The science behind wheel sizes

[topwelshman]

What's the science behind wheel sizing, by that what effects on speed & handling does say a 15" wheel have over 17" wheels? What difference does the width of the tyre make and how does adverse weather affect these choices?

I need to buy 2 new sets of wheels (1 for dry and 1 wet)and would like to make an informed choice rather than one on aesthetics.

[graham bahr]

ok here goes...the following is nearly all based on my own experiences on my bmw 2002 race car.

a 17" wheel will give a bigger footprint than a 15", however some of the gains will be lost due to the bigger wheel being heavier and having its weight spread further out, as wheels act just like flyheels, however i find that wheel diameter has little effect other than to alter the gearing, infact i use either 15,16 or 17 rear wheels depending on the ciruit, it sure beats the hell out of keep changing diffs.

going back to the weight of wheels acting like flywheels, back to back testing with the same size tyres shows my car definatly accerlates better with my 7X15 wheels, compaired to my much heavier 7x8's, however dry lap times are faster with the 8x15's as the wider wheel stretches the tyre more and gives a wider footprint as well as stiffer sidewalls, it has to be noted that the ideal tyre pressure are several psi different for the two wheel sizes even with the same tyres, so i reserve the narrower wheels for the wet.

for best handling on a race car it pays to have the tyres on the narrow side of what the wheel will accept, avoid over tyreing the car as you will get better lap times with a narrower tyre nice and hot compaired to a wider tyre thats only warm, as for the wet, narrow tyres are definatly the way to go, to give the rubber a chance to cut throught the water and grip the tarmac. in the dry at least you can use bigger offsets or wider wheels to increase the width of the track which will give you better corner stability and make the car less twitchy.
one final point, as you go wider with your wheels you have to run less camber or you might find wider wheels give a smaller contact patch as i found when i first fitted my 8 inch rims.

[greenamex2]

Graham, sort of going to contradict you but not, if you get what I mean.

Tyre footprint is (almost)totally dictated by tyre pressure and force (ok weight) on the given wheel. Dig out your old Physics notebook from school (covered in the obiligatory wallpaper/sticky backed plastic etc) and you will find the following formula -

Area=Force/Pressure

Funnily enough this also dispells the common myth that wider tyres give a bigger footprint, they don't.

HOWEVER, what both a larger diameter TYRE (and wider one for that matter) give you is a more optimal tyre footprint shape. The bigger the diameter (and width) the more oblong the footprint. This is good for two reasons.

A suprising amount of a tyres footprint does surprisingly little due to unequal load across it and some other stuff. By going to a bigger diameter (and width) you make more effective use of what footprint you have.

The second benefit is cooling. The bigger diameter and wider a tyre is the cooler it will run. This means the tyre can either be 'softer' for a given condition or will run a lower hot pressure. Obviously a softer tyre will give more grip, less obviously a lower pressure will in increase the size of the contact patch (see above formula).

Another benefit of a bigger diamater wheel is potentially having a shorter stiffer sidewall for the same outside diameter. The sidewall being stiffer means that it will flex less. All other things being equal this will make the steering feel much more responsive and also stop the tyre deforming and hence losing it's optimal contact patch shape. In addition you can lose a big of your new found stiffness and drop your tyre pressures, referring to formula above we know that this will increase the area of our contact patch.

This is also the reason why having the widest rim on the narrowest tyre is a very good thing.

The disadvantage of a stiffer less flexible sidewall is the tyre will be less tolerant of poor camber control.

[dtype38]

Can anyone tell me why open wheel cars, dragsters and Nascars mostly run high profile tyres on quite small diameter rims, whereas closed wheel cars like touring cars and Le-Mans sportscars tend to run rubber bands on enourmous rims? Is it just the tyre rules of each type of racing or is there a technial reason? :confused:

[1200Datto27]

Most of the series that run on smaller diameter wheels have either a set size of wheel/tyre, or a maximum size allowed. Drag racing is different, in that they run special "Wrinkle Wall" tyres, that are designed to run at around 8psi, with a secondary support tyre internally mounted. These sidewalls are designed to flex and squat to allow the dragsters to get the best launch possible, but you would not want to have to turn quickly on them.

[HiRich]

dtype,
When designing from scratch, one of the first questions is "how big a brake do I want/can I have?"

If tyre size is restricted, but disc size is relatively free (and you're running in a relatively heavy series like Touring Cars), you'll fit the biggest, meatiest discs you can get away with - hence rubber bands on giant rims.

[dtype38]

Ok, that makes sense. Does it then follow that a good place to start choosing wheels and tyres would be to pick the smallest front brake discs that can give the necessary braking, then pick the smallest rims that fit around the calipers, then pick the the deepest profile tyres that comfortably fit under the wheel arches? Personally I prefer deep profile tyres because they seem to be the most forgiving of imperfect camber control and small variations in tyre pressure. It does mean, though, that I seem to have to run very stiff springs to keep control of the car.

[greenamex2]

Light cars such as 'open wheelers', Caterhams etc don't need as much sidewall stiffness as heavy cars such as any saloon and Le Mans prototypes.

They also don't need such big brakes (and big brakes are heavy, as I just found out trying to lift a couple of Porsche GT3RS disks!!!).

All they above and much more (gearing, unsprung weight, cost, rules, suspension geometry priorities etc) combine to dictate what wheel/tyre size is chosen.

There is also the issue, particularly in Saloons, of image. The general public (or certain sections of it) believe that low profile tyres grip better and large diameter wheels look better so the manufacturer supported teams have to have large tyres with rubber band wheels.

If you are designing from scratch then low profile is probably better. If you are modifying a saloon car with a 40 year old suspension design that can't be totally changed then a mid section tyre would probably be more suitable.

Another (un)interesting point - I once spent a couple of days building virtual wheels and tyres and found that for a given outside tyre diameter and tyre width, a low profile tyre on a big rim is ALWAYS heavier than a high profile tyre on a small diameter rim.

[dtype38]

sorry, mispost - cant delete ??

[dtype38]

Hmm interesting about the weight thing.. I always try to fit the lightest option. Definitely some food for thought.

[avsfan733]

the weight thing is mostly a function of air weighing less than aluminum, even pressurized air in tires weighs less than going to a biger wheel and less tire then you have to make the wheel stronger. A lot of this has to do with the type of chassis. In F1, its probably somewhat restricted by rules (im not sure i'll look) but a lot of it comes down to the tires acting as the springs. the more sidewall the more spring. I can tell you for sure that Bridgestone and Michelin are playing with that tire to tire race to race. The function on a road car is that of reducing that sprign when you go to a smaller profile tire. this stiffens up the suspension and the handling as the tire isn't left to wander around. The dragsters you mention actually use this sidewall flex to the extreme. If you watch superslowmoion replays of drag launches, then you can actually see the sidewall winding up and then releasing (cthey run 2-5psi) this creates some forgiveness in the launch and helps to prevent wheelspin in that case

[Tim Falce]

Originally posted by dtype38
Can anyone tell me why open wheel cars, dragsters and Nascars mostly run high profile tyres on quite small diameter rims, whereas closed wheel cars like touring cars and Le-Mans sportscars tend to run rubber bands on enourmous rims? Is it just the tyre rules of each type of racing or is there a technial reason? :confused:

Don't know abut Nascars but dragsters run very large tyres at low pressure on the rears because the tyre diameter gets larger as the rotational speed increases so in effect the gearing alters as the car goes faster, watch a dragster doing a burnout and you can see the tyre size increase.

[topwelshman]

Ok, so are we basically saying that Smaller diameter wheels accelerate faster due to their lower weight but larger diameter wheels give a better footprint and which allows you run lower tyre pressures which in turn gives better grip and puts less stress on the tyres due to lower temperatures? And, in the wet you're better off with a Larger diameter & narrower wheel to cut through the rain?

[dtype38]

My race car weighs about 1000kg and is front engine / rear wheel drive. I use Yokohama A032R 225/60-R15s and a front spring rate of 925lb/in. I've got a head on picture of my car half way round a corner at Donnington and its clear that my loaded front tyre is significantly more "squashed" than the unloaded one. Also, if I "wobble" my car when its standing still, virtually all the movement is in the tyre walls not the suspension. Strange then that it feels completely and solidly planted on the track while I'm actually driving. There is no feeling of "wander" from the steering... and I'm comparing to when I used to drive karts! Thoughts anyone ??

[dtype38]

topwelshman.. I use 225/60 inters on 7J15s in the dry / damp and 205/65 on 6J15s in the wet. They have pretty much the same overall diameter but the latter are indended to ride puddles better - they also have much deeper tread. On past experience, though, I find its only worth going to the narrower tyres if it so wet that there's standing water about that can't be avoided. If there aren't actually any puddles, then the more rubber on the track the better!

[topwelshman]

Ok cheers for that people, good to uderstand these things

[greenamex2]

dtype38 - You are running a spring rate 925lb. Your tyre has probably got a spring rate of the same OR LESS!!!

It's no wonder you are seeing as much compression on the tyre as the suspension!

In reality your spring rate at the wheel is probably lower due to motion ratios but you get the picture.

This is the reason behind the common F1 quote "most of the suspension movement is in the tyre".

[dtype38]

I have been progressively increasing my spring rate in steps of around 100lb/in starting from 425lb/in. Each increase has improved my handling (and lap times).

Incidentally, and this might raise some eyebrows, I had thought I'd reached the limit around 750lb/in due to very bad understeer in slow corners. But I'd been reading the ideas on suspension set-up by an American called Fred Phun, and using his advice I threw away my front anti-roll bar and continued to increase the spring rates. Not completely sure of all the technicalities about why it works, but the car now handles great!!

Having said that, I agree that I'm probably a bit "over-springed" for the weight of the car now and so won't be going any higher.

[greenamex2]

dtype38 - Welcome to the club. I keep trying new adjustable antiroll bars and keep giving up and going back to the standard bar and playing with dampers, springs and camber. I think the problem is road tyres just aren't sticky and stiff enough to work with stiff bars.

[HiRich]

dtype,

Going back a few steps, your theory about choosing the smallest brake discs practical first, then packaging rims and tyres around them is fine - in theory. In practice, many cars are brake limited. A bigger brake might weigh more, and might compromise your tyre choice, but will offer greater deceleration, more consistently, and give better feel. The odds are that you'll need/benefit from a bigger disk than you expect.

As Dennis says, you're spring and tyre rates are probably comparable. It's worth remembering that stiffness of springs in series works on an inverse law:
1/spring stiffness
+
1/tyre sifnness
=
1/total stiffness

If you're two rates are similar, the total, 'real' stiffness could be half what you think it is.What's more, bumping up the spring stiffness in big lumps may only be having a small effect on actual stiffness (which, from the formula, will always be less than the softest spring). Also, whilst your body may feel very stable, the hub could be bouncing around like billyo between the two springs (tyre and coil), with consequent variation in the wheel load.

It's far too long since I did this for a living to make any sort of recommendations, but (presuming that you don't have underbody downforce, which changes the rules entirely), I always liked the idea of running relatively soft springs. Yvan Muller runs his car this way, and his engineer put it succinctly "it takes longer for the grip to arrive, but when it does it stays there"

[greenamex2]

Only things that I would add to HiRich's comments are -

Your brakes only need to be big enough for YOU to lock the wheels. Any bigger and they are costing you time.

I also subscribe to the softer is better school of thought BUT you musn't run out of wheel travel both in terms of bump/droop and valid suspension geometry (principally camber and bump steer) AND you need decent dampers that won't fade with either the large amount of movement or the stiff settings they may end up with to control/balance the car.

By decent dampers I mean REAL gas pressurised dampers not something with a crisp packet in it. Not that I am knocking this design (I use them on my track day kit car) it's just that they MAY cost you time at the end of a race for the sake of a few extra quid. It's a case of if you buy cheap you may end up buying twice.

[avsfan733]

I think the idea behind the brake sizing comments wasn't so much a brake torque reaction thought but one of endurance, the ability to fit heftier rotors. you can then change piston sizers master cylinder sizes or pedal ratios to fit the feel you want to it. I agree with HIrich, you should really be running the softest springs you can get away with. More force can do bad thigns like inhibiting weight transfer and proper tire loading... PLus it destroys any sort of control when things get bumpy (ex: williams at China). The antiroll bar thign goes back and forth I have heard both sides...Your best bet is to leave it in but soft and just stiffen it up as needed. It does help especially with balancing the car. Haven't really tried it around a circuit but my rear bar gets unhooked for autcrossing and I set the front softest (of three) Just MHO

[dtype38]

OK interesting set of reactions to that one.

HiRich: completely understand what you're saying about adding effective spring rates. I know that if I had low profiles (ie. stiffer side walls) I wouldn't be getting away with my high spring rates. I would say that your estimate that I've similar rates in my tyres and springs is sound, and that I've got a real rate from the chassis to the ground in the 400-500lb.in range. That's what I understand is more reasonable for my car and all ties together with the theories I'm working to. I think its also worth condsidering, though, that the tyre isn't a pure spring and has a certain amount of integral damping. This means that the hub isn't moving around "completely" uncontrolled.

Denis: could you expain a bit more about what "the softer the better" means. I've come from karting and find all cars horrendously soft and squishy in the suspension department. On my own car I've been striving towards maximum rigidity and a "flat" ride. As far as I have been able learn, the only limit to how stiff a car can be run is when the surface of the tyres no longer completely follow the surface of the track. To this end, I'm running minimal damping settings so that the springs can move quickly to take up irregularities in the track, but keeping the springs stiff to minimise roll and pitch.

avsfan733: I understand what you say about endurance of the brakes being as important as stopping power. Its a similar function to tyre size and overheating. Fortunately I only run in 15 and 20 min sprint races so can get away with quite small discs with large pistons to give me plenty stopping power (although it gets through pads quite quickly). I'm not convinced about the soft springs and the problems of the Williams in China though. I think that might be more to do with the ripples in the track being a bit too close to the harmonic requency of their damper / tyre setup. That isn't necessarily a problem though, as I remember watching the Merc CLKs (I think) stomping on McLaren F1s and Porsche GTs at the old German GP track (Hockenheim or Nurburgring?? dunno) and doing the same dancing up and down in the braking zones. Didn't slow them down though.

[HiRich]

dtype,
In many ways you are right, and you certainly want the car set up a way you want, which may not be the theoretical ideal - works for Michael Schumacher!

I will pick you up on one point, though, which does get to the heart of the argument. You say:
"As far as I have been able learn, the only limit to how stiff a car can be run is when the surface of the tyres no longer completely follow the surface of the track."
That's not completely true. ANY variation in the wheel load affects the grip the tyre can produce, the slip angle, and the load on the other three corners (it has to go somewhere). Also, if the road surface is imperfect the input is a displacement (think the sawtooth kerbs at Silverstone, a "pothole" dip, or when you hook up the apex on a heavily cambered road).
With stiff springs, a 1" bump on the outside front wheel (say, riding the kerb on the exit) kicks that wheel up. The car balance moves dramatically (and it may happen faster than you can react), the car may twitch. It feels cool, but may not be fastest. You may react at the wheel, you might even lift off (OK, maybe not!)
With soft(er) springs, the input (displacement) is the same, but the load change is smaller and slower. The forces on each wheel have only changed slightly, and the car remains more balanced. You can keep your foot in, make fewer corrections, and keep all four tyres working closer to their optimum. And you've exited Becketts Hairpin 5mph faster, so you'll reach Brooklands two tenths earlier.

Of course, all this depends on a whole load of other things, like how good your camber/articulation is. It takes a lot of learning (both the engineering and the driver feedabck/assessment), and a helpful mate with a stopwatch (or a telemetry system) - apart from the stopwatch, skills I'll never claim to have had.

I am intrigued by your lack of reliance on the dampers. That feels very wrong, and I would suggest a decent test session to 'learn' them. My gut reaction is that you appear to be using stiff springs to provide body control, when the dampers could be doing much of this - giving the 'quickness' and reaction to input that you want whilst allowing more suppleness over the bumps and dips.
A trip to Llandow would be a good idea (nice & quiet, lots of tracktime, good selection of corner. And cheap). Try the car in sequence on:
- Full soft
- Full hard
- Hard front, soft rear
- Soft front, hard rear
Not only should you measure times, but write out fully how the car reacted at each different corner type. Then work your way to a setting that works for you and the clock.

But hey, what do I know!

[greenamex2]

I tend to agree with HiRich, adding the softer springs give the tyres an easier time meaning they run cooler and hence more consistent pressures, larger contact patch and last longer.

There is also the issue that whilst a hard spring will stop the outside of the car dropping it won't do much to stop the inside of the car lifting. Then you start adding stiffer antiroll bars which sends the weight transfer god knows where plus silly static camber that plays havoc with braking!

I prefer controlling a car with dampers, partly because I am fortunate in having quite expensive Koni double adjustable gas mono tube dampers, but mostly because I can adjust the cars 'effective stiffness' without constantly buying new springs (especially as my rears have to be custom made).

In the end if your car beats everything in it's class, who cares. If it doesn't then what are the people beating you doing differently?