I’ve been researching curves and splines for a videogame project of mine.
I’m not 100% sure what it means to have a curve ‘banked’.
It seems to help vehicles with turns on curvy roads, but I don’t quite understand how exactly a curve is banked / what it means to bank a curve (visually) / how it helps with turns.
I have seen some formulas / math for it, but I’d like to understand the concept before exploring potential implementations.
In: Physics
So other comments have explained what a banked curve is. But why, and how do you determine how strongly it has to be banked?
When you drive straight, the most important force (apart from braking/accelerating) applied to your car is gravity. Gravity pulls you straight down, toward the center of the earth; when the road is fully level, it is therefore exactly perpendicular to the pull of gravity. If the road is inclined to the left or right, and the force of gravity therefore stands at an angle to the surface, your car would tend to slide down the incline (though under good conditions, the wheels have so much grip that many cars, especially trucks with a high center of mass, might tip over before sliding sideways. Still not something you want).
When you drive in a curve, you can feel the centrifugal force pushing you to the outside of the curve. Depending on your speed and how hard you turn, this force might become as strong or even stronger than gravity. When two forces are simultaneously applied to an object, they add up to a force that points in a direction somewhere between them (for the exact details of the resulting direction and force, you need some trigonometry). So, in a curve on level ground, the force exerted on your car now stands at an angle to the surface – as above putting you in danger of sliding sideways or tipping over.
To get the same situation in a curve that you have while driving straight on level ground, the road surface should be inclined so the resulting force on a car driving through the curve will be perpendicular to the surface again. Of course, this means that you have to know beforehand how fast cars will pass through the curve to calculate the correct bank angle. A car coming too fast will still have the effect of centrifugal force (though weaker) while one coming too slow will be at risk of sliding (or tipping) towards the inside of the curve. Therefore, bank angles on public roads are usually minimal, as there is always the possibility of a vehicle having to drive through the curve slowly. On racetracks, where you can usually assume that all cars will be fast, you can have steeper bank angles (or, of course, not have them in order to pose more of a challenge to the drivers).
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