# Will a car on ice have its maximum speed reduced?

1. Oct 17, 2009

### Omnirizon

suppose we have a car on ice stuck in first gear.

intuitively, I thought it should still be able attain maximum speed (in first gear) in a straight line, but it would take longer because it couldn't apply as much force before the force it applies is greater than the static friction between the car's tire and the icy surface.

however, after trying some calcs (I may be doing them wrong): it seems that the icy surface would limit the car's speed because rolling resistance will soon bring the small amount of force the car can apply to accelerate to a net total of zero.

that is, when the car attempts to apply force to accelerate, the current rolling resistance at a given velocity will reduce that force to zero. because force is limited by low static friction (the ice) it is unable to obtain the same velocity it could on something with greater static friction (like pavement).

is this correct? if not what am I doing wrong?

this is all assuming the car is stuck in first gear (I can't quite wrap my head around how higher gears would work, but it seems that they essentially 'store' inertia in another form different from the inertia in the car's tires).

2. Oct 17, 2009

### Bob S

The major force that limits a car's velocity is the air-drag force, and maintaining a specific velocity requires a balancing torque (force) at the drive wheels. The maximum torque at the drive wheels is limited by the coefficient of static friction (as you pointed out) of the wheels on the ice. (If the car had all-wheel drive, would the tire rolling resistance limit the maximum velocity?)
Bob S

3. Oct 17, 2009

### Danger

This might be useful.
http://www.casc.on.ca/iceRacing.php" [Broken]
You can Google 'ice racing' for a lot more hits.

Last edited by a moderator: May 4, 2017
4. Oct 17, 2009

### mender

Considering that with reasonable tires, the C of F on ice is about .3 and the acceleration rate of the average family car in top gear is rarely above that, the top speed of a car is going to be quite close to what it can attain on pavement. Not recommended as the stopping distance will be considerable. As a former ice-racer I can attest to that.

The salt flats can sometimes offer less traction than ice yet the cars running there certainly manage some pretty stout speeds.

5. Oct 18, 2009

### Omnirizon

Ok. Thanks for all your responses, they have been helpful, but are not quite getting at what I was asking.

I'm not interested in ice racing, nor the real coefficient of friction on ice. I also know that rolling resistance is very small for a car compared to air drag. I'm attempting to get at a conceptual point; namely that low C of F can actually limit the top speed of a car (which doesn't seem very intuitive to me, at first).

so lets suppose the car is stuck in first gear on something really slippery, even more slippery than ice. Also, the car is in a vacuum. This surface has a C of F of 0.0001.

is it the case that because the C of F limits the amount of force the car's wheels can apply to the surface, the rolling resistance (which will much sooner become equal to the force the car's wheels can apply) will act to limit the car's speed to a much lower speed than if the car was on dry pavement?

Please try to keep your responses in a simple conceptual space. Ice racing and salt flats have little to do with this question because those situations involve an array of other factors that render the conceptual point here much less important (namely, that they have gears to carry inertia and lessen the amount of torque actually applied at the wheels, and foils to press the car into the ground).

6. Oct 18, 2009

### mender

And what are you using for Crr (coefficient of rolling resistance) since you are using such a small number for Csf (coefficient of static friction)?

The essence is that if the static friction is higher for the drive wheels than the rolling resistance of the non-driven wheels, in the absence of any other forces (drag from air for instance) the vehicle will be able to continually accelerate until something limits that process, such as the max rpm of the engine or a cliff.

Different gears change the amount of torque available to accelerate the vehicle by trading torque for speed. You've probably noticed that your car goes faster but accelerates at a lower rate in higher gears. You can't have both at the same time!

Last edited: Oct 18, 2009