tag:blogger.com,1999:blog-379365072024-03-07T21:13:28.952+00:00McCabismThe only philosophy-physics-motorsport blog in the world!Gordon McCabehttp://www.blogger.com/profile/09151162643523937086noreply@blogger.comBlogger892125tag:blogger.com,1999:blog-37936507.post-12076014963550342452021-04-15T13:54:00.003+01:002021-04-15T13:54:31.930+01:00The Winner Takes it All - Williams 2013-2018<p> Sung to the tune of ABBA's classic:<br /><span>
</span></p><p class="yiv3382466112ydpd95567b9MsoNormal"><i>I don't wanna talk<br />
About races we've gone through<br />
Though it's hurting me<br />
Now it's Autocourse history<br />
I've played all my stops<br />
And that's what you've done too<br />
Nothing more to say<br />
No more Quali compounds to play<br />
<br />
The winner takes it all<br />
Paddy Lowe standing small<br />
Beside the victory<br />
That's his destiny<br />
<br />
I was in Lawrence Stroll’s arms<br />
Thinking I belonged there<br />
I figured it made sense<br />
Building me a fence<br />
Building me a DIL<br />
Thinking I'd be strong there<br />
But I was a fool<br />
Playing by Jakob’s rules<br />
<br />
The FIA may throw the dice<br />
Their minds as cold as ice<br />
And someone way down here<br />
Loses one point held dear<br />
The winner takes it all<br />
Ed Wood has a trackday fall<br />
It's simple and it's plain<br />
Why should I lodge a protest within the specified timeframe?<br />
<br />
But tell me Valterri, does Toto kiss<br />
Like Johnny used to kiss you?<br />
Does it feel the same<br />
When Tony Ross calls your name?<br />
Somewhere deep inside<br />
You must know we miss you<br />
But what can I say?<br />
Claire must be obeyed<br />
<br />
Charlie Whiting will decide<br />
The likes of me abide<br />
Spectators of the show<br />
Correlation with tunnel figures staying low<br />
The Grand Prix is on again<br />
A lover or a friend<br />
A big thing or a small<br />
The winner takes it all<br />
<br />
I don't wanna talk to the media<br />
If it makes you feel sad<br />
And I understand<br />
You've come to shake Felipe’s hand<br />
I apologize<br />
If it makes you feel bad<br />
Seeing me so tense<br />
No downforce, but plenty of gearbox compliance<br />
But you see<br />
The winner takes it all<br />
The winner takes it all…</i></p><p></p>Gordon McCabehttp://www.blogger.com/profile/09151162643523937086noreply@blogger.com0tag:blogger.com,1999:blog-37936507.post-46144562616354885832021-03-13T16:52:00.003+00:002021-03-13T17:07:06.952+00:00Brands Hatch F1 Tyre Test 1985<div style="text-align: justify;"><p>A beautiful summer's day in 1985, the greatest circuit in Britain, and the greatest F1 cars and drivers of all time, preparing for the European Grand Prix. No zoom lens, so there's something of a polite distance maintained between photographer and object.</p></div><div style="text-align: center;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJGKFfEQTky3DZ23u9rEpe0MbfCUcxPUSZuiJijPNAmcUeu6r_3aXcgeXGFeGinfVpvEHmeQ3-Z5Imr6diPppWXSGAHLeg2wn6jziaoHRi9YXYw2wnUZCDtv5EtWYgr0_HBdv4/s1733/Surer.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1173" data-original-width="1733" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJGKFfEQTky3DZ23u9rEpe0MbfCUcxPUSZuiJijPNAmcUeu6r_3aXcgeXGFeGinfVpvEHmeQ3-Z5Imr6diPppWXSGAHLeg2wn6jziaoHRi9YXYw2wnUZCDtv5EtWYgr0_HBdv4/s320/Surer.jpg" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b>Marc Surer passes through the cutting at Pilgrim's drop.</b></td></tr></tbody></table></div><div style="text-align: center;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitt7ZBGcEkTkIIjKOWWzYbJdXmm_EOmSdlHGYIgi3rDtyUaDWGzOOH8Lp9PkU15ZQ6spHi24WNGFYyRo-EhPihh5x8jB6sKhf4v_PpzXjenbZQIP5GBKX1y3pVEJ9bfrNxF4v3/s2048/Senna.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1319" data-original-width="2048" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitt7ZBGcEkTkIIjKOWWzYbJdXmm_EOmSdlHGYIgi3rDtyUaDWGzOOH8Lp9PkU15ZQ6spHi24WNGFYyRo-EhPihh5x8jB6sKhf4v_PpzXjenbZQIP5GBKX1y3pVEJ9bfrNxF4v3/s320/Senna.jpg" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b>Senna turning into Hawthorn Bend. Don't turn left.</b></td></tr></tbody></table></div><div style="text-align: center;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirHMpk7mxqsBbHRQA2jWfm3Up0jEElDMOq9joy8VBrprfgvxmzy35oWFdqYdPbC7HKXbnxtA3kzhNw_u_Vzjxq0tBbzRVpM0mQTjMGw-lBKodw7wxMzPc6uIH_yvC5eLmr1oKo/s1725/keke.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1065" data-original-width="1725" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirHMpk7mxqsBbHRQA2jWfm3Up0jEElDMOq9joy8VBrprfgvxmzy35oWFdqYdPbC7HKXbnxtA3kzhNw_u_Vzjxq0tBbzRVpM0mQTjMGw-lBKodw7wxMzPc6uIH_yvC5eLmr1oKo/s320/keke.jpg" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b>Keke in the FW10. The FW10B would only make its debut at the European Grand Prix itself.</b><br /></td></tr></tbody></table></div><div style="text-align: center;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-bH9cxlZD0Ju2d32KT2rLEOVIO7_5PbC9SxznGK_ZelAm6KCWsuA1KnoLtwRjcMohNwOsT3mNoyYKNEsLcvek3cd2m437bekbdlMXIHcVrNT0pRdZMsRnhvnlFNRWA9E5gaBb/s1737/Alain1.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1169" data-original-width="1737" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-bH9cxlZD0Ju2d32KT2rLEOVIO7_5PbC9SxznGK_ZelAm6KCWsuA1KnoLtwRjcMohNwOsT3mNoyYKNEsLcvek3cd2m437bekbdlMXIHcVrNT0pRdZMsRnhvnlFNRWA9E5gaBb/s320/Alain1.jpg" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b>Prost coasting through the apex of Hawthorn. Don't want to overheat the left-front</b>.</td></tr></tbody></table></div><div style="text-align: center;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiLFfmQDSySx_vosO_h_6bl3_4lGFIfs7LPirnXce7tLVh-EA6ZXvScnJM9ANcKBRVdY1mglB3IIcN7AqVYLwfjCw9swwVR5XqRbZ3LDl3FU2N5RshlfZvgB-TVNdJcSD2WSFjI/s1729/Alain1b.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1169" data-original-width="1729" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiLFfmQDSySx_vosO_h_6bl3_4lGFIfs7LPirnXce7tLVh-EA6ZXvScnJM9ANcKBRVdY1mglB3IIcN7AqVYLwfjCw9swwVR5XqRbZ3LDl3FU2N5RshlfZvgB-TVNdJcSD2WSFjI/s320/Alain1b.jpg" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b>Prost gently easing through the dappled light into Stirling's. Careful with the right-front temperature.</b></td></tr></tbody></table></div><div style="text-align: center;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmK6KjEKWMfWEEyGkju_CzSZ54u3Gr_p1mmgEUXdlDhZuxxmqubGkFv_RjlvaEXqZEoDogMKbVtiOe7EggAVQ__HESAivNvPkRZECfwOJCYu5AzEBxBqkq16rT528zRTB2tVDD/s1745/Alain2.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1101" data-original-width="1745" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmK6KjEKWMfWEEyGkju_CzSZ54u3Gr_p1mmgEUXdlDhZuxxmqubGkFv_RjlvaEXqZEoDogMKbVtiOe7EggAVQ__HESAivNvPkRZECfwOJCYu5AzEBxBqkq16rT528zRTB2tVDD/s320/Alain2.jpg" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b>Prost carefully accelerating out of Stirling's. Don't want to overheat those rears.</b></td></tr></tbody></table></div><div style="text-align: center;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyw1SzHnptBHEp5EHGBp9RKLR2soqYu1MkgczV5VD-Lm6MS3x0RGXq9UihGCZx-Hi5rJMHJQLyJCmaR-QZAgQ_WX6sdlCu3a5t7TI7Pv_HROpclVxn38-M3AuG96h2yt62K7rt/s2048/Johan.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1209" data-original-width="2048" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyw1SzHnptBHEp5EHGBp9RKLR2soqYu1MkgczV5VD-Lm6MS3x0RGXq9UihGCZx-Hi5rJMHJQLyJCmaR-QZAgQ_WX6sdlCu3a5t7TI7Pv_HROpclVxn38-M3AuG96h2yt62K7rt/s320/Johan.jpg" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b>Stefan Johansson's Ferrari at Hawthorn Bend. Note how far forward the drivers still are in 1985.</b></span></td></tr></tbody></table></div><div style="text-align: center;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNhbhk1OPzDR8-sktHElyyDyxdaDeZI3IZSe9HAruOWODkiWmk_l2QlEhsp6nZuu_WoEb4-mSqPEk-EEW03l3nKOtYfBA6KU8hurwNhi7U-K0ZQTi84CtaGBm82rO5V_eQTCUq/s1665/Clearways.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1157" data-original-width="1665" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNhbhk1OPzDR8-sktHElyyDyxdaDeZI3IZSe9HAruOWODkiWmk_l2QlEhsp6nZuu_WoEb4-mSqPEk-EEW03l3nKOtYfBA6KU8hurwNhi7U-K0ZQTi84CtaGBm82rO5V_eQTCUq/s320/Clearways.jpg" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b>Bernard Asset-style atmospheric shot of Clearways.</b></td></tr></tbody></table></div><div style="text-align: center;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgEXKIwdSbxs4sfeInHgHcGWnU_lecniDyAZhxGrcbUHM1H7xDGomiwN33elQcYHLD4G0LE55untnFs8ZlamKS9TREvNueNRe_2QFmXVMnHNDzThAziohqLu72EXi9i1hmyiV0d/s1733/Senna2.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1173" data-original-width="1733" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgEXKIwdSbxs4sfeInHgHcGWnU_lecniDyAZhxGrcbUHM1H7xDGomiwN33elQcYHLD4G0LE55untnFs8ZlamKS9TREvNueNRe_2QFmXVMnHNDzThAziohqLu72EXi9i1hmyiV0d/s320/Senna2.jpg" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b>Ayrton Senna da Silva turning into Graham Hill Bend.</b></td></tr></tbody></table></div><div style="text-align: center;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTv4gnDc1zuK225Zt52EACKxllU1VdfR_rIW4fmzPo-AzjavVT-dh4SkmFfWqaM6RxJ5MlEAFmgPOuWqrab0LwJz2AvQbEQQDLOnptQ0qZ-Bf_ED3Mx1Ok-HEfEguCgAdzCqSz/s1733/Boutsen.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1073" data-original-width="1733" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTv4gnDc1zuK225Zt52EACKxllU1VdfR_rIW4fmzPo-AzjavVT-dh4SkmFfWqaM6RxJ5MlEAFmgPOuWqrab0LwJz2AvQbEQQDLOnptQ0qZ-Bf_ED3Mx1Ok-HEfEguCgAdzCqSz/s320/Boutsen.jpg" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b>Boutsen's Arrows up the hill towards Druids. </b></td></tr></tbody></table></div><div style="text-align: center;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj9XIFo1JexamTyrU2dweTu6MUm_59HRNL5aXl9Q_oGAUy8sS-BdORf0k9jO9D5Jqn5wm3k8kM8-xr7r96TQQNA7SbAVwolo9NntShCCx4V7eycaW6qrxSwyi7ETmZ63T_Mt7Ak/s1753/bellof.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1025" data-original-width="1753" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj9XIFo1JexamTyrU2dweTu6MUm_59HRNL5aXl9Q_oGAUy8sS-BdORf0k9jO9D5Jqn5wm3k8kM8-xr7r96TQQNA7SbAVwolo9NntShCCx4V7eycaW6qrxSwyi7ETmZ63T_Mt7Ak/s320/bellof.jpg" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b>Stefan Bellof (Tyrrell), shortly before his death at Spa in a Porsche 956.</b></td></tr></tbody></table></div><div style="text-align: center;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixRuocs4yzkb70EHWg57yJm4iPqIsK5BTtLNQ2l_5Y-5tqN__YSG8nGlM19l5ka-1ci-aMbPPydz5pqRkXWMlwN2kWTzZO76I5q0WDgl3pSMMd0iZ_n2-6VTgJ4gfkZjnLYIaJ/s1733/Dingle+Dell.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1121" data-original-width="1733" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixRuocs4yzkb70EHWg57yJm4iPqIsK5BTtLNQ2l_5Y-5tqN__YSG8nGlM19l5ka-1ci-aMbPPydz5pqRkXWMlwN2kWTzZO76I5q0WDgl3pSMMd0iZ_n2-6VTgJ4gfkZjnLYIaJ/s320/Dingle+Dell.jpg" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b>Toleman plunging down from Westfield through Dingle Dell.</b></td></tr></tbody></table></div><br />Gordon McCabehttp://www.blogger.com/profile/09151162643523937086noreply@blogger.com0tag:blogger.com,1999:blog-37936507.post-34383776601241635882020-06-23T18:58:00.001+01:002020-06-23T18:58:25.383+01:00Thruxton British F3 - March 1988<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; 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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibVz02SKPVX4pLTE4m_1OJztDKR1dJkpCQzH1mNnQbKjr70TgVidFskC_cJYaywzdgqmsIXg71xYjBIr0Cztaj52LyQMChQYtcKfBXHf4FmkdrCr9jc4EyjWkJTUjk3qG4o2Ah/s1600/T1.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1067" data-original-width="1600" height="213" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibVz02SKPVX4pLTE4m_1OJztDKR1dJkpCQzH1mNnQbKjr70TgVidFskC_cJYaywzdgqmsIXg71xYjBIr0Cztaj52LyQMChQYtcKfBXHf4FmkdrCr9jc4EyjWkJTUjk3qG4o2Ah/s320/T1.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Pitlane walkabout: Jyrki Jarvilehto shows off his blisters</b></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJd5dPo9zgoN50NUppEtsCOQtHoM5WVI9UbNcFxRtbVVpZqJ6yCFaJEXlJ5k9MwBDrIi7qpGx4TZ6tgHr_xY-Nao5dwmOFqK4rQbFy1_ngn7QqKIMkEIxvuJXeCdqdhjhOHY4G/s1600/T2.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1083" data-original-width="1600" height="216" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJd5dPo9zgoN50NUppEtsCOQtHoM5WVI9UbNcFxRtbVVpZqJ6yCFaJEXlJ5k9MwBDrIi7qpGx4TZ6tgHr_xY-Nao5dwmOFqK4rQbFy1_ngn7QqKIMkEIxvuJXeCdqdhjhOHY4G/s320/T2.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Exhaust-blown rear wing</b></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrbAaaCLABpCvA1VXpyTVHcSp9H5GcWqEtusev_-ILq7rB_BqXot2CrgOGG-f1sFCxIqJcvMPKC3Ki9Suc3JYybKiHWktk4ceiaE_Rnp9pgrJ2bYINFo5AaBYqvd2CYugB6gwK/s1600/T4.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1086" data-original-width="1600" height="217" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrbAaaCLABpCvA1VXpyTVHcSp9H5GcWqEtusev_-ILq7rB_BqXot2CrgOGG-f1sFCxIqJcvMPKC3Ki9Suc3JYybKiHWktk4ceiaE_Rnp9pgrJ2bYINFo5AaBYqvd2CYugB6gwK/s320/T4.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Ample opportunity for future Ferrari engineers to 'top-up' the fuel tank</b></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQl8ROo0DGd9ZEJXxB273kFA_Syu2Gk1bDohFoHE0ziFLM6o6OrE_gJYp7TpMJCjYH2pSwqaz6-EqlwmlrYP1zuyWltFV2VYQPMZ9LWyCUe6hFJUkmis0_RxYo3aCpvMH6fPjE/s1600/T5.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1087" data-original-width="1600" height="217" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQl8ROo0DGd9ZEJXxB273kFA_Syu2Gk1bDohFoHE0ziFLM6o6OrE_gJYp7TpMJCjYH2pSwqaz6-EqlwmlrYP1zuyWltFV2VYQPMZ9LWyCUe6hFJUkmis0_RxYo3aCpvMH6fPjE/s320/T5.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Derek Warwick. For sure.</b></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBAw1bxUz9aQZDjntfH04xdbpiy66VjK_I5IqtXUd4L7K-ZAGYJI2wtHt21NmyXQdtXxSM-FnQdCW5Iw6Y4shaUQx6jIGvlL0B53MCeVsYHabQm1PfoQXQhzobGpElz_1vx04h/s1600/T6.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1025" data-original-width="1255" height="261" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBAw1bxUz9aQZDjntfH04xdbpiy66VjK_I5IqtXUd4L7K-ZAGYJI2wtHt21NmyXQdtXxSM-FnQdCW5Iw6Y4shaUQx6jIGvlL0B53MCeVsYHabQm1PfoQXQhzobGpElz_1vx04h/s320/T6.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Steve Rider, looking haunted after being boot-lidded down the A303 by Des Lynam.</b></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjFMBMET9p7fyI6KtqYvWntuY7U6gJeKN_qPOs6kjLL-CgIIZAwE1fSFrhO-pr120JHseILnJoqdw3iGaOTZuPn5085ZD0drJXcU1OpYjE4EhF8YMbOEb3Vqs-98bcC5jYaMswX/s1600/T7.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1083" data-original-width="1600" height="216" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjFMBMET9p7fyI6KtqYvWntuY7U6gJeKN_qPOs6kjLL-CgIIZAwE1fSFrhO-pr120JHseILnJoqdw3iGaOTZuPn5085ZD0drJXcU1OpYjE4EhF8YMbOEb3Vqs-98bcC5jYaMswX/s320/T7.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Interesting front anti-roll bar design. Note for aerodynamicists: those spiral things are called 'springs'.</b></td></tr>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjbF3KEzvD_pbI6yG4gIPli6VyteCNm-JDsyBLuWpeU1TkZd6J9ft3qx-gZUCihrH3SKdxlg7a5G0-aW_-wCFzmVVdFnmmZAQjSEE8o-pCjH9DgnQSTr4OtpsPaL-sYt4HaZI7o/s1600/T9.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="979" data-original-width="1600" height="195" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjbF3KEzvD_pbI6yG4gIPli6VyteCNm-JDsyBLuWpeU1TkZd6J9ft3qx-gZUCihrH3SKdxlg7a5G0-aW_-wCFzmVVdFnmmZAQjSEE8o-pCjH9DgnQSTr4OtpsPaL-sYt4HaZI7o/s320/T9.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>And we're off! Martin Donnelly is on pole, but makes a poor start. In yellow is Philippe Favre, behind is Lehto, and to the outside is Damon Hill.</b></td><td class="tr-caption" style="text-align: center;"><br /></td></tr>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOMZSTEqm5PbtaIE0UdRhVD4RmbdYSpLrfi-U4vCMxubM5D1UctwxxGkA8SOTwCBbkQJV_ycphfZy-2KVuUzvUdhpUufpH4P-0OF0ssf54OfTWXRu3DutRZrKx1YASIVjnt_51/s1600/T10.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="871" data-original-width="1600" height="174" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOMZSTEqm5PbtaIE0UdRhVD4RmbdYSpLrfi-U4vCMxubM5D1UctwxxGkA8SOTwCBbkQJV_ycphfZy-2KVuUzvUdhpUufpH4P-0OF0ssf54OfTWXRu3DutRZrKx1YASIVjnt_51/s320/T10.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Donnelly and Favre are wheel-to-wheel through Allard, with Hill trying the wide-line, and Lehto sneaking through on the inside (hidden by Eddie Irvine).</b></td></tr>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyGwHmW7R_K0Cao7q7po099YIl9k28uJJreN30iVB8BuVC0IPBcGY3hW9NMXexCs_azhItj7gi7qFHYMEfvdI86ymna2dxII2tNhMKe2QAJRIaFfPOL9jWyrcyOiytBR0smNc-/s1600/T11.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="954" data-original-width="1600" height="190" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyGwHmW7R_K0Cao7q7po099YIl9k28uJJreN30iVB8BuVC0IPBcGY3hW9NMXexCs_azhItj7gi7qFHYMEfvdI86ymna2dxII2tNhMKe2QAJRIaFfPOL9jWyrcyOiytBR0smNc-/s320/T11.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>By the end of lap 1, Favre has run wide into the complex, and both of the Cellnet cars of Hill and Donnelly have missed a gear. Lehto leads, and holds his lead to the finish.</b></td></tr>
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Gordon McCabehttp://www.blogger.com/profile/09151162643523937086noreply@blogger.com0tag:blogger.com,1999:blog-37936507.post-21149645636060430892020-06-07T15:54:00.002+01:002020-06-07T15:54:33.277+01:00Brands Hatch F3000 1988<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhS_6DDyrm397P9LPPzao5DilfmGboISAPbUKLt3pWeCxvP_he6jxHlgoBJZk4O7rW32WH4pTUoPa8LmvRZydYK0gJ91-wnZD-mU5tKm9mpJ7EMMsMb4Yfz02z_kMAoC_dc4opK/s1600/19881.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1074" data-original-width="1600" height="214" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhS_6DDyrm397P9LPPzao5DilfmGboISAPbUKLt3pWeCxvP_he6jxHlgoBJZk4O7rW32WH4pTUoPa8LmvRZydYK0gJ91-wnZD-mU5tKm9mpJ7EMMsMb4Yfz02z_kMAoC_dc4opK/s320/19881.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Johnny Herbert leads out of Paddock Hill Bend from Donnelly, Martini, Grouillard, Foitek, Moreno, Blundell, Alesi, Langes, Ferte and the rest.</b></td></tr>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgj-fIqawVNSSm2FqyPXR0WYSEEbGWYU1VxqSk9dRHxCt75Urk6QNo9AjsJnxJx67MfB_QL7zj4Rra5U_UtW2a_G1l6VyCeCaELizKv0ETwmgLatIuoQqjCC4w92_YmzZrYR9ZS/s1600/19883.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1090" data-original-width="1600" height="217" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgj-fIqawVNSSm2FqyPXR0WYSEEbGWYU1VxqSk9dRHxCt75Urk6QNo9AjsJnxJx67MfB_QL7zj4Rra5U_UtW2a_G1l6VyCeCaELizKv0ETwmgLatIuoQqjCC4w92_YmzZrYR9ZS/s320/19883.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Alesi exits stage left at Druids.</b></td></tr>
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<div class="separator" style="clear: both; text-align: center;">
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjK9J1T8VD7b437yGEcB7IhDBXIf-S0t8miCY-5ijanU_9mJQCshPd3U3KgrasqNbF7_eN_bgVakdm5n8tBnr17WV5dsVvK_eOCVyFunboJazPb_5IHwxtIHF4SKJJ-XfHHWtzO/s1600/19884.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1088" data-original-width="1600" height="217" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjK9J1T8VD7b437yGEcB7IhDBXIf-S0t8miCY-5ijanU_9mJQCshPd3U3KgrasqNbF7_eN_bgVakdm5n8tBnr17WV5dsVvK_eOCVyFunboJazPb_5IHwxtIHF4SKJJ-XfHHWtzO/s320/19884.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Martin Donnelly pressures Herbert in the early stages.</b></td></tr>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiSM2BQ2156N_iSNNyMbZMBOsHGc-lGcYE1w8DBclTrNUW7m0iLGNY8Wh0RJ6a0qMXA5K60slnOsj_saHESmwfgZAio02NfXtP1q7_GkYicxHM6TtOgZzb3xoGjbkQ58H0y5LOZ/s1600/19885.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1089" data-original-width="1600" height="217" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiSM2BQ2156N_iSNNyMbZMBOsHGc-lGcYE1w8DBclTrNUW7m0iLGNY8Wh0RJ6a0qMXA5K60slnOsj_saHESmwfgZAio02NfXtP1q7_GkYicxHM6TtOgZzb3xoGjbkQ58H0y5LOZ/s320/19885.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>A battle for 3rd develops between Martini, Foitek, Moreno, Grouillard and Blundell. </b></td></tr>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPFKtcOdQjsCN1L4AIcBtaBEI6gwPygSLL80Hi-ppx5tIvKolrYaM4eH3D4hSY-B0Bquej37OMVMEwJ7U-NyNIP1_ZtEz_RqyW0UWMIQynpYd9MCHwEEzwqu5Jq4VHeFotixsX/s1600/19886.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1070" data-original-width="1600" height="213" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPFKtcOdQjsCN1L4AIcBtaBEI6gwPygSLL80Hi-ppx5tIvKolrYaM4eH3D4hSY-B0Bquej37OMVMEwJ7U-NyNIP1_ZtEz_RqyW0UWMIQynpYd9MCHwEEzwqu5Jq4VHeFotixsX/s320/19886.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Foitek creams Moreno into the tyre barrier at the top of Paddock.</b></td></tr>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEis6PfDyTqe0raOHcY614V-qbWwafLpaekXGxR4Mr5pGgMfyJwXg0Wi8cr0GMKGvhkGylAslFM9-OW_5DL3Px5xm9iNyI_Y-qLbu6vqHl9YUVwprv8L_Mf-0zjt4etJByGeUzL6/s1600/19887.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1097" data-original-width="1600" height="219" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEis6PfDyTqe0raOHcY614V-qbWwafLpaekXGxR4Mr5pGgMfyJwXg0Wi8cr0GMKGvhkGylAslFM9-OW_5DL3Px5xm9iNyI_Y-qLbu6vqHl9YUVwprv8L_Mf-0zjt4etJByGeUzL6/s320/19887.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Moreno's Reynard 88D sustains heavy damage.</b></td></tr>
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<b></b></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjEPbb0QFPJrSeJOXJUAZfZXqM8Su5Qlco0bMzL-bZk0sv7BB5RR4l4zPNn-jtLknvfj705zYt3KGSCOC3KbyL_DfZv5j8T_D-7pQgDngw9U9eae_TNCI4LUZGYSQNYLM_KqrWk/s1600/19888.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1075" data-original-width="1600" height="214" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjEPbb0QFPJrSeJOXJUAZfZXqM8Su5Qlco0bMzL-bZk0sv7BB5RR4l4zPNn-jtLknvfj705zYt3KGSCOC3KbyL_DfZv5j8T_D-7pQgDngw9U9eae_TNCI4LUZGYSQNYLM_KqrWk/s320/19888.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>At the restart, Donnelly leads away this time, followed by Martini, Herbert, Foitek, Grouillard, Blundell and the rest.</b></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-6JqfUIb0NR6ELrr4SF3gSlWEAxHpZK_jjTDDntHi0okkVenyeLa7YK8mt8yloKV9y6V81AtTyW-IgLQk70ptZQI-GZHkZHfokcq9SrOO6Qwj3zP3M5bjRa7xvQo93RereR3d/s1600/19889.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1092" data-original-width="1600" height="218" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-6JqfUIb0NR6ELrr4SF3gSlWEAxHpZK_jjTDDntHi0okkVenyeLa7YK8mt8yloKV9y6V81AtTyW-IgLQk70ptZQI-GZHkZHfokcq9SrOO6Qwj3zP3M5bjRa7xvQo93RereR3d/s320/19889.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Catastrophe at Pilgrim's Drop.</b></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMdRJUGnMfsI8oAVDenTbD8hevRxCMPtgZ1aReTHM6DPuSWJ2xZRw2Kop0WLY8-4f2LID3bVFUPjLjkEEPc9LHFXHtbZMgT7kRpEx5yah0cWRK9VgFmB5VKR0wT2jVjVDBKUP6/s1600/198810.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1096" data-original-width="1600" height="219" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMdRJUGnMfsI8oAVDenTbD8hevRxCMPtgZ1aReTHM6DPuSWJ2xZRw2Kop0WLY8-4f2LID3bVFUPjLjkEEPc9LHFXHtbZMgT7kRpEx5yah0cWRK9VgFmB5VKR0wT2jVjVDBKUP6/s320/198810.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Foitek is still in the car adjacent to the far barrier, and Grouillard is being freed from his GDBA Lola.</b></td></tr>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhK_5jVtwi_42J9K8rLYo5fJv_4YUOMc59TaIo4mhCUJVeV38IOz1vj2hXYCZj8ByOXsMNh_TTUALutVPXI6QjOHx6LRzLjZPfz76oduzlUZiILB02M-I1_3d_U83kdlPEEq-u7/s1600/198811.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1082" data-original-width="1600" height="216" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhK_5jVtwi_42J9K8rLYo5fJv_4YUOMc59TaIo4mhCUJVeV38IOz1vj2hXYCZj8ByOXsMNh_TTUALutVPXI6QjOHx6LRzLjZPfz76oduzlUZiILB02M-I1_3d_U83kdlPEEq-u7/s320/198811.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Medical assistance arrives for Johnny Herbert.</b></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJ03VvoxdtcpheCykm_xNiWdzxLcQmMgXBUL_rYcfod32XhpQKJDRXQ3zPe4D2TQd7fJ2rePS29baoNZCJIG75T4Q-WbaqAZSMMSt80j98CZbEQKXZC0bgf4Xz4klaD51bzdAA/s1600/198812.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1090" data-original-width="1600" height="217" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJ03VvoxdtcpheCykm_xNiWdzxLcQmMgXBUL_rYcfod32XhpQKJDRXQ3zPe4D2TQd7fJ2rePS29baoNZCJIG75T4Q-WbaqAZSMMSt80j98CZbEQKXZC0bgf4Xz4klaD51bzdAA/s320/198812.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Andy Wallace is carried away, accompanied by GEM team-mate Gary Evans.</b></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6PiiOtkrMG0pUYAtwp4w9_y3iYfUEyb3-_cNn8BNnYX85kqMK9LbA5DJx-_9VvZAuspB7mtoRMft0yfT0jIgqyQxk2j4-eiO1ODhdnfuMYVGQ0RBvqLtGJxADy0M0i4nYATPo/s1600/198813.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1093" data-original-width="1600" height="218" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6PiiOtkrMG0pUYAtwp4w9_y3iYfUEyb3-_cNn8BNnYX85kqMK9LbA5DJx-_9VvZAuspB7mtoRMft0yfT0jIgqyQxk2j4-eiO1ODhdnfuMYVGQ0RBvqLtGJxADy0M0i4nYATPo/s320/198813.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Herbert is worked on for something in the region of 40 minutes, during which time marshals fought a frequent battle to repel spectators trying to crawl up the undergrowth on the right of the track.</b></td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg78cgNj74vIKhdla58IVtxlhhI2E6JCE5R47kGV6FmfYAvJobc4H1CijNp4YJG3E_RVOqRyLO7XhYmdC2NgIEuQIwxpldhyphenhyphentUp6bDQd0TXFWn3W9zFV8OUFJSZL0TnNBxAm6N6/s1600/198814.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1081" data-original-width="1600" height="216" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg78cgNj74vIKhdla58IVtxlhhI2E6JCE5R47kGV6FmfYAvJobc4H1CijNp4YJG3E_RVOqRyLO7XhYmdC2NgIEuQIwxpldhyphenhyphentUp6bDQd0TXFWn3W9zFV8OUFJSZL0TnNBxAm6N6/s320/198814.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Martin Donnelly wins the re-started race.</b></td></tr>
</tbody></table>
Gordon McCabehttp://www.blogger.com/profile/09151162643523937086noreply@blogger.com0tag:blogger.com,1999:blog-37936507.post-84656177770660903702020-01-18T22:59:00.000+00:002020-02-12T12:21:20.956+00:00Trump and opinion dynamics<div style="text-align: justify;">
The January 2020 issue of <i>PhysicsWorld</i> includes an article on '<a href="https://physicsworld.com/a/the-physics-of-public-opinion/">The physics of public opinion</a>', written by Rachel Brazil. The article focuses on the claim made by French physicist, Serge Galam, that Donald Trump's victory in the 2016 US Presidential election can be explained using his model of 'minority opinion spreading'.</div>
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Galam's work models how opinions evolve in a network of human agents. The idea is that an individual's beliefs can be changed by social interactions with people holding other beliefs. However, Galam also represents the fact that some people can be more stubborn in retaining their initial beliefs. In particular, he models the way in which an initial minority opinion can eventually become the majority opinion, if the proportion of stubborn people is larger in the initial minority group than it is in the initial majority group:</div>
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<i>'An opinion that starts in the minority can quickly spread as long as it is above a base threshold...As few as 2% more stubborn agents on one side puts the tipping point at a
very low value of around 17%, which leads to the unfortunate conclusion
that to win a public debate, what matters is not convincing a majority
of people from the start, but finding a way to increase the proportion
of stubborn agents on your side.'</i></div>
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This is interesting work, but more problematic is Galam's attempt to use a variation on this theme to explain Trump's 2016 victory:</div>
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<i>'I<span class="s1">n the case of the 2016 US presidential elections, Galam
says the prevailing factor was peoples’ "frozen prejudices". He argues
that Trump’s outrageous statements, though initially seen as repellent
by most voters, managed to activate their hidden or unconscious
prejudices. First, many Trump supporters shifted to Hillary Clinton,
rejecting his statements with great outrage, leading to a decrease in
support. But the initial outrage led to more public debates with an
automatic increase in the number of local ties. At those points, “it’s
like flipping a coin, but with a coin biased along the leading
prejudice”, Galam says. Then many voters started to swing in favour of
Trump.'</span></i></div>
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There are two problems with this. The first is the explanatory dependence upon<i> </i>the theoretical concept of<i> </i>'frozen' or 'unconscious' prejudices. This sounds almost like a retreat into the mysterious world of Freudian psychoanalysis, with its array of unverifiable unconscious motives.</div>
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Moreover, the notion that there is some form of latent fascism or Nazism within society, just waiting for an opportunity to gain ascendancy, plays the role of a tribal myth within Progressive politics. The Enlightened Ones urge continual vigilance against this ever-present threat, and such appeals perform the function of enhancing group cohesion. Galam's work therefore falls into an extant genre of Progressive literature, which has flourished in the wake of the Brexit referendum and Trump's election victory. </div>
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The second problem with Galam's proposal is that there is already an adequate and much simpler explanation: </div>
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<i>Trump won the 2016 election because a critical proportion of blue-collar voters rationally assessed their changing economic circumstances and prospects, and concluded that their interests were <a href="https://www.theguardian.com/commentisfree/2017/feb/05/trump-not-fascist-champion-for-forgotten-millions">better represented by Trump than the Democrats</a>. </i></div>
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Unfortunately, to accept this explanation would require those within Progressive politics to accept their own culpability in bringing Trump to power. Better, perhaps, to believe in the existence of sinister, hidden prejudices. </div>
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Indeed, if there's one phenomenon which <i>does</i> call out for an explanation within social physics, it's the very spread of Progressive politics and political-correctness in recent decades. Back in the 1980s, politically-correct opinions were minority opinions held only by vocal, stubborn and fanatical groups. Today, these ideas have spread to become mainstream within the professional middle-classes. </div>
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Sadly, one suspects that those working in academia are prejudiced about the nature of prejudice.</div>
Gordon McCabehttp://www.blogger.com/profile/09151162643523937086noreply@blogger.com0tag:blogger.com,1999:blog-37936507.post-29704828592564225132020-01-09T17:02:00.000+00:002020-01-09T17:02:18.233+00:00Formula One and Machine Learning<div style="text-align: justify;">
The power of Machine Learning, based upon artificial neural networks, has become all-too-obvious over the past decade. Early this year, it was <a href="https://www.nature.com/articles/s41586-019-1799-6.epdf?referrer_access_token=WbvHGBJrYbHBvKiJaNQapdRgN0jAjWel9jnR3ZoTv0M5zwPVx5jT4z_z-YkUZTBTbM27UWphyoF6vHoR667kKgqCi8GNWj2oxgaEK9QGM_L12Qj2XG2htlhQgMs-Jn1mKBUd25SpdBhOjYDX_GFMLTK44y2K7v497ZLTwD8IKoL8lTzPLsWB4xXOKg4LogkW0Es0jjHxbQhkY9oYXszziIjRwreH15wQ8EIioG0jIqs%3D&tracking_referrer=www.bbc.co.uk">announced in <i>Nature</i></a> that a Deep Learning algorithm, developed by Google Health, is better than human experts at identifying breast cancer in mammograms.</div>
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Naturally, there's also been much chatter in recent years about the potential use of such Artificial Intelligence (AI) in Formula One. For example, one can find Jonathan Noble's article, '<a href="https://www.autosport.com/f1/feature/8009/why-artificial-intelligence-could-be-f1-next-big-thing">Why Artificial Intelligence could be F1's next big thing</a>', on Autosport.com, apparently suggesting that AI could be used by both trackside engineers and those in race-support roles:</div>
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"Getting through the mountains of data generated in Formula 1 can be a
'needle in a haystack' process for teams searching for performance.
There's technology on the way that could make a huge difference...The AI being talked about right now will be used at first to help better manage access to data. The
computers will learn to know which data needs to be saved; which data
needs to be prioritised so there can be rapid access to it. Plus it
needs to be one step ahead and bring up data that is needed next."</div>
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Perhaps the idea is that if AI can spot patterns in a bunch of tits, then it could also be used by a bunch of tits to spot patterns in data. </div>
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From inside the teams, the arrival of the Machine Learning advocates sometimes resembles a flock of seagulls swooping noisily from one landfill site to another, seeking easy pickings from the technically clueless decision-makers, squawking and chirping happily about 'convolutional neural networks', and 'GPUs running in the cloud' as they descend upon unwitting mechanical engineers and aerodynamicists.</div>
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Perhaps Formula One needs to carefully scrutinise some of the claims made by the Machine Learning (ML) community, particularly <i>vis-a-vis</i> its capabilities in the fields of forecasting and data-mining. A recent paper <a href="https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0194889&type=printable">published in PLoS by Makridakis, Spiliotis, and Assimakopoulos</a> compares the performance of ML algorithms, versus standard statistical methods, for making future predictions from time-series data. The aggregated errors were quantified using two measures, symmetric Mean Absolute Percentage Error (sMAPE), and the Mean Absolute Scaled Error (MASE). Unfortunately for the Machine Learning advocates, the statistical methods had the lowest error levels, as represented in the chart below. </div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjR_KDyE3qZIhP5Ac8joFoMGuN4Z9o1I-LSsj9L8T47ijMsK2oZ8WSdBIxoPhlI3Q3gTRUZBtC-VhO3vaIasM9wG_8Ca3o4J3Fh4ZsC0c3y7naGSpMvIo94onTUC2NnbX4e27DS/s1600/journal.pone.0194889.g002.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="770" data-original-width="1600" height="192" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjR_KDyE3qZIhP5Ac8joFoMGuN4Z9o1I-LSsj9L8T47ijMsK2oZ8WSdBIxoPhlI3Q3gTRUZBtC-VhO3vaIasM9wG_8Ca3o4J3Fh4ZsC0c3y7naGSpMvIo94onTUC2NnbX4e27DS/s400/journal.pone.0194889.g002.PNG" width="400" /></a></div>
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So, good news if you're an F1 engineer: you can cling onto your Excel spreadsheets for at least a little longer. Or better still, learn to use the statistical package <i>R</i>.</div>
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As Makridakis <i>et al</i> justifiably assert, "the importance of objectively evaluating the relative performance of the ML methods in forecasting is obvious but has not been achieved so far raising questions about their practical value to improve forecasting accuracy and advance the field of forecasting. Simply being new, or based on AI, is not enough to persuade users of their practical advantages over alternative methods." </div>
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Also provided in the paper by Makridakis <i>et al</i> is a useful table (below), which can be used as a guide to distinguish those applications where Machine Learning is demonstrably powerful (games, image and speech recognition), from those applications where it isn't (currently) the right tool for the job.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXSrzB1mFU2eTv9wXOLlbDtXt252NeXbksx5WCjKHTXTgr8ejh1Vw9pAPkEsRgOj8dd0Ah4BJVuHoFs2XMwzXDJePTy86qnZMOVRGfh91VECzW1BwW4pjz7xhUGOILZhjphBjH/s1600/journal.pone.0194889.t010.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="473" data-original-width="1600" height="116" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXSrzB1mFU2eTv9wXOLlbDtXt252NeXbksx5WCjKHTXTgr8ejh1Vw9pAPkEsRgOj8dd0Ah4BJVuHoFs2XMwzXDJePTy86qnZMOVRGfh91VECzW1BwW4pjz7xhUGOILZhjphBjH/s400/journal.pone.0194889.t010.PNG" width="400" /> </a></div>
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Machine Learning advocates can be expected to thrive in an environment lacking technically knowledgeable management. Coincidentally, there are two articles on Autosport.com extolling the virtues of Artificial Intelligence, the aforementioned '<a href="https://www.autosport.com/f1/feature/8009/why-artificial-intelligence-could-be-f1-next-big-thing">Why Artificial Intelligence could be F1's next big thing</a>', and '<a href="https://www.autosport.com/f1/feature/8795/the-dangerous-ai-tool-that-could-dominate-f1">The dangerous AI tool that could dominate F1</a>'. In the latter, <span class="article_text">Serguei Beloussov, boss of Acronis, asserts: "</span><span class="article_text">In F1, there are ultimately three areas that
you can apply machine learning - one is the race strategy, [the others are claimed to be logistics/operations and design]. There is some advantage, but not so much - because a race is a highly
random activity, so it is relatively difficult to make a sustainable
project because there is a lot of randomisation."</span></div>
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<span class="article_text">Now, Serguei is right about the difficulty of applying Machine Learning to race strategy, but he's completely misunderstood the principal reason. The problem is not the random element, and indeed, the random element (safety-cars and suchlike) is not the factor which dominates the logic of F1 race-strategy. </span></div>
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<span class="article_text">To the disappointment of many, F1 race-strategy is a perturbation of deterministic logic: when teams devise their race strategies, they do the deterministic calculations involving tyre-compound offsets, tyre-degradation, pit-losses, fuel-consumption and so forth, and then apply perturbations to the timing of pitstops based on game-theoretic considerations of undercuts and overcuts, and the importance of hedging against (or catching) safety-car and virtual safety-car periods. There's a random element, but it's not the dominant element.</span></div>
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<span class="article_text">No, what makes Machine Learning so difficult (at present) to apply to F1 race strategy is the fact that F1 is a game in which the rules are constantly changing. The sporting and technical regulations are constantly changing from one year to the next, altering the rules on starting tyre-sets, how many tyre compounds are available or need to be used, how difficult overtaking is, whether refuelling is permitted etc.; moreover, the performance characteristics of the tyres change from one race to the next, and the compounds and construction change from one year to the next. It's much more difficult to train an artificial neural network when the past data is, like this, essentially a collection of similar, but different games. </span></div>
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<span class="article_text">For example, you might try and estimate the overtaking difficulty at Paul Ricard based upon one year of data, without taking into account the fact that there was a headwind down the Mistral on that particular weekend, or the fact that the DRS effect was much stronger/weaker under the set of aero regulations in force that year; there might even have been a higher level of tyre degradation that year, which can have a disproportionate effect on traction, reducing the overtaking difficulty more than the pure lap-time deficit alone would indicate. </span></div>
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<span class="article_text">So, whilst it's difficult to see a long-term future in which all aspects of F1 activity are not influenced by artificial intelligence, in the short and medium-term, perhaps it's best to employ standard engineering practice: look at the nature of the problem, and choose the right tool for the job, rather than grabbing a sexy new tool and trying to find an application for it. </span> </div>
Gordon McCabehttp://www.blogger.com/profile/09151162643523937086noreply@blogger.com0tag:blogger.com,1999:blog-37936507.post-63348279062628783302019-07-14T13:35:00.002+01:002019-07-15T10:59:02.466+01:00The problem of refuelling<div style="text-align: justify;">
FIA President Jean Todt has floated the idea of <a href="https://www.bbc.co.uk/sport/formula1/48971037">re-introducing refuelling</a> to Formula 1, largely it seems to reduce the running-weight of the cars. According to Andrew Benson's BBC report, "Todt said he had been warned that the reintroduction of refuelling would
likely lead to teams' race strategies being too similar to each other
but countered that that was a product of there being too much simulation
in F1."</div>
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Quite. So let's have a quick look at why refuelling doesn't necessarily make race-strategy more interesting. Suppose we have the following fairly typical parameter values:</div>
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<b>Tyre-deg</b>: <b>0.05 sec/lap</b></div>
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<b>Fuel-effect: 0.033 sec/kg</b></div>
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<b>Fuel-consumption: 1.5 kg/lap</b></div>
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Suppose that the deterministically optimal first pit-stop would be after 20 laps. That requires a fuel-load of 30kg. Suppose that the second stint would also require a fuel-load of 30kg. The lap-time penalty for 30kg of fuel would be 30*0.033 = 1 sec.</div>
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After 20 laps, the cumulative tyre degradation would be 20*0.05 = 1 sec.</div>
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Suppose two cars with identical zero-fuel-load lap-times are racing each other. As we approach the first pit-stop window, there would be no benefit of the car behind trying to pit first to undercut the car ahead: the penalty of taking on 30kg of fuel cancels out the advantage of switching to a fresh set of tyres. The conventional undercut logic, which permits overtaking between equally matched cars, would be lost. </div>
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With this set of parameter values, there would also be no benefit to the car behind running longer: the cumulative tyre deg cancels out the benefit of lapping on almost empty fuel tanks. However, one might suspect that this result only follows from choosing a special set of parameter values, so let's assume that the tyre-deg is lower, at 0.03 sec/lap. Surely this would tip the balance in favour of running longer? </div>
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Well, suppose the car behind is planning to run 3 laps further in the race, to lap 23. That requires a starting fuel-load of 23*1.5 = 34.5kg. That's an extra 4.5kg which the car behind needs to carry around for the first 20 laps of the race. With a fuel-effect of 0.033 sec/kg, that's a lap-time penalty of 0.033*4.5 = 0.15 secs on every lap of the first 20 laps. So, if we assume both cars are running in free air, the car behind would have lost 3 secs of cumulative time after 20 laps (assuming the extra weight didn't also increase the tyre-deg).</div>
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With the assumed tyre-deg of 0.03 secs/lap, the cumulative deg after 20 laps would be 0.6 secs. Which is less than the 1 sec penalty for taking on 30kg of fuel. Hence, the car running to lap 23 would make up 0.4 secs/lap on the car which has pitted on lap 20. Over 3 laps, that would be 1.2 secs.</div>
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Would the car behind be able to overcut the car ahead? Unfortunately not. That extra fuel-weight has already cost it 3 secs over the first 20 laps of the race. The 1.2 secs regained still leaves a net loss of 1.8 secs when it finally pits on lap 23.</div>
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Obviously, if both cars were running in traffic, and the car ahead was unable to exploit its superior potential lap-time over the first 20 laps, then the overcut might still work.<br />
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In summary, however, we can see why refuelling pushes strategies towards the deterministic optima: if you try to overcut an opponent, the greater fuel-weight necessary for that is counter-productive; conversely, if there's any benefit to be had from undercutting an opponent, that benefit would be even greater in the absence of refuelling. </div>
Gordon McCabehttp://www.blogger.com/profile/09151162643523937086noreply@blogger.com0tag:blogger.com,1999:blog-37936507.post-16806099521867047632019-06-29T13:37:00.000+01:002019-06-29T13:46:08.789+01:00Flocculation and the Payne effect<div style="text-align: justify;">
With the quality of racing in contemporary Formula One reaching something of a nadir, some parties have sought a quick-fix by proposing that Pirelli revert to their thicker-gauge 2018 tread design. With tyres back on the agenda, then, perhaps it's a good moment to look a little bit deeper at the composition of a racing tyre tread. </div>
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A modern pneumatic tyre-tread contains rubber. Rubber itself consists of long chains of polymer molecules. The chains are mutually entangled, and in its raw form it is a highly-viscous liquid. It is not, however, elastic. It only becomes a viscoelastic solid when it undergoes 'vulcanization', whereby sulphur crosslinks are created between the molecular chains. This transforms the already entangled collection of polymer chains into a 3-dimensional network. </div>
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So far, so familiar. However, a modern tyre-tread is a rubber composite. In addition to the network of vulcanized rubber, it contains a network of 'filler' particles. These filler particles are not just dispersed as isolated particles in the rubber matrix; rather, they agglomerate into their own 3-dimensional network. (The term for this agglomeration is 'flocculation').</div>
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The rubber network and filler network interpenetrate each other. Hence, the elasticity, viscosity, and ultimately the frictional grip of a tyre-tread is attributable to three sources: (i) the cross-links and friction between rubber polymer molecules; (ii) the bonds between filler particles; and (iii) the bonds between filler particles and the rubber molecules.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgkDHqwcxFcdUvbssY2rGtH3U-A1SDWe7BnwHGq46PbXgvtqzDOBZbfO4UMpKop7i8bslFu6YqeCM-xzeQqWIHKtlct35krS5EB8YonOZd8bMf3GdJXOVhrmjqYL002baFm-AZM/s1600/carbon+rubber.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="446" data-original-width="329" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgkDHqwcxFcdUvbssY2rGtH3U-A1SDWe7BnwHGq46PbXgvtqzDOBZbfO4UMpKop7i8bslFu6YqeCM-xzeQqWIHKtlct35krS5EB8YonOZd8bMf3GdJXOVhrmjqYL002baFm-AZM/s400/carbon+rubber.jpg" width="295" /></a></div>
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'High-performance' racing tyres, of course, are something of a world of their own, and tend to use carbon-black as a filler in high concentrations because it increases hysteresis (i.e., viscous dissipation) and grip. One can find statements in the academic literature such as the following:</div>
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"For a typical rubber compound, roughly half of the energy dissipation during cyclic deformation can be ascribed to the agglomerated filler, the rest coming from [rubber polymer] chain ends and internal friction [of polymer network chains]," (Ulmer, Hergenrother and Lawson, 1988, '<i>Hysteresis Contributions in Carbon Black-filled rubbers containing conventional and tin end-modified polymers</i>').</div>
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Given the higher concentration of filler in a racing tyre, one might expect more than half of the energy dissipation, and therefore the frictional grip, to come from the agglomerated filler.</div>
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<div style="text-align: justify;">
And now comes the interesting bit. Filled rubber compounds suffer from the 'Payne effect'. This is typically defined by the variation in both the storage modulus, and the loss modulus (or tan-delta) of the tyre when it is subjected to a strain-sweep under cyclic loading conditions. (The storage modulus is related to the elasticity or stiffness of the material, and the loss modulus is related to the viscous dissipation).</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwrYoVYX0SbpNe-6Z-VWvHniLLff0NsDYeSAEcFYG2N6YkJtTT9DuLgJrQy64zkQVKP8elOhmYC8QwdmggjnuBIz67JrgXg1xJNlvI1-bqWHDxGHkhCCs3BsquDnd9hUpK8dNK/s1600/Payne+effect.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="561" data-original-width="816" height="275" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwrYoVYX0SbpNe-6Z-VWvHniLLff0NsDYeSAEcFYG2N6YkJtTT9DuLgJrQy64zkQVKP8elOhmYC8QwdmggjnuBIz67JrgXg1xJNlvI1-bqWHDxGHkhCCs3BsquDnd9hUpK8dNK/s400/Payne+effect.jpg" width="400" /></a></div>
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Typical graphs, such as that above, show that the storage modulus decreases as the amplitude of the strain is increased, whilst the loss-modulus or tan-delta reaches a peak at strains of 5-10%.</div>
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The Payne effect is typically attributed to the breaking of bonds between filler particles, as Pirelli World Superbike engineer <a href="https://www.cycleworld.com/2014/07/13/world-superbike-the-payne-effect/">Fabio Meni attests</a>:</div>
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<i>'Riders constantly talk about how their tires "take a step down" after a few laps, so I asked Meni what physical process in the rubber is responsible for this perceived drop in properties. "This has a name", he began. "It is called the Payne effect."</i></div>
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<i><br /></i>
<i>"In the compound," Meni continued, "the carbon-black particles are not present as separate entities but exist as aggregates - clusters of particles. As the tire is put into service, the high strains to which it is subjected have the effect of breaking up these aggregates over time, and this alters the rubber's properties."</i></div>
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<i>Meni went on to say that it is not so much that the tire loses grip as it feels different to the rider. This is 'the step' that the rider feels after a few laps, after which the tire's properties may change little through the rest of the race.</i></div>
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In fact, I would quibble with this slightly: in the world of Formula One tyres, the way in which a tyre is treated at the beginning of a stint will often determine the subsequent degradation slope. If you abuse a tyre, it remembers it, and punishes you. Damage to the filler network appears to reduce grip, not merely soften a tyre.</div>
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One intriguing twist to the Payne effect is that there may be circumstances in which it is possible for a tyre to recover from damage to the filler network: "Much of the softening remains when the amplitude [of the strain in a cyclic strain-sweep] is reduced back to small values and the original modulus is recovered only after a period of heating at temperatures of the order of 100 degrees C or higher," (A.N.Gent, '<i>Engineering with Rubber'</i>, 2012, p115).</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiockDe9Y3S4QAGx3Q5RbEHIWNaujKg9aQBaNEwArYyk-C1u1l3Bofpzf_Gy9c0T_GO0sWGTUOLKjjCAbIZG0mMc6ItO-ldtxU3o6L_YTRcBlG4Hjwi_Gtjypbj2SDrpFVupDEM/s1600/c5ra25423j-s2_hi-res.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="316" data-original-width="980" height="128" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiockDe9Y3S4QAGx3Q5RbEHIWNaujKg9aQBaNEwArYyk-C1u1l3Bofpzf_Gy9c0T_GO0sWGTUOLKjjCAbIZG0mMc6ItO-ldtxU3o6L_YTRcBlG4Hjwi_Gtjypbj2SDrpFVupDEM/s400/c5ra25423j-s2_hi-res.gif" width="400" /></a></div>
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So heat is capable of annealing a damaged filler network, restoring the bonds between filler particles. The anneal temperature quoted here by Gent is not dissimilar to the maximum tyre-blanket temperatures currently permitted by Pirelli in Formula One...</div>
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As a final flourish on this subject, for those who like a bit of scanning electron microscopy, images of filler-reinforced rubber which has been in a state of slip across a rough surface, reveal that there is a modified 'dead' surface layer, about a micron-thick, in which the carbon-black filler particles are absent, (image below from work conducted by Marc Masen of Imperial College).</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglrw-6XKuUkDrB3T0xdpQBC99L_HbB_ltUpTUlHIg6qbzZkWMJR00-2fSFW_Xwr5LvsNwg_L2MO-W8c6c8nFnT_LKQb-ElHnReWw4oIKgqmFOWo3VcrTuqtYOzxWXfHaKrFdWc/s1600/Surface.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="581" data-original-width="493" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglrw-6XKuUkDrB3T0xdpQBC99L_HbB_ltUpTUlHIg6qbzZkWMJR00-2fSFW_Xwr5LvsNwg_L2MO-W8c6c8nFnT_LKQb-ElHnReWw4oIKgqmFOWo3VcrTuqtYOzxWXfHaKrFdWc/s400/Surface.jpg" width="338" /></a></div>
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To paraphrase Homer Simpson, "Here's to tyres: the cause of, and solution to, all of Formula One's problems."</div>
Gordon McCabehttp://www.blogger.com/profile/09151162643523937086noreply@blogger.com0tag:blogger.com,1999:blog-37936507.post-66984558971614684112019-02-06T18:38:00.000+00:002019-05-13T00:46:49.749+01:00Assessing the nuclear winter hypothesis<div style="text-align: justify;">
After falling into disrepute for some years, the nuclear winter hypothesis has enjoyed something of a renaissance over the past decade. In the January 2010 edition of <i>Scientific American</i>, two of the principal proponents of the hypothesis, Alan Robock and Owen Brian Toon, published an article summarising recent work. This article focused on the hypothetical case of a regional nuclear war between India and Pakistan, in which each side dropped 50 nuclear warheads, with a yield of 15-kilotons each, on the highest population density targets in the opponent's territory.</div>
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Robock and his colleagues assumed that this would result in at least 5 teragrams of sooty smoke reaching the upper troposphere over India and Pakistan. A climate model was developed to calculate the effects, as Robock and Toon report:</div>
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"<i>The model calculated how winds would blow the smoke around the world and how the smoke particles would settle out from the atmosphere. The smoke covered all the continents within two weeks. The black, sooty smoke absorbed sunlight, warmed and rose into the stratosphere. Rain never falls there, so the air is never cleansed by precipitation; particles very slowly settle out by falling, with air resisting them...</i><br />
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<i>"The climatic response to the smoke was surprising. Sunlight was immediately reduced, cooling the planet to temperatures lower than any experienced for the past 1,000 years. The global average cooling, of about 1.25 degrees Celsius (2.3 degrees Fahrenheit), lasted for several years, and even after 10 years the temperature was still 0.5 degree C colder than normal. The models also showed a 10 percent reduction in precipitation worldwide...Less sunlight and precipitation, cold spells, shorter growing seasons and more ultraviolet radiation would all reduce or eliminate agricultural production.</i>," (<a href="http://climate.envsci.rutgers.edu/pdf/RobockToonSciAmJan2010.pdf"><i>Scientific American</i>, January 2010</a>, p78-79).<br />
<br />
These claims seem to have been widely believed within the scientific community. For example, in 2017 <i>NewScientist</i> magazine wrote a Leader article on the North Korean nuclear problem, which asserted that: "those who study nuclear war scenarios say millions of tonnes of smoke
would gush into the stratosphere, resulting in a nuclear winter that
would lower global temperatures for years. The ensuing global crisis in
agriculture – dubbed a “nuclear famine” – would be devastating," (<a href="https://www.newscientist.com/article/mg23431223-300-talk-of-a-localised-nuclear-conflict-is-ignorant-and-dangerous/"><i>NewScientist</i>, 22nd April 2017</a>).<br />
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But is there any way of empirically testing the predictions made by Robock and his colleagues? Well, perhaps there is. In 1945, the Americans inflicted an incendiary bombing campaign on Japan prior to the use of nuclear weapons. Between March and June of 1945, Japan's six largest industrial centres,
Tokyo, Nagoya, Kobe, Osaka, Yokohama and Kawasaki, were devastated. As
military historian John Keegan wrote, “Japan's flimsy wood-and-paper
cities burned far more easily than European stone and brick...by
mid-June...260,000 people had been killed, 2 million buildings destroyed
and between 9 and 13 million people made homeless...by July 60 per cent
of the ground area of the country's sixty larger cities and towns had
been burnt out,” (<i>The Second World War</i>, 1989, p481).<br />
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This devastation created a huge amount of smoke, so what effect did it have on the world's climate? Well Robock and Brian Zambri have recently published a paper, '<a href="http://Did Smoke From City Fires in World War II Cause Global Cooling?">Did smoke from city fires in World War II cause global cooling?</a>', (<i>Journal of Geophysical Research: Atmospheres</i>, 2018, 123), which addresses this very question.<br />
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Robock and Zambri use the following equation to estimate the total mass of soot $M$ injected into the lower stratosphere:<br />
$$<br />
M = A\cdot F\cdot E\cdot R \cdot L \;.<br />
$$ $A$ is the total area burned, $F$ is the mass of fuel per unit area, $E$ is the percentage of fuel emitted as soot into the upper troposphere, $R$ is the fraction that is not rained out, and $L$ is the fraction lofted from the upper troposphere into the lower stratosphere. Robock and Zambri then make the following statements:<br />
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"<i>Because the city fires were at nighttime and did not always persist until daylight, and because some of the city fires were in the spring, with less intense sunlight, we estimate that L is about 0.5, so based on the values above, M for Japan for the summer of 1945 was about 0.5 Tg of soot. However, this estimate is extremely uncertain.</i>"<br />
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But then something strange happens at this point, because the authors make no attempt to quantify the uncertainty, or to place confidence intervals around their estimate of 0.5 teragrams.<br />
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I'll come back to this shortly, but for the moment simply note that 0.5 teragrams is one-tenth of the amount of soot which is assumed to result from a nuclear exchange between India and Pakistan, a quantity of soot which Robock and his colleagues claim is sufficient to cause a worldwide nuclear winter.<br />
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Having obtained their estimate that 0.5 teragrams of soot reached the lower stratosphere in 1945, Robock and Zambri examine the climate record to see if there was any evidence of global cooling. What they find is a reduction in temperatures at the beginning of 1945, before the bombing of Japan, but no evidence of cooling thereafter: "The injection of 0.5–1 Tg of soot into the upper troposphere from city fires during World War II would be expected to produce 0.1–0.2 K global average cooling...when examining the observed signal further and comparing them to natural variability, it is not possible to detect a statistically significant signal."<br />
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Despite this negative result, Robock and Zambri defiantly conclude that "Nevertheless, these results do not provide observational support to counter nuclear winter theory." However, the proponents of the nuclear winter hypothesis now seem to have put themselves in the position of making the following joint claim:<br />
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<i>'5 teragrams of soot would cause a global nuclear winter, but the 0.5 teragrams injected into the atmosphere in 1945 didn't make a mark in the climatological record.'</i><br />
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Unfortunately, their analysis doesn't even entitle them to make this assertion, precisely because they failed to quantity the uncertainty in that estimate of 0.5 teragrams. The omission rather stands out like a sore thumb, because there are well-known, routine methods for calculating such uncertainties.<br />
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Let's go through these methods, starting with the formula $M = A\cdot F\cdot E\cdot R \cdot L \;.$ The uncertainty in the input variables here propagates through to the uncertainty in the output variable, the mass $M$. It seems reasonable to assume that the input variables here are mutually independent, so the uncertainty $U_M$ in the output variable can be inferred by a simple formula from the uncertainties attached to each of the input variables:<br />
$$<br />
U_M = \sqrt{(U_A^2 + U_F^2+U_E^2+U_R^2+U_L^2)} \;.<br />
$$ $U_A$ is the uncertainty in the total area burned, $U_F$ is the uncertainty in the mass of fuel per unit area, $U_E$
is the uncertainty in the percentage of fuel emitted as soot into the upper troposphere,
$U_R$ is the uncertainty in the fraction that is not rained out, and $U_L$ is the uncertainty in the fraction
lofted from the upper troposphere into the lower stratosphere.<br />
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Next, to infer confidence intervals, we can follow the prescriptions of the IPCC, the Intergovernmental Panel on Climate Change. The 2010 <i>Scientific American</i> article boasts that Robock is a participant in the IPCC, so he will surely be familiar with this methodology.<br />
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First we note that because $M$ is the product of several variables, its distribution will tend towards a lognormal distribution, or at least a positively skewed distribution resembling the lognormal. The IPCC figure below depicts how the upper and lower 95% confidence limits can be inferred from the uncertainty in a lognormally distributed quantity. The uncertainty $U_M$ corresponds to the 'uncertainty half-range' in IPCC terms. <br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhy3Xis1aQQaMbatw4QGhALud77p48QHjvJBQoikhJNcFKD6wAw6EXd5Mvb5KbzDmWBJW2WOSOp9nc0etf0Mz5St20uLvRZ40n8XDqIvA3Zad_KEWiYMG21GATlSN1T1iwFtAVN/s1600/confidence.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="474" data-original-width="984" height="192" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhy3Xis1aQQaMbatw4QGhALud77p48QHjvJBQoikhJNcFKD6wAw6EXd5Mvb5KbzDmWBJW2WOSOp9nc0etf0Mz5St20uLvRZ40n8XDqIvA3Zad_KEWiYMG21GATlSN1T1iwFtAVN/s400/confidence.jpg" width="400" /></a></div>
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The IPCC figure "illustrates the sensitivity of the lower and upper bounds of the 95 percent probability range, which are the 2.5th and 97.5th percentiles, respectively, calculated assuming a lognor<span class="highlight begin selected">mal</span><span class="highlight end selected"> distr</span>ibution based upon an estimated uncertainty half-range from an error propagation approach. The uncertainty range is approximately symmetric relative to the mean up to an uncertainty half-range of approximately 10 to 20 percent. As the uncertainty half-range, U, becomes large, the 95 percent uncertainty range shown [in the Figure above] becomes large and asymmetric, "(<i><a href="https://www.ipcc-nggip.iges.or.jp/public/2006gl/pdf/1_Volume1/V1_3_Ch3_Uncertainties.pdf">IPCC </a></i><i><a href="https://www.ipcc-nggip.iges.or.jp/public/2006gl/pdf/1_Volume1/V1_3_Ch3_Uncertainties.pdf"><i>Guidelines for National Greenhouse Gas Inventories - Uncertainties</i>, 3.62</a></i>).</div>
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So, for example, given the large uncertainties in the input variables, the uncertainty half-range $U_M$ for the soot injected into the lower stratosphere in 1945 might well reach 200% or more. In this event, the upper limit of the 95% confidence interval would be of the order of +300%. That's +300% relative to the best estimate of 0.5 Tg. Hence, at the 95% confidence level, the upper range might well extend to the same order of magnitude as the hypothetical quantity of soot injected into the stratosphere by a nuclear exchange between India and Pakistan. </div>
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Thus, the research conducted by Robock and Zambri fails to exclude the possibility that the empirical data from 1945 falsifies the nuclear winter hypothesis for the case of a regional nuclear exchange. </div>
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In a sense, then, it's clear when Robock and Zambri refrained from including confidence limits in their paper. What's more perplexing is how and why this got past the referees at the <i>Journal of Geophysical Research...</i></div>
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Gordon McCabehttp://www.blogger.com/profile/09151162643523937086noreply@blogger.com0tag:blogger.com,1999:blog-37936507.post-65033703342540772332019-01-13T12:34:00.000+00:002019-01-13T12:37:49.563+00:00Thruxton British F3 1989<div style="text-align: justify;">
The thickness of the atmospheric thermal boundary layer falls to a global minimum over Thruxton. Hence Thruxton is very cold. So much so, in fact, that the British Antarctic Survey have a station there, built into the noise-attenuation banking at the exit of The Complex, (much like a Hobbit-hole), where the younger scientists train to work in a frozen environment before travelling to the Halley Research Station on the Brunt ice shelf.</div>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVIliyM0oBjzId7VmLrcRisfSaMk2-3BO523eMXlbXagKE9nSVLZmMchP7PoHJ1aIIxR6vatBC_qSUZm3o116aTrWIvjXWeM0R63_-eZ5LlhFnB0bm1Ln_TYN6r4_0haH9jqt0/s1600/Thrux2.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="588" data-original-width="863" height="272" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVIliyM0oBjzId7VmLrcRisfSaMk2-3BO523eMXlbXagKE9nSVLZmMchP7PoHJ1aIIxR6vatBC_qSUZm3o116aTrWIvjXWeM0R63_-eZ5LlhFnB0bm1Ln_TYN6r4_0haH9jqt0/s400/Thrux2.jpg" width="400" /></a></td></tr>
<tr align="justify"><td class="tr-caption"><b>The late Paul Warwick in the Intersport Reynard. Puzzlingly, in the background there appear to be no takers for the shelter provided by the parasols.</b></td><td class="tr-caption"></td></tr>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuogcERC8YZxJyCY4Rpuh9RBrUB62cPKOMybYjVyENoaq1J-ZlvS-TYcZsLFyUEamqOVIHW_Qyxz9no2A3oTMZM_kLdK5vfp-uK9xVVHHDfwhKv5N-iONorKr7uPi8V5d1D-Wj/s1600/Thrux1.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="591" data-original-width="849" height="277" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuogcERC8YZxJyCY4Rpuh9RBrUB62cPKOMybYjVyENoaq1J-ZlvS-TYcZsLFyUEamqOVIHW_Qyxz9no2A3oTMZM_kLdK5vfp-uK9xVVHHDfwhKv5N-iONorKr7uPi8V5d1D-Wj/s400/Thrux1.jpg" width="400" /></a></td></tr>
<tr align="justify"><td class="tr-caption"><b>In 1869, <a href="http://www.rigb.org/our-history/iconic-objects/iconic-objects-list/tyndall-blue-sky">John Tyndall discovered why the sky is blue</a>. If he'd lived in Thruxton, the question wouldn't even have occurred to him. Note the characteristic Wiltshire combination of distant mist, a stand of lifefless trees, and flat wind-swept expanses. </b></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8C7V_IfxmZ397IYCv9xyDXwaqCEP4YuiZR2eDsB_vyIZ58Mf1t28htY30D6XgbhxZwCfyYXhnXAj_zr_xKx9l966W2gcAZ0sIfgTG2V8w6R696zJVT7x3posnROltl8CtZFAT/s1600/Thrux3.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="575" data-original-width="850" height="270" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8C7V_IfxmZ397IYCv9xyDXwaqCEP4YuiZR2eDsB_vyIZ58Mf1t28htY30D6XgbhxZwCfyYXhnXAj_zr_xKx9l966W2gcAZ0sIfgTG2V8w6R696zJVT7x3posnROltl8CtZFAT/s400/Thrux3.jpg" width="400" /></a></td></tr>
<tr align="justify"><td class="tr-caption"><b><b>Marshals assist a driver who has entered a turnip field. </b>The Wiltshire economy is entirely dependent upon (i) the annual turnip yield, and (ii) government subsidies into the thousand-year consultation process for a Stonehenge bypass/tunnel. The buildings in the background are what people from Wiltshire refer to as a 'collection of modern luxury flats and town-houses.' </b></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjUDUh2Wth_Y4bHTIiXnX7chW56v7XJ3mMs3jvAYXXjRogAIIlmrwvCtrsI0yD0ATyxttZWRSPHlTJImNtvpyBxkeNYtKWcgxCK62hDECvQFwJpC5XF4_5HWihCwVrNlJpBXjKq/s1600/Thrux4.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="451" data-original-width="865" height="207" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjUDUh2Wth_Y4bHTIiXnX7chW56v7XJ3mMs3jvAYXXjRogAIIlmrwvCtrsI0yD0ATyxttZWRSPHlTJImNtvpyBxkeNYtKWcgxCK62hDECvQFwJpC5XF4_5HWihCwVrNlJpBXjKq/s400/Thrux4.jpg" width="400" /></a></td></tr>
<tr align="justify"><td class="tr-caption"><b>One of the drivers is distracted by an ancient ley line running tangential to the Brooklands kink. </b></td></tr>
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Gordon McCabehttp://www.blogger.com/profile/09151162643523937086noreply@blogger.com0tag:blogger.com,1999:blog-37936507.post-48832465924013428732019-01-11T00:42:00.000+00:002019-01-11T00:42:12.338+00:00Silverstone Tyre Test 1990<div style="text-align: justify;">
Generally speaking, it was impossible to see a car with the naked eye at Silverstone. However, with the assistance of the world's best astronomical optics, I was occasionally able to pluck an image out of the infinitesimally small strip separating the cold, grey sky from the wooden fence posts and metal railings.</div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIfRh3iBW41JrSb9EtUPyBl3l73SVIf7GylnxrwN0_iQnuUODBjrvtjRDXdnlYwGK0smxFBdvoXVl46ZnNWtFMDp74SE-XpPVAmjGrgz-sw_BWC3lvy9nup7yi3fr0aTBPE8-K/s1600/90_2.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="582" data-original-width="874" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIfRh3iBW41JrSb9EtUPyBl3l73SVIf7GylnxrwN0_iQnuUODBjrvtjRDXdnlYwGK0smxFBdvoXVl46ZnNWtFMDp74SE-XpPVAmjGrgz-sw_BWC3lvy9nup7yi3fr0aTBPE8-K/s400/90_2.jpg" width="400" /></a></td></tr>
<tr align="justify"><td class="tr-caption"><b>Satoru Nakajima in the pioneering raised-nose Tyrrell 019. This image was obtained with the Wide Field and Planetary Camera on the Hubble Space Telescope.</b></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZVHr7IImuEyxVisPgQmPFSzyPD0ua7FtQ59fVchOstos6qLFEit1oVflv_TPxz37EY30cnXKJIABgJWHk71Fhyphenhyphen506ShXt88GUA9Td7-AWazKmiFfu8PBIi71v19_tp7FodUlE/s1600/90_1.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="580" data-original-width="765" height="302" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZVHr7IImuEyxVisPgQmPFSzyPD0ua7FtQ59fVchOstos6qLFEit1oVflv_TPxz37EY30cnXKJIABgJWHk71Fhyphenhyphen506ShXt88GUA9Td7-AWazKmiFfu8PBIi71v19_tp7FodUlE/s400/90_1.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Alessandro Nannini in the Benetton. This shot was taken with the 100-inch reflector on Mount Wilson.</b></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGQx-zVR_R0biPkPgL7fHzd0nxS9oDIm3pyIaEippp5OfXr_3QCDmVMRcTZv6ftxwJoSYNYls90Kycrvj_LTkjh2rfRZ1l7gDxG4PjNoS3gaGvKyIMAWuYWSjDx2z8xRv75mTj/s1600/90_3.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="558" data-original-width="778" height="286" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGQx-zVR_R0biPkPgL7fHzd0nxS9oDIm3pyIaEippp5OfXr_3QCDmVMRcTZv6ftxwJoSYNYls90Kycrvj_LTkjh2rfRZ1l7gDxG4PjNoS3gaGvKyIMAWuYWSjDx2z8xRv75mTj/s400/90_3.jpg" width="400" /></a></td></tr>
<tr align="justify"><td class="tr-caption"><b>Nigel Mansell, lighting up the front brake discs as he prepares for the turn-in to Copse. Nigel set the fastest lap on the day I attended the test; a mid-season pattern of performance which led Ferrari to reward Nigel by handing his chassis over to Prost.</b></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdXix1GJ9eA1j92FGV58AfrNQubfQH6UZQolFn7zUPm2NbgzF4ruOhGO3MyJLhMQT2O8Pdu-JjdjTdeB_n4fiZbEP2LDK-0tIVZ4-l_0M648vd3K7OKo4uWQoz-RC6xiJ45YFk/s1600/90_4.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="556" data-original-width="870" height="255" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdXix1GJ9eA1j92FGV58AfrNQubfQH6UZQolFn7zUPm2NbgzF4ruOhGO3MyJLhMQT2O8Pdu-JjdjTdeB_n4fiZbEP2LDK-0tIVZ4-l_0M648vd3K7OKo4uWQoz-RC6xiJ45YFk/s400/90_4.jpg" width="400" /></a></td></tr>
<tr align="justify"><td class="tr-caption"><b>Ayrton Senna in characteristic pose, head dipped forward and tilted towards the rapidly approaching apex of Copse corner . </b></td></tr>
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Gordon McCabehttp://www.blogger.com/profile/09151162643523937086noreply@blogger.com0tag:blogger.com,1999:blog-37936507.post-19323164699678383552019-01-03T17:09:00.003+00:002019-01-05T12:41:26.389+00:00Formula One and Electro-Aerodynamics<div style="text-align: justify;">
Most travelling Formula One engineers probably think that an 'ionic wind' is the result of over-indulgence at the end-of-season curry night. On the contrary, in late 2018 a group of researchers from MIT <a href="https://www.theguardian.com/science/2018/nov/21/first-ever-plane-with-no-moving-parts-takes-flight">published a paper in <i>Nature</i></a> detailing how an ionic wind was used for the first-ever flight of a heavier-than-air, self-propelled device with no mechanical moving parts. </div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEialnfBcHrx3uo7OB1rtdJ3gq5uF88dbTjlIbgjF7iM9t2OMMj8kYg1YU7fndb2HXs5ep4gG0gEsHiZgoayUjbjwMNWBct7wOp3MjLZ4hDBTBEFQw6-ym14xqRTfu8ERJdoJiwg/s1600/ionic+wind.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="606" data-original-width="642" height="377" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEialnfBcHrx3uo7OB1rtdJ3gq5uF88dbTjlIbgjF7iM9t2OMMj8kYg1YU7fndb2HXs5ep4gG0gEsHiZgoayUjbjwMNWBct7wOp3MjLZ4hDBTBEFQw6-ym14xqRTfu8ERJdoJiwg/s400/ionic+wind.jpg" width="400" /></a></div>
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The ionic wind was created by generating an ionic cascade between the paired elements in an array of high-voltage electrodes. Each positive electrode was a 0.2mm stainless-steel wire supported in front of a wing-section. The corresponding negative electrode was a thin layer of aluminium foil on the downstream wing-section. The ions are accelerated in the electric field, and impart some of their momentum to the ambient air-flow, thereby generating a forward thrust, (and in this case, presumably, some lift). </div>
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Ultra-light power-sources were used: a custom-made 600W battery, and a custom-made High-Voltage Power Converter (HVPC), yielding a DC voltage of ~40kV. The battery weighed only 230g, and the HVPC weighed 510g.</div>
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The thrust generated by the experimental device was ~3N, from a wing-span of 5.14m, so the thrust itself isn't about to grab the attention of the Formula One community. However, one might instead be tempted to re-task such ionic wind devices with accelerating the boundary layer flow in certain areas, enabling one to avoid separation at moments of <i>extremis</i>.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjo1Mx2wlevcf9ITPZXXHogejTVfsmDJ6Iak-RIPfCS_uNvrRbW6bFBvB68MHoRSNcxBe-1MV9e1ARR0shMD-kHfVKhNJMVOC8cp5vm5updghgcsEDpO-ZNyKC0k6FYrDLtXEqq/s1600/IW.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="384" data-original-width="451" height="340" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjo1Mx2wlevcf9ITPZXXHogejTVfsmDJ6Iak-RIPfCS_uNvrRbW6bFBvB68MHoRSNcxBe-1MV9e1ARR0shMD-kHfVKhNJMVOC8cp5vm5updghgcsEDpO-ZNyKC0k6FYrDLtXEqq/s400/IW.jpg" width="400" /></a></td></tr>
<tr align="justify"><td class="tr-caption"><b>Ionic wind accelerating the flow at the bottom of the boundary layer. (From '<i>Ionic winds for locally enhanced cooling</i>', Go, Garimella, Fisher & Mongia, Journal of Applied Physics 102, 2007). This retards separation by delaying the point at which the slope of the velocity profile, at the wall, becomes zero. </b></td></tr>
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Plasma-actuators for boundary layer control have been under aeronautical development for some years, and unfortunately their use in Formula One seems to have already been proscribed. The Technical Working Group notes for December 2006 contain a request for clarification on the issue from James Allison, and in response Charlie Whiting declares that he had "already given a negative opinion, based on moving parts influencing the car's aerodynamics."</div>
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This is a slightly puzzling response, because the whole point about plasma actuators and ionic winds is that they involve no moving mechanical parts. The objects in motion are electrical currents, and the ambient airflow itself, both of which are considered to be consistent with the regulations, and indeed necessary for the function of a Formula One car.</div>
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So perhaps there's a future here for electro-aerodynamics in Formula One. It would be an exciting line of research, and one which might also be considered beneficial to Formula One's environmental credentials. </div>
Gordon McCabehttp://www.blogger.com/profile/09151162643523937086noreply@blogger.com0tag:blogger.com,1999:blog-37936507.post-34714415612850132222018-12-31T20:39:00.000+00:002018-12-31T20:39:38.839+00:00Andrew Ridgeley crashes at Brands<div style="text-align: justify;">
It's the 1986 Cellnet Superprix, the rain is relentless, and it's dark, very dark. Too dark, in fact, for those amateur photographers foolish enough to have arrived with nothing other than 100 ASA film...</div>
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The field is strong, containing future luminaries such as Martin Donnelly, Perry McCarthy, Damon Hill, Gary Brabham, Andy Wallace, David Leslie and Julian Bailey. Also entered is Andrew Ridgeley, George Michael's partner in contemporary pop-duo <i>Wham!</i> </div>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHBO-wHHzpcMMbYyr85fAThKD5UBzVQ0q2emSvIcg_LyaVENeNJbeLAGao8FQ3NhnFbSuDJI1s-ImCTqNlgwjB52xpia0Ynf1rYA8NhH0KhM00HI5jqNqzLhg627EiJSel9b8d/s1600/AR0.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="586" data-original-width="879" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHBO-wHHzpcMMbYyr85fAThKD5UBzVQ0q2emSvIcg_LyaVENeNJbeLAGao8FQ3NhnFbSuDJI1s-ImCTqNlgwjB52xpia0Ynf1rYA8NhH0KhM00HI5jqNqzLhg627EiJSel9b8d/s400/AR0.jpg" width="400" /></a></td></tr>
<tr align="left"><td class="tr-caption"><b>Failing to compensate for the reduction in the effective power-spectrum of the road-surface, Ridgeley Go-Goes into the gravel at Druids...</b></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0zUDNfiUHWlyMVu4OJXRaHQ6AEmV-LO4XkBaVaT2NDur_o-Ddexp_Neo7KiJB2fshYCNnNcK18QUj2n4JreDvVOs9Au0hpx5oYLV_7X97_dvZ1I08nu8K32zfmOAxE01WEEID/s1600/AR1.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="592" data-original-width="853" height="277" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0zUDNfiUHWlyMVu4OJXRaHQ6AEmV-LO4XkBaVaT2NDur_o-Ddexp_Neo7KiJB2fshYCNnNcK18QUj2n4JreDvVOs9Au0hpx5oYLV_7X97_dvZ1I08nu8K32zfmOAxE01WEEID/s400/AR1.jpg" width="400" /></a></td></tr>
<tr align="left"><td class="tr-caption"><b>His momentum is somewhat checked by the Cellnet cars of Ross Cheever and David Hunt, which have already found the tyre-wall.</b></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhf_I-tTTfD9Rs4iVyuUmC5xYnM-OZrOVeSsVREQv2CtLr1Ot5yV7NsYp5Nw38ayKjN6VmuVzN-CDcWjfX0afY2Ki77NmSd_fCcLNwVqmTkzV3xN5D6rmtJ5qUPYfiBSXCEER5K/s1600/AR2.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="584" data-original-width="873" height="267" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhf_I-tTTfD9Rs4iVyuUmC5xYnM-OZrOVeSsVREQv2CtLr1Ot5yV7NsYp5Nw38ayKjN6VmuVzN-CDcWjfX0afY2Ki77NmSd_fCcLNwVqmTkzV3xN5D6rmtJ5qUPYfiBSXCEER5K/s400/AR2.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Nothing for it but to head back to the Kentagon for a warming cup of tea.</b></td></tr>
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Gordon McCabehttp://www.blogger.com/profile/09151162643523937086noreply@blogger.com0tag:blogger.com,1999:blog-37936507.post-59716302898877089802018-12-28T12:50:00.000+00:002018-12-29T15:40:41.591+00:00Brands Hatch F3000 1987<div style="text-align: justify;">
Second installment of the McCabism photographic archive. The place once again is Brands Hatch, this time for a round of the European F3000 championship. By 1987 the Grand Prix had moved to the numbing wind-swept expanses of Silverstone, so this was very much Brands' biggest single-seater race of the year.</div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1GAdAs3Nq70XHyV3C0Cv2Knz2NJ-_6Sgr58UGPQb6KnwrwRm6RxWZwPs-uJVFdjDRJTS6EodTuijp2hmVPO62s9IboLkkCvuuoAVQPb2FFDkgo6ioBjoOHCtZZUlfilDdDl_u/s1600/87a.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="594" data-original-width="853" height="277" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1GAdAs3Nq70XHyV3C0Cv2Knz2NJ-_6Sgr58UGPQb6KnwrwRm6RxWZwPs-uJVFdjDRJTS6EodTuijp2hmVPO62s9IboLkkCvuuoAVQPb2FFDkgo6ioBjoOHCtZZUlfilDdDl_u/s400/87a.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>F3000 cars of the era tended to be<i> sans</i> engine cover. This is the Madgwick Motorsport Lola of Andy Wallace.</b></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgCAJbFPjgH0OEIbIKtmUBRJZNfjWhAEbTQB792UXqawIe0HTRxEqulTmV4EkiPz-skrdiCKfMaxO54hSeFNFRnKC9ampZZE5OEcVyqOYXmcse6ZuKyEnegnC109fPA_XQCYj4w/s1600/87b.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="583" data-original-width="872" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgCAJbFPjgH0OEIbIKtmUBRJZNfjWhAEbTQB792UXqawIe0HTRxEqulTmV4EkiPz-skrdiCKfMaxO54hSeFNFRnKC9ampZZE5OEcVyqOYXmcse6ZuKyEnegnC109fPA_XQCYj4w/s400/87b.jpg" width="400" /></a></td></tr>
<tr align="justify"><td class="tr-caption"><b>The absent engine cover facilitated tall intake trumpets, which maximise torque at lower revs, F3000 engines being restricted to 9,000rpm. (When the intake valve opens, it creates a rarefaction wave, which propagates to the top of the open-ended trumpet, and reflects as a compression wave. The lower the revs, the longer the necessary trumpet length so that the compression wave returns just as the intake valve is closing, pushing more mass into the combustion chamber). This is the Pavesi Racing Ralt of Pierluigi Martini.</b></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizDkAhfpaXW_AU8jVFvJ3av0ivVigmnr_xwYdnM9y-GVCiPG_b1mDEIashHD3dL3z0kgMflekNBxqtuuxQNcU93NTcF_b-jGi1b4Y4T7-UlYN6jC3YTLaIRItbfvM0uf47Q1TJ/s1600/87g.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="583" data-original-width="870" height="267" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizDkAhfpaXW_AU8jVFvJ3av0ivVigmnr_xwYdnM9y-GVCiPG_b1mDEIashHD3dL3z0kgMflekNBxqtuuxQNcU93NTcF_b-jGi1b4Y4T7-UlYN6jC3YTLaIRItbfvM0uf47Q1TJ/s400/87g.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>This is a <i>motor racing circuit</i>. It possesses gradient and contour, exists in a natural setting, and is distinguishable from a go-kart track.</b></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-_YuGmOXkpebK0X30VYKJ_9xKjh1tj700JGfaRu15JKAxO44M_nyv9fJQ9qjgpR3k7zQFaLtczhInqU8z0fZ3RPeUvnepDYH-gTmr7zTZ5O3W9W1Gj8IddZaTalTaweeNNFeu/s1600/87c.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="587" data-original-width="851" height="275" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-_YuGmOXkpebK0X30VYKJ_9xKjh1tj700JGfaRu15JKAxO44M_nyv9fJQ9qjgpR3k7zQFaLtczhInqU8z0fZ3RPeUvnepDYH-gTmr7zTZ5O3W9W1Gj8IddZaTalTaweeNNFeu/s400/87c.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>First corner of the race, and Julian Bailey has immediately overtaken the front-row sitters, Gugelmin and Moreno in their Ralts.</b></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmNcF8GE90yg-4feyFlMOD08_FQiJXHyEpAnNNFulc1wpcJJQWSLtN6uLdiZpD1yNSJH9Bllu-TeCMYRCJ6ZYG5xeej6LiNrBlBmR7KVxNuAkED4QTNKPdCKNMaxYqpZT7oKtJ/s1600/87e.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="583" data-original-width="872" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmNcF8GE90yg-4feyFlMOD08_FQiJXHyEpAnNNFulc1wpcJJQWSLtN6uLdiZpD1yNSJH9Bllu-TeCMYRCJ6ZYG5xeej6LiNrBlBmR7KVxNuAkED4QTNKPdCKNMaxYqpZT7oKtJ/s400/87e.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Andy Wallace moves past Moreno into 3rd, but Bailey looks comfortable in the lead.</b></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6vFXgWOw6WaBY_cdjtFe0C4U7BbTP07d1Sm3WHqYITlEnIFBC9Wa0PScF25NqOOCqucUXDeAFTOEyZjVPtt13-oa6A-W3VbrugUd-JwgRGDU8jBbrL-y1IMuc78-tKXS79I24/s1600/87d.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="592" data-original-width="848" height="278" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6vFXgWOw6WaBY_cdjtFe0C4U7BbTP07d1Sm3WHqYITlEnIFBC9Wa0PScF25NqOOCqucUXDeAFTOEyZjVPtt13-oa6A-W3VbrugUd-JwgRGDU8jBbrL-y1IMuc78-tKXS79I24/s400/87d.jpg" width="400" /></a></td></tr>
<tr align="justify"><td class="tr-caption"><b>Stefano Modena ahead of Yannick Dalmas, the latter displaying a black tyre-mark on his nose-cone as evidence of prior contact with Modena. Dalmas had tapped Modena into a spin at Druids, but courteously waited for Modena to resume ahead of him.</b></td><td class="tr-caption"></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhjBW3wFa1OD76T_Ex4DC4AvQ-k8z_CwPUDqZwBJzaCOX5d4GobX8XBhPk8laGpibKd1rx2DIgKT2UCn9wmK75fW-53P1OguKN3t2l8PJNStS4SQudKnrJMfJgFc-RxAfHbia13/s1600/87h.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="588" data-original-width="871" height="270" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhjBW3wFa1OD76T_Ex4DC4AvQ-k8z_CwPUDqZwBJzaCOX5d4GobX8XBhPk8laGpibKd1rx2DIgKT2UCn9wmK75fW-53P1OguKN3t2l8PJNStS4SQudKnrJMfJgFc-RxAfHbia13/s400/87h.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Michel Trolle has a territorial dispute at Druids with A Yorkshireman. This inevitably results in a large accident, Trolle's car flipping upside down onto the top of the tyre-wall.</b></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEifACARndP_xKEm-dQWhmfakypy8d2k8ffCx3y0Bn11mzMP7gLZ6_E5Oey5bF2jOC2jhsNCl6vSv3_ss_cq5ovdWog7YW3aXbSiqu0lcQAzPamPTzaksdqJyE-c8ChajiFknhfE/s1600/87f.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="586" data-original-width="617" height="378" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEifACARndP_xKEm-dQWhmfakypy8d2k8ffCx3y0Bn11mzMP7gLZ6_E5Oey5bF2jOC2jhsNCl6vSv3_ss_cq5ovdWog7YW3aXbSiqu0lcQAzPamPTzaksdqJyE-c8ChajiFknhfE/s400/87f.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>A slightly shocked Trolle stumbles to his feet after being hauled from the upturned car.</b></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNZ7-obhJFiV5OVQxdqnPO2JIs1wZ0aLTf_v5PlgrtfB3iqYpujQOF4o-lhuhcZI2izoZgla8i2psEGpsLficAgKVEFp0_6IFtVBraROF2F8C_vjbKn87Hu-4XEo4GJpWq40fp/s1600/87g.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="582" data-original-width="868" height="267" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNZ7-obhJFiV5OVQxdqnPO2JIs1wZ0aLTf_v5PlgrtfB3iqYpujQOF4o-lhuhcZI2izoZgla8i2psEGpsLficAgKVEFp0_6IFtVBraROF2F8C_vjbKn87Hu-4XEo4GJpWq40fp/s400/87g.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>The race is red-flagged and Bailey awarded victory.</b></td></tr>
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<br />Gordon McCabehttp://www.blogger.com/profile/09151162643523937086noreply@blogger.com0tag:blogger.com,1999:blog-37936507.post-57156398886118821242018-12-23T21:24:00.004+00:002018-12-24T00:05:11.044+00:00Brands Hatch Tyre Test 1986Time to dip into the McCabism personal photographic archive. The occasion here is the 1986 pre-Grand Prix Tyre Test at Brands Hatch.<br />
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Proper drivers, proper cars, and a proper circuit. <br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxxgKOBr5B6EauwtzbkkNjiZwQj3CgvRa2Z22w474px_TAcX5ohf48xCyp3xjF3F1j3P9LKOpn5HPFn9rCFTTi-ovnmvnRom821b7RB_JzbjSc7xZZoEoDUz6pLAr5BfwjrqzI/s1600/BH1.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="632" data-original-width="957" height="263" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxxgKOBr5B6EauwtzbkkNjiZwQj3CgvRa2Z22w474px_TAcX5ohf48xCyp3xjF3F1j3P9LKOpn5HPFn9rCFTTi-ovnmvnRom821b7RB_JzbjSc7xZZoEoDUz6pLAr5BfwjrqzI/s400/BH1.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Nigel Mansell zipping down the pit-straight in a car weighing less than 700kg.</b></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyz-uUOK3ylGX1z6OIlpzhPeX4LTMqmgiPWxJNoq28OKe5q8UVw6YaIKQj8UwoKhNfBhOigIVSpxJhElzBgWJt6-nMVC85Q2MaSaVWv3AbMXkV5Pf-5ocBTwh-UAAGNlO-lS25/s1600/BH3.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="625" data-original-width="915" height="272" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyz-uUOK3ylGX1z6OIlpzhPeX4LTMqmgiPWxJNoq28OKe5q8UVw6YaIKQj8UwoKhNfBhOigIVSpxJhElzBgWJt6-nMVC85Q2MaSaVWv3AbMXkV5Pf-5ocBTwh-UAAGNlO-lS25/s400/BH3.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Stefan Johansson's Ferrari, in the days before people from Northern Europe and South Africa introduced the Scuderia to the exciting world of stable balanced downforce.</b></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1WL7vhNDQ5d83FAImEzdIKSJSipMu9Ney_dzV5z0oLISB3KRKzKdlzdHTKjnrFXSEe9SSpMsX1Y-7u_TfQyEzfZAmrtjiz9FaOy_S6lAiSc-AtxsBrnl99wlyh0w9kXb1djxV/s1600/BH2.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="626" data-original-width="902" height="277" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1WL7vhNDQ5d83FAImEzdIKSJSipMu9Ney_dzV5z0oLISB3KRKzKdlzdHTKjnrFXSEe9SSpMsX1Y-7u_TfQyEzfZAmrtjiz9FaOy_S6lAiSc-AtxsBrnl99wlyh0w9kXb1djxV/s400/BH2.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Nelson Piquet, plotting and scheming as he brakes for the hairpin at Druids.</b></td><td class="tr-caption" style="text-align: center;"><b><br /></b></td><td class="tr-caption" style="text-align: center;"><b><br /></b></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-UOh0z7AmDulRbFermYhg9rjA_wcBh56L4du6g72oRCMIzSKr6Tk4XatKu6G3GmgqWd5U3Tua2swtdjrdvGPN9Yd1DayC7HcKVkg5CjBCZc3SkP9va1o_iJf11bxQm-x5C6ND/s1600/BH4.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="619" data-original-width="899" height="275" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-UOh0z7AmDulRbFermYhg9rjA_wcBh56L4du6g72oRCMIzSKr6Tk4XatKu6G3GmgqWd5U3Tua2swtdjrdvGPN9Yd1DayC7HcKVkg5CjBCZc3SkP9va1o_iJf11bxQm-x5C6ND/s400/BH4.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Ayrton Senna negotiating the curved flow at Hawthorns. </b></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmoYIh__lZuOzRTen39Xhf7gv550p-C_zn-5IhGgnzy8_IZAZBxvh2t29IzCgKQLLEg3pxjXVwmobXWr2SUDBihi4LquMGF1rlZ4qJ3KHt6iDJBlVeSdXZHC6QYq6zIvy6grTi/s1600/BH5.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="592" data-original-width="844" height="280" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmoYIh__lZuOzRTen39Xhf7gv550p-C_zn-5IhGgnzy8_IZAZBxvh2t29IzCgKQLLEg3pxjXVwmobXWr2SUDBihi4LquMGF1rlZ4qJ3KHt6iDJBlVeSdXZHC6QYq6zIvy6grTi/s400/BH5.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Poking my camera over the bridge parapet to get a shot of Keke Rosberg accelerating down the hill to Clearways.</b></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGFnx7LEmhOqleH6QyUeSZaZgVJeNBPZe2A2DpVEZM4rdBZqU92lPhQAWETRmyq9_N0JMp2DbljM169rtiHtcAJipCaOA1IG9JoMiRiB9cyP-EGp9N_CfkEzBYNJ_BSaG631mo/s1600/BH6.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="589" data-original-width="869" height="270" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGFnx7LEmhOqleH6QyUeSZaZgVJeNBPZe2A2DpVEZM4rdBZqU92lPhQAWETRmyq9_N0JMp2DbljM169rtiHtcAJipCaOA1IG9JoMiRiB9cyP-EGp9N_CfkEzBYNJ_BSaG631mo/s400/BH6.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Nigel Mansell in the pits, complaining of an excessive surface/bulk tyre temperature delta, and some inconsistent behaviour from the Y250 vortex.</b></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgv2CfZEIMVLzu4N9y_Teu11L4cbHcdNYEq9j3YUBCZh6FBlwhwHLcr86kwMcJXX8NB8vl0LIrEAE9bdp0p8rK5nROKbm7XpfZwKmGsjNRjoXibHMye1jq-m7gvwPkc1jU_lXt1/s1600/BH7.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="579" data-original-width="843" height="273" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgv2CfZEIMVLzu4N9y_Teu11L4cbHcdNYEq9j3YUBCZh6FBlwhwHLcr86kwMcJXX8NB8vl0LIrEAE9bdp0p8rK5nROKbm7XpfZwKmGsjNRjoXibHMye1jq-m7gvwPkc1jU_lXt1/s400/BH7.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Ayrton Senna cresting the rise after the sylvan delights of Dingle Dell, and preparing to turn into Dingle Dell corner.</b></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhftHcjzbcUp3fm1-GvU-IVvGolpY3aWUoYxXcAmY5saWrdjTSVzqSw9VW5IURoRBZPXmUlAL7MuriOXIxvmy-TxL4hw-4ii5c0lh1_HHtE7f_ZvE-dvq9IgCgDwIt_nxlAwkuf/s1600/BH8.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="582" data-original-width="868" height="267" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhftHcjzbcUp3fm1-GvU-IVvGolpY3aWUoYxXcAmY5saWrdjTSVzqSw9VW5IURoRBZPXmUlAL7MuriOXIxvmy-TxL4hw-4ii5c0lh1_HHtE7f_ZvE-dvq9IgCgDwIt_nxlAwkuf/s400/BH8.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Keke Rosberg in the McLaren, somehow living to tell the tale without a halo for protection.</b></td></tr>
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Gordon McCabehttp://www.blogger.com/profile/09151162643523937086noreply@blogger.com0tag:blogger.com,1999:blog-37936507.post-45385098381717831862018-07-19T22:14:00.000+01:002018-07-31T11:44:45.544+01:00Understanding tyre compound deltas<div style="text-align: justify;">
Pirelli revealed at the beginning of the 2018 F1 season that it was using new <a href="https://www.autosport.com/f1/news/134906/new-pirelli-software-to-spice-up-f1-strategies">software to help it choose the three tyre compounds</a> available at each race. Pirelli's Racing Manager Mario Isola commented:</div>
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<div style="text-align: justify;">
<i>"It's important that we collect the delta lap times between compounds to decide the selection. If
we confirm the numbers that we have seen in Abu Dhabi [testing in
November] - between soft and supersoft we had 0.6s, and supersoft to
ultrasoft was 0.4s - depending on that, we can fine tune the selection
and try to choose the best combination."</i></div>
<br />
<div style="text-align: justify;">
Getting the tyre compound deltas correct is indeed a crucial part of F1 race strategy, so let's review some of the fundamental facts about these numbers. The first point to note is that tyres are a performance <i>multiplier</i>, rather than a performance <i>additive</i>. </div>
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<div style="text-align: justify;">
To understand this in the simplest possible terms, consider the following equation:</div>
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$$F_y = \mu F_z $$<i> </i>This states that the lateral force $F_y$ generated by a tyre is a product of the coefficient of friction $\mu$, and the vertical load $F_z$. All other things being equal, the greater the lateral force generated by a car in the corners, the faster the laptime. (Note, however, that in many circumstances one would wish to work with lateral acceleration rather than lateral force, given the influence of car-mass on lateral acceleration).</div>
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<br /></div>
<div style="text-align: justify;">
Now, suppose we have a base compound. Let's call it the Prime, and let's denote its coefficient of friction as $\mu_P$. Let's consider a fixed car running the Prime tyre with: (i) a light fuel-load, and (ii) a heavy fuel-load. </div>
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<br /></div>
<div style="text-align: justify;">
Let's really simplify things by supposing that the performance of the car, and its laptime, can be reduced to a single vertical load due to downforce alone, and a single lateral force number. When the car is running a heavy fuel load, it will generate a downforce $F_z$, but when it's running a light fuel load it will be cornering faster, so the vertical load due to downforce will be greater, $F_z + \delta F_z$. (Recall that the contribution of greater fuel weight to vertical load results in a net loss of lateral acceleration due to weight transfer). The lateral forces will be as follows:</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<b><u>Prime tyre. High fuel-load</u></b></div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
$\mu_P F_z $</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<b><u>Prime tyre. Low fuel-load</u></b><br />
<br /></div>
<div style="text-align: justify;">
</div>
<div style="text-align: justify;">
$\mu_P (F_z + \delta F_z) = \mu_P F_z + \mu_P\delta F_z$</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Now, let's suppose that there is a softer tyre compound available. Call it the Option. Its coefficient of friction $\mu_O$ will be greater than that of the Prime, $\mu_O = \mu_P + \delta \mu$. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Consider the performance of the same car on the softer compound, again running a light fuel-load and a heavy fuel-load:</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<b><u>Option tyre. High fuel-load</u></b><br />
<br /></div>
<div style="text-align: justify;">
</div>
<div style="text-align: justify;">
$\mu_O F_z = ( \mu_P +\delta \mu ) F_z $</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<b><u>Option tyre. Low fuel-load</u></b><br />
<br /></div>
<div style="text-align: justify;">
</div>
<div style="text-align: justify;">
$\mu_O (F_z + \delta F_z) = ( \mu_P +\delta \mu )(F_z + \delta F_z) $</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
So far, so good. Now let's consider the performance deltas between the Option and the Prime, once again using lateral force as our proxy for laptime. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<b><u>High-fuel Option-Prime delta</u></b></div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
$( \mu_P +\delta \mu ) F_z-\mu_P F_z = \delta \mu F_z$</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<b><u>Low-fuel Option-Prime delta</u></b><br />
<br /></div>
<div style="text-align: justify;">
</div>
$( \mu_P +\delta \mu )(F_z + \delta F_z)-\mu_P (F_z + \delta F_z)=\delta \mu (F_z + \delta F_z)$<br />
<br />
<div style="text-align: justify;">
Notice that sneaky extra term, $\delta \mu \delta F_z$, in the expression for the low-fuel compound delta? As a consequence of that extra term, the Option-Prime delta is greater on a low fuel load than a heavy fuel-load. As promised, tyre-grip is a performance multiplier.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
If you scrutinise the compound deltas in each FP2 session, you'll see that the low-fuel compound deltas from the beginning of the session are indeed greater than those from the high-fuel running later in the session. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Given that the compound deltas input into race-strategy software are generally high-fuel deltas, one could make quite a mistake by using those low-fuel deltas. In fact, parties using low-fuel deltas might be surprised to see more 1-stop races than they were expecting.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
There is another important consequence of the fact that tyres are performance multipliers: the pace gap between faster cars and slower cars increases when softer tyres are supplied. The faster cars have more downforce, and therefore more vertical load $F_z$ than the slower cars, at any equivalent fuel-weight. The delta in vertical load is multiplied by the delta in the coefficient of friction, and all things being equal, the faster cars duly benefit from that extra $\delta \mu \delta F_z$. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Of course, that qualification about 'all things being equal', hides some complex issues. For example, softer tyres have a lower 'cornering stiffness', (i.e., the gradient of lateral force against slip-angle). A softer tyre therefore generates peak grip at a higher slip-angle than a harder tyre. If the aerodynamics of a car are particularly susceptible to the steering angle of the front wheels, then such a car might struggle to gain proportionately from the greater grip theoretically afforded by a softer tyre. Such a car would also appear to gain, relative to its opposition, towards the end of a stint, when the tyres are worn and their cornering stiffness increases.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Notwithstanding such qualifications, the following problem presents itself: the softer the tyres supplied to the teams in an attempt to enhance the level of strategic variety, the greater the pace-gaps become, and the less effect that strategic variety has... </div>
Gordon McCabehttp://www.blogger.com/profile/09151162643523937086noreply@blogger.com0tag:blogger.com,1999:blog-37936507.post-14585809683867582272018-05-15T20:34:00.002+01:002018-05-15T20:48:54.417+01:00Front-wing in yaw<div style="text-align: justify;">
Armchair aerodynamicists might be interested in a 2015 paper, '<a href="https://dspace.lib.cranfield.ac.uk/bitstream/handle/1826/12288/Yaw_Paper_June-15%20(2).pdf?sequence=1">Aerodynamic characteristics of a wing-and-flap in ground effect and yaw</a>'. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
The quartet of authors from Cranfield University analyse a simple raised-nose and front-wing assembly, consisting of a main-plane and a pair of flaps, equipped with rectangular endplates. On each side of the wing, three vortices are created: an upper endplate vortex, a lower endplate vortex, and a vortex at the inboard edge of the flap. (The latter is essentially a weaker version of the Y250 which plays such an important role in contemporary F1 aerodynamics). </div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh26oI4_JP8XSgn3KvJrhVKFLB_-_DdbjngEMrtV5OOv5-j_9v5aodtoPDcTjPmZekE5kCXabQD7zfMHVQ1Nc5uLWBhFUY5IrgDbEOEhXp6ZnOv5Nu_SBOSlHPbqFgpx2CTmUBq/s1600/Yaw1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="599" data-original-width="776" height="308" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh26oI4_JP8XSgn3KvJrhVKFLB_-_DdbjngEMrtV5OOv5-j_9v5aodtoPDcTjPmZekE5kCXabQD7zfMHVQ1Nc5uLWBhFUY5IrgDbEOEhXp6ZnOv5Nu_SBOSlHPbqFgpx2CTmUBq/s400/Yaw1.jpg" width="400" /></a></div>
<div style="text-align: justify;">
<br />
The authors assess their front-wing in yaw, using both CFD and the wind-tunnel, and make the following observations:</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
1) In yaw, vortices generated by a lateral movement of air in the same direction as the free-stream, increase in strength, whereas those which form due to air moving in the opposite direction are weakened.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
2) The leeward side of the wing generates more downforce than the windward side. This is due to an increase in pressure on the leeward pressure surface and a decrease in suction on the windward suction surface. The stagnation pressure is increased on the inner side of the leeward endplate, and the windward endplate partially blocks the flow from entering the region below the wing.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
3) A region of flow separation occurs on the windward flap suction surface.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
4) Trailing edge separation occurs in the central region of the wing. This is explained by the following: (i) The aluminium wing surface was milled in the longitudinal direction, hence there is increased surface roughness, due to the material grain, for air flowing spanwise across the surface; (ii) There is a reduction in the mass flow-rate underneath the wing; (iii) The effective chord-length has increased in yaw.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
5) The vortices follow the free-stream direction. Hence, for example, the windward flap-edge vortex is drawn further towards the centreline when the wing is in yaw. </div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLB9kzII-sEUtyiA1TPTq30ccXq3N4xcH4K0Be7mC42ydrChngkXSpqhcIX74s6i2X3OVuyZ6DiQRHc9qB0cMPvcQ1W8SDCFWLMMAzcGL-5BCi4lP3amg5BNIaLDlU97oJFO8b/s1600/Yaw2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="630" data-original-width="714" height="352" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLB9kzII-sEUtyiA1TPTq30ccXq3N4xcH4K0Be7mC42ydrChngkXSpqhcIX74s6i2X3OVuyZ6DiQRHc9qB0cMPvcQ1W8SDCFWLMMAzcGL-5BCi4lP3amg5BNIaLDlU97oJFO8b/s400/Yaw2.jpg" width="400" /></a></div>
<br />
One comment of my own concerns the following statement:<br />
<br />
<div style="text-align: justify;">
"The yaw rate for a racing car can be high, up to 50°/sec, but is only significant aerodynamically during quick change of direction events, such as initial turn-in to the corner. The yaw angle, however, is felt throughout the corner and is usually in the vicinity of 3-5°. Although the yaw angle changes throughout the corner the yaw rate is not sufficiently high, other than for the initial turn-in event, to warrant any more than quasi-static analysis."</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
This is true, but it's vital to point out that the stability of a car in the dynamic corner-entry condition determines how much speed a driver can take into a corner. If the car is unstable at the point of corner-entry, the downforce available in a quasi-static state of yaw will be not consistently accessible. </div>
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<br /></div>
<div style="text-align: justify;">
Aerodynamicists have an understandable tendency to weight conditions by their 'residency time'. i.e., the fraction of the grip-limited portion of a lap occupied by that condition. The fact that the high yaw-rate corner-entry condition lasts for only a fraction of a second is deceptive. Minimum corner speed depends not only on the downforce available in a quasi-static state of yaw, but whether the driver can control the transition from the straight-ahead condition to the quasi-static state of yaw.</div>
Gordon McCabehttp://www.blogger.com/profile/09151162643523937086noreply@blogger.com0tag:blogger.com,1999:blog-37936507.post-77825993915056383182018-04-29T22:09:00.002+01:002018-04-29T23:21:40.845+01:00Local cosmography and the Wiener filter<div style="text-align: justify;">
The local cosmic neighbourhood has recently been mapped in spectacular fashion by the <a href="https://arxiv.org/pdf/1306.0091.pdf">Cosmicflows</a> research programme, yielding papers in <i>Nature</i>, and an article in <i>Scientific American</i>. The images generated are stunning. <br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3WF507DKhKluKWGHVhb5CS1iOtQkY5G9nJrkkuWjfXy8Y97ThlK3gJOE6yr724i9jJrK9Tes7hOOSSTVA4FFaIKdNI23Qb0SkDqTIdrepmtINAdrtQiNRurB8Y4Wz7HtB50Hq/s1600/Mog4.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="567" data-original-width="1009" height="223" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3WF507DKhKluKWGHVhb5CS1iOtQkY5G9nJrkkuWjfXy8Y97ThlK3gJOE6yr724i9jJrK9Tes7hOOSSTVA4FFaIKdNI23Qb0SkDqTIdrepmtINAdrtQiNRurB8Y4Wz7HtB50Hq/s400/Mog4.jpg" width="400" /></a></td></tr>
<tr align="left"><td class="tr-caption">Perspective view of the X-Y equatorial plane of our cosmic neighbourhood in supergalactic coordinates. The density of matter is represented by colour contours, deep blue regions
indicating voids, red indicating zones of high density. The velocity streams are represented
in white, with individual galaxies as spheres.</td><td class="tr-caption"><br /></td><td class="tr-caption"><br /></td></tr>
</tbody></table>
</div>
<div style="text-align: justify;">
There's also an interesting mathematical back-story here because the work has been underpinned by techniques developed over 20 years ago by Yehuda Hoffman and colleagues. Drawing upon the <a href="https://link.springer.com/chapter/10.1007%2F978-3-540-44767-2_17">exposition provided by Hoffman</a>, let's take a look at these methods, beginning with Gaussian fields.<br />
<br />
<b><u>Gaussian fields</u></b><br />
<br />
A random field is a field in which the value at each point is sampled from a univariate probability distribution, and the values at multiple points are sampled from a multivariate distribution. Typically, the sampled values at different points are spatially correlated, with a degree of correlation that declines with distance.<br />
<br />
A Gaussian field is a type of random field in which the distribution at each point is Gaussian, and relationship between the values at different points is given by a multivariate Gaussian distribution. The properties of a Gaussian field are specified by its covariance matrix. Assuming a Gaussian field $\mathbf{s}$ of zero mean, this is denoted as:<br />
$$<br />
\mathbf{S} = \langle \mathbf{s} \mathbf{s}^T\rangle <br />
$$ Treating $\mathbf{s}$ as a vector of random variables, this expression is understood as the 'outer-product' of the column vector $\mathbf{s}$ with its transpose row vector $\mathbf{s}^T$:<br />
$$<br />
\mathbf{S} = {\langle s_i s_j \rangle} <br />
$$<b><u>Convolution</u></b></div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Given the Gaussian field $\mathbf{s}$, the generation of the measured data-set $\mathbf{d}$ is represented as follows: <br />
$$<br />
\mathbf{d} = \mathbf{Rs} + \mathbf{\epsilon} <br />
$$ $\mathbf{R}$ represents the characteristics of the measuring instrument, and $\epsilon$ represents measurement noise. The covariance matrix of the noise is denoted as follows:<br />
$$<br />
\mathbf{N} = \langle \mathbf{\epsilon} \mathbf{\epsilon}^T\rangle <br />
$$ The transformation $\mathbf{R}$ is typically a convolution. In astronomical measurements of the sky it is often referred to as the Point Spread Function. It specifies how the energy detected to belong to a particular pixel of the sky is actually a weighted sum of the energy belonging to a range of adjacent pixels. Similarly, in spectroscopy it specifies how the energy detected at each particular wavelength is actually a weighted sum of the energy belonging to adjacent wavelengths, thereby smearing out the energy spectrum.<br />
<br />
Given the true spectrum $f(\lambda)$, and the convolution kernel $g(\lambda - \lambda_1)$, the measured spectrum $I(\lambda)$ is defined by the convolution:<br />
$$<br />
I(\lambda) = f * g = \int f(\lambda_1) g(\lambda - \lambda_1) d\lambda_1<br />
$$</div>
<div style="text-align: justify;">
<b><u>Wiener filter </u></b></div>
<div style="text-align: justify;">
<br />
Stochastic filtering provides a collection of techniques for constructing estimates of the true values of a quantity or field from sparse and noisy measurement data. The Wiener filter is one such technique. It provides a transformation $\mathbf{F}$ that maps a measured dataset $\mathbf{d}$ into an estimate of the true field:<br />
$$<br />
\mathbf{s}^{WF} = \mathbf{F} \mathbf{d} <br />
$$ The discrepancy between the true field and the estimated field is called the
residual:<br />
$$<br />
\mathbf{r} = \mathbf{s} - \mathbf{s}^{WF}<br />
$$ The residual possesses its own covariance matrix $\langle \mathbf{r}\mathbf{r}^T \rangle$. The Wiener filter is defined so that it minimizes the covariance of the residual.<br />
<br />
The Wiener filter possesses another property which makes it the natural choice of filter for cosmography: Given the prior distribution of the true field $\mathbf{s}$; given the relationship between the true field and the measured values; and given the measured values, a posterior Bayesian distribution $p(\mathbf{s}|\mathbf{d})$ can be obtained over the true field. In the case where the true field is a Gaussian field, and the noise is also Gaussian, the Wiener filter picks out the mean value of the posterior distribution.<br />
<br />
The Wiener filter is given by the expression:<br />
$$<br />
\mathbf{F} = \mathbf{SR}^T (\mathbf{RSR}^T + \mathbf{N})^{-1} <br />
$$</div>
<b><u>Constrained realizations</u></b><br />
<br />
<div style="text-align: justify;">
The method of constrained realizations goes back to a paper by Yehuda Hoffman and Erez Ribak in 1991 ('<i>Constrained realizations of Gaussian fields - A simple algorithm</i>', Ap. J. Lett., vol 380, pL5-L8). It's based upon a simple but crucial point:
the application of the Wiener filter to a measured dataset will produce
an estimated field which includes the covariance of the residual: $$\mathbf{s}^{WF} = \mathbf{s} - \mathbf{r}$$</div>
<div style="text-align: justify;">
Hence, the estimated field will be smoother than the true field. The idea proposed by Hoffman and Ribak is simple: to generate a realistic realization of the true field, you need to add a sampled realization from the residual field.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Their method works as follows:</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
(i) Generate a random realization $\tilde{\mathbf{s}}$ of the true field. (The tilde here indicates a realization).</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
(ii) Generate a realization of the measurement noise, and apply the measurement transformation to $\tilde{\mathbf{s}}$ to yield a random dataset realization: $$\mathbf{\tilde{d}} = \mathbf{R\tilde{s}} + \mathbf{\tilde{\epsilon}}$$ </div>
<div style="text-align: justify;">
(iii) Apply the Wiener filter to $\mathbf{\tilde{d}}$ to create an estimate of the true field realization: $\mathbf{F} \mathbf{\tilde{d}} $.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
</div>
<div style="text-align: justify;">
(iv) Generate a realization of the residual: </div>
<div style="text-align: justify;">
$$\mathbf{\tilde{r}} = \tilde{\mathbf{s}} - \mathbf{F} \mathbf{\tilde{d}} $$ </div>
<div style="text-align: justify;">
(v) Add the realization of the residual to the estimated field which has been obtained by applying the Wiener filter to the actual measured dataset: </div>
<div style="text-align: justify;">
$$\eqalign{\mathbf{s}^{CR} &= \mathbf{\tilde{r}} + \mathbf{Fd} \cr &=\tilde{\mathbf{s}}+ \mathbf{F} (\mathbf{d-\tilde{d}})}$$</div>
<div style="text-align: justify;">
</div>
<div style="text-align: justify;">
<b><u>Reconstruction of continuous fields from finite data</u></b><br />
<br />
Here the Gaussian field $\mathbf{s}$ is assumed to be a function $f(\mathbf{r})$, so that the covariance matrix becomes the auto-correlation function $\xi$:<br />
<br />
$$<br />
\mathbf{S} = \langle f(\mathbf{r}_i) f(\mathbf{r}_j)\rangle = \xi(\mathbf{r}_i,\mathbf{r}_j) <br />
$$ Assume that measurements are made of this field at a finite number of points, ${F_i}$. If there is no convolution operation, so that $\mathbf{R} = \mathbf{I}$, then in this case the combined application of the Wiener filter and constrained realization yields the following expression:<br />
$$<br />
f(\mathbf{r})^{CR} = \tilde{f}(\mathbf{r})+ \xi(\mathbf{r}_i,\mathbf{r})
( \xi(\mathbf{r}_i,\mathbf{r}_j) + \mathbf{N}_{ij} )^{-1}(F_j-\tilde{f}(\mathbf{r}_j))<br />
$$ Repeated indices are summed over here.</div>
<div style="text-align: justify;">
<b><br /></b>
<b><u>Cosmicflows</u></b><br />
<br />
The Cosmicflows research programme applied these techniques to a finite collection of sparse and noisy galaxy recession velocities to reconstruct the full 3-dimensional peculiar velocity field in our local cosmic neighbourhood. (The latter is defined to be a length-scale of the order 100 Mpc). 'Peculiar' velocities in this context are those which remain after the recession velocity due to cosmic expansion has been subtracted.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSTFW5Ff1qp3_nGDnm31AndQI8o9G8X02i68nunDXvs_g3PTBjd9_1dFNYbYWWzYqkV7vOWGPpp6GNrW58ILV7FDCHORctIjtadygj2Nfz1LgiijZR6ZPF2W2kjUBuV99tPmMN/s1600/Mog5.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="511" data-original-width="606" height="336" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSTFW5Ff1qp3_nGDnm31AndQI8o9G8X02i68nunDXvs_g3PTBjd9_1dFNYbYWWzYqkV7vOWGPpp6GNrW58ILV7FDCHORctIjtadygj2Nfz1LgiijZR6ZPF2W2kjUBuV99tPmMN/s400/Mog5.jpg" width="400" /></a></td></tr>
<tr align="left"><td class="tr-caption">Our cosmic neighbourhood,within a cube 200Mpc on each side. The Milky Way is located at the origin of coordinates. There are three isodensity colour contours. The velocity flows are depicted as black lines.</td></tr>
</tbody></table>
Assuming that cosmic structure formation has been seeded by perturbations sampled from a Gaussian random field, and assuming that the expansion of the universe followed the Lambda-Cold Dark Matter ($\Lambda$CDM) model, the combination of the Wiener filter and Constrained Realization was applied to a sample of galaxy recession velocities along the line-of-sight. The density field in our neighbourhood was then inferred from the reconstructed velocity field.<br />
<br />
Some of the most striking images produced by the Cosmicflows team are those which depict the streamlines of the peculiar velocity field in our cosmic neighbourhood. These reveal regions in which the streamlines converge, due to concentrations in the density of matter such as the Great Attractor, and regions in which the streamlines diverge from cosmic voids. In particular, the Cosmicflows team have attempted to identify the surface of divergent points that surrounds us. They define the volume within that watershed as our local galaxy Supercluster, which they name '<a href="https://arxiv.org/ftp/arxiv/papers/1409/1409.0880.pdf">Laniakea</a>'.<br />
<br />
The Cosmicflows programme assumes only linear deviations from homogeneity and isotropy. This assumption preserves the Gaussian nature of the peculiar velocity field and the density perturbation field. But it does have the consequence that the velocity field is irrotational. i.e, it possesess zero vorticity. Hence, the images of cosmic streamlines contain watersheds, but no whirlpools. Whilst the linear theory should prevail on large scale, the non-linearity should dominate on smaller scales. The Cosmicflows team claim that the non-linearity should only dominate on the Mpc length-scale, and that their approach is therefore valid.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhbx7K1prkfq14NeaHgEkDjeLJmWAho3RHu9jTWqxRqJ49uoUPK-k7_3ypN_njW61vcDYmuW584eeUyaKNLDS-MpZRpFRPxE-NjnUycqF-H7kDk1I7PpPZCJ0roWYlpWYaoaDJU/s1600/Mog6.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="520" data-original-width="928" height="223" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhbx7K1prkfq14NeaHgEkDjeLJmWAho3RHu9jTWqxRqJ49uoUPK-k7_3ypN_njW61vcDYmuW584eeUyaKNLDS-MpZRpFRPxE-NjnUycqF-H7kDk1I7PpPZCJ0roWYlpWYaoaDJU/s400/Mog6.jpg" width="400" /></a></td></tr>
<tr align="left"><td class="tr-caption">A slice through the equatorial plane in the supergalactic coordinate system. The boundary of the Laniakea supercluster is depicted as an orange line. The diagram is shaded with density contours, deep blue regions indicating voids, and red regions indicating zones of high density. The velocity streams within the Laniakea basis of attraction are represented in white.</td></tr>
</tbody></table>
<br /></div>
Gordon McCabehttp://www.blogger.com/profile/09151162643523937086noreply@blogger.com0tag:blogger.com,1999:blog-37936507.post-77391327589533114312017-12-03T09:54:00.001+00:002017-12-03T18:26:46.364+00:00Neural networks and the neutron transport equation<div style="text-align: justify;">
<br />
The Monte Carlo simulation technique was <a href="http://permalink.lanl.gov/object/tr?what=info:lanl-repo/lareport/LA-UR-88-9067">conceived at Los Alamos in the late 1940s by Stanislaw Ulam and John von Neumann</a> with a specific application in mind: neutron transport and nuclear fission chain-reactions. Perhaps, however, other simulation techniques are now available. I'd like to propose one such alternative below, but first we need to understand what the neutron transport problem is.<br />
<br />
The neutron transport equation is a special case of the Boltzmann transport equation, the primary equation of non-equilibrium statistical mechanics. In the general case of the Boltzmann equation, the quantity of interest is a distribution function on phase-space, which specifies the expected number of particles per unit of phase-space volume. (At low particle-number densities, one might refer to the probability of particle occupancy per unit of phase-space volume). </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
In the case of the neutron transport equation, the quantity of interest can be taken to be $n(\mathbf{r},\mathbf{v},t)$, the expected number of neutrons per unit of physical space about $\mathbf{r}$, per unit of velocity space about $\mathbf{v}$, at time $t$. (Whilst, strictly speaking, phase space deals with position and momentum, it is often interchangeable with position and velocity).</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
The Boltzmann equation is of some philosophical interest because it can be used to describe the approach of a system towards equilibrium. Certainly, a population of high-energy neutrons in a region of space
occupied by non-fissile atomic nuclei at room temperature, would transfer energy to the atomic nuclei by means of elastic and inelastic scattering interactions, and approach a state of
equilibrium. The neutrons would 'thermalise', their energy spectrum
approaching that of a Maxwell-Boltzmann distribution, with a temperature
equal to that of the background nuclei.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
However, the neutron transport equation can be deployed to describe the evolution of the neutron population in a nuclear reactor, and such a system remains, for a reasonable period of time, and with the appropriate control systems, in a stable state far-from-equilibrium.<br />
<br />
A fissile chain reaction occurs when neutrons are absorbed by heavy atomic nuclei, which fission into smaller, more stable nuclei, and emit high-energy neutrons in the process. By means of this fissile chain reaction, the neutron temperature, flux and number density can be maintained at a constant level, despite intensive interactions with a background population of atomic nuclei at a much lower temperature. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
There are two populations of particles here, which remain at different temperatures despite being in contact with each other. The system therefore remains out of thermal equilibrium. Nevertheless, the entropy of the system is
still increasing because the fission reactions release the free energy of the
heavy fissile isotopes, and transform it into heat. A nuclear reactor is, of course, far from being a closed system, and stability far-from-equilibrium is only possible in this case if the heat generated by the fissile reactions is transported away, typically by conduction into a liquid or gas, which convectively transports the heat to a location outside the reactor vessel. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Before we define the neutron transport equation, let's begin with some definitions. Let's start with the neutron flux, $\phi(\mathbf{r},\mathbf{v},t) = v \;n(\mathbf{r},\mathbf{v},t)$. For each neutron energy level $E = 1/2 m_n v^2$, (where $m_n$ is the rest-mass of a neutron), this is the number of neutrons at a point $\mathbf{r}$ passing through a unit surface area, per unit time. For each energy level $E$, it is equivalent to the total path length travelled by the energy-$E$ neutrons per unit volume at $\mathbf{r}$, in a unit of time.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
To calculate the rate at which neutron reactions take place, the flux is multiplied by a 'macroscopic cross-section' $\Sigma_j(\mathbf{r},\mathbf{v},t)$. The macroscopic cross-sections are the product of the microscopic cross-sections with the number density of the target nuclei $\Sigma_j(\mathbf{r},\mathbf{v},t) = \Sigma_i \sigma_{ij}(\mathbf{r},\mathbf{v},t) N_i(\mathbf{r},t)$. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
The microscopic cross-sections $\sigma_{ij}(\mathbf{r},\mathbf{v},t)$ express the probability of a reaction of type $j$ between a neutron and a target nucleus of species $i$. There are microscopic cross-sections for neutron absorption, fission, elastic scattering and inelastic scattering. The microscopic cross-sections have units of area per atom, and depend upon the energy (velocity) of the incoming neutron, as well as the temperature of the target nuclei.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
The macroscopic cross-sections have units of inverse distance. As such, they define the probability of a reaction per unit of neutron path-length. When multiplied with a neutron flux (equivalent to the total path-length travelled by the neutrons per unit time per unit volume), this yields the reaction rate per unit volume.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
One other definition to note is the distinction between 'prompt' and 'delayed' neutrons. The prompt neutrons are released in the fission event itself, whilst the delayed neutrons are emitted after the beta decay of certain fission product fragments, and typically occur some time after the fission event. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
With those definitions in place, let's proceed to the neutron transport equation itself. (The equations which follow are adapted from <i>Mathematical Methods in Nuclear Reactor Dynamics</i>, Z.Akcasu, G.S.Lellouche, and L.M.Shotkin, Academic Press, 1971). We will assume for simplicity that there is a single type of fissile isotope. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
The time evolution of the neutron distribution function is governed by the following equation:</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
$$\eqalign{\partial n(\mathbf{r},&\mathbf{v},t)/\partial t = - \mathbf{v} \cdot \nabla n(\mathbf{r},\mathbf{v},t) - \Sigma(\mathbf{r},\mathbf{v},t) \;v \;n(\mathbf{r},\mathbf{v},t) \cr &+ f_0(\mathbf{v}) (1-\beta)\int \nu(\mathbf{r},\mathbf{v}',t) \Sigma_f(\mathbf{r},\mathbf{v}',t) \;v' n(\mathbf{r},\mathbf{v}',t) d^3 \mathbf{v}' \cr &+ \Sigma_{i=1}^{6} f_i(\mathbf{v}) \lambda_i C_i(\mathbf{r},t)\cr &+ \int \Sigma_s(\mathbf{r},\mathbf{v}' \rightarrow \mathbf{v},t) \;v' n(\mathbf{r},\mathbf{v}',t)d^3 \mathbf{v}'}$$ Let's consider the various terms and factors in this equation one-by-one.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
$\mathbf{v} \cdot \nabla n(\mathbf{r},\mathbf{v},t)$ is the loss of neutrons of velocity $\mathbf{v}$ from the volume about a point $\mathbf{r}$ due to the flow of neutrons down a spatial concentration gradient $\nabla n(\mathbf{r},\mathbf{v},t)$. The loss is only non-zero if the concentration gradient has a non-zero component in the direction of the velocity vector $\mathbf{v}$.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
$\Sigma(\mathbf{r},\mathbf{v},t) \;v \;n(\mathbf{r},\mathbf{v},t)$ is the loss of neutrons of velocity $\mathbf{v}$ from the volume about a point $\mathbf{r}$ due to \emph{any} reaction with the atomic nuclei in that volume. $\Sigma$ is the sum of the macroscopic cross-sections for neutron capture $\Sigma_c$, fission $\Sigma_f$, and scattering $\Sigma_s$.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
$\Sigma_f(\mathbf{r},\mathbf{v}',t) \;v' n(\mathbf{r},\mathbf{v}',t)$ is the rate at which fission events are triggered by incoming neutrons of velocity $\mathbf{v}'$. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
$\nu(\mathbf{r},\mathbf{v}',t)$ is the mean number of neutrons output from a fission event triggered by an incoming neutron of velocity $\mathbf{v}'$. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
$\beta$ is the fraction of fission neutrons which are delayed, hence $1-\beta$ is the fraction of fission neutrons which are prompt.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
$ f_0(v)$ is the probability density function for prompt fission neutrons. i.e., it specifies the probability that a prompt fission neutron will have a speed $v$, (and a kinetic energy $E = 1/2 m_n v^2$). It is equivalent to the energy spectrum of prompt fission neutrons.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Assuming the outgoing prompt fission neutrons are emitted isotropically, the probability of a prompt fission neutron having a velocity $\mathbf{v}$ is $f_0(\mathbf{v}) = f_0(v)/4 \pi$. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Hence $f_0(\mathbf{v})(1-\beta) \int \nu(\mathbf{r},\mathbf{v}',t) \Sigma_f(\mathbf{r},\mathbf{v}',t) \;v' n(\mathbf{r},\mathbf{v}',t) d^3 \mathbf{v}'$ is the rate at which prompt neutrons of velocity $\mathbf{v}$ are created at position $\mathbf{r}$ in the reactor, by incoming neutrons of any velocity $\mathbf{v}'$.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
$C_i(\mathbf{r},t)$ is the concentration of species $i$ delayed neutron precursors, and $\lambda_i$ is the decay constant of that species, hence $\lambda_i C_i(\mathbf{r},t)$ is the decay-rate of the $i$-th delayed neutron precursor. This is equivalent to the production-rate of delayed neutrons from the $i$-th precursor. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
$f_i(\mathbf{v})$ is the probability density function over velocity for delayed neutrons produced by the $i$-th precursor species, hence $\Sigma_{i=1}^{6} f_i(\mathbf{v}) \lambda_i C_i(\mathbf{r},t)$ specifies the rate at which delayed neutrons of velocity $\mathbf{v}$ are created at position $\mathbf{r}$ in the reactor.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
$\Sigma_s(\mathbf{r},\mathbf{v}' \rightarrow \mathbf{v},t)$ is the macroscopic cross-section for elastic or inelastic scattering events in which an incoming neutron of velocity $\mathbf{v}'$ transitions to an outgoing neutron of velocity $\mathbf{v}$ by colliding with a target nucleus. Hence $\int \Sigma_s(\mathbf{r},\mathbf{v}' \rightarrow \mathbf{v},t) \;v' n(\mathbf{r},\mathbf{v}',t) d^3 \mathbf{v}'$ specifies the rate at which neutrons of velocity $\mathbf{v}$ are created at position $\mathbf{r}$ in the reactor by incoming neutrons of any velocity $\mathbf{v}'$ scattering with target nuclei.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
The concentration of each delayed neutron precursor satisfies the following equation:</div>
<div style="text-align: justify;">
$$\eqalign{\partial C_i(\mathbf{r},t)/\partial t &= \beta_i \int \nu(\mathbf{r},\mathbf{v}',t) \Sigma_f(\mathbf{r},\mathbf{v}',t) \;v' n(\mathbf{r},\mathbf{v}',t) d^3 \mathbf{v}' \cr &- \lambda_i C_i(\mathbf{r},t)} $$ $\beta_i$ is the fraction of fission neutrons produced by the delayed neutron precursor of species $i$. Hence, $\beta = \Sigma_i \beta_i$.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
The rate at which delayed neutron precursors of species $i$ are produced by fission events is given by $\beta_i \int \nu(\mathbf{r},\mathbf{v}',t) \Sigma_f(\mathbf{r},\mathbf{v}',t) \;v' n(\mathbf{r},\mathbf{v}',t) d^3 \mathbf{v}'$, and the rate at which they decay is given by $\lambda_i C_i(\mathbf{r},t)$. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Note that, unlike the general Boltzmann equation, there is no term for neutron-neutron interactions. Neutron densities in a reactor are only of the order of $10^9/cm^3$, compared to the number density of atomic nuclei, which is of the order $10^{22}-10^{23}/cm^3$. Hence, neutron-neutron interactions can be neglected.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Now, the interesting point about the neutron transport equation is that the most important terms have the form of integral transforms:</div>
<div style="text-align: justify;">
$$(Tf)(x) = \int K(x,y)f(y) dy \, $$ where $K(x,y)$ is the 'kernel' of the transform. In discrete form, this becomes:</div>
<div style="text-align: justify;">
$$ (Tf)(x_i) = \Sigma_{j} K(x_i,y_j)f(y_j) \,.$$</div>
<div style="text-align: justify;">
The neutron transport equation takes neutron fluxes as the input, and calculates reaction rates, and thence heat production, by integrating those fluxes with macroscopic cross-sections. The macroscopic cross-sections provide the kernels of the integral transforms. In general schematic terms:</div>
<div style="text-align: justify;">
$$\text{Output}(\mathbf{r},t) = g\left(\int \Sigma(\mathbf{r},\mathbf{v'},t) \;\text{Input}(\mathbf{r},\mathbf{v}',t)d^3 \mathbf{v}' \right)\, ,$$ where $g$ is some function.<br />
<br />
For example, given the heat produced per fission event, $W_f$, the rate of fission-product heat-production throughout the reactor is given by: $$H_f(\mathbf{r},t) = W_f \int \Sigma_f(\mathbf{r},\mathbf{v}',t) \;v' n(\mathbf{r},\mathbf{v}',t) d^3 \mathbf{v}'\, .$$ Neural networks which implement convolutions have become immensely powerful tools for pattern recognition in recent years. Convolutions are a particular type of integral transform, so let's briefly recall how such neural networks are defined.<br />
<br />
On an abstract level, a neural network consists of a set of nodes, and a
set of connections between the nodes. The nodes possess activation
levels; the connections between nodes possess weights; and the nodes
have numerical rules for calculating their next activation level from a
combination of the previous activation level, and the weighted inputs
from other nodes.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
The nodes are generally divided into three classes: input nodes,
hidden/intermediate nodes, and output nodes. There is a directionality to a neural network in the sense that
patterns of activation propagate through it from the input nodes to the
output nodes, and in a <i>feedforward</i> network there is a partial
ordering relationship defined on the nodes, which prevents downstream
nodes from signalling those upstream.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
For the implementation of integral transforms, feedforward neural networks with strictly defined layers are used. The activation levels
of the input layer of nodes represents the values of the input function
at discrete positions; the weights represent the values of the discretized kernel;
and the values of the nodes in the layer beneath represent the
discretized version of the transformed function. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Thus, the activation levels $x^l_i$ of the neurons in layer $l$ are given by weighted sums over the activation levels of the neurons in layer $l-1$:</div>
<div style="text-align: justify;">
$$x^l_i = f \left(\sum_{j=1}^{n}W^l_{ij}x^{l-1}_j \right), \, \text{for } \, i = 1,\ldots,n$$ $W^l$
is the matrix of weights connecting layer $l-1$ to layer $l$, with $W^l_{ij}$ representing the strength of
the connection from the $j$-th neuron in layer $l-1$ to the $i$-th neuron in layer $l$. $f$ is a non-linear threshold function. </div>
<div style="text-align: justify;">
<br />
Now, the empirical cross-section data required for nuclear reactor kinetics is far from complete. The cross-sections are functions of neutron energy, and can oscillate wildly in some energy ranges, (see diagram below). The cross-section curves are therefore not defined to arbitrary levels of resolution.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgFkuwpotGFA3hQBSpsFvDgOrlIzwwaoDDUet1loeUDtNrJay1CHmB7Ufd1iiGCCTA4qtCTzRHueNFcNiIe8S1TpJEhKjxFaGNiF9qATQH3kfP5Hzq8hRyFV65Ijidt-es_Qsb/s1600/crosssection.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="313" data-original-width="696" height="178" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgFkuwpotGFA3hQBSpsFvDgOrlIzwwaoDDUet1loeUDtNrJay1CHmB7Ufd1iiGCCTA4qtCTzRHueNFcNiIe8S1TpJEhKjxFaGNiF9qATQH3kfP5Hzq8hRyFV65Ijidt-es_Qsb/s400/crosssection.gif" width="400" /></a></div>
<br />
Perhaps, however, neural networks can offer a solution to this problem. If the input layer of a neural network is used to represent the neutron flux at various positions throughout a reactor, and the output layer is used to represent, say, the temperature levels measured throughout the reactor, such a network could be trained to predict the correct temperature distribution for any given pattern of neutron flux. It would do so by adjusting its weights, and because the weights would represent the nuclear reaction cross-sections, this would provide a means of filling in the gaps in the nuclear physics datasets.<br />
<br />
Questions one might pose immediately include the following: (i) are the neutron flux measurements in a reactor sufficiently accurate to facilitate this technique; and (ii) how many neurons would one need in a layer of the neural network to provide the necessary degree of spectral resolution?<br />
<br />
These are questions I don't yet know the answer to...</div>
Gordon McCabehttp://www.blogger.com/profile/09151162643523937086noreply@blogger.com0tag:blogger.com,1999:blog-37936507.post-41966413094597394072017-11-01T21:11:00.000+00:002017-11-01T22:12:02.281+00:00The problem with Fred Pearce<!--[if gte mso 9]><xml>
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<div class="MsoNormal" style="text-align: justify;">
Environmental journalist Fred Pearce published an article on William
Penney (‘<i>Atomic Briton who brought home the bomb</i>’) in <i>NewScientist</i> magazine on 14<sup>th</sup>
October 2017, (p42-43). The article concludes with some brazen distortion of the facts.<br />
<br />
Pearce claims
that the Orange Herald device, a large fission bomb detonated as part of the
Grapple operation in May 1957, misled “US legislators in Congress…Congress
amended the McMahon Act, believing they would be sharing science with a fellow
H-bomb nation.” Pearce refers to this as "Penney's nuclear bluff."<br />
<br />
The definitive reference work on
the history of British H-bomb development is Lorna Arnold’s ‘<i>Britain and the
H-bomb</i>’ (2001). Here she reports that “weapon debris, radioflash data and
microbarograph readings…showed that [<i>Grapple</i>] had only been partially
successful. A ‘thermonuclear bluff’ had never been seriously contemplated; the
Americans had regularly been assisted to take measurements and collect data at
several British trials, including <i>Grapple</i>,” (p151).<br />
<br />
The British went on to
conduct a successful 3 megaton H-bomb test, Grapple Y, in April of 1958.
Strangely, this fact is absent from Pearce’s article. The amendment
of the McMahon Act was passed by Congress some months later, on June 30<sup>th</sup>
1958, and the US-UK Mutual Defence Agreement was signed on 3<sup>rd</sup> July
1958.<br />
<br />
These dates are also omitted from Pearce's article. It's easy to see why, because their inclusion destroys Pearce's argument. <br />
<br />
Sadly, then, the only bluff here comes from Mr Pearce. If <i>NewScientist</i> magazine wishes to mislead its readers, publishing Mr Pearce's work is certainly the most effective way of so doing.</div>
Gordon McCabehttp://www.blogger.com/profile/09151162643523937086noreply@blogger.com1tag:blogger.com,1999:blog-37936507.post-73283532380379800772017-10-21T19:17:00.001+01:002017-10-21T19:30:49.870+01:00Diffusers and rear-wheel wakes<div style="text-align: justify;">
There is a persistent notion amongst some Formula One technical analysts that the low pressure wake behind the rear wheels can be connected to the lateral extremities of the diffuser airflow, thereby enhancing the flow capacity of the underbody, and its downforce-generating potential. In particular, the notion has been repeatedly promoted by <i>Autosport</i> Technical Consultant Gary Anderson:</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<i>"Mercedes has worked very hard in making
the low pressure area behind the rear tyres connect up to the trailing
edge of the diffuser. In effect this gives the diffuser more extraction capacity," (</i><i>
<span class="article_title article_uid51640"><a href="http://classicplus.autosport.com/premium/feature/7454/">The key technical developments from Australia</a><b>, </b></span>25th March 2017).</i></div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Now, it's certainly true that if the diffuser is expanded in a lateral direction without causing separation of the boundary layer, then the expansion ratio of the diffuser will be increased, and it'll generate more downforce. It's also true that the wakes shed by the wheels are areas of low pressure, situated as they are behind rotating bluff bodies. So surely, one might think, there will be a pressure gradient directed towards those rear-wheel wakes, and surely the airflow exiting the diffuser can be connected to them, thereby increasing its effective expansion ratio? </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Unfortunately, whilst the wakes behind bluff bodies do indeed tend to be regions of low pressure, they are also regions of high turbulence, and the airflow 'sees' a region of turbulence as an obstruction. Directing the lateral extremities of diffuser airflow towards the rear wheel wakes does not therefore offer a straightforward boost in the power of the diffuser, and could even promote diffuser separation.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
One illuminating way to understand this is to look at the Reynolds-averaged Navier-Stokes (RANS) equations for a flow-field containing turbulence. A solution of these equations represents the mean velocity flow field $\overline{u}$ and the mean pressure field $\overline{p}$ in a region of space. For a time-independent incompressible flow, each component $\overline{u}_i$ of the mean velocity vector field is required to satisfy the equation</div>
<div style="text-align: justify;">
$$<br />
\rho (\mathbf{\overline{u}} \cdot \nabla) \overline{u}_i = - \frac{\partial \overline{p}}{\partial x_i} +\frac{\overline{\tau}_{ij}}{\partial x_j} - \rho \frac{\overline{u'_i u'_j}}{\partial x_j} \;.<br />
$$ This equation is simply a version of Newton's second law, $F=ma$, albeit with the accelerative term on the left-hand side, and the force terms on the right-hand side.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
In the case of a continuous medium, the density $\rho$ is substituted in place of the mass, and $(\mathbf{\overline{u}} \cdot \nabla) \overline{u}_i$ represents the acceleration experienced by parcels of air as the velocity field changes from one spatial position to another. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Each term on the right-hand side of the equation represents a different type of force. The first term $- \partial \overline{p}/\partial x_i$ is the familiar pressure gradient. The negative sign indicates that the force points in the opposite direction to the gradient: the fluid will be pushed away from high pressure, and sucked toward low pressure.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Pressure, however, is only the isotropic component of stress. When the isotropic component has been subtracted from the total stress, what remains is called the 'deviatoric' stress $\tau_{ij}$. This represents the stresses which occur due to viscosity $\nu$. These are the forces which occur within a continuous medium when there are shear motions. In the case of a Newtonian fluid such as air, the deviatoric stress is a function of the viscosity and the velocity shear:</div>
<div style="text-align: justify;">
$$ \tau_{ij} = \rho \nu \bigg[ \frac{\partial u_i}{\partial x_j}+ \frac{\partial u_j}{\partial x_i} \bigg] $$In general, forces are generated by spatial gradients of the stress, and the second term on the right-hand side of the RANS equation represents the force due to the spatial gradient in the mean deviatoric stress. These 'tangential' forces are crucial inside the boundary layer of a fluid, but more generally they play a role wherever one layer of fluid runs parallel to another layer travelling at a different speed. Here, the viscosity entails that momentum is transferred from the higher velocity layer to the lower velocity layer, helping to pull it along. This is a source of acceleration in the flow-field which cannot be explained by pressure gradients alone.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
The third term on the right-hand side of the RANS equation represents the effective force due to spatial gradients in the turbulence. In a turbulent flow-field, the velocity at a point is decomposed into a sum $u_i = \overline{u}_i + u'_i$ of the mean-flow $\overline{u}_i $ and the turbulent fluctuations, $u'_i$. The expression $\overline{u'_i u'_j}$ represents a type of turbulent stress, hence its spatial gradient provides another source of acceleration in the mean flow-field.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
This third term is crucial to understand why the rear wheel wakes behave like obstructions in the flow-field. Note the negative sign associated with the turbulent-stress term. That entails that the force vector points away from a region of turbulence. Airflow exiting a region of low turbulent intensity will effectively experience a repulsion force as it approaches a region of high turbulence. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Hence, trying to join the diffuser-flow to the rear wheel wake is not necessarily a good idea. A better idea is to create vortices from the edges of the diffuser which push the rear wheel wake further outboard. This might enable one to increase the expansion ratio of the diffuser without provoking separation.</div>
Gordon McCabehttp://www.blogger.com/profile/09151162643523937086noreply@blogger.com1tag:blogger.com,1999:blog-37936507.post-55960307726768630332017-10-08T16:05:00.002+01:002017-10-08T16:14:44.417+01:00Why nuclear disarmament is wrong<div style="text-align: justify;">
The 2017 Nobel Peace Prize was <a href="http://www.bbc.co.uk/news/world-europe-41524583">awarded this week to the International Campaign to Abolish Nuclear Weapons</a> (ICAN), a coalition of 468 non-governmental organisations across 101 countries. Berit Reiss-Andersen, the chair of the Nobel committee, stated that the award recognised ICAN's work “to draw attention
to the catastrophic humanitarian consequences of any use of nuclear
weapons and for its groundbreaking efforts to achieve a treaty-based
prohibition of such weapons”. According to the BBC, ICAN's supporters “include actor Michael Sheen.”</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Now, whilst one contradicts a B-list actor at one's peril, it is nevertheless a good juncture to review exactly why organisations such as ICAN are wrong, and why nuclear disarmament would be a bad thing. Let's begin with those “catastrophic humanitarian consequences of any use of nuclear
weapons”, by returning to 1945 and the use of nuclear weapons to end the Second World War.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
The image of the mushroom cloud, and the destruction inflicted on Hiroshima and Nagasaki dominates modern media coverage of these events. Rarely, however, does the media also recall the incendiary bombing campaign conducted by the Americans prior to the use of nuclear weapons.<br />
<br />
Between March and June of 1945, Japan's six largest industrial centres, Tokyo, Nagoya, Kobe, Osaka, Yokohama and Kawasaki, were devastated. As military historian John Keegan wrote, “Japan's flimsy wood-and-paper cities burned far more easily than European stone and brick...by mid-June...260,000 people had been killed, 2 million buildings destroyed and between 9 and 13 million people made homeless...by July 60 per cent of the ground area of the country's sixty larger cities and towns had been burnt out,” (<i>The Second World War</i>, 1989, p481).</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Unfortunately, this mass bombing campaign, conducted with conventional chemical munitions, and inflicted upon civilians and military alike, did not stop the war. Only the bombing of Hiroshima and Nagasaki stopped the war.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
In terms of the number of deaths, “reported numbers vary, but it has been estimated that by the end of
1945, 90 000 to 120 000 out of a civilian population of about 330 000 in
Hiroshima, and 60 000 to 80 000 out of 280 000 in Nagasaki, would be
dead as a result of exposure to the intense heat, physical force, and
ionizing radiations emitted by the bombs,” (<i><a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3907953/">Long-term Radiation-Related Health Effects in a Unique Human Population: Lessons Learned from the Atomic Bomb Survivors of Hiroshima and Nagasaki</a></i>).</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
So, the first conclusion to draw from this is that conventional munitions killed more people, and didn't stop the war, while nuclear weapons killed less people, and did stop the war. In terms of “humanitarian consequences”, being burnt alive by incendiary weapons rather than the blast wave, thermal radiation or ionising radiation of a nuclear detonation, seems scant consolation. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
In the decades since the Second World War, the presence of nuclear weapon stockpiles have been justified on the basis of deterrence: as long as the use of nuclear weapons by one side will result in a retaliatory strike that guarantees their own destruction, then a nuclear war is unwinnable, hence there is no incentive to use nuclear weapons. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Despite the logic of deterrence, many continue to argue that nuclear weapons should now be abolished by means of multi-lateral disarmament. A recent article in <i>NewScientist </i>by Debora Mackenzie argued that deterrence is unstable:<br />
<br />
“The growth in US missile defence systems...undermine deterrence by, in theory, allowing a country to launch a first attack safe in the knowledge that it can intercept any retaliatory strikes...deterrence is only ever a temporary stand-off, lasting just until the enemy finds a way to neutralise your deterrent. Ultimately, the technological capacity to see, hear and otherwise detect and destroy other countries' weapons could become so good that first strikes will become winnable, and deterrence will no longer work...What else will keep the nuclear peace? Optimists are promoting a UN treaty to ban all nuclear weapons,” (<i>Accidental Armageddon</i>, 23rd September 2017).</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Which brings us back to ICAN, who promoted the 'Nuclear Weapons Ban Treaty'. The nine recognised nuclear powers refused to sign this at the United Nations in July. And they were right not to do so, for the following reason:</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
A world without nuclear weapons is a world in which a nuclear war <i>is</i> winnable. As demonstrated in the 1940s, it only requires one nation to secretly begin the production of nuclear weapons, (breaking whatever treaty they may have signed), to gain a head-start on their enemies, and they will be able to use nuclear weapons without fear of reprisal. A world without nuclear weapons is a world in which there is an incentive to use nuclear weapons. Multi-lateral nuclear disarmament would therefore take us into the most unstable and dangerous state of all.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Once nuclear weapons have been invented, there is no going back to a world without them. It's not a question of optimism or pessimism, it's a question of logic.</div>
Gordon McCabehttp://www.blogger.com/profile/09151162643523937086noreply@blogger.com2tag:blogger.com,1999:blog-37936507.post-84574745173360002682017-09-13T23:02:00.000+01:002017-09-25T22:21:23.309+01:00F1 1980 - Separation and curvature<br />
<div class="MsoNormal" style="text-align: justify;">
As noted in the previous post, the airflow in the aft section of a venturi duct has a propensity to separate. Whilst the primary cause of
boundary layer separation is the severity of the adverse pressure gradient
experienced during pressure recovery, curvature upstream of the pressure
recovery region can also exert a significant influence. In this context, a
useful rule-of-thumb to remember is that the thicker the boundary layer at the
start of the pressure recovery region, the earlier separation will occur. The
rate at which the thickness of the boundary layer on a flat surface increases
with distance from the leading edge is generally used as a baseline, with
respect to which the effects of curvature can be compared. </div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
To understand the influence of
curvature, let’s first introduce a distinction between 2-dimensional and
3-dimensional boundary layers. In a 2-dimensional boundary layer, the velocity
profile and thickness of the boundary later vary only in a longitudinal
direction, along the direction of streamwise flow. The boundary-layer velocity
is a function only of height above the solid surface and longitudinal distance;
it is therefore 2-dimensional. In contrast, in a 3-dimensional boundary layer
the velocity profile and thickness vary in both a longitudinal and a lateral
direction.<span style="mso-spacerun: yes;"> </span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
Consider first a 2-dimensional
boundary layer on a surface with either convex or concave curvature. Concave
curvature increases the rate at which a boundary layer thickens (compared to a
flat surface), whilst convex curvature either thins a boundary layer, or
reduces the rate at which the thickness would otherwise increase. </div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
One way to understand this is in
terms of radial pressure gradients. For a flowfield to negotiate a curve, a
pressure gradient develops which is directed towards the centre of the radius
of curvature, balancing the centrifugal force associated with the curved flow. </div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
A flowfield bounded by a concave
curve is such that the centre of curvature is located inside the fluid itself,
hence a pressure gradient develops which points upwards from the solid surface
into the fluid, effectively trying to peel the boundary layer off the surface</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
In contrast, a flowfield bounded
by a convex surface is such that the centre of curvature is located the ‘other
side’ of the solid surface, hence a pressure gradient develops which points
downwards onto the surface, effectively pushing the boundary layer onto it. </div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
Hence, concave curvature is
liable to trigger boundary layer separation, while convex curvature promotes
boundary layer adhesion.</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
So much for the influence of
curvature on a 2-dimensional boundary layer. Most actual flowfields tend to
possess ‘crossflow’ velocity components in addition to streamwise components.
Crossflow components point in a lateral direction. In the context of wings,
this is often referred to as ‘spanwise flow’. The representation of separation
under these circumstances requires the introduction of the aforementioned
3-dimensional boundary layers.</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
The crossflow velocity components
correspond to the existence of crossflow pressure gradients. These pressure
gradients will induce streamline curvature both inside the boundary layer
attached to the solid surface, and in the adjacent outer-flow streamlines. The
streamline curvature, however, will be greater inside the boundary layer.
Hence, the skin-friction lines on the solid surface (otherwise known as the
shear stress at the wall), have greater curvature than the streamlines just
outside the boundary layer. (<i>Understanding Aerodynamics</i>, Doug McLean,
Wiley, 2013, p88).</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
Inserting a bend or kink into the
wall of a venturi tunnel will generate a radial crossflow pressure gradient,
pointing towards the centre of the radius of curvature. The outer-flow
streamlines will turn the corner due to this radial pressure gradient. The
skin-friction lines on the ceiling of the tunnel, however, will turn the corner
at a tighter angle. </div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
The curvature of a surface will
itself generate streamline curvature, but this effect is distinct from the
streamline curvature generated by a crossflow pressure gradient. If an
outer-flow streamline is projected onto a curve in the solid surface, the
curvature at each point of that curve can be decomposed into a component which
is parallel to the tangent plane of the surface at that point, and a component
which is perpendicular to the tangent plane. The perpendicular component
represents the part of the curvature which is due to the streamline simply
following the extrinsic curvature of the surface in 3-dimensional space. In
contrast, the parallel component represents the intrinsic curvature of the
projected streamline due to a crossflow pressure gradient. If there is no
crossflow, then the projected streamlines are geodesics of the surface, with
zero intrinsic curvature. (McLean, p306-307).<span style="mso-spacerun: yes;"> </span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
A similar but distinct type of
curvature effect occurs when a solid is bounded by an axisymmetric surface,
whose radius varies in a longitudinal direction. If the lateral extent of a
surface tapers in a longitudinal direction, then successive lateral slices
through the surface possess an increasingly smaller diameter. For example, in
the special case of a cone-shaped surface, oriented with the tip of the cone
pointing downstream, successive lateral slices through the surface of the cone
have a smaller diameter. A boundary layer attached to such a surface will
thicken at a faster rate than it would over a flat surface with the same
streamwise pressure gradient, (McLean p124). This occurs as a consequence of
the preservation of mass and the relative incompressibility of the air: the
boundary layer air is forced to thicken as its lateral dimensions contract.
This makes such a boundary layer more liable to detach. </div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
Conversely, consider a surface
which flares outwards with longitudinal direction, an extreme case of which
would be a cone-shaped surface with its tip pointing upstream. The boundary
layer on such a surface will either get thinner as the lateral extent of the
surface increases, or its thickness will increase at a slower rate than it
would on a flat surface in the same streamwise pressure gradient. Hence, a
surface which spreads outwards promotes boundary layer adhesion.</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
In both cases the outer-flow
streamlines are following longitudinal geodesics of the surface, and there is
no pressure-driven crossflow, (ibid). A Formula 1 car, however, is rarely
equipped with axisymmetric appendages. Rather, it exhibits reflection symmetry in
a longitudinal plane, and as a consequence the flow around the nose and engine
cover are special cases of ‘plane of symmetry’ flows (ibid., p125-126). In such
flows, the boundary layer along the plane of symmetry resembles a 2-dimensional
boundary layer, with no crossflow component, but either side of the symmetry
plane there are crossflow components which either induce divergence or
convergence. </div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
In the case of a Formula 1 car,
the flow over the nose will be a divergent plane-of-symmetry flow, and that
over the engine cover will tend to be a convergent plane-of-symmetry flow.<span style="mso-spacerun: yes;"> </span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
So, equipped with this
understanding of the effects of curvature, let’s consider an example of its
impact on F1 ground-effect aerodynamics. In 1980, some of the teams created vertical
surfaces at the rear of the sidepods to partially seal the venturi tunnels from
the effects of the rotating rear wheel. The motive for this may have been
twofold: to enhance underbody performance, and also to reduce rear wheel lift
and drag. However, these plates, when considered in horizontal cross-section,
traced a sinuous curve which started with concave curvature, passed through a
point of inflection, and ended with convex curvature. Hence, whilst such plates
may have prevented the flow in the venturi tunnels from directly interacting
with the rotating wheel, the geometrical restriction imposed by the presence of
the wheel was in no way eliminated. </div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
If a venturi tunnel entered a
constriction towards the rear of the sidepod, then the reduced cross-sectional
area would have a tendency to thicken the boundary layer. Moreover, at just
this point, the initial concave curvature on the outer wall of the tunnel would
also contribute towards thickening the boundary layer. Exacerbating matters yet
further, the turbulent jet from the inner contact patch of the rotating rear
wheel would be injected into this region of the underbody. All three factors,
in conjunction, would have tended to promote boundary layer separation in this
part of the underbody. The only mitigation here is that the cross-sectional
constriction would have weakened the adverse pressure gradient.</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoBodyText" style="text-align: justify;">
As a specific example of the challenges in this region of
the underbody, the Williams FW07B MKIV underwing, as specified in a design
drawing from April 1980, contained a dashed outline of an alternative profile
for the sinuous section of the outer wall as it passes inside the rear wheel.
The rationale behind this is alluded to in a briefing note written by Patrick
Head, dated 1<sup>st</sup> April 1980, (just in advance of the introduction of
the MKIV underwing at the Belgian Grand Prix). Here, he notes that Williams
would be “running the wide rear track with new rear plates and engine fairings
plus a wheel fairing which will reduce leakage into the rear of the side wing
and increase the velocities. A new side wing profile is also to be made with an
altered profile in the defuser (<i>sic</i>) section to reduce proneness to
separation.”</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
The alternative profile reduced
the concave curvature, but it did so at the expense of beginning the transition
further upstream, therefore sacrificing channel width. Hence, there was a
trade-off here: concave curvature or convergence; both would have thickened the
boundary layer. </div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Frank Dernie has since testified that “most people’s diffusers stopped at the rear suspension. It was very difficult to keep the flow attached any further back…I am told the Brabham BT49 never had attached flow rearward of the chassis because they never found a solution to keeping the flow attached after the sudden change of section.” (Motorsport Magazine, November 2004, X-ray Spec: Williams FW07, p77). </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
In fact, the initial underbody profile on the Williams FW07B in 1980 did attempt to extend the diffuser tunnels beyond the leading edge of the rear suspension. These gearbox enclosures and sidepod extensions appeared on the car during practice in Argentina, but serious porpoising problems were experienced, and the sidepods and underbodies were returned to 1979 MKIII specification for the race. The porpoising was attributed to the skirts jamming, hence the extensions were tried again in conjunction with the MKIII sidepods and underwing during practice in South Africa. They were, however, notable by their absence when the MKIV underwing made its debut in Belgium. </div>
<div style="text-align: justify;">
<br /></div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWJje0AGylAowOR9xYV8vzu1iZR9bVLf-NNyQj5GpkXyuqy0IlM42j1o2gH0HL_0L1F-bPRVio_1RDNyE78uEH8i5FiQdKpr5lpLvD5hEjYdNG1d447zPGVVaOEZrtyyTXVLS1/s1600/FW07B+South+Africa.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="602" data-original-width="732" height="328" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWJje0AGylAowOR9xYV8vzu1iZR9bVLf-NNyQj5GpkXyuqy0IlM42j1o2gH0HL_0L1F-bPRVio_1RDNyE78uEH8i5FiQdKpr5lpLvD5hEjYdNG1d447zPGVVaOEZrtyyTXVLS1/s400/FW07B+South+Africa.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>FW07B venturi extensions, as seen at Kyalami. (Grand Prix International magazine)</b></td></tr>
</tbody></table>
Gordon McCabehttp://www.blogger.com/profile/09151162643523937086noreply@blogger.com0tag:blogger.com,1999:blog-37936507.post-87358705560928574632017-09-13T19:52:00.001+01:002017-09-25T22:25:21.845+01:00F1 1980 - Nozzles and streamtubes<!--[if gte mso 9]><xml>
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<br />
<div class="MsoNormal" style="text-align: justify;">
Let’s delve a little more deeply
into the nature of ground-effect downforce. The underbody of a ground-effect
car can be treated as a type of (subsonic) converging-diverging nozzle. Such a
nozzle consists of a mouth, a throat, and a diffuser. The mouth consists of a
duct with a contracting cross-section, which accelerates air into the narrowest
section, the throat. In accordance with the Bernoulli effect, the pressure is
at its lowest in the throat, and the airflow velocity is at its highest. The
air then flows from the throat into the diffuser, a duct with an expanding
cross-section, which decelerates the air, and thereby returns it towards the
freestream pressure, a process referred to as ‘pressure recovery’. </div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
To give an illustration of the
relative proportions here, the MKIV underbody on the Williams FW07B had a
throat about 30 inches (762mm) in length, compared with a mouth only about 10
inches (254mm) long. The diffuser was about 45 inches (1143mm) in longitudinal
extent.</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
Pressure recovery is a delicate
process because it creates an ‘adverse pressure gradient’. The pressure
increases in the direction of flow, hence there is a force pushing against the
flow in the diffuser. Such an adverse pressure gradient tends to promote
separation of the boundary layer. When separation occurs, the boundary layer is
released into the interior of the fluid, where it breaks up into turbulence.
This reduces the effective cross-sectional area and flow capacity of the
diffuser, which in turn reduces the low pressure upstream at the throat.
Separation also transforms a portion of the mean-flow kinetic energy into
turbulent kinetic energy, which eventually dissipates as heat energy. To avoid
separation, the diffuser tends to be much longer than the mouth and throat,
with a more gradual slope than that between mouth and throat. </div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
At a fixed freestream velocity
(determined by the car-speed), the steady-state mass-flow rate through this
nozzle is determined by the area of the diffuser outlet (assuming there is no
separation), and by the ‘base pressure’* at the diffuser exit. The latter will be
lower than the freestream pressure due largely to the low pressure created by
the suction surface of the rear-wing, but also due to the low-pressure wake
behind the car. </div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
To understand this further, it’s
useful to introduce the concept of a ‘streamtube’. This is defined by taking a
closed loop in the flowfield, identifying the streamline which passes through
each point of the loop, and extruding the loop along those streamlines. This
defines the surface of the streamtube. By definition, because the surface of a
streamtube is constructed from streamlines, the velocity field is tangent to
the surface of the tube, hence no mass can flow through the surface. Moreover,
in a steady flow the mass flow-rate is the same through any cross-section of
the streamtube.</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
Now, whilst the underbody of a
ground-effect car has a solid mouth, (defined in 1980 by the geometry of the
sidepod inlets), the flow upstream of the mouth is not confined by solid walls.
Instead, it is defined by the streamtube of the flow which enters each venturi
tunnel. </div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
At a fixed car-speed, the greater
the exit area of the diffuser, and/or the lower the base pressure created by
the rear-wing, the greater the cross-sectional area of the streamtubes feeding
the sidepod inlets. The greater the cross-sectional area of the streamtube
feeding the mouth of each venturi tunnel, the greater the contraction as the
air enters the throat of the tunnel, hence the greater the acceleration of the
air and the greater the pressure drop. Therefore, “the degree of expansion of
the air in the diffuser rather than the physical dimensions of the mouth
determines the effective contraction of air into the throat, hence the maximum
airspeed that will be obtained,” (Ian Bamsey, <i>The Anatomy and Development of
the Sports Prototype Racing Car</i>, Haynes, 1991, p63). </div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
A principal concern in the design
of the underbody mouth is the avoidance of separation. Depending upon the
car-speed and the base-pressure, the stream-tubes entering the venturi tunnels
may either expand or contract as they approach the mouth. There will be a
stagnation line somewhere around the upper-lip of each mouth: flow below this
line will enter the venturi duct, while flow above it will pass over the top of
the sidepod. If the stream-tubes expand approaching the mouth of each tunnel,
(as they might do at high car speeds), then the stagnation line might lie just
inside the upper lip of the tunnel, and the external flow might separate as it
accelerates over and around the upper lip. Conversely, if the stream-tubes
contract approaching each mouth, the stagnation line might exist just outside
the upper lip, and the flow might separate as it accelerates under that lip
into the tunnel. The latter condition would inject turbulence into the throat
of the underbody tunnel, leading to a significant loss of downforce.<br />
<br />
*Note that whilst the ‘base pressure’ is lower than the static pressure of the freestream, it is <i>not</i> the point of lowest pressure, the latter being located in the throat of the venturi. The air doesn't flow towards the rear of the car because of a pressure gradient; it flows to the rear because the car is in motion with respect to the air!</div>
Gordon McCabehttp://www.blogger.com/profile/09151162643523937086noreply@blogger.com0tag:blogger.com,1999:blog-37936507.post-60251001100233528912017-08-11T12:38:00.001+01:002017-08-11T15:26:20.906+01:00Curved flow and the Arrows A3<!--[if !mso]>
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<div style="text-align: justify;">
After something of a sustained gestation period, the publication of <a href="https://shop.motorsportmagazine.com/product/View/productCode/F1RETRO1980/">F1 Retro 1980</a> is imminent, so it's a good opportunity to take a look at one of the more interesting aerodynamic experiments seen that season: the underbody venturi extensions on the Arrows A3 at Brands Hatch. </div>
<div class="MsoNormal">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgEFUDo2jsxrsM0oPEBzABL8pNN6IlgbZp2orv2M4qk_VVpnEpwlKOjT9f_7yRDaoGASdhDyTFNGlGeDLVUAVRnfodyOQvEHiT5T28HR8YzQ1YbSFtfWqhNsJi83PMxlbvUW92S/s1600/Arrows+A3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="369" data-original-width="553" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgEFUDo2jsxrsM0oPEBzABL8pNN6IlgbZp2orv2M4qk_VVpnEpwlKOjT9f_7yRDaoGASdhDyTFNGlGeDLVUAVRnfodyOQvEHiT5T28HR8YzQ1YbSFtfWqhNsJi83PMxlbvUW92S/s400/Arrows+A3.jpg" width="400" /></a></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
This was the latest in a series of attempts to improve upon the original F1 ground-effect concept. In 1979, the Lotus 80 and
the Arrows A2 had both attempted to extend the area of the underbody, but both had failed to reap the expected benefits.</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
The Lotus 80, in its initial
configuration, featured skirts under the nose, and separate skirts extending
all the way from the leading edge of the sidepods, inside the rear wheels, to
the back of the car. The failure of the Lotus 80 is commonly attributed both to
an ineffective skirt system, and an insufficiently rigid chassis.<span style="mso-spacerun: yes;"> </span> </div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
The Arrows A2 featured an engine
and gearbox inclined at 2.5 degrees in an attempt to exploit the full width of
the rear underbody. In its original configuration the A2 also dispensed with a
conventional rear-wing, replacing it with a flap mounted across the rear-deck.
The sidepod skirts were complemented by a parallel pair of skirts running
inside the width of the rear wheels to the back of the car. Unfortunately, the
higher CoG at the back entailed the car had to be run with a stiff rear
anti-roll bar, detracting from the handling, (Tony Southgate - <i>From Drawing
Board to Chequered Flag</i>, MRP 2010, p108).</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
The 1980 Arrows A3 was a more
conventional car, with the engine and gearbox returned to a horizontal
inclination. However, at Brands Match in 1980, Arrows experimented, like the
initial Lotus 80, with skirts under the nose. Developed in the Imperial College
wind-tunnel, the Arrows version of the idea
had skirts suspended from sponsons attached to the lower edges of the
monocoque, running back beneath the lower front wishbones to the leading edge
of the sidepods. At the same event, the team also tried extending
the rear underbody all the way to the trailing edge of the rear suspension,
with bulbous fairings either side of the gearbox fairing. This was done with
the avowed intention of sealing the underbody from the detrimental effects of
rear wheel turbulence.</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
Sadly, although the nose-skirts were intended to cure understeer, it was reported that they actually
<i>exacerbated </i>the understeer.</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
Now, many aerodynamic difficulties encountered in this era of Formula One were actually just a manifestation of inadequate stiffness in the chassis or suspension. However, for the sake of argument, let's pursue an aerodynamic hypothesis to explain why the nose-skirts on the A3 worsened its understeer characteristic.</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
The nose skirts on the Lotus 80
and Arrows A3 would have suffered from the fact that a Formula 1 car has to
generate its downforce in a state of yaw. Thus, in a cornering condition, a
car is subjected to a curved flow-field. This is difficult to replicate in a
wind-tunnel, hence a venturi tunnel design which worked well in a
straight-ahead wind-tunnel condition could have failed dramatically under
curved flow conditions. To understand this better, a short digression on curved flow and yaw angles is in order.</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
The first point to note is that a car follows a curved trajectory through a corner, hence if we switch to a reference frame in which the car is fixed but the air is moving, then the air has to follow a curved trajectory. If we freeze the relative motion mid-corner, with the car pointing at a tangent to the curve, then the air at the front of the car will be coming from approximately the direction of the inside front-wheel, while the air at the back of the car will be coming from an outer direction.</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
That's the simplest way of thinking about it, but there's a further subtlety. The negotiate a corner, a car generates: (i) a lateral force towards the centre of the corner's radius of curvature; and (ii) a yaw moment about its vertical axis.</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
Imagine the two extremes of motion where only one of these eventualities occur. In the first case, the car would continue pointing straight ahead, but would follow a curved path around the corner, exiting at right-angles to its direction of travel. In the second case, it would spin around its vertical axis while its centre-of-mass continued to travel in a straight line.</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
In the first case, the lateral component of the car's velocity vector corresponds to a lateral component in the airflow over the car. The angle which the airflow vector subtends to the longitudinal axis of the car, is the same along the length of the vehicle.</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
In the second case, the spinning motion also induces an additional component to the airflow over the car. It's a solid body spinning about its centre of mass with a fixed angular velocity, and the tangential velocity of that spin induces an additional component to the airflow velocity along the length of the car. However, the further away a point is from the axis of rotation, the greater the tangential velocity; such points have to sweep out circles of greater circumference than points closer to the centre of mass, hence their tangential velocity is greater. </div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaPCg1v0ZrS8RrRvWA66dkFXitbdNsSqovMx1IzJ-71SC3XXXNplyu1DaWU-ZBzQVXgwaGNMgICbZWDK0asYad1mvZB2x3s44T8U-0eFg5RLsTopNaS8S0VbwBenKUSPHR8yCi/s1600/Yaw.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="636" data-original-width="726" height="350" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaPCg1v0ZrS8RrRvWA66dkFXitbdNsSqovMx1IzJ-71SC3XXXNplyu1DaWU-ZBzQVXgwaGNMgICbZWDK0asYad1mvZB2x3s44T8U-0eFg5RLsTopNaS8S0VbwBenKUSPHR8yCi/s400/Yaw.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Curved-flow, side-slip and yaw-angle. (From 'Development methodologies for Formula One aerodynamics', Ogawa et al, Honda R&D Technical Review 2009).</td></tr>
</tbody></table>
<div class="MsoNormal" style="text-align: justify;">
Now imagine the two types of motion combined. The result is depicted above, in the left-part of the diagram. The white arrows depict the component of the airflow due to 'side-slip': the car's instantaneous velocity vector subtends a small angle to the direction in which its longitudinal axis is pointing. In the reference frame in which the car is fixed, this corresponds to a lateral component in the direction of the airflow which is constant along on the length of the car.</div>
<div class="MsoNormal" style="text-align: justify;">
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When the yaw moment of the car is included (indicated by the curved blue arrow about the centre-of-mass), it induces an additional airflow component, indicated by the green arrows. Two things should be noted: (i) the green arrows at the front of the car point in the opposite direction from the green arrows at the rear; and (ii) the magnitude of the green arrows increases with distance from the centre of mass. The front of the car is rotating towards the inside of the corner, while the rear of the car is rotating away, hence the difference in the direction of the green arrows. And, as we explained above, the tangential velocity increases with distance from the axis of rotation, hence the increase in the magnitude of the green arrows.</div>
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The net result, indicated by the red arrows, is that the yaw-angle of the airflow has a different sign at the front and rear of the car, and the magnitude of the yaw angle increases with distance from the centre-of-mass. (The red arrows in the diagram are pointing in the direction in which the car is travelling; the airflow direction is obtained by reversing these arrows).</div>
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So, to return to 1980, the Arrows A3 design
trialed at Brands Hatch moved the mouth of the venturi tunnel forward to the nose of the car. The
further forward the mouth, the greater the angle of the curved onset flow to
the longitudinal axis of the car, and the further away it is from the
straight-ahead condition. Hence, the curved flow might well have separated from the
leading edge of the skirt on the side of the car facing the inside of the
corner, injecting a turbulent wake directly down the centre of the underbody. In this respect, the conventional location of the venturi inlets on a 1980 F1 car, (i.e., behind the front
wheel centreline), would have reduced yaw sensitivity.</div>
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Front-wings and rear-wings certainly have to operate in state of yaw, and do so with a relatively high level of success. However, such devices have a larger aspect-ratio than an underbody venturi, which has to keep its boundary layer attached for a much longer distance. </div>
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It should also be noted that the
flow through the underbody tunnels, like that through any type of duct, suffers
from ‘losses’ which induce drag. The energy budget of a flow-field can be
partitioned into kinetic energy, pressure-energy, and ‘internal’ heat energy.
Viscous friction in the boundary layers, and any turbulence which follows from
separation in the duct, creates heat energy, and irreversibly reduces the sum
of the mean-flow kinetic energy and the pressure energy.</div>
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These energy losses are
proportional to the length of the duct, the average flow velocity through the
duct, and inversely proportional to the effective cross-sectional diameter of
the duct. Due to such losses, it is not possible for full pressure recovery to
be attained in the diffuser and its wake, and this will contribute to the total
drag of the car. Hence, whilst underbody downforce comes with less of a drag
penalty than that associated with inverted wings in freestream flow, it is nevertheless
true that the longer the venturi tunnels, and the greater the average velocity
of the underbody flow, the greater the drag of the car.<span style="mso-spacerun: yes;"> </span></div>
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Moreover, the longer the mouth
and throat of a venturi tunnel, the thicker the boundary layer at the start of
the pressure recovery region, and the more prone it will be to separation in
that adverse pressure gradient. All of which mitigates against a quick and easy
gain from extending the area of the underbody. </div>
Gordon McCabehttp://www.blogger.com/profile/09151162643523937086noreply@blogger.com6