# At what steepness does a vehicle start rolling?

At what exact gradient does a typical vehicle in the following classes start to roll away when the brakes are released and the transmission is in neutral? I'm trying to design a super-safe parking lot/garage in which vehicles won't start rolling even with all brakes released and the transmission not in park. The following classes are:

D-segment midsize car

3-row SUV/minivan/half-ton truck

Class 6-7 construction truck/school/transit bus

Class 8 semi-truck trailer

• Just design it level. Commented Feb 4, 2022 at 13:49
• and place a low curb at each end of a parking space Commented Feb 4, 2022 at 16:15
• If you want it to be "super-safe" then you should not be asking for typical values. You should be asking for the minimum value. To answer this question someone will need data on all vehicles, past and present. The only reasonable choice is to make the parking spaces level. Commented Feb 4, 2022 at 16:50
• @SolarMike If level isn't an option, you can always paint the parking spaces to be perpendicular to the slope - you only really need to worry about the effective slope along the axis of the car, rather than the actual slope of the ground. A wheel will spontaneously roll down a hill, but not across it (although you'll still have some small effective slope since people won't park perfectly perpendicular). Commented Feb 4, 2022 at 17:13
• @NuclearHoagie or you could design it so cars are parked on metal plates, secured then stacked vertically - wasn't it GM that shipped cars like that? Also shown in the film I Robot? Commented Feb 4, 2022 at 17:15

A car on a slope has to overcome rolling friction before it starts to move.

Rolling friction is usually much less than static or even kinetic friction and depends on many factors, road material, road surface texture, tire pressure, texture, tire radius. The interesting thing is rolling resistance increases with the speed of the car.

Usually, for a midsize car on concrete or asphalt road, C is 0.01 to 0.015. The driving force is $$mg* sin\alpha$$

$$mg*sin\alpha \geq mg*cos\alpha* C \rightarrow tan \alpha \geq C$$

• m = mas of the car

• g= gravity acceleration

• $$\alpha$$ = slope angle.

I attach a table of some common rolling coefficients.

Source

.

• And also include all the bearing friction, oil between gears etc etc Commented Feb 4, 2022 at 17:16
• @Solar Mike, they say the car is in neutral. a bit of more inflation on the tires would more than cover that. Commented Feb 4, 2022 at 19:45
• But what about the coefficients of friction of the transmission output seal, differentials, transfer cases, and the wheel bearings? Commented Feb 5, 2022 at 6:24
• It may be in neutral, but the oil still gets between gears plus total rotating mass, unless it is one of the Saabs with the freewheel... Commented Feb 5, 2022 at 6:58
• Designing to "typical" values means that half of the vehicles will roll away, doesn't it? I don't see anything "super safe" here. Commented Feb 5, 2022 at 12:48

Theoretically, the rolling won't happen if the sliding force is less than the friction force:

$$Wsin\theta \le \mu Wcos\theta$$

$$tan\theta \le \mu$$

$$\theta \le tan^{-1} \mu$$

• $$\mu$$ is the sliding friction coefficient of the contact surfaces. You shall select a coefficient for the "wet" condition.

But, practically, you shall apply a safety factor to the result, because parking on a slope, the tire will deform and causes uneven pressure distribution on the contact surface that results in reduced resistance of motion. Once the motion is started, the friction quickly changes to the rolling friction, which is much smaller than the sliding friction.

Note: There is great confusion between sliding friction and rolling friction, the text below may help to clear the air (hopefully):

• I think you've missed the main point. There's no sliding friction. It's all about vehicles with their brakes off and rolling resistance holding them in position. Commented Feb 4, 2022 at 17:33
• @Transistor Agreed. The friction cofficient should be that of the rolling resistance coefficient of the tire.
– r13
Commented Feb 4, 2022 at 20:23
• @Transistor After reviewing this article, I am not so sure that using the rolling resistance is the correct way to go. Please have a look. en.wikipedia.org/wiki/Rolling_resistance
– r13
Commented Feb 5, 2022 at 1:17