The science behind wheel sizes

[dtype38]

Dennis... aha, you're running standard road tyres I gave that up long ago as a non-starter in the competitiveness stakes. First time I ran a set of road tyres I overheated the tread blocks so badly that the tread patteren actually melted and closed up most of the grooves I tried a harder compound, but that just made the car slide sideways in fast corners... no grip

Anyway, I'm surprised the increase in rear spring rate should make such a difference to your tyre wear. Afraid that goes past my level of understanding of the situation. I now run Yoko A032Rs which are road legal (only Caterham owners seem to actually use them on the road) but are much much softer compound than most normal ruad tyres. They have quite soft side walls and are very compliant to the road. I haven't seen any graining on them regardless of suspension setup. The 32Rs still have tread blocks so can suffer overheating in hot weather, so I'm thinking of going to the new A048Rs when these wear out. I'm told they have different side wall stiffness so might affect my handling, but I'll deal with that when I get them.

How much toe-in / toe-out do you use front/rear?

[greenamex2]

None.

[Goran Malmberg]

Originally posted by Denis Bassom
Graham, sort of going to contradict you but not, if you get what I mean.


Area=Force/Pressure

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

wider tyres give a bigger footprint, they don't.

[/B][/QUOTE]

Well, this issue has been discussed before, and it sounds logical that the footprint should bee as described. However, wider tires does gives a larger footprint. Check out my site, http://hem.passagen.se/hemipanter/
where I have som charts and prints of two size Avon racing tyres of the same diameter. I run across this issue at first when reading the book of Paul Haney, which is a very good book about the racing tires. I find this sort of problems interesting, and interesting problems makes me set up a real life experiment to see what it says. In my site there is just a few pictures of what I found out, but newer the less it shows what happens.
Regards
Goran Malmberg

[greenamex2]

Goran - Interesting site. I have come across it beforebut never got as far as the tyre footprint diagrams.

A quick couple of questions about them -

For a 30% increase in width you only got a 10% increase in contact patch. Any ideas why?

There are a number of splodges of paint outside of the measured area, particularly on the narrower tyre. Why weren't these included?

Did the measurement allow for the tread pattern?

Were the tyres of equal sidewall stiffness, both due to the construction of the tyre and as a result of the relative width of the wheel rim they were mounted on?

[Goran Malmberg]

Originally posted by Denis Bassom
Goran - Interesting site. I have come across it beforebut never got as far as the tyre footprint diagrams.

A quick couple of questions about them -
1.
For a 30% increase in width you only got a 10% increase in contact patch. Any ideas why?
2.
There are a number of splodges of paint outside of the measured area, particularly on the narrower tyre. Why weren't these included?
3.
Did the measurement allow for the tread pattern?
4.
Were the tyres of equal sidewall stiffness, both due to the construction of the tyre and as a result of the relative width of the wheel rim they were mounted on?

1.
I am told that sidewall stiffness is varying in proportion to total tire size. In this case we got the same type tire, the same diameter. The only difference is width. Cant tell the influence of this. It might also have to do with that it is harder to deform the tire in to a longer footprint with a narrower tire as the sidewall must deflect more then. Much guesswork here.

We may also use less inflation with wider tires resulting in even more footprint.

2.
Some of the paint actually dropped off the tires or there was more paint pressed out the sides. I simply draw a line around the clearly marked print area when WET. Paint was water with candy colour. It is also so that we don’t know the exact pressure distribution on the patch. It was much easier to see the difference (footprint shape)on the footprint when colour was still wet.

3.
The area is strictly over the whole marked area including pattern.

4.
Rim is about the same as tread width, and as recommended “ideal” by Avon.

Goran Malmberg

[ianselva]

I have only one arguement with all these posts .You all talk about spring rates , but surely the effective spring rate is what counts . ie the spring, as seen by the wheel including the suspension leverage.

[greenamex2]

ianselva - We did cover motion/leverage ratios at some point in the past and you are right, it is more important than actual spring rate.

We even covered the spring/damper 'angle' in relation to the lower arm which can also have quite a drastic effect on it's effective spring rate.

Just to give you an idea, my kit car has a spring rate of around 275lb but because of the ridiculous angle the damper sits at I have to pretend that it is closer to 225 lb. And by the time you factor in motion ratio I end up with a wheel rate of about 150lb!!!

Worse still, the effective rate REDUCES massively as the suspension compresses, by upto another 10%

Straightening the front coilover is up there on my priority list, right after fixing a leaky petrol tank, being able to see out of my side window and filling all the gaping great holes in my body work!

[Goran Malmberg]

Originally posted by ianselva
I have only one arguement with all these posts .You all talk about spring rates , but surely the effective spring rate is what counts . ie the spring, as seen by the wheel including the suspension leverage.

Absolutley right so! The important thing is "wheelrate".
But we can stretch it futher. If we know the wheelrate, the car may be of different weight. Then the important thing will be "spring Hz" rating. My own car is sprung to 3Hz, which is quite stiff to be a road car. By comparing the Hz number we can compare cars of different weight and wheelrate.

If someone you dont mind, here is some formulas to calculate spring rates. First we must find the motion-ratio (Mr). Mr=D1/D2. D2 is the lenght of the under A-arm.
D1, is the distance from the inner pivot centre of the A-arm to the centre line of the coilover an a 90 degree angle.

To calculate wheelrate (Kw), Kw=(Mr^2)*Ks. Where Ks is spring constant.

Now, what we should take notice of is that Motionratio is powered to Mr*Mr. This means that if D1 is half the distance of the A-arm we got this figures. D2 is 12" and D1 is 6". 6/12=0,5.
Mr=0,5. Then 0,5*0,5=0,25. If springrate are 400p/inch, then Kw=0,25*400=100. In other word Wheelrate is only 100p/inch!

This might surprice some of the readers, but that is the way it is.

(Hope I get everything straight in mat and English now)

Regards
Goran Malmberg

[dtype38]

Hmmmm... somewhat lost me on that one Goran. Maybe we aren't using the same terms as you, but I think your definition of "Motion Ratio" and "Wheel Rate" look more like dynamic load formulae relating the the first moment and second moment of inertia of the wheel relative to the inner pivot - rather than simple static deflection values.

If I follow what I think you mean, then you're quite right that so far we've only been talking about simple lever arm calculations when it comes to spring rate. (You possibly also missed that we discussed tyre side wall stiffness due to different constructions and tyre aspect ratios, which also affects effective spring rates). Regarding the dynamic situation, once the wheel is in motion vertically, it gains a momentum of its own and, if memory serves correct, that varies as the square of the lever arm. That's why its very important to keep unsprung weight (wheel, tyre, brake etc) to as low as possible. It could be that at very high speed, there are even a few gyroscopic effects that come into effect, but I haven't seen any figures to know if that's significant on ordinary track cars.

I suppose what I'm saying is that our discussions so far are mostly about the principles involved and not the detailed maths. On that basis I think most of the issues and points raised are valid, but only a guide rather than a rigerous analysis of the subject.

[dtype38]

Goran... oh, I forgot to say that I'm also interested in your calcuation of "spring Hz", by which I think you mean the "natural freqency" of the spring. Do you measure/calculate that and vary it for the weight of the car, or do you use it calcuate the damping you need. If the latter, do you aim for "critical damping", or allow for a bit of bounce?

[foolio]

Originally posted by Goran Malmberg
wider tyres give a bigger footprint, they don't.



Well, this issue has been discussed before, and it sounds logical that the footprint should bee as described. However, wider tires does gives a larger footprint. [/B]

I would like to agree with Goran. You can't simply use the air pressure to determine contact patch, since much of what holds the tire off the ground is the sidewall stiffness. Just look at those run-flat tires in the corvettes.

- Eli

[Goran Malmberg]

Its a little late here and I have to get my kids to sleep, but here is a fast answer anyway. I give you the Hz formula tomorrow.

Mr is what is regulary meant as USA term. Wheel rate is how many pounds it takes to move the wheel one inch. If the lever arm is 0,5:1 it follows that a static spring force of say 400 pounds become 200 at the wheel. But the RATE PER INCH becoms as shown by the formula. It is a change of leverage AND the distance of movement at the spring. Its a little tricky, but think of it overnight at you catch it.


Ok, back to critical dampening. I newer calculate critical dampening. We hawe two main damper speed to use. Called Hig and low speeds. The dampening curve is raising with speed. (I am talking the speed of the shock movement).
As my dampers ar separatley adjustable in high and low speed and also in compression and rebound, where the rebound has less resistance than compression, the dampening resistance will maybe happen to become "critical" only for a short moment. So, I use the low speed dampening to set cornering caracter and high speed to follow road irregularities. No matter where the critical effect may land.

Sleep well
Goran Malmberg

[dtype38]

Well run me over with a Corvette if you aren't spot on. Of course the bl**dy tyre moves twice as far as the spring as well as having twice the lever arm = 4x lb/in!! But....... errr, not actually quite sure what that means. See, we've so far only been talking about individual cars and the relative front and rear stiffness. I guess it may mean that the relative stiffness balance front/rear actually varies as the square of the lever arm ratio rather than directly. I'd have to do some calcuations to see if that meant the comparison Denis did with my car would actually show the difference was more or less than he thought. But as you say.. its late and my brain is now somewhat slowed by quite a lot of....


Oh, and if you're still following this one Dennis, NO toe Is that normal for your car? Have you tried playing with it? I found that a bit of front toe out makes a massive difference to the turn in, and the amount of toe in at the back definitely affects traction out of corners (although I have a "powerlock" diff so that isn't necessarily representative!)

Oh and for anyone who didn't see it elsewhere, I loved the quote from the American Commentator who said "And for those viewers who are more used to the sophisticated European terms - understeer and oversteer, then what we mean by Push is when you can see the accident coming, and Loose is when you can't!"

[greenamex2]

No I haven't tried playing with toe yet. I always viewed this as fine tuning and my car is not at the fine tuning stage yet.

Besides, can't change the rear anyway because it's a solid axle. Although, spookily enough, I do seem to have ended up with a solid axle with a reasonable amount of negative camber. I didn't bend it but I did a large supply to select from ;-)

[Goran Malmberg]

I made the formula in a Word document but pasting this in her failed as the parantese did not show. Hopefully this will be possible to understand.

This is what the Hz formula looks like. The starting point is to select a Hz number. 2Hz may be suitable for a street sportscar visiting tracks once in a while. 3Hz is better for a 3-4 inch of ground setting and more track oriented cars. Wsf is sprung weight over the wheel in question.

Desired
Wheel konstant Kw=((((Wsf/9786)rot)*Hz-nr/0,159)^2


I made an example.

Front wheel left.
242kg / 9786 =0,0247rot * 2 = 0,3145 / 0,159= 1,978 ^2 = 3,91kg/mm Kw-f
Ws Hz
Rear wheel left.
363 / 9786 = 0,0371rot * 1,8= 0,3470 / 0,159 = 2,180 ^2 = 4,75kg/mm Kw-r.

Then all 4 wheel together gives a total wheel constant of… Kw tot = 17,36kg/mm.

If the car has no rollbars, this is the roll-resistance that keeps the car from rolling in corners, and also vertical spring stiffness. As seen even as the car has stiffer rear springs due to the greater rear weight the rear Hz number is lower and showing that the car is SOFTER in the rear. Softer in the rear is not common streetcar theory, but often used on race cars. In my own case for preventing the car from splitter to ground connection while braking.
Goran Malmberg

[Goran Malmberg]

See, a happy face showed up in the middle of the formula without me kowing. I newer klick on anyone. The word "desired was also supposed to be located over Hz in the formula as it meant "deired Hz number".

Sorry for this.

Goran Malmberg

[dtype38]

Goran.. I think we're on a losing battle trying to deal with proper maths in this forum. It's difficult to get the formulae to look right and it could be that the happy face was the web page interpreting something like : - ) together as a face. I get your general drift though. Do you know any good books that deal with this in a fairly basic way?

RE: the front/rear stiffness and frequency - I have a front engined car with a relatively narrow track so the situation is a bit different to your Pantera.

Just out of interest, why the figure of 3Hz? Is this something you've worked out from experience or is there a theoretical basis?

Denis, does that mean if you rotate the axle half shaft tubes you could get toe-in but no camber

[Goran Malmberg]

Just out of interest, why the figure of 3Hz? Is this something you've worked out from experience or is there a theoretical basis?

This is a little like walking in circles. In order to maitain proper weight distribution the CGH has to be low.
Low ride height makes it nessesary to use stiffer springs not to hit ground. Depending on track surface harder springs may destroy grip if bumpy. As I use quite high a tire profile i can run a little more spring, so the Hz number desired is really an experiment factor to select.
And I change springs when nessesary.

But we can use those mentioned numbers as a starting point.

If lower profile radial is used, camber change during wheel travel gets more of a concerne. Which also calls for less roll to be keept under controll. Now, moost tracks is not that bumpy so stiffer springs becomes to much of a problem.

Goran Malmberg

[greenamex2]

dtype38 - The trouble with that idea is I would then have to rotate the rest of the car to get the suspension pickups back in the right place!!!!

At the moment due to unequal length unparallel rear links my whole axle 'bumpsteers' when the car rolls anyway so it probably won't help much anyway.

If I ever change to a series that allows suspension pickup points to be moved/located inside the car then the trusty angle grinder and welder will be be into use.

I'll chop the car up and turn into something useful, like a coffee table!

[Goran Malmberg]

Originally posted by dtype38
Goran..
Do you know any good books that deal with this in a fairly basic way?

I have been reading a lot books, and i dont think there is any "racing people language" books that explain things in a proper way. In fact i dont think it is to properley described in many books at all. Magazine explain things in a way that makes readers buy the next issue and the next again. Books seem to miss the relation to practical use, even if VERY correct description is used. You sort of must be "educated" to be educated.
Taking the risk of beeing refused by the moderator I can say that I have been written a book myself. The only problem is that it is releast only in Swedish. So this is in fact no comercial anyway. What I am trying to say is that I am very much awheare of the of the problems with this sort of books, and by listening to the respons from customers.
Hopefully one day I will get in contact with a person that is able to help with translation, without me getting bankrupt.

Goran Malmberg

[greenamex2]

Totally sympathise with Goran. Most British car mags seem to have more breasts than cars in them now, or concentrate solely on the non-technical aspects of F1/Touring cars/WRC. The notable exception being Tracks & Race Cars which, with the exception of about a 1/3 of the waffle Dave Walker can come out with, is really good.

A lot of American books concentrate on how wonderful the author is, name dropping to prove it and contain remarkably little substance. If you took out the filling you could reduce them to a thrid of the size. That is not to say aren't worth reading, you just need to know what to skip.

Most British books are iutdated. Anything written by Alan Staniforth or Simon McBeath should be immediately purchased and read cover to cover, several times.

From the contents of your website and forum responses I'd say go for it, there is a lot more thought in it than some of the rubbish I have paid good money for. I am sure if your were to make a good stab at translating it yourself you would be able to find a native English (or American) to then tidy it up. If it isn't too thick I'd volunteer.

[dtype38]

Goran, Dennis. Thanks for all that. I'll see if I can hunt anything out by Messrs Staniforth & McBeath. In the mean time, good luck with the book Goran and look forward to it in English. Maybe we should put this one to bed for the moment to be revisited after a bit of experimentation.
Ken

[R59]

This has been a very interesting, technical, thread.
I need to print it off and read it steadily.

One thing that has been lost is that the dampers must match the springs in terms of damping rate vs spring rate. Look at the kids on the street with their lowered cars with silly stiff springs (because the car is now lower, and the spring rate is thus higher) on standard dampers. They bounce like the dampers are not there!

Like Denis, I spent a lot of time working out spring rates for my Nova. ended up with 325lb on the rear, and 375lb on the front. Before hand, I could get a season out of the rear tyres with little or no wear, which meant that they weren't doing much. After Empress Race Developments worked their magic, I shaved 2 seconds a lap off of my times! Rear tyres now last three to four races.

Just like Denis, I ran on Toyo rubber - as I was in the BRSCC Super Road Saloon Championship, which was amalgamated with the BARC Modified Production Saloon Championship, both running on Toyo road tyres.

Back to the springs. With the rate known, I took the dampers back to Koni who re-valved them to match the springs, and the change was very noticeable.

Overall, I'm very happy with the handling of the Nova (well it was good until the shell got bent at Thruxton last year!)
It's very forgiving, changes direction very well, and works well over kerbs (except for the "wall" on the inside of the second part of "Mountain Bottom" at Cadwell, which used to be a joy when you could get all four wheels inside the line!!)

As far as road-going type cars are concerned, it's probably the best fun I've ever had in a race car.

Goran, that Pantera is MAD! I drove a 1974 version, and at anything over 100, it felt like all of the panels were going to fall off, and over 140, it felt like it wanted to get airborne! Though they did a fiarly good job at sorting out their aero problems as the production went on...

Rob.

[Goran Malmberg]

Originally posted by racing59
This has been a very interesting, technical, thread.
I need to print it off and read it steadily.
1
One thing that has been lost is that the dampers must match the springs in terms of damping rate vs spring rate.
2
Goran, that Pantera is MAD! I drove a 1974 version, and at anything over 100, it felt like all of the panels were going to fall off, and over 140, it felt like it wanted to get airborne! Though they did a fiarly good job at sorting out their aero problems as the production went on...

Rob.

Rob,
1
I left the dasmpers out of discussion in order to stay on the springproblem issue.
Damper is among the most vital to get the car to run
properley. And if we got the money, spend it on the best damers there is. Also, where you can get good service from the shop, becouse the damper needs to change settings now and then. I prefere dampers that has separate low and high speed adjustments so cthat cornering settings can be done fairley separate from high speed dampening. By speed I mean the speed of shock movement.

Futher discussion on shock absorbers may be "off topic" in this tread.
2
My Pantera is not very great as a race car since it will not fit in to any rules with success. I use it for fun driving and to test specific behaviour. Like aero devices, braking power etc. Like on a rough pavement track I may test some light unsprung weight to get a fast single lap.
But then the brakes cant take to many lap. Just to see the difference.
The Pantera is quite slick with a Cv 0,30. My friend managed 220 mph at Bonnewille last year without ballast.
But many times those cars acts as your experience. But the basic geometry is almost the same as most other cars of the kind. To me it just happened to be a Pantera 30 years ago...

Regards
Goran Malmberg

[greenamex2]

dtype38 et all

Experimeted with stiffening and softening my front anti roll bar on the kit car at Brands yesterday.

Yep the car car rolled less and felt more sporty.

Yep it understeered more.

I have come to the conclusion they are great for fixing problems but not much else.

When I get an engine that doesn't dump 1/4 of a litre a lap into the catch tank the research will continue. Getting back on thread (a bit) I will be concentrating on getting the front and rear tyre tenperatures the same.

Oh, and stopping the car bottoming out.