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# I thought I understood Milliken!

## I thought I understood Milliken!

(OP)
Hi!

Could someone here tell me if I have to eat humble pie or not?

I have become embroiled in a fairly heated 'debate' about 'grip and slip'.

My view is simply that a tyre has a certain level of 'grip' by which I mean it has a quota of Adherence and Conformity that ensures you have traction, after a certain load on the tyre it can no longer gain this 'grip' in either the short time it is in contact with the road or the load has meant there is no further conformity available.

So a graph with even rates on each axis [x-y] would show [as most tyres have a 'static friction' of more than 1.4/1] a line at 55degrees [approx] then as we reached the point where the tyre could be said to be slipping at a real discernible rate the graph line would fall away in the manner of a parabola or missile trajectory plot.

The other side to this states catagorically that this does not happen, and that the fall off is immediate from 0 or 1kg

Now this wouldn't be so bad and I would normally dismiss any counter arguement as just the ramblings of a novice... HOWEVER... the guy who is turning upside-down all my old thinking says he sorta knows Doug Milliken, is part of the FIA World Rally set-up, is a test driver and all sorts of things... he's a big cheese!

So simply, do I have to eat humble pie?

Have I completely mis-understood all I was taught?

Am I woefully out of date and all I learnt years ago has been overturned in the last year?

### RE: I thought I understood Milliken!

What are the axes on your graph?

If you are plotting cornering force vs slip angle, all other things being equal, then I suspect you are both right.

The curve is roughly linear up to a certain point, but it almost certainly has some funnies near zero, depending on how it is being tested. However, although the main part of the curve looks like a straight line, it isn't. There is a slight downward curve away from the straight line. (or more technically, the gradient reduces with increasing slip angle).

Linear is a good enough assumption though, for most practical purposes.

Cheers

Greg Locock

### RE: I thought I understood Milliken!

btw Doug hangs out on the Usenet newsgroup sci.engr.mech

Cheers

Greg Locock

### RE: I thought I understood Milliken!

(OP)
My apologies, I appear to have put this in suspension not tyres!!!

### RE: I thought I understood Milliken!

(OP)
Cheers Greg.

The graph is a traction graph as you say, I did say the same thing as yourself in that at the start and even along that line there will be some vagueness simply due to inherent testing tolerances, interstices etc, but he still maintains that the tyre is always losing grip as soon as any weight is applied and it is never a straight line but a constant falling away from around zero, the old graphs I remember show a notional line travelling straight for a time then at the threshold of slip the line falling away!

### RE: I thought I understood Milliken!

(OP)
Except to say that this is not a cornering situation.

Straight line stuff, we both agree that the across axle weight shift will lessen overall traction and that this loss will occur.

The point came about due to me saying that there was a way to work out an ideal width of tyre for the weight of the car and that tyres need to be matched, there is a point along the sliding scale of tyre sizes were the weight of the car most closely matches that of the tyre, this it seems is not so!

I am perplexed slightly.

### RE: I thought I understood Milliken!

I was just thinking about this. In the real world this is (painfully) obvious - imagine driving a constant radius test, and accelerating.

As the car goes faster, even in the 'linear' range you have to apply more lock than you'd expect. This is partly because of compliance steer effects, partly weight transfer, partly just vehicle understeer, and partly that the tyre is non linear from the get-go.

This is most clear on lightly laden tyres, which often have no discernible linear section before they curve over toward stheir max grip point.

Cheers

Greg Locock

### RE: I thought I understood Milliken!

(OP)
I equated it to simple ground pressure, I said if the ideal ground pressure for a given tyre is 'x' then upto that point the tyre will behave in a linear fashion upto a point then after that any weight added will not give an equal return in traction.

If the tyre is is loaded with 0.5 'x' then as it is not 'idealised' it will not have more traction for the same weight but less, as said 'that is just a simple ground pressure thing', this is I think what you are saying?

### RE: I thought I understood Milliken!

Now I'm confused, I was 'plotting' lateral force vs slip angle.

You now seem to be talking about (maximum?) traction for a given vertical load.

In that case you will (almost) always get a higher coefficient of friction as you reduce the load. That is, the actual maximum tractive force will drop as you reduce the load, but not as fast as the load is dropping.

One reason for this is that at zero load there is still some grip, due to cogging.

As to sizing tyres for maximum grip, sadly the graphs that would allow you to make a rational choice are not easily available. But so far as I know, a wide tyre will usually develop more grip than a 'similar' but narrower tyre, when correctly set up, in the dry, at the same temp.

Cheers

Greg Locock

### RE: I thought I understood Milliken!

(OP)
Hmmmm...

I asked if he meant cogging difference at the start of the slope and that was not it.

I remember back in the late 70's some tests done [admittedly Static friction] on Austin Mini wheels [10in. diameter] and tyres where a reading was taken for traction vs load using a simple 'pull test'

20lb needed 26lb of force to make it break traction
this carried on until [IIRC] 170lb at that point this 'constant' 1.3:1 was demonstrably starting to decrease.

This was explained as the limit of Adherence and Conformity had been reached, it was not exactly linear but was for all intents and purposes assumed to be so.

Somewhere on the 'net [apparently] there is a set of  these figures for modern tyres.

### RE: I thought I understood Milliken!

I wouldn't use a static friction test.

Cheers

Greg Locock

### RE: I thought I understood Milliken!

Vbird,

Greg already eluded to this, but I think your friend's point could be illustrated by plotting a graph of         Fymax(Fz)/Fz vs. Fz (where Fymax(Fz) means the maximum lateral force that can be obtained from the tire @ the vertical load Fz @ whatever slip angle it occurs).  This plot is something like the "effective" coefficient of friction of the tire as a function of vertical load.  In this sense, grip (effective coefficient of friction) does decrease as load is applied b/c the frictional properties of rubber are pressure dependant (higher pressure gives lower friction -- it's TRUE! ...don't listen to your physics teacher b/c he/she is always talking about rigid body behavior when he/she says that friction is independant of load and/or contact area).  If the contact patch area increased in exact proportion to the load (it does not b/c of the tires structural stiffness and a whole bunch of other minute construction details) and if the sliding velocities of every point in the contact patch were always exactly opposing the macroscopic direction of travel, then what our physics teachers told us would be approximately correct.  The fact that the slip velocities within the contact patch can vary a tremendous amount is as important a reason as any as to why the tire cannot reach the theoretical limit of grip based on the rubber coefficient of friction (which can certainly be greater than 1 and even over 2).
I agree that both you and your friend are correct, but he is talking about effective coefficient of friction and you are probably thinking about the maximum grip that can be attained at a specified load with varying slip angle.

Hope this helps,
bhart

### RE: I thought I understood Milliken!

(OP)
Thank-you bhart,

I think that that is indeed how we view it!

I see it from the Design point of view that I must spec. the right size of tyre to 'put off' the time when the bifurcation of traction vs load line becomes a serious concern.

Yes a lot of the old thinking is constantly being raked over, the pressure thing accounts for some of the additional grip of larger tyres.

I think he sees it as a driver and the car is already correctly 'loaded' and then doubling the weight imposed really will see a loss of 'grip'.

Thank-you.

### RE: I thought I understood Milliken!

Another interesting slant on the question of tires and traction is put forth by the late Chuck Hallum in a couple of SAE papers and an article in the July, 2003 issue of Racecar Engineering.  He spends time on the  single particle behavior in the CP, and the short term changes in avilable traction as the surface tempeature of the tread changes.  It alters some of the conclusions based on the classic steady state tire behavior.  Especially as it relates to available lateral force on initial turn in and how it is affected by vertical loading.  The 2 SAE papers are:

#2002 -01 -3302  Dynamic Traction Characteristics of Tires
#2000-01-3571  How to Work Race Tires on Nascar Ovals

They are well worth the read and there are enough graphs and formulas to satisfy anyone I would think.  They are available from SAE at $9.60 ea. for members, non-members should not be more than$1.00 to \$2.00 higher.  They are aimed primarily at a racing environment, but should relate well to road vehicles.

Dave

### RE: I thought I understood Milliken!

Enough, already! Why don't you just buy Doug and Bill (Doug's father) Millikens' book, "Race Car Vehicle Dynamics," and you'll have all the tire data, both cornering and traction, to answer any questions you might have? It's available through Amazon.com and the SAE. I believe the Amazon price is a bit lower, however.

### RE: I thought I understood Milliken!

When did Chuck Hallum pass on. I was in a seminar with him 10 months ago and was corrosponding with him via e-mail earlier this year. He seemed OK. Does anyone have any info???

### RE: I thought I understood Milliken!

Chuck Hallum was killed in an automobile accident a few months back.  He was driving his "Viper", that is the only information that I have.

Dave

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