Tyre contact patch vs Spring rates 1

[willeng]

If we have a large tyre contact patch due to the use of wide tyres & then we change to a narrower tyre with a smaller contact patch, do we assume that we will have to go to a softer spring rate to achieve around the same level of grip as the wider tyre???
I am aware of the many variables involved with this, but is there a general rule of thumb sort of thing regarding this?

Thanks

 

[GregLocock]

Wow, dissapointing lack of reaction.

I can't give you a rule of thumb other than softer= better and to be honest I'd be a bit surprised if you have not already got your suspension as soft as possible.

However, I'd split it up into three tasks

1) How will the grip change as you change the spring rate?

2) What is the likely change in grip from a change in tire width?

3) How to determine the necessary change in spring rate?

1) is pretty much controlled by the weight transfer. the general rule seems to be the lateral grip at a given slip angle is proportional to the vertical load^0.7

So, if you double the weight on the wheel, the grip goes up by 60% or so. Obviously the other wheel on the axle will drop to zero, so a stiff suspension has only 80% of the grip potential of a completely compliant one.

2) haven't seen much in the publc domain on this. A cynic would say that according to the simple rules of friction the contact patch area and shape is irrelevant, so grip = k*width^0

An optimist, or marketing man, might think that grip =k*width

I'll use the data from (1) and say a fatter tyre is a little bit like having an extra tyre in there, so grip=k*width^0.7, only not as good, so grip=k*width^0.4.

3) Using the above equations and the track, spring rate, motion ratio, geometry, cg height and sta bar rates you should be able to work out the required change in weight transfer. I imagine you'll want less weight transfer with a narrower tire.







Cheers

Greg Locock

 

[willeng]

Thanks Greg, it sure is quite!

 

[mloew]

Quite what?

Best regards,

Matthew Ian Loew
"I don't grow up. In me is the small child of my early days" -- M.C. Escher

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

 

[GregLocock]

Dunno. here's a worked example, for a 10% reduction in tyre width, based on an axle that is currently overpsrung so the inner takes 250 kgf and the outer 750 kgf, at a given condition, and for grins we'll give say it gives 600 kgf of lateral force at a nominal design load of 500 vertically.
Current lateral force from inner wheel= (250/500)^.7*600=369kgf

outer wheel=600*(750/500)^.7=797 kgf

so the overall lateral force is 1166 kgf

Now drop the tyre width by 10%, so the nominal grip at 500 kgf is 600*.9^.4, 575 kgf

Using the same suspension the overall grip from the axle is now 354+764=1118 kgf.

Well, in this case, even with no lateral weight transfer the best that can be done is 1150 kgf, still not as good as the previous tyre.







Cheers

Greg Locock

 

[willeng]

Sorry guy's, a DUMB spelling mistake on my part. I meant, it sure is quiet!!

I bet it got you thinking though!!

Thanks again Greg.

 

[Tmoose]

With this talk of changing "weight transfer" via spring rate, are we assuming a 4 wheel vehicle whose "other" end is providing a constant roll stiffness contribution?
Then, assuming temporarily that all these changes were made at the front end-
- smaller tires = more understeer
- softer springs = less understeer
The handling balance could be adjusted to maintain the original level of understeer, but, as the rear's roll stiffness contribution is now a greater percentage of the whole, the rear tires have less cornering power, and the car will have less overall cornering power.

Am I correct thinking changing front and rear spring rate together would not change "weight transfer" much at all? (discounting the slight change in CG height that reduced roll might produce)

 

[GregLocock]

If you reduce the overall roll rate of each end by the same proportion, then, with GRCs at zero, yes, the weight transfer won't change. That roll stiffness will include contributions from road springs and sta bar. In a typical production car the road springs provide around 50% (not a hard and fast rule, just the last one I remember) of the roll rate.

Cheers

Greg Locock

 

[NormPeterson]

Reducing the roll rates will have a couple of indirect effects regardless of how such a reduction is accomplished.

Lateral weight transfer through the roll centers and from the unsprung masses will become a larger proportion of the total and will likely shift the total lateral load transfer distribution a bit.

More roll can be expected to cost you more camber at one end than at the other, meaning that there will be a change in the relative slip angles and ultimate grips. The narrower tire will likely have a different sensitivity to camber, though that could push things either way in the overall picture.

willeng - As far as the narrower tire with the smaller contact patch - what is known about its vertical spring rate relative to that of the wider tire? Between the sprung mass and the contact patches, this is just one of a collection of "springs in series/parallel"; hence its stiffness will affect the LLTD. For that matter, are the smaller tires envisioned at all four corners or only on one axle?

Greg - Thanks for those rules of thumb. Pure cosmic timeliness.

Norm

 

[NormPeterson]

"Lateral weight transfer through the roll centers and from the unsprung masses will become a larger proportion of the total and will likely shift the total lateral load transfer distribution a bit."

As a bit of clarification - I'm thinking in terms of transient maneuvers here, such as during an autocross slalom. Load transfer through the RC's and from the unsprung masses are fully developed, but that from the sprung mass isn't for a significant portion of the time.

Norm

 

[GregLocock]

Yes, I've just been investigating the forces in the suspension in the first 200 milliseconds of a step steer event.

Very interesting stuff, I even have a grudging respect for geometric roll centres now.

Unfortunately I can't publish the results, but it is safe to say that the plots at the back of Milliken in RCVD Fig 22.38 are along the right lines, so if you superimpose your arm and tie rod loads on that sort of diagram then it makes a great deal of sense, to the extent that they are likely to become a standard method for setting hardpoints for us.

Cheers

Greg Locock

 

[willeng]

Norm:

The tyres will be used on all four corners & at this stage we have no data on the tyres.
I will keep you informed as we get into it a bit deeper!

Thanks

 

[JakubMech]

Guys

Correct me if im way out of the ball park, but from doing a quick analysis (actually already had a spreadsheet) going to thiner tyres will give a softer tyre rate (assuming all other variables remain the same). So then to have the same effective rate we would need to increase tyre pressure - or use a stiffer springs (to go from thin to fat tyres).

Contact patch areas should remain the same, assuming the same tyre pressures, but grip would decrease because of the change in patch shape with the thiner tyres (patch shape being less aligned to the lateral direction).

Therefore for a change to thinner tyres and changing springs to stiffer to have the same roll resistance would lead to a type of double grip decrease (patch shape and spring rate increase or higher tyre pressure leading to increased tyre rate - smaller patch).

Jakub

 

[JakubMech]

typo : please disregard "(to go from thin to fat tyres)" in the first paragraph. Or simply reverse to say fat to thin.

Jakub

 

[GregLocock]

Do narrower tyres of the same sidewall height have a different radial stiffness? Not much, I'd guess.

We aren't trying to get to the same ride rate, I was trying to change the weight transfer to restore grip to the axle.



Cheers

Greg Locock

 

[JakubMech]

I just had a simple model, neglecting sidewall stiffness, basically using tyre pressure and dimensions.

Thats cool, this topic encopasses quite a bit of stuff, just thought that ride rate would partly effect the balance, hence weight transfer.

Jakub

 

[mloew]

Thats cool, this topic encopasses quite a bit of stuff, just thought that ride rate would partly effect the balance, hence weight transfer.

How do rates effect weight transfer? Do you mean load transfer?



Best regards,

Matthew Ian Loew
"I don't grow up. In me is the small child of my early days" -- M.C. Escher

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

 

[JakubMech]

yes, lateral load transfer.