How is ackerman calculated?

[Villanuevas_BMW]

One of the things I have to take care of this year on our FSAE team is the steering geometery. I have no idea how ackerman is calculated, I read the Tune to Win part on this along with the Milliken book. There are a couple explanations on the fsae forums of how its calculated but nothing seems concrete. The one Im hearing the most is that "the distance of the point at where extended drawn lines of the fully turned wheels meet, with relation with the rear axle line" is how its calculated. So the distance of the left and right wheel intersection to the axle line divided by the wheelbase times 100 is your percent ackerman? Sorry, i know there are a ot of words to try to explain this but any help would be appreciated. thanks heres some pics to help explain.

and heres our car http://www.csupomona.edu/~fsae/

[snook...]

http://www.rctek.com/handling/ackerm...principle.html

one of the nice things about race quality rc cars is that they give so many adjustments, that one can "play" with setup on the coffee table...its going to be a greater than/less than number....i've heard oval guys say it in terms of "positive" or "negative...or neutral....positve meaning in front of rear centerline, negative behind rear centerline.......but they'll put rear steer into the car, so i don't know if that jacks stuff up....anyway i'm no expert, and i'm just repeating what i overheard in the pits......

i may/they might be wrong with the terminology, just recall how it was described and the terms used.....

[Steve J.]

http://fsae.com/eve/forums?a=search&reqWords=ackerman

[Chris@RRT]

Oops, posted with the wrong account. See below:

[RRT]

Ackermann geometry is meant to optimize the kinematics of the steering system under low lateral acceleration, steady-state conditions. For these conditions, force generation is low and consequently the slip angle at each tire is low. Therefore, the cornering is geometric: An ideal vehicle will have each tire pointed in the direction tangent to the path the contact patch is traveling on (i.e., the slip angle is zero for all four tires). Of course this isn't the case for real vehicles.

It's basically a way to get in the ballpark for your steering design. The optimization isn't exact for higher lateral acceleration, steady-state conditions for various reasons. It falls apart further under dynamic conditions, because the yaw acceleration of the vehicle becomes a significant contributor to the slip angle at a given point on the vehicle. Remember, even under steady-state conditions, the slip angle is different at different points on the vehicle.

Probably a good approach to the design would be to have more than "ideal" ackermann at small steering angles (small meaning probably just a few degrees) because it would cause a yaw moment that would improve turn-in. Then at larger steering angles, move to less than "ideal" ackermann in an attept to optimize the lateral force generation on the front tires.

Sorry if it doesn't make much sense but to really explain it in detail would take pages with formulas including cross products etc. and this just isn't the place for that.

For what it's worth, you really have to use the information in Milliken's book carefully, because it presents a largely classical, simplified, steady-state approach. To really get into the handling of the vehicle, numerical simulations (CarSim, Adams, etc) are very useful.

Good luck and have fun.

[Villanuevas_BMW]

Thanks a bunch snook and RRT,
I guess i was also pretty vague in my question though.
The models i posted are some calcs i did off our 2007 car, we have a rear steer setup(the tierods connect behind the steer axis). Since Formula SAE tracks are tighter with bigger steering angles, positive ackerman works for us. I guess my real question is how percentages are calculated, eg 110% and it not a the simple degree or radian difference between left and right wheels. Ive been reading the the fsae forums, but like I said in my first post nothing seems concrete. People are saying 100% is para steer, when some teams are claiming 100% ackerman with 25 degree/31 degree steer at full lock. Out of the Smith books, Engineer to Win was the most promising and gave a good explanation but it doesnt have the calcualtions i need to show judges at comp.

[RRT]

I think for your purposes these points might be helpful:

Parallel steer is NOT 100% ackermann.

The "lines through the control arm and tie rod balljoints intersecting at the rear axle" method is just an approximation and I wouldn't recommend presenting it at FSAE.

For the case where only the front axle steers, you basically assume that both of the rear tires are traveling with zero slip angle. Which, incidentally, includes the implicit assumption of zero toe angle. This constrains the body slip angle (i.e., the slip angle at the center of gravity) and the slip angles at the body points above each of the front contact patches. The optimized case (100% ackermann) is when you set your steering angle at each front wheel equal to the slip angle of the body at the point above the contact patch (so the tire slip angle equals zero). The kinematics of the steering system don't make this possible throughout the steering range, so you have to do some engineering and decide which way you want your error to occur, at each point throughout the steering travel.

Since you have front and rear steering, things get more interesting because you have more unknowns. I think if you look in the Milliken chapter "Simplified Steady State Stability and Control" there are some figures that will help.