Tyre contact patch + friction physics discussions

[Driftin_AW]

alright guys, I know some of you are very intelligent engineers, so this is something that's been puzzling me for a while, please help:

Everyone knows that widers tyres = more grip....or does it?

Frictional force is found by the following formula

F = (mu) * N

where F = friction force
(mu) = coefficient of friction
N = normal reaction force (for our purposes, just assume this = weight force)

so what this means is that friction force is proportional to coefficient of friction between the two surfaces, and also proportional to weight force on the surfaces.

it's also worth pointing out that friction is a reactive force, ie this figure above is the maximum friction force a system can generate in reaction to an opposing force trying to accelerate the object, not a constant force.

Anyway, here's a simple thought experiement:
1. Take a block of steel, with a weight of 100 Newtons (that's about 10kg mass)
2. On the bottom of the steel block, affix a large piece of rubber
3. Place the block on smooth asphalt, rubber side down
4. Attach a rope to the steel block and pull with increasing force until it moves - let's say it takes X amount of force to move it.

Now, take an identical steel block, with rubber on the bottom, place it next to the other, and repeat the experiment. We now have twice the weight, 200N, and as you can obviously imagine, the force required to move them would be 2X

So what this all means, if you look at the formula from above:

F = (mu) * N
with our values from the first experiment, we have
X = (mu) * 100
so (mu) = X/100

from the second experiment we have
2X = (mu) * 200
or (mu) = 2X/100
which is the same as
(mu) = X/100

also from this relationship we can see that if we had 2 steel blocks of only 50N each, the force required to shift them would be half as much as 2X, so again we would have (mu) = X/100

so what this shows is that the coefficient of friction has not changed whatsoever, despite the fact that the contact patch has doubled from the first experiment to the second, and therefore the larger contact patch has not given us any increase in maximum available friction force....

so, does a wider tyre/larger contact patch really give you more available friction force?
(please don't answer this by saying you put bigger tyres on and got more grip, because that's not what I'm trying to establish)

Anyway, one reason I can think of for the apparent increase in traction when you increase tyre width, is that you're also increasing the mass moment of inertia for the wheel/tyre (basically the rotational equivalent of the linear value of mass), which means if you apply the same amount of torque to the wheel, the angular acceleration will be less because:
M = I * (alpha)
where M = moment (torque)
I = mass moment of inertia
(alpha) = angular acceleration

and btw M = I * (alpha) is the rotational equivalent of Newton's 2nd Law, F = m * a (force = mass * accelertion)

[Driftin_AW]

well, I posted this on another forum and got a rather concise response.
this is a scan from racecar engineering magazine

http://www.users.on.net/~fivebob/Images/tyres1.jpg
http://www.users.on.net/~fivebob/Images/tyres2.jpg
http://www.users.on.net/~fivebob/Images/tyres3.jpg
http://www.users.on.net/~fivebob/Images/tyres4.jpg

[Paul Woods]

moving to technical malcolm,this is good stuff!

[boondougal]

Does this help

Rolling Friction


When a cylinder rolls on a surface the force resisting motion is termed rolling friction. Rolling friction is generally considerably less than sliding friction. If W is the weight of the cylinder converted to force, or the force between the cylinder and the flat surface, and R is radius of the cylinder and F is the force required to overcome the rolling friction then.

F = f x W/R
f is the coefficient of rolling friction and has the same unit of length as the radius R -in the example below m (metres)


Typical values for f are listed below

Note: Values for rolling friction from various sources are not consistent and the following values should only be used for approximate calculations.

Steel on Steel f = 0,0005m
Wood on Steel f = 0,0012m
Wood on Wood f = 0,0015m
Iron on iron f = 0,00051m
Iron on granite f = 0,0021m
Iron on Wood f = 0,0056m
Polymer of steel f = 0,002m
Hardrubber on Steel f = 0,0077m
Hardrubber on Concrete f = 0,01 -0,02m
Rubber on Concrete f = 0,015 -0,035m

[adamh]

](*,) i see where your coming from malcolm, i thought of this.. if you increase the width of the tyre, you are indeed spreading the load across a wider surface, and unless you have an increased weight to proportionally increase your ratio.. which ever ratio you have chosen, you wont have any increased 'traction' theoretically. put a row of 5 points across a tyre width.. lets say each point supports a load of 50kg..

double the width, each point now only takes 25kg, no increase in the ratio, half the friction across the doubled whole. 250/5 same as 500/10
all things are equal and a ratio. in theory, should you have the correct gauges its hard to find a difference of that rule :nuts: almost an impossibilty when experimenting with even the best gauging, after scribbling some theory. :-(


i would think why people claim to have better grip from wider tyres.. there is 99.999999999999999999999999999999999999999999% <--:lol: dork,
truth from that, generally, i'd say the car manufacturers dont engineer cars/wheels to stick to the road inside of the tyre width/weight ratio minimum for continued traction throughout the rev range of lets say... first gear,.. had they engineered the weight/tyre spread efficiently (an engineers type view), no car would spin in first gear.. hence every joe go's and buys wider tyres for their under engineered stock wheels. its only stock wheel tyre combo's your up against. including me :D i got 8 inchers for the rear.. ! they will still smoke the same as the 185/60/14's unless i have proportional weight to hold them down.. i dont, i just have more power, but wil have much better cornering ability due to the center of grav and all that balls. ask me what that proportinal weight/traction figure is, id say it aint worth the brain ache, and once you did arrive you'd have a car that weighed in something silly, you will never have a car with the perfect accelration/traction cos there is always a forces acting against it, like mr erm.. newty says. i know you appreciate that, and all that disection and analyzing of tyre theory, its as broad as it is long :lol: i'd agree, wider tyres do not mean improved traction, they only do in peoples minds because they have not increased the Pressure, proportionally also, giving a better footprint, but more importantly, improving the tyre that was never perfect in the first place.. i'd like a perfect tyre please cap'.. "impossible!" and performance sacrificial to traction control, drag, cross dressing, i hate engineering, but it keeps me in work :D... improving and re-engineering stuff is most annoying, cos you know at the end of it, friction will get the better of allthings mechanical. then theres no gravity.. how does friction come into that.. any super duper brains about.. thats something i want to know.. is there any resistance ..air type thing..in space? malc, can you pop your head out the window and let me know? :moon:

[adamh]

i guess im a conceited engineer, just my opinion mate

[Driftin_AW]

adam, what you said is pretty much what I was thinking, but after reading the article I posted I changed my mind entirely :) The way I understand it is that the friction coefficient isn't actually linear, and it reduces as more weight is applied above a certain point, I imagine because the interface between the two surfaces reaches a point where the two can't interfere with each other any more, and therefore can't increase friction (much).

Also you get shearing of the "sticking up bits" of the tyre, on a small scale, and the amount of force parallel to the surface required to shear the bits of rubber will not change at all when more weight (perpendicular to the surface) is applied. However, by increasing the contact patch you will increase the area resisting shear, and as you know:
Force (required to shear) = shear stress of material * area resisting shear (or area of shear plane)

However as discussed in the article, the contact area doesn't actually change with a wider tyre, rather it's shape changes, however that only occurs to a certain point, ummm or something.


Anyway basically the way I see it, what you effectively have is a coefficient of friction which is constant to a contact pressure (force/area), and above that point the cof gradually reduces. Let's say a tyre has a coefficient of friction of 0.5 but above 200psi contact pressure it decreases at a rate of 0.001 per 1psi.
Now let's say our particular car/tyre set up gives us a contact pressure of 250psi. This means the CoF will effectively be 0.5-(0.001 * 50) of 0.45.
If we then increased the tyre width by 20%, we would get a contact pressure of 200psi, which would mean our CoF would now be 0.5. Since the weight force on the tyre hasn't changed, but the CoF has increased by about 10%, we will get a 10% increase in available friction.
Further increasing the width of the tyre, however, would have no effect as we are now in the contact pressure region where the CoF is linear...

understand what I mean? It's obviously a bit of an over-simplification, as the CoF isn't really changing, but the microscopic relationship between the surfaces is, but I think it does ok to explain what actually occurs.


As for friction in space...hmm...there obviously wouldn't be wind resistance, but I guess if you were for instance travelling toward the sun, the solar radiation would actually slow you slightly (kind of like a solar sail).
Friction in space could work if you were in a ship that constantly rotated to provide centripedal acceleration (although you would get heavier as you moved toward the perimeter of the ship, and would be weightless in the middle...fun :) )

[adamh]

yup, i dig that bit about the microscopic stuff.
one to remember is top fuel tyres, they change into torus shape with a big foot print at the bottom, when taking off! achieve super grip, thats with laying their own rubber creating higher co-ef aswell. thats the way to do it. low low pressures! if you get the chance a slow motion start on a quarter run is quite revealing, i'm sure youve seen a good few matey.

alas, too much math is not good for the health! can become a bit stressful when every waking moment is spent calculating, before now ive actiually taken calculators in the bath 8-[ only this last year or so ive learnt to lay off the analysing so much, curiosity always leads to periods punching numbers and getting headaches :D :lol: engineering is an affliction to be taken in moderation :D
i spent 6 weeks calculating and designing my last work project which has taken me 3 months to build manualy, just solid sesh's o the calc and number crunching.. horrible stuff mate, but its alive! and nearly ready for a bit of limelight.

[chris99]

arrghhhhhhhhhh this thread hurts my head!!!!! Top work lads. When you work it out can you post in simple terms for stupid folk like me please :D

[superchargedsam]

christ just been through all this and it so reminds me of uni and why I didnt carry on with it ! malc, adam some truly sterling work there and makes for interesting (if not headache inducing) reading thats for sure ! Is it to cheeky to ask what the conclusion actually is ? I have seen first hand a top fuel cars tyres change shape as I walked behind one as it took off down the then avonpark raceway (now shakespear county raceway) and there was no real security so I just walked from one side to the other so get to my mates, needless to say I was blown back as all 8 straightthough exhuasts blasted nitromethane at me (needless to say I supplied mucho mucho enjoyment to the crowd that day)! But as I was being blown backwards I saw the tyres go from what would have been about 4-5 foot tall to an easy 6-7foot as it spun off the line into the distance with me going backwards at a force equal but not the same and certainly non linear to the car going forward(bolocks to physics it sounded funny in my head) ! This brings me to another point, if every force has an equal and opposite reaction then how many 1000bhp cars would it take to line up side by side to do a burn out that would then cause the earth to stop and maybe even spin the other way (well if every force has an equal and opposite reaction this must be possible) !