The Fun but Useless Similarity between an Airfoil and a Tire

This blog mainly discusses some interesting observations about the mathematical models for an airfoil (aerofoil) and a tire (tyre).

My professor stressed that the essential external forces applied to an automobile only include aerodynamic ones and ones through the tires. And I find it quite interesting that some forces acting upon an airfoild and a tire can all be expressed in the form of:

F = ka + C

For an airfoil, F can be seen as the lift and k the lift coefficient. a in this case would be the angle of attack (AOA). C is the result of an airfoil's camber.

For a tire, F can be seen as the lateral force, k the cornering stiffness and a the slip angle. C is due to the tire's camber and is known as the "camber thrust".

It is also noticed that this linear expression only holds true for a limited range of a, which is nevertheless where an airfoil or a tire normally opereates. The following two graphs would be helpful to explain this.

fig. 1  The linear range a symetrical airfoil's lift over AOA.

(http://slideplayer.com/slide/3520095/)

fig. 2  The linear range of an umcambered tire's lateral force over slip angle.

(https://drracing.files.wordpress.com/2014/12/slip-curve.jpg)

fig. 3  A cambered airfoil has an offset in lift.

(https://drracing.files.wordpress.com/2014/12/slip-curve.jpg)

fig. 4  Camber thrust shown in the tire's F_y curve.

(https://www.tut.fi/ms/muo/vert/11_tyre_as_car_component/handling_cornering_camber.htm, alfa = slip angle, gamma = camber angle)

Furthermore, F_max can be increased, in a certain range, by increasing the airfoil's thickness or the tire's width.

How useful are the above observations? Probably not so much. But making connections help me understand and memorize concepts. And maybe the linearity and similarity observed here could give us a tiny bit of relief in a world of randomness and non-linearity.