Duke University Motorsports is a student group that designs and builds open wheel, single seat race cars to compete in the Formula SAE competition sponsored by the Society of Automotive Engineers. The team consists of Duke students from both Pratt and Trinity, in all classes. The purpose of the team is to provide students with a way to gain practical design and manufacturing experience in a fun and challenging setting.

Wednesday, July 27, 2011

Aerodynamics and Vehicle Dynamics

The following write-up is  quick introduction to aerodynamics and how it relates to vehicle dynamics, for those interested.  After the break are snippets of an email I sent to the aero team almost a year ago, and I think it's a good place for those on the team interested in aerodynamics to start.

Vehicle Dynamics and Aerodynamics
Increasing performance can be done in a number of ways, i.e. more power, less weight, or in our case, more grip.  How does aero increase grip?  A car has four tires, which are the only points of contact between car and road.  Under cornering, the tires generate lateral force proportional to load to first order.  These lateral forces act on the car's mass, causing the car to turn.  As I mentioned, the lateral force created by the tires increases with load.  However, if you just add weight to the car, you have to move more mass with the tires, thus canceling the effect of the extra grip.  In addition, the relationship between load and grip is less than linear, which means you lose grip by increasing weight.  By increasing the load on the tires without increasing the mass and inertia of the car, the car can corner harder.

Now how much extra grip can we produce? The average speed for a FSAE track is about 30mph.  Now, say we produce 100lbf of downforce at 30mph, which is about 1/6 of the weight of car + driver.  If tires were ideal, that would translate into an extra 16.6% lateral force, but it's going to be less than that.  How much less?  Well that depends on your tire- look at the tire data.  As the extra grip goes as v^2, the contribution is even higher if there are many high speed corners.  The downside?  Drag.

There are many ways to generate downforce.  Any device that can create a pressure differential over a decently large surface area can create usable downforce.  Racing cars have used wings, diffusers, sealing skirts to take advantage of ground effects, fans that create a vacuum under the car, and all sorts of other contraptions.  For our purposes, FSAE does not allow powered aero, so no fans.  That limits us more or less to wings, diffusers, and body panels.

Aerodynamic Balance
All four tires must work together to produce cornering forces, and the tires with the least grip will limit the cornering performance.  There's no point in running too much downforce in the rear if there's no downforce in the front since then there's no extra grip on the front, and the car corners no harder.  In addition, we must keep the car balanced for vehicle dynamics purposes - a car that lifts on the front because of too much rear downforce defeats the point of having the downforce, and vice versa (lifting the rear is unstable and can be very dangerous).  Typically on aero cars there is a slight rear bias on aero loading for stability purposes, especially at high speeds.

The numbers are going to be somewhat arbitrary after all - the ultimate goal is to get as much downforce as possible, while minimizing drag.  It becomes an optimization problem of lift to drag - we can keep increasing downforce, but at some point drag is going to outweigh the benefits of the additional downforce.  What's that point for Formula SAE?  Well, that's what we're going to try to figure out.

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