Track differences case study

[thewoundedsoldier]

Has anyone seen a successful team compete with a car featuring more than 4" track width difference? Has anyone ever built one?

I am interested in building a very short rear-tracked vehicle this year (44-46" in the rear vs. 51" in the front). The purpose is to better serve a rear spool. My thinking is that during corner entry the wide track of the front wheels will keep the car stable, and during corner exit the short rear track will help unload the inner tire and actually help handling by putting more power on the outside wheel. Our school just got tire data, so hopefully I can piece together a better picture in the coming weeks. Just hoping for feedback from those who have seen something like this done (or not done for a reason). Am i missing anything obvious? Anything not-so-obvious?

[Vaibhav Kumar]

You can have a look at the FSG_2009_Programme document on FSG website. It has wheelbase, track and other basic information of all participating cars.

[Pennyman]

Rule B2.4 says you could go even narrower in the rear if you wanted!

I would compare designing suspension/ wheel packages for a spool to being pregnant. There is no middle ground of you want it to handle at its best.

Our team built a suspension that accommodated a spool and a diff last year. I wouldn't say it was completely successful with either the diff or the spool, but we learned a lot in the process.

I won't give away everything just yet, but let's just say that there's more than just unloading the inner rear tire that affects your design considerations.

There are some very interesting loads fed into the suspension/ chassis during corner entry and exit (when the inner tire isn't unloaded) that need to be accounted for, and the fact that you are sacrificing a significant amount of rear grip to maintain vehicle stability. Not to mention your tires wear in ways you wouldn't normally think they would...

[thewoundedsoldier]

Thanks Vaibhav, I've had my eye on this idea as well as a few others while looking at recent years' cars. I haven't really seen a setup similar to what I am looking for in a recent car, so I'm wondering if anyone has seen this done in years past.

I am aiming more for the experience of the old-timers who browse the forums.

Pennyman, wait until you see the suspension I've
dreamed up to account for the turning/torsion force. Hopefully you come by the shop this year to check it out..

[Ben K]

You might even be able to get rid of the diff if you consider you are constantly lifting that tire....but you gotta enter every corner with some feeling

Yeah we thought about this last year--then we decided to build a solid, good car instead of going crazy trying to tune it

[Dash]

I made a spreadsheet with the top eleven teams for each event, and overall for 2009 and 2010 Michigan events. None that I can directly remember have differences of more than 3 inches. I would say most floated around the 1-2 inch mark.

[flavorPacket]

Maryland was 52/46 this year according to the handbook. Won skidpad by a wide margin at MIS.

[Ockham]

I wonder if a diff-less rear and a minimal rear track (think ~18in) with an extremely stiff front anti-roll bar would be workable... That seems to be the direction this thread is headed. You'd sure get a grilling from the design judges, but I like the audacity of that setup. It'd certainly be light (bye-bye twelve kilos of differential), but how well would it grip?

[Kirk Feldkamp]

Originally posted by Ben Kolodner:
You might even be able to get rid of the diff if you consider you are constantly lifting that tire...

Agreed. If you're going to build a kart, you might as well incorporate the simplicity of a kart! Try to hunt down some pictures of Cal Poly SLO's car from a few years back if you're interested in seeing how others have done this before. The SLO concept was great, they just didn't get their engine tuning together in time to put together a solid effort at comp. Had they, I think the ideas they incorporated into the car would have garnered a lot more attention. At ~330lbs, it's hard to argue with the case of simplification for the sake of weight savings. One thing I'd recommend if you're planning on traveling down this path is to allow for quick adjustability in track width (both front and rear), just like you have in a kart. That's one of the most significant parts of a kart setup, after all.

To take the concept a step further, if you can somehow utilize off-the-shelf kart axles and hubs, you could put yourself many steps ahead in the fabrication process. Plus, if you do something like this, you will always have a vast network of inexpensive and easy to source replacement parts available.


Originally posted by Ockham:
It'd certainly be light (bye-bye twelve kilos of differential), but how well would it grip?

Ever driven a 'real' kart? They do ok. http://fsae.com/groupee_common/emoticons/icon_wink.gif

-Kirk

[Bobby Doyle]

Originally posted by flavorPacket:
Maryland was 52/46 this year according to the handbook. Won skidpad by a wide margin at MIS.

Any idea what their weight distribution was?

[Mike Cook]

Yes we did have a 52 front 46 rear. I liked it a lot because it was really about the right ratio not to hit cones with the inside rear tire, so that made it a little bit easier to drive. On the whole, thats probably too wide. Its really course dependent, and in tight slaloms that wide front track kills us. For instance, in autocross we were maybe .25 seconds off the pace, and then in endurance we were about .8 off the pace. The autocross track was actually a lot slower average speed then the endurance, so we thought we would pick up some on the endurance track due to aero, but there was a really tight section that teams like Oregon could just drive straight through. Not so much for us, and it cost us big.


Oh, and about spool cars -

They are very difficult to drive. Driving around on three wheels takes a lot of work to get right. There is a ton of adjustment built into shifters to get them to work well, and when the conditions change, or grip level changes, those guys are all out there changing track widths and everything else. Most teams lack the resources to test enough to figure this all out in one year, so unless your driving a legacy car, I would shy away from a spool.

[thewoundedsoldier]

Originally posted by Bobby Doyle:

Any idea what their weight distribution was?

This is sharp! I am extra concerned about this because it looks like our car will be rear heavy (close to 58/42). I'd imagine this setup would be optimized somewhere around 50/50. Any thoughts?

Mike, thanks for the feedback. Is the plan for the next terps car to be similarly ratio-ed, just smaller?

[Mike Cook]

The easiest thing for us to do is cut the front track back down to about 47ish, I'd like to go narrower with the rear too, but that requires a lot more work with making new half shafts and everything else...so we will see.

In terms of weight distro, i'm not going to say what ours is, but it has a bit of junk in the trunk.

[js10coastr]

The Audi R10 ran with a spool (if I recall correctly).

There are a lot of adjustments built into a shifter kart, however there is a lot more adjustment in an FSAE car that you don't have in a shifter kart.

[Kirk Feldkamp]

Originally posted by js10coastr:
There are a lot of adjustments built into a shifter kart, however there is a lot more adjustment in an FSAE car that you don't have in a shifter kart.

Given your contact with a FSAE car that's sort of a shifter kart, would you say someone designing such a system should look at making it more kart-like, or more standard FSAE-like? Obviously, the SLO concept went more kart-like, but I'm curious to hear your opinion on what about that approach is good, and what's bad.

-Kirk

[Dash]

Originally posted by flavorPacket:
Maryland was 52/46 this year according to the handbook. Won skidpad by a wide margin at MIS.


Also, If i remember correctly, they had something like a 72 inch wheelbase. Far longer than any FSAE vehicle i've seen.

[Mike Cook]

Yes, we also had a 72" wheelbase...probably one of the biggest fsae cars in a long time. It was basically built as an AMOD car. Our goal was to do well at FSAE but also win SCCA Nationals.

There are a lot of performance advantages to setting your car up like a shifter but I think in the end it makes a FSAE car harder to drive, so it kinda depends on how good your drivers are. If you have any specific questions feel free to ask

[Bobby Doyle]

Originally posted by Mike Cook:
If you have any specific questions feel free to ask

What was/is your weight distribution?


EDIT: Just saw above that you politely declined. Fair enough. http://fsae.com/groupee_common/emoticons/icon_smile.gif

[Dash]

Did you find it hard to get around any part of the course with the longer car? I know your track setup probably helped with cone issues, but still, seems large in comparison with other teams. I'm afraid to make our car much longer ( 65 in wheelbase ), but for some packaging issues we had last year, another two or three inches would have helped a ton.

[js10coastr]

Originally posted by Kirk Feldkamp:


Given your contact with a FSAE car that's sort of a shifter kart, would you say someone designing such a system should look at making it more kart-like, or more standard FSAE-like? Obviously, the SLO concept went more kart-like, but I'm curious to hear your opinion on what about that approach is good, and what's bad.

-Kirk

I never drove the solid rear axle cars, so I can't speak from that end. However I was in on the initial design and concept considerations and watched the build (or attempts thereof) of three generations. The main reasons for going in this direction was the coming of the 450 single cylinder engines. To achieve similar power to weight numbers the car would have to weigh close to 300 lbs. One of the other factors was that during that time, there weren't many FSAE specific tires and so getting temperature into them was an issue. By cornering on three we figured more heat would go into the tires, therefore providing more grip.

The concept was never developed to anywhere near its full potential. Engine tuning plagued the team the first year, and then amidst leadership turmoil/turnover the understanding of vehicle dynamics, upper level decision making, and the basics of ground vehicles was lost. On top of that CP SLO has never been a good "race team"; always a better "design team".

While it may seem simple to design a "solid axle" because there are less parts, the few parts end up being more complex (to design and manufacture). There are also less resources to learn from, nobody does the solid rear like this but you can look anywhere and see a double wishbone and learn from theirs. On top of that, the car is generally more difficult to work on. Design wise... well the entire rear end is unsprung and you have one damper trying to control that. I'm also not convinced (anymore) that being that light is that advantageous.

On the positive side, the system should weigh less and you get to cut out a damper from your cost report.

From my view, IF you were to try and do a solid rear axle you better hell know your tire spring rates well, and I would make a steel tube frame chassis with adjustable members (like a go kart) to adjust the chassis stiffness/TLLTD. I'm sure the car would be as light as a carbon one, but you would save a lot in the cost report.

I would prefer an independent rear with a spool... see my formula hybrid car (search for cal poly formula hybrid on youtube). I think this is a decent tradeoff, and with a few hours of testing its pretty easy to tune the car with a spool. PS. You only have to unload the tire, not lift it completely off the ground.

From working in pro racing (GT cars) for a few years, I think tuning a diff is what separates the top teams from the not so top teams... however I think it is beyond the scope of most FSAE teams.

[js10coastr]

...one more thing. The solid rear axle cars always had a forward biased weight distribution to allow for "neutral handling". From my opinion it is a terrible compromise you have to make in braking and traction limited acceleration to corner properly.

[jdstuff]

Originally posted by js10coastr:
From working in pro racing (GT cars) for a few years, I think tuning a diff is what separates the top teams from the not so top teams...

I've been saying this for years....although my experience was in Atlantics instead of GT's. I think JS and I even had discussions over a beer about this very topic in SLO once or twice.

To thewoundedsoldier, good questions, and keep on this path. Once you understand the implications of driveline design, it will really open your eyes to the suspension system as well.

You can approach this problem from either end: 1) Fix your driveline, as in a spool, and then focus all of your design energy into developing adjustability in the suspension to accommodate it. As has been stated previously, your component count will decrease, and the overall package will be come lighter, but those remaining components will become increasingly complex. Or 2) design a vanilla suspension system, and build loads of adjustability into your driveline...as in a salisbury-type differential. The overall package will probably be heavier, but there may be design and/or manufacturing simplifications that result.

There is no wrong answer. Both options will require 10x more testing than you have planned to figure out. http://fsae.com/groupee_common/emoticons/icon_wink.gif Cheers.

[Mike Cook]

Originally posted by Dash:
Did you find it hard to get around any part of the course with the longer car? I know your track setup probably helped with cone issues, but still, seems large in comparison with other teams. I'm afraid to make our car much longer ( 65 in wheelbase ), but for some packaging issues we had last year, another two or three inches would have helped a ton.

One thing we did is modeled all the basic maneuvers on a autocross track (slalom, box turn, hairpin, skidpad) in solidworks. Then we modeled our car and generated paths that it would need to travel through the cones. We looked at how the radius and path length changed when we changed basic geometric parameters like track and wheelbase. I don't think the longer wheelbase actually hurts you very much at all, however it will require more steering so you need to make sure you have all that figured out. It seems to me that track width plays a much larger role on affecting your path than wheelbase.

[Drew Price]

I think the geometric approach is basic and valid and easy to visualize, but did you take slip angle into account for this, particularly since it changes with lateral acceleration, and probably won't be symmetric front v. rear?

Standing out on the enduro and Auto-x track at CA this year I did not see a single car even clip a cone with a rear wheel, unless the car was going in way too hot and got sideways.

What about YMOI?

Best,
Drew

[Mike Cook]

Yeah, you need to take slip angle into account and its best to have a real idea of what your slip angles are because it will change the results quite a bit. We had a slip sensor available to us a few years ago and got a good idea of what slip angles we were running...although like you said it changes with maneuver (i.e. slalom vs. skidpad).

Generally with our cars, our yaw inertia isn't changing that much when we lengthen our wheelbase because all the main components are still packaged close to the CG. If you look in Millikens book about yaw response, you can see that yaw response improves greatly with a longer wheelbase so as long as you attempt to keep your YMOI small, longer is probably better.

About clipping cones on the rear tire, we clipped two in autocross. Obviously if you're running equal front and rear tracks you will need to drive different lines than a car with a 52/46 track. It all depends on what you want to optimize for. For a long slalom or kink you will be limited by front track. For a tight slalom you will be limited by your rear track.

Mike

[thewoundedsoldier]

Mike, what you did for slalom is pretty close to what I have in mind. Once I have tire data, I plan to use simulink to create curves pitting steering angle vs. lateral g and create overlays onto a track of when the inner wheel will be unloaded a given amount. I'll then optimize that overlay to take most advantage of corner exit.

One of the input parameters I am interested in is how track width (both front and rear) affect the diagonal load transfer. I am, of course, expecting a smaller rear track to unload easier than a larger rear track. Does this sound right by your experience?

[Mike Cook]

I think you are on the right track. The one thing I have realized is that a lot of the formulas in text books have a lot of small angle approximations that don't work for what we are doing - simply because were steering so much. Obviously to go through a slalom, we need to yaw the car back in forth. What yaws the car? Not that outside front tire whose force vector passes near the CG. Its all about keeping that weight on the inside front.

Some problems you run into when trying to pick the inside rear tire off the ground is that you need to be really rear stiff. It sounds obvious, but how do you do that? Really stiff springs, stiff bars, etc. Of course all those things ultimately hurt grip so you try to find other ways to help like roll centers and track widths and dampers.

Don't get to confused with what shifter carts do though. Yes they want to unload the inside rear tire but they do it through jacking. On a shifter cart, just by steering you can pick the rear tire off the ground - so essentially go from a 50% cross to a 0% cross. Changing the track widths drastically affects their jacking and thats why they tune with it so much. On a FSAE car steering the car might give you 5% wedge or thereabouts so playing with your track widths aren't going to be a very sensitive parameter.

Mike
Happy 4th

[oz_olly]

I think Mike is really on the money where he says

"The one thing I have realized is that a lot of the formulas in text books have a lot of small angle approximations that don't work for what we are doing - simply because were steering so much."

With the amount of steering we use in FSAE the longitudinal force component of the tyre lateral force (in the vehicle coordinates) becomes significanlty large. The main way we can balance this component of the yaw moment is to add tractive force at the rear outside wheel, but the more we add there the less lateral capacity the rear outside tyre has and so on. This is where alot of the linearised bicycle models fall down for FSAE (at least that is what I am starting to think).

[Mike Cook]

We're getting warmer.

[Drew Price]

Very cool Mike, I think steering towards what you need to be competitive in A-Mod is a good way to go towards actually tuning a race car. I wish I could have seen your car this year, it looks pretty stunning in the photos, and it definitely does not look like the wheelbase is that long, how did it look amidst everyone else's car?

Best,
Drew

[Mike Cook]

I mean, it didn't look that big, but there are a couple neat things about it. For one, the frame really isn't longer than any other fsae frames, but the centerline of the front axle is in front of your feet which puts the front of the tire much in front of the front bulkhead. Also, we were probably the only team that used 10" diameter front tires and 13" rear. I still think in retrospect, we were probably too wide...But in SCCA the car just kills, much faster than anything else and I reckon that if we had to go head to head with the best amod car (bowland) it might win. It's a cool car, bc you could actually sell it to someone that wanted to race AMOD and all they really need to do is add some ballast and pull the restrictor off. I will step off my soap box but you can find some pretty wicked videos of it on facebook.

[thewoundedsoldier]

Originally posted by Mike Cook:
I think you are on the right track. The one thing I have realized is that a lot of the formulas in text books have a lot of small angle approximations that don't work for what we are doing - simply because were steering so much. Obviously to go through a slalom, we need to yaw the car back in forth. What yaws the car? Not that outside front tire whose force vector passes near the CG. Its all about keeping that weight on the inside front.

Aren't you assuming a particular steering design? I'm finding that for a locked rear end, my design options in the front are becoming more and more limited.

I think I can tell from the pictures, but just to be sure, what kind of ackermann are you running?

[Mike Cook]

No, steering design does not have much to do with it. To be more blunt, in a steady state corner, forces and moments must be equal to 0. What happens when you enter a corner? You steer, and the front tires build up slip angles and cornering forces. These forces yaw the car. The yaw generates slip angle on the rear axle which then builds up force. How much force does the rear axle build up? Enough such that the yaw moment is balanced and = 0.

Now think about how much yaw moment the front axle produces? What produces more moment, if all the weight is on the outside front tire or split equally between the front tires? Since the inside front tire has a longer moment arm than the outside front tire (at high steer angles, (i.e. no small angle aprox.)) the more weight you keep on the inside front, the more yaw you get. And this is important, because for the tight turns, your rear tires are rarely saturated, so you aren't getting as much work out of them as possible. If you increase the front yaw moment, the rear yaw moment will need to increase, which means the rear tire cornering force will increase. This means more lat accel.

[thewoundedsoldier]

Sorry if these questions are trivial...

Saying that the inside tire has a longer moment arm definitely does make steering assumptions. I can see positive ackermann creating a situation where the outer tire has the longer moment. Especially with wider track widths and longer wheelbases.

Also, for the same turn, doesn't the longitudinal force component of the outside tire give a longer moment arm than the longitudinal force component of the inside tire? Do these not serve to yaw the car?

Going back to unloading the inner-rear, do you think that rear tires rarely saturate because the front-to-rear weight transfer takes so much weight off of them? Then is it like a trade--the greater yaw moment will also give a greater longitudinal grip? Does this question even make sense?

[Pennyman]

Originally posted by thewoundedsoldier:
Sorry if these questions are trivial...

Saying that the inside tire has a longer moment arm definitely does make steering assumptions. I can see positive ackermann creating a situation where the outer tire has the longer moment. Especially with wider track widths and longer wheelbases.

Also, for the same turn, doesn't the longitudinal force component of the outside tire give a longer moment arm than the longitudinal force component of the inside tire? Do these not serve to yaw the car?

Going back to unloading the inner-rear, do you think that rear tires rarely saturate because the front-to-rear weight transfer takes so much weight off of them? Then is it like a trade--the greater yaw moment will also give a greater longitudinal grip? Does this question even make sense?

Josh,

If you have positive ackermann, you could increase the FORCE component of the yaw moment (as opposed to the distance component) of the inside tire relative to the outside tire.

If you think about it, wouldn't the longitudinal component of the outside tire serve to de-yaw the car? (Like if you all of a sudden locked up just the outer front while it was steered, it would just want to put the car straight again).

Finally, regarding your last question ( I assume you're referring to the use of a spool). Why would you be interested in increasing longitudinal grip during a turning event? wouldn't this just reduce your cornering capability? During turn in, you have a positive slip ratio on the inner rear tire and a negative slip ratio on the outer, which resists turn in and also reduces your available lateral grip. Then once the inner rear is unloaded, guess what? You still have less lateral grip because your inner rear is pretending it's an airplane.

[thewoundedsoldier]

Originally posted by Pennyman:
Josh,

If you have positive ackermann, you could increase the FORCE component of the yaw moment (as opposed to the distance component) of the inside tire relative to the outside tire.

If you think about it, wouldn't the longitudinal component of the outside tire serve to de-yaw the car? (Like if you all of a sudden locked up just the outer front while it was steered, it would just want to put the car straight again).

Finally, regarding your last question ( I assume you're referring to the use of a spool). Why would you be interested in increasing longitudinal grip during a turning event? wouldn't this just reduce your cornering capability? During turn in, you have a positive slip ratio on the inner rear tire and a negative slip ratio on the outer, which resists turn in and also reduces your available lateral grip. Then once the inner rear is unloaded, guess what? You still have less lateral grip because your inner rear is pretending it's an airplane.

Is the force component increased because the ackermann gives a higher slip? I would still argue that the simple geometry would be significant in a wide and long car.

I get why the longitudinal force would de-yaw the car on the outside tire, but don't understand why we ignore it just because we are turning. Don't you want longitudinal force all the time, except for the very apex of the turn? We should go straight from braking to accelerating?

I'll spend tonight getting cozier with yaw moment terms and effects.

[thewoundedsoldier]

Update time:

So putting myself through the ringer has definitely shown me that experience trumps assumption. I thought I knew, or at least had a solid grip on, what the basic parameters were with this issue. I didn't.

First off, I finished a *decent* steady state cornering model in simulink based off the MMM. By "decent" I mean "it sucks", but I think it is a step in the right direction. Two main lessons are standing out to me.

1) CG height is a much more critical design parameter than I gave it credit for. I am doing all these small design changes to fine tune lateral weight transfer, and then I make tiny changes in CG height and it has some strong effects! I always thought it was best to simply get your CG as low as possible, but to get big rear weight transfer, a higher CG seems to help... This was essentially my visualization of a shorter rear track unloading the inner rear better--shorter rear track and higher CG give increased weight transfer (sorry, I know that that was already obvious to everyone else--I'm still learning!)

2) We recently committed to a spool drive, and shortly thereafter decided that it'd be easier on us to make a solid beam axle than a spool with IRS. This decision wasn't necessarily made for weight savings, but for manufacturing/assembly speed and the ease of implementing it on last year's Formula-Hybrid car (plan to use the car for driver training and data acq, as well as parts testing). This is giving me some good amounts of work to do getting caster, scrub, trail, etc to live in harmony.

There is another guy on our team who is doing a really good job developing an acceleration model, and we plan to mesh the two relatively soon to work within a lapsim within a points-optimization model.

Thanks to everyone who has provided feedback along the way, especially Mike and Joey!

Any further thoughts/ideas are much appreciated, and I hope this thread helps more people than just me.

[exFSAE]

Ahh yes. Vehicle simulation work.

How do you know the tire data is remotely realistic and not junk?

[thewoundedsoldier]

Haha it's funny you ask, because...

We've decided on 10" LC0s or LC3s this year, and obviously have no data to go off of. So, since the only TTC data on 10" tires was on goodyears, I found myself creating tables that compared the 10" goodyear performance to the 13" goodyear performance, then extrapolated from the 13" hoosier data to make phony 10" hoosier data. It is obviously junk, but the best I can do. (let's not even talk about the fact that the 13" goodyears, 10" goodyears, 13" hoosiers, and our chosen 10" hoosiers are all different compounds!)

Once we buy the tires I can get the essentials like spring rate and deflection, but anything dynamic is gonna be all guess work.

I have learned a lot just assuming our tires from last year (20.5x7x13 R25B). My diabolical plan has been to develop completely different wheel packages for 10" and 13" wheels, then try them both out and finetune. It is proving harder than I thought, especially with the vehicle simulation.

[Mike Cook]

There is some tire data on the Hoosier 10" from the first round I think. Its not the LC0, but its a start I think. I would expect the LC0 peak grip to be at a little bit higher slip angle because they have less ply which will make it more compliant.

Anyways, you can get your car pretty much in the ball park with some basic assumptions. I sometimes think that tire temperature probably has a lot more to do with peak grip than camber or tire pressure, so the tire data is at most good for only comparing brand g to brand H, but not necessarily optimizing a setup.

[thewoundedsoldier]

Wow now I feel like an idiot. I looked at the first contents file and they have it written as 20x6x10 and I only saw the 20". They make the same error in the title of their .mat files. Now I have a 10 inch vs. a 13 inch in the same compound, this is HUUUGE!

As for the tire temp, it is part of the data, so can't you introduce it as a third or fourth dimension? I am seeing that tire temp vs. Fy is nearly as valuable as Fz vs. Fy.

[Mike Cook]

I was just pointing out that you have no idea what your on track tire temp will be. So even if you know how it affects your FY, its hard to simulate.

[thewoundedsoldier]

For concept and initial setup you're definitely right.

Our strategy at this point is to build the current solid beam axle design and retrofit it onto last year's car (with the entire rear frame cut out). That way we can get testing as soon as possible, and work things like tire temperature back into the models before starting to build the final product (which will be an entire new car, frame up). Also, come March or April it should give us two working cars to do a lot of parallel concept/product testing.

In your second to last post, you said that you can get your setup ballparked by making some basic assumptions. By that did you mean tire parameter assumptions (slip angle, camber curve, Mz, etc)?

[Horace]

I hope this is not going off topic. But after reading this thread and the one about 10"/13" wheels I was wondering how certain track/wheelbase would be more suitable for certain cornering stiffnesses of the tires. Anyone want to comment on that?

[Mike Cook]

Horace,

Off the top of my head I'm not sure how I would necessarily relate track/wheelbase to cornering stiffness. However one thing to consider is that the 10" tires have a lot of load sensitivity, while the 13"s aren't nearly as bad. So if using 10", you kinda need to be conscientious of how much weight you are transferring. Also, generally you are going to want the highest cornering stiffness rear tires as possible, as this will have a large effect on your transient behavior.