Friday, August 11, 2017

Curved flow and the Arrows A3

After something of a sustained gestation period, the publication of F1 Retro 1980 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. 

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.

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.  

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 - From Drawing Board to Chequered Flag, MRP 2010, p108).

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.

Sadly, although the nose-skirts were intended to cure understeer, it was reported that they actually exacerbated the understeer.

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.

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.

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.

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.

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.

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.

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.

Curved-flow, side-slip and yaw-angle. (From 'Development methodologies for Formula One aerodynamics', Ogawa et al, Honda R&D Technical Review 2009).
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.

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.

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).

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.

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.

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.

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. 
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.


Unknown said...

This is one of your best F1 articles. I plan to get this book, plus Adrian Newey's book "How to Build a Race Car" (released in the UK November 2nd). Oddly enough I emailed Red Bull to pass along the notion while there was still time Adrian might beef up the technical content of the book. Generally these autobiographies are very underwhelming. I knew the FW14B Haynes manual was coming out a year and half ahead of time, emailed Steve Rendle twice to try to get the aero maps to highlight the difference between the 91 and 92 aero maps. The book is very good on the suspension components: pictures, anecdotal stories and some nice details how the car was run.
One of my favorite details was the fact that the car had a dial to control low speed
and high speed ride height. Reading a book chapter by Willem Toet dating a few years
back he mentions an untrained (non aero person) doesn't tend to think separation
is most likely at slow speeds (lower Reynolds number). In a 1992 article by Andy Brown of Leyton House fame he too mentions at higher speeds the air can do more work. Hence the higher ride height at slow speeds for the 1992 Williams (I am inferring this.) The book's aero treatment was very poor. A few paragraphs with
Brian O'Rourke (the composites guy at Williams). Given that Steve Rendle did the Red Bull Haynes manauls (two of them). I could not fathom why he did not speak to Adrian Newey. There was some nice stuff about the electronics (Paddy Lowe interview
with EEPROMS and the Psion Organizer units). On the aero front, I think the book needs a redo or a new updated edition. The Mark Hughes piece on Adrian's favorite
6 cars in Motorsport magazine a couple of years ago was much better.
Even the Japanese reporters got more out of him in the GP Car Story book on the FW14B Williams (which was a bit of a chore to translate).

Unknown said...

You mention yaw, Willem Toet told me the losses on the 1994 Williams FW16 in yaw (slow corners) were even larger than the peaky aero losses. Williams didn't do yaw testing, and McLaren still didn't when Newey was there in 98, 99. Adrian's forte
has been (for most of his career is my understanding, but probably not so much now)
the long high speed flowing corners. Many people were astounded by the slow speed
prowess of the 94 Benetton and they did have "traction control", but it was more
than just better mechanical grip. In an issue of Bernoulli magazine in an article
by Rob Lewis of Total Sim, he includes some plots of a few CFD models,
and in slow corner yaw conditions (where the wind tunnel really struggles
even with discrete runs at different yaw angles or the full transient sweeps these
days, they really need CFD to manage it correctly (something called the Coriolos effect and some other things). But the pressures under the car where completely
different for the two cases. Hence the Benetton makes a huge step forward,
while Williams has dial back their car, which still left something to be desired
in the slow corners even at the end of 94 (this is my understanding).
Oddly enough, there is probably way more to it than that too, in 92, 93, and 94
the Benetton car was mega in Spa at Eau Rouge, Pouhon, Blanchimont. Schumacher would have probably won in 93 if not for a bad pit stop. I asked Willem to release
the aero maps of the 93 and 94 Benetton, but he did not want to !!!!
My interest is where the gains were made. Many of the cars had more downforce in 94 than in 93 ( Harvey Postlethwaite mentioned it was just case of redistributing
it differently - I don't know whether he meant across the broad set of ride heights
or physically on the car or probably both). In an issue of "Motorings News" he mentioned that where you get your two pennies back for the one you put in
was the ground effect, peak downforce vs variation and sensitivity, and he mentioned the top teams had tonnes of data of what would work and what would
be so optimal while the smaller teams had not the money to acquire all that tunnel
data). He was referring to the controversies about the 94 Ferrari flexure pivot
joints and the rear suspension of the Williams and whether it was a moveable aero device. That was not where the gains would be made in his view.

Great post.

- Pete from Canada

Gordon McCabe said...

Thanks Pete, a blizzard of ideas as ever.

There's some good stuff from Adrian Newey in Maurice Hamilton's 2009 book on Williams.

Unknown said...

Really interesting Article!!

The subject of curved air flow was in my mind for a long time. This article really explains it very well.

I guess this diagrams show the reason why a shark fin is useful. It will create a side force in the direction of the center of the curve right? although it creates a yaw moment that works against turning in...

Please continue writing this great articles.


Gordon McCabe said...

Thanks Pedro.

When Penske introduced their shark-fin back in the 90s, it was indeed about the side-force.

However, the tip of the shark-fins also create a vortex in yaw. In 2017 F1, the shark-fins are raised so that the vortex doesn't plough into the rear-wing.

Unknown said...

There are problems with the cited paper and image regarding the path of the car and air flow. The magenta travel/flow path arc in the image is actually incorrectly placed and it suggests the rear wheels are travelling at an angle to their rolling direction. There is side slip to be considered in any cornering vehicle but this amount of exaggeration ignores the rolling direction of the wheels. To have these velocity directions rearward of the CoP/CoM it would need to be a four wheel steered car. I think it’s best to first approach this subject with the mindset that the instantaneous velocity direction of a wheel is the direction it points.

The rear wheels of the car in the image are fixed to roll at an angle parallel to the car longitudinal axis. The center of the turn will always lie on the axis of the rear wheels. When this vehicle is cornering, the further forward a point is from the rear the larger is the angle of that point’s velocity direction relative to the vehicle’s longitudinal axis. Imagine two fins aligned with the car’s longitudinal axis where one is attached at the nose and the other at the rear. When the car corners, the fin at the nose would point at an angle to its velocity direction while a fin at the rear would point parallel to its velocity direction and thus have less drag. In other words, the further forward the fin is placed from the rear wheels the larger the lateral force.

A vertical plane coinciding with the rear wheel axis is the boundary between left or right air flow. So any part of the car behind the rear wheel axis will experience air flow from outside the turn.

Below is a link to an image showing the correct velocity directions of a cornering car.

A cornering vehicle does have angular velocity centered at its CoM but all parts of the vehicle only proceed through the air and along the road with instantaneous velocities perpendicular to the turn center because the vehicle is constrained to this travel by the wheels at their contact points. One can point to a vertical axis rotation about the CoM but the velocity directions of the rotating car parts also include the velocity of the CoM. The following video describes this rotation of a cornering vehicle with and without linear velocity.

A cornering vehicle has angular momentum and rotates about its CoM while the contact points change the direction of linear velocity at the CoM. Through our eyes we perceive a rotation of the cornering vehicle about the turn center point ICP.

I won’t attempt to describe what the air does after it is influenced by any part of the car as you have more knowledge on the subject, but I can say the turn center is the reference point for predicting the travel of the cornering vehicle along the road and through the air. Aerodynamic forces become more influential the higher the speed and the main goal is to use those forces to keep the wheels pressed on to the road so that they can control where the car goes.