Why are mountain roads generally made winding upwards rather than going straight up?

The mountain roads are generally constructed in a winding fashion so as to increase friction and thereby reduce skidding of vehicles. This comes from the definition of friction for an object placed at a slope of angle θ .

Here, f is the frictional force, μ is the coefficient of friction, m is the mass of the object, g is the acceleration due to gravity and θ is the angle made by the object with the surface.

Now, winding the road means decreasing the θ with respect to ground. This will increase friction as cosine will increase. Hence the frictional force increases. Going straight up means going at a larger angle so the friction will decrease.

Here, θ’ is the angle made by the slope of the mountain with the ground whereas, θ is the angle made by each turn with the ground. As it is clear that θ ’> θ.

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