rolling circumference of tyres
rolling circumference of tyres
(OP)
Here is a paradox that automotive engineers can solve for me.
Because a tyre is slightly flattened at the point of contact with the road, the height of the axle above the road is less than the radius of the tyre.
The driving torque of the axle produces a forward force at the point of contact of T/r, where r is the height of the axle above the road. OK.
But when the wheel turns a full 360 degrees, the distance the vehicle moves is 2piR where R is the unloaded radius of the tyre. While the wheel is rotating, the effective force would appear to be T/R.
Is the driving force greater when the vehicle is stationary than when moving?
If not, what happens to the extra rubber in the circumference?
I realise this is trivial, but I have worried about this now for some years, (not very hard though)
Jeff
Because a tyre is slightly flattened at the point of contact with the road, the height of the axle above the road is less than the radius of the tyre.
The driving torque of the axle produces a forward force at the point of contact of T/r, where r is the height of the axle above the road. OK.
But when the wheel turns a full 360 degrees, the distance the vehicle moves is 2piR where R is the unloaded radius of the tyre. While the wheel is rotating, the effective force would appear to be T/R.
Is the driving force greater when the vehicle is stationary than when moving?
If not, what happens to the extra rubber in the circumference?
I realise this is trivial, but I have worried about this now for some years, (not very hard though)
Jeff
RE: rolling circumference of tyres
No it isn't.
1) In order for the tyre to create grip it has to move relative to the road surface.
2) The tractive force is t/r2 where r2 is the laden radius, not the unladen.
Cheers
Greg Locock
RE: rolling circumference of tyres
Then does the vehicle move 2piR or 2pir2?
Does the tyre have to move relative to the road surface to create grip? Railway wheels don't. (The rail and wheel have the same elasticity and presumably do not move relative to each other at the contact patch)
I can see that the tyre and the road must move relative to each other to solve the paradox, or perhaps the tyre structure (including the tread)deforms while the contact patch retains its momentary shape.
Jeff Stanton
RE: rolling circumference of tyres
Eventually the discussion gets around to providing some experimental data, with the actual distance traveled measured for a bias tire given at 96% of what the free radius predicts but the loaded radius being only 94% of the free radius (yes, this dates my reference material somewhat). For radials, it gives 98% distance traveled with the loaded radius being only 92% of loaded radius. Data for more recent tires may differ in the specific percentages, but I'd certainly expect the general relation to hold.
Norm
RE: rolling circumference of tyres
jeff
RE: rolling circumference of tyres
RE: rolling circumference of tyres
"Does the tyre have to move relative to the road surface to create grip? Railway wheels don't. (The rail and wheel have the same elasticity and presumably do not move relative to each other at the contact patch)".
Actually, a railway wheel does a very similar thing, although the effect is very small. The rail and wheel do not have the same "elasticity" since they are different shapes, although of course the E values are effectively the same. Relative sliding within the contact patch is one of the sources of rolling resistance, which you can read about in texts on ball bearing analysis for example.
RE: rolling circumference of tyres
Jeff
RE: rolling circumference of tyres
1) chemical grip - bonding between the rubber and the road - doesn't need slip
2) cogging grip - intermeshing of asperities on the surface of the tyre and road - doesn't need slip
3) hysteresis grip - deformation of the rubber as it drags over the surface needs energy, so it need sa force and a velocity. Needs slip
I don't know the relative proportions of those in a given situation, but it is worth pointing out that standard tyre results are presented with slip on the x axis - implying that slip is a very important factor.
Cheers
Greg Locock
RE: rolling circumference of tyres
RE: rolling circumference of tyres
RE: rolling circumference of tyres
Jeff
RE: rolling circumference of tyres
RE: rolling circumference of tyres
RE: rolling circumference of tyres