Tire Dynamics

This is my first (long winded) post. Having lots of shelter-in-place time (i.e., the track is closed), I’ve been reading obsessively about kart set-ups. Most of my 11 years karting has been spent testing this and that and listening to better drivers (not too hard to find, in my case).

Now, everything I’ve read, including Michelin’s complex pdf “The Tyre – Grip”, says that WIDENING the rear track allows a tire to go FASTER around a set curve before beginning to skid, once the kart has jacked and has taken a set. Obviously this maximum speed is also controlled by a specific tire, psi, track surface, etc., etc. But the principles, as I read them (e.g., the moment arm from CG to contact patch, the contact patch deformation, and on and on) all seem to lead to this conclusion. Push back?

Is Michelin specifically referring to karting tires here? I ask because in a car, obviously a wider track width is going to allow for better cornering ability in most cases, but in a kart it’s a little more nuanced, since the inside rear wheel has to unload for the kart to rotate effectively. To do that, you need to get the kart to flex and tip onto the outside rear tire. With a wider track width, you effectively are lowering the relative center of gravity, and diminishing the kart’s ability to lift the inside rear through weight jacking. You’re also relatively softening the rear of the kart, as you’re exposing more axle and allowing more flex. I find that wider rear track widths offer more stability, as the kart isn’t as narrow and reactive to steering inputs, so that’s how I use rear track width when fine tuning the balance.

This comes back to the constant struggle to separate “grip” from “rate of lift”. A kart that is too narrow will be reactive and unstable, and some drivers may perceive this as “lack of grip”, when in reality, they have the opposite problem. The kart is unstable because it is digging too hard on the outside tire from the excessive weight jacking. Conversely, a kart that is too wide can start to get too soft to the point where the rear end just squats in the corner and the kart flat slides or drags the inside rear wheel.

You are absolutely correct about this interplay between jacking and lateral grip at different points in the turn – it seems to be the a constant battle and brings into play all kinds of variables, from seat struts to castor (that is, from all the front-of-the-kart adjustments to all those in the rear). That is why I tried to keep those out of the equation by assuming a kart that has jacked (properly) and has taken a set.

I assume I have a lot to learn about when and how quickly and how much a kart should jack (and, in reverse order, set back down). And I agree with you that the stability of this transition is aided by a wider width. As you know, there is a lot of that in the discussion of axles on this forum. You are also correct to point out that cars (4 wheels with suspensions) are different than karts (fast tricycles), since a car wants to get as much grip as possible out of all 4 tires, including the inside rear.

Thus all the stuff about shortening the distance between the roll center and the CG, etc. However, Michelin (and others) point out that the transverse coefficient of friction for a tire in a turn is not a constant and goes down as LOAD on the tire increases. Assuming all my “constants” in my original post, the wider the track, the lower the vertical load placed on the outside rear tire of a kart in a turn. Since velocity around a turn is directly proportional to the transverse coefficient of grip (Michelin’s words) times radius, then if there is less load on the tire as it is moved out on the axle, there should be an increase in the potential for velocity as the coefficient remains high(er).

Let me admit that I am struggling with this – not only with the principles laid out by Michelin but also with trying to identify all variables that I can hold constant without violating the principles.

I have been reading the Michelin document for about 20 minutes now and it’s pretty much over my head. But I think I hear what you’re saying. Let me take a stab at it.

There are two radii on the kart when going around a corner. The inner wheels and the outer wheels. When we widen the rear track width, the outer radius increases and the inner radius decreases. However, since we are lifting the inside rear wheel, that inner radius doesn’t really matter. But the outer wheel is now on a wider radius, so can tolerate more friction and therefore corner faster. Am I understanding correctly?

I think I’ve caused myself too much brain damage. As a starting point, it is hard to keep track of what Michelin is talking about at any given point in their article. Velocity (probably linear or how fast you are truckin’ around the corner), vertical load on the tire, weight (or load) shift, lateral friction, lateral grip, etc. What you made me realize is that we probably cannot answer my original question: Does a wider track mean faster linear velocity around a given curve until you finally start to skid?

I do not think we can answer this because we have 2 conflicting principles. First, as the rear tire is brought in, you shorten the lever arm from the CG to the contact patch. This increases the absolute load on the tire AND thus the grip (all be it at a declining, non-linear, rate). However, as you increase the load, you decrease the transverse coefficient of friction, and, thus, you decrease the grip. Which one rules? I have no idea.

I started my research and this post because, over the years, I’ve been following the advice of really good (national level) drivers and mechanics, without really understanding why they believed what they do. AND one guy’s input it was frequently contradicted by another.

Now I have come full circle and believe that I’ll just have to keep experimenting with set-up on my own. I’ve resisted this because I wasn’t sure what made sense to try and because I’m a painfully slow wrench. My friends at the track should set up a GoPro while I’ve got tools in my hand and sell the footage to the Comedy Channel for big bucks…But thanks for taking this on and making me think – it only happens occasionally!

Hey Evan – It turns out, according to Michelin, that tires have one relatively constant coefficient of friction longitudinally (accelerating and braking) and another entirely different “transverse coefficient of friction” in a turn. This second one is not a constant at all, but is variable and goes down in value as the vertical load on the tire increases. Go figure.

Interesting! I appreciate the info. Could some of this variation be due to side wall response, and would tires of various side wall stiffnesses each have their own unique curve?

The real issue here is this is all relative to the gazillion other variables in a kart chassis, track surface, etc.

Good topic to make you think though. Definitely melted my brain a little.

I’m not a tire engineer, but somehow that never stops me from having an opinion. :grin:

If I’m looking at the correct document, then it states this:

Tire%20loads

That all seems fine in theory, but what kart running anywhere close to competitive speeds is generating 4 degrees (or less) of slip angle other than during the time when load is initially being transferred to the outside front tire to initiate a turn, or load is being transferred from the front tire to the outside rear tire to manage the kart’s trajectory from the corner’s rotation point to the exit? This idea of driving the outside front tire into turns and the outside rear tire out correlates to TJ’s point about the radius of the inner tires being relatively unimportant to maximum performance.

Then they say:

Again we have theory (slip angle remains constant), which it never does in real life, but more importantly, the whole statement is unclear (seemingly contradicting itself). It says traction increases as load increases until the tire reaches optimal ‘load’ (which presumably correlates to optimum drift angle… aka the slip Vs G-load curve).

That all makes sense, and we can intuit that once the tire is at optimal load, adding additional load will simultaneously increase drift angle and reduce traction (while also scrubbing speed and increasing tire temperatures and wear). However, then they go on to say “THE” load transfer leads to a reduction in force (traction), when based on what they said previously they mean “Excessive” load transfer leads to reduced traction.

So ultimately it seems like they are saying what we all already understand empirically and/or intellectually… The outside tires MUST be optimally loaded to produce optimal traction. The inside tires contribution in terms of cornering force is minimal, however, for karts, their contribution to the management of load transfer to the outside tires (jacking weight into the inside front to influence how the inside rear lifts) is critical to effective tire load management.

That just my $0.02

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After I read all this, I was talking it out to myself in Michelin’s technical terms, and then I went, “oh, they’re saying a tire grips more as load is applied, to a point where too much load causes the tire to slip. Well I knew that!” The technical jargon hurt my brain, but when it comes down to it, I think they’re just explaining with algebra what we already know subconsciously about how a tire works.

TJ is spot on about the gazillion variables, full stop. And that doesn’t even include the driver’s own variables… I was hoping, with the virus-imposed time I had to “research”, that I would find my own rational approach to tuning my kart chassis (after all these years). The thread “Do different stiffness axles do anything?” contained a lot of good information in the back and forth; I did learn some new things and had other things reinforced. “Learning how to diagnose tires” also helped. These threads plus the one we are on now, “Tire dynamics”, leads to a question about balance. While some sites talk about the location of CG, it seems to me that balance is a tire issue. Specifically, in a turn, when the kart has jacked and has taken a set, I think balance is defined as the grip of the front tires being equal to the grip of the rear outside tire. I notice this most when I overcook a turn and slide; if front and back slide sideways at the same rate, I’m balanced. Thoughts?

In a shifter especially, but sometimes with x30, in fast, loaded up turns, you can have two sets of traction circles going on, fronts headed one way with the rears a bit behind, going in another direction, but playing catch up. Each arc in perfect grip, balanced, just in different parts of the turn. In this state the grip is equal across the tires.But, they are all in that interlock state with the underlying rubber, so max grip. But, I think balance is a number of things working together. Grip is a byproduct.

Maybe, but not necessarily. The way I would define “balance” would be that one end of the kart isn’t making the other end of the kart do something it shouldn’t. The front isn’t too twitchy, causing the rear to oversteer. The rear isn’t too bound up, causing the front to understeer.

It’s hard to say what the kart’s balance is like if you overcook a corner for example, since you made an input beyond the kart’s limit to get to the state of “overcooking”, and you’re having to make inputs outside of the kart’s limits to keep the kart on the correct trajectory, so you’re automatically inducing an unusual balance into the kart at that point anyway.

When I go out for morning warm-up on a cold track, and the kart is feels pretty good and predictable, but I’m 0.5 down on the leaders, I know the balance is good and I’m just lacking overall grip, and once I slap new tires on for qualifying, I should be okay.

In our last club race before the lockdown, I went into one corner too fast, started skidding sideways, and was heading toward some raised curbing. (Flip imminent… My input was to freeze at the wheel until I stopped skidding.) Kart never oversteered or understeered during this brief “moment”. Actually, kart felt very good all day and tires looked good after qualifying, heat, and final. Probably as close to balanced as I get. By the way, we never have a rubbered-up track except for 3 days a year when the national teams come out for the Challenge of the Americas. At best, we race on a good clean, green track. Also, my kart is a Zanardi KZ2 with Rotax Evo on Envinco Reds; Dom was correct to bring into the discussion the specific kart involved.

Make sense to me that it makes a corner a little less tight. As you also state this is a trade off against all the other variables and may not be a net gain.