# Questions regarding Cornering Stiffness for RC Car

I am a bachelor's level student tasked with modeling the vehicle dynamics of an RC Car that will be made to drive autonomously. I lack prior experience or particularly specific education with vehicle dynamics so I have been studying the field a bit, particularly Vehicle Dynamics and Control by Rajesh Rajamani. By advice from a supervisor I will not be using the Pacejka Magic Formula. I think I have a good enough idea of the problem and how to approach it but I've hit a wall quite badly regarding the parameter 'Cornering stiffness'. As I understand this is a property of the tires, and something that I would find on data sheets on tires. However in my case the tires are considerably more simple, they're just solid rubber rings around the wheels. I have tried to read up on Cornering Stiffness to see if I can determine it myself somehow but I haven't really found anything I've understood.

So, how should I go about determining the cornering stiffness? Otherwise, considering the shape of these tires are there any assumptions I can make that would simplify the model?

• How fast do you intend to go, especially compared with typical track speeds for racing RC cars? I suspect you'll get much more info if you hop on over to various hobbyist forums. Feb 5, 2018 at 18:18
• The intent is to go as close to the top speed of the car as possible ~5.5 m/s. But thanks for the advice on checking hobbyist forums.
– user14808
Feb 6, 2018 at 20:50
• What kind of application is intended? What scale/size is the vehicle? If you plan to race it on a concrete floor, soft rubber slicks are the best tyres, on grass or other rough terrains, spiked tyres will give a better result. You can't really calculate cornering stiffness there. You can try different tyres on a skidpad test(google it) to get an idea.
– Bart
Feb 6, 2018 at 21:47

Cornering stiffness is usually measured on Force And Moment Machine (for example: https://www.smithersrapra.com/testing-services/by-sector/automotive/tire-testing/force-and-moment). Basically, the tire is in contact with a moving surface --either a flat track or a large drum-- which drives the tire at a particular speed under a particular load. Then the turn angle changes and sensors measure the lateral forces as a function of turn angle.

This is expensive, specialized equipment; probably not easily available to a university. But you could approximate something by pulling the tire behind a vehicle and measuring the lateral forces. Still not easy, though.

If the tires are not steel belted, there is a very old book which had formulas for these things, Mechanics of Pneumatic Tires, edited by Samuel Clark.

• You did read the question and realised that it is about a Radio Control car... :) Nov 25, 2018 at 21:27
• They did not state how big the RC car was. If it is a small car --or tiny car-- it is a valid and useful answer. If it is a radio controlled Porsche, then it is still valid, but maybe not so practical :-) Nov 25, 2018 at 21:37
• Solid rubber tires are a bit of a giveaway though.... Nov 25, 2018 at 21:45
• I had to re-read a couple of times. I also missed the "...NOT using Pacejka's formula..." part. Ugh. Nov 25, 2018 at 22:49

Oh my, if you mean an RC car as in a hobbyist car I would think weight and the lack of weight(inertia) would be a far greater problem, at 5.5 m/s I doubt the tires would be of much concern for a tiny car (100 g or so), unless you put glue on the tires it will be the least of the problems...just go for rubber ..safety first ;D...

In the absence of anything better pretend it is a pneumatic tire, this will give about 0.1mu/deg of cornering stiffness. If you want to get fancy you could incorporate tire load sensitivity, that is the grip falls off as vertical load increases.

Slot car fanatics or R/C racers may have a better idea of the CS of solid tires.