Wednesday, September 25, 2013

Chapman, side-thrust, and the America's Cup

In the summer of 1975, Colin Chapman composed a list of requirements for a Future F1 Car.  Reproduced in Karl Ludvigsen's excellent engineering biography (Colin Chapman - Inside the Innovator), many of the points continue to be relevant today. In particular, the list includes the following laudable objectives:

5...We must get maximum cornering force from the tyres. This is maximised by:
(i) The largest possible contact patches.
(ii) With the softest compound.
(iii) Kept in contact with the ground as long as possible.
(iv) With highest possible download.
(v) Spread as evenly as possible over the contact patch.
(vi) And spread as evenly over the four contact patches in proportion to the sideloads they have to carry.

In a more quirky vein, Chapman includes the following speculative thought:

9. Total cornering force can also be increased aerodynamically
Should we try to use vertical lifting surfaces to provide additional side load derived from the speed and yaw angle of the car whilst cornering?

Which is interesting, because apart from the use of fins atop the engine cover, there appears to have been little effort in Formula 1 to generate a direct aerodynamic side-thrust. In contrast, it seems to be an extremely important part of racing yacht design, of which The America's Cup might be held as the foremost example.

If a yacht is your chosen mode of travel, and the wind rather inconveniently happens to be blowing from a direction close to the direction in which you wish to travel, you can still generate a thrust in that direction by means of some aerodynamic and hydrodynamic magic.

Firstly, you use your sail as an aerofoil, and generate low pressure on one side of it, so that an aerodynamic force is produced at right angles to the effective direction in which the wind is travelling. This alone wouldn't get you to where you want to go, but here you can use the fact that there are actually two fluids in play: air and water. Whilst your sail can generate a force from the airflow, the hull of your yacht can also generate a force from the flow of water. With a yaw angle between your direction of travel and the effective wind direction, the water will accelerate around one side of the hull, creating a hydrodynamic side-force which can be used to cancel out the sideways component of the force generated by the sail. What remains of the aerodynamic force is a component pointing in the direction you wish to travel!

As Alfio Quarteroni explains (Mathematical Models in Science and Engineering, from which the diagram above is taken), the presence of two fluids with different densities and viscosities, separated by a free surface endowed with surface tension and variable curvature, adds many interesting dimensions to the fluid mechanical problem. Moreover, the sail itself needs to be treated as an aero-elastic medium, deforming in response to the pressure field upon it, and thereby changing the airflow, in a coupled manner. Seen in this light, it's no surprise that The America's Cup once exerted such a pull over the imagination of Chapman's modern counterpart, Adrian Newey.


Unknown said...

Do you have or know where to find the famous road vehicle aerodynamics 1994 paper by Gino Sovran on underbody diffusers ? He co-authored two more papers with Kevin Cooper fours years later also on difffuers.

Gordon McCabe said...

Hi Peter,

Are you sure it's a 1994 paper? There's a 1967 paper by Sovran and Klomp (Experimentally determined optimum geometries for rectilinear diffusers with rectangular, conical or annular cross-section). It is, however, of such a vintage that you'd need a university library to obtain a copy.