Kart style rear end tire forces?

[adambrouillard]

Hi guys, I have been trying to work through the physics at the rear of a kart and I know some of you guys run kart style rear ends. Basically I am trying to figure out what is going on at the tire as the forceline between the CG and the outer rear tire changes. It seems once the inside rear is unloaded the outside rear sees all the load so wouldn't the potential grip be a constant no matter where the CG is located in relation to the outside rear tire. Basically I am wondering if there is maybe an advantage to (raising the CG/narrowing the track) to the point of just barely not overturning, or just keeping it as low/wide as possible. I was thinking there might be some change in the center of pressure at the tire possibly. Hopefully someone can help me out with this as I have been trying to wrap my brain around this for a few days pushing cans around on desks and whatnot.

[Adambomb]

Hmm, interesting question, good "thinking outside the box." First, a disclaimer, I don't have any direct cart experience. To my knowledge, the issue is that most carts run spools and no rear (or any) suspension, therefore the strategy is to use various methods to cause the inside rear to lift under cornering.

So, like you've said, rear cornering forces provided by the rear tires would, in fact, be more or less constant (assuming it doesn't lift the inside to the point you start getting camber effects on the outside). To maintain more or less neutral handling, adding grip to the front wouldn't do any good, so yes, in this case I imagine there would be less incentive (at least in cornering) to reduce lateral weight transfer. So IMHO that could be a reasonable input to a strategy to choose track width.

As for CG height, I would consider the effects it would have on acceleration and braking before developing a strategy for that.

[adambrouillard]

The traditional wisdom in karting is that narrowing the rear track increases rear grip up until the point of overturning, but this sounded a little fishy to me. I was thinking that assuming you can keep the rear inside unloaded there would be no change in potential lateral grip no matter what the track or cg height was because the load on the outside rear would not change. I do think there probably is benefit of a narrow rear track under acceleration though as there is not as much of a yawing torque in the direction of oversteer. But on the other hand I would think a wider track would reduce the overturning torque and minimize any positive camber affects. I suppose though that there could be other methods, such as lowering the cg, to minimize the overturning torque.

Okay, so as a basic strategy I was thinking lowest cg and widest feasible front track to increase front grip. Narrowest rear track (without 2 wheeling, and keeping camber as negative as possible) to help minimize oversteering yaw, and then I could adjust balance by moving CG forward and backward.

I think a higher cg would help acceleration and hurt braking, and I do have a higher powered kart so it might be more beneficial than the reduced frontal load transfer, but I understand the tradeoff.

Does this all sound right?

[exFSAE]

Not following your bit on the rear grip being constant..

[adambrouillard]

Okay, well since because of load sensitivity a tire develops a certain amount of lateral force based on a certain load if the load doesn't change shouldn't the potential lateral force also remain the same. If one rear tire has totally unloaded that would mean that all the rear load is on one tire and no more load can be added to it, not counting longitudinal load transfer or aero or the like. That how I understood it anyway.

[Drew Price]

Originally posted by exFSAE:
Not following your bit on the rear grip being constant..


I am interpreting the thinking that once the inside rear tire is unloaded the outside rear will have constant load, and thus constant tractive capacity.

I think for analysis and rough design you could use this method, but I don't think it would be safe to assume that normal load on the outside rear would ever be constant with the inside rear lifted off the ground - you can still have lateral load transfer between the two front wheels, and longitudinal from front to rear distributed between those three wheels.

Imagine coming hot into a decreasing radius corner - inside rear lifts at some point entering into the corner, but as you go deeper the steer angle or even brake force may keep increasing, taking load from the single rear wheel and distributing it to the front two wheels in some fashion.

Not sure what exactly you're asking though, could you clarify a little more?

Best,
Drew

[adambrouillard]

I think I am mainly looking for a strategy to determine the optimum rear track, or at least the tradeoffs involved with deciding. So basically I am asking if the following thinking is correct.

"I was thinking that assuming you can keep the rear inside unloaded there would be no change in potential lateral grip no matter what the track or cg height was because the load on the outside rear would not change. I do think there probably is benefit of a narrow rear track under acceleration though as there is not as much of a yawing torque in the direction of oversteer. But on the other hand I would think a wider track would reduce the overturning torque and minimize any positive camber affects."

I also just thought that under braking a wider track would have a greater understeer torque.

I was just wondered if there was some variable I was missing.

[exFSAE]

I'm not convinced the load will truly be constant. Furthermore, the inclination angle will change the more you lift it.

[Ross_K]

Changing the rear track has a big effect on the relative stiffness of the rear axle...look into that idea a little bit as rear axle stiffness has a major impact on the handling of karts.

You will find in karting though is that there is no "optimum" rear track width..this is like trying to find the optimum rear spring rate on a racing car...it's more about tuning to the conditions that you face and what the driver likes.

You're correct that having a wider track will reduce the overturning moment. If you've ever seen a kart "bicycle" or get up on two wheels, this is because the driver has far too much rear grip mid corner and should widen the rear track to compensate.

It would be interesting to look at a tire model for a kart tire...you're right that if you come from a background in racing cars, a lot of kart dynamics doesn't make sense. It all has to do with that solid rear axle...

Ross

[DJHache]

There's also a big geometrical problem with karts. Since there's no diff in the back if you don't get that inside rear wheel up you will have a huge understeer moment. The front tires will never have enough grip to overcome the grip of the rear tires and the kart will just plow. setting the rear track on the kart is more about unloading the inside rear than loading the outside.