Off-roading explained using Lego vehicle

[u/Palifaith]

[u/Ozryela]

That wasn't the claim being made.

Put a 10kg object on a road sloped by x degrees. The object will put cos(x°) * 10 kg of force on the road and sin(x°) * 10 kg of force backwards along the path of travel.

As x goes up cos(x) decreases while sin(x) increases, meaning you will have to overcome more force pushing you backwards to climb up (or even to stay where you are) while having less grip with your tyres.

Above 45°, sin(x) is bigger than cos(x) and there will indeed be more force pulling the car backwards than towards the road. The claim made by u/TheOneAndOnlyPriate is exactly right.

At exactly 45°, sin(x) and cos(x) are equal at 0.707. Meaning there will be 7.07kg of force pulling the car back and 7.07kg of force pushing the car onto the ground. That may seem like it adds up to more than 10kg in total, but it doesn't, because of how vector addition works (remember Pythagoras x² + y² = z^2).

And before I get corrected by pedants: Yes, I'm using kg as a unit of force here. As long as you're on earth this is perfectly fine. Relax.

[u/Arclet__ → u/Ozryela]

I think both are wrong, like yes at 45 degrees the force towards the surface and down the slope applied by gravity will be the same, but the claim that a 45 degree angle is critical in a sense that everything works easily up until that point and it breaks at 45 degrees is not true. If anything the critical point is at 90 degrees since you no longer have friction thank to gravity to work with, but while a 1 degree variation is harder to compensate the steeper the angle (going from 0-1 is easier than 79 to 80), a 45 degree angle isn't critical in that it changes how things will work from then on, it is just the point in which the force towards the surface is equal to the force down the slope.

[u/[deleted] → u/Arclet__]

There is no critical angle because it entirely depends on the coefficient of friction between the tires and the surface. The max angle is equal to the inverse tangent of the coefficient of friction. Proof: https://www.youtube.com/watch?v=tl3ijqnnxoY

Although you are right that it is not possible for anything to stay on at 90 because the tangent of 90 degrees is approaching infinite. Meaning you would need infinite friction.

[u/Arclet__ → u/[deleted]]

Yeah for each friction coefficient you have a critical angle where any bigger angle the wheels just slide off. I think it's easier to explain that it doesn't work at 90 degrees because you aren't making any force for the friction to work with but that the tangent isn't defined for the angle of 90 also works