What are banked curves / turns?

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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

It means the outside of the curve is raised up in elevation, putting that section of road at an angle to reduce the risk of sliding off due to the centrifugal forces involved when taking turns at high speeds.

It means that the surface of the road tilts to the side – down on the inside of the curve, and up on the outside. Imagine an airplane turning. When it turns left, the left wing drops, and the right wing goes up. A road can do exactly the same thing, and for the same reasons.

The old Brooklands racing circuit in England is a great example of one.

There are quite a few pictures on https://www.brooklandsmuseum.com/explore/exhibitions/race-track but if you do a search for “Brooklands track” you should see plenty, including some video clips.

EDIT: You can see the banking in action at https://www.youtube.com/watch?v=NORWAfl3ihU from 1938.

Think of a velodrome (cycling track). The corners are higher at the outside than the inside which helps guide the bikes around the bend. If bikes take flat turns too quickly, they’ll topple. If they don’t topple, they’d slide out. The banking basically gives them something to push off to prevent this. Same goes for cars, though they’re less likely to topple!

The reason for this is that things that are moving tend to keep moving in a straight line (Newton’s first law). Changing the way they’re moving requires force (Newton’s second law). This includes turning. So, when you turn the steering wheel in a car, you are trying to use friction between the road and the wheels to change the direction.

If the car is going too fast for the angle of the turn, the wheels don’t provide enough friction. This means the car will continue to go straight on, and fly off the track.

The banking redirects some of the force. Because you can’t go *through* the road, the surface of the road forces you around. There’s a balance between the momentum keeping you going forwards (or outwards) and gravity pulling you towards the middle.

The curve has a pitch, where the outside edge is a higher elevation than the inside edge. The normal force is the force of an object perpendicular to the ground. You can think of this as an arrow from the car’s center axis pointing down. Cars are very good at this. When that force and lateral forces diverge enough, and the tires lose traction, the car tends to fall off the road. This will happen most often in curves. I can personally attest to falling into a ditch on a flat curve at 30 mph (the speed limit) a day after it rained in my high school shitbox. It doesn’t take much. So by banking the curve, you close that angle of difference between the normal and lateral forces. That lateral force just points more down, so you get more down force in the curve. With an extreme bank, this can contribute significantly to traction. The turns on some NASCAR tracks are a lot higher than you might imagine, than you can appreciate on TV. For normal roads, there might be a bank of just a couple degrees to facilitate traction at the posted speed limit.

It means the surface of the road isn’t level, which helps the car go around a turn faster because it’s leaning into the turn.

Ever seen NASCAR? It’s like that.

If you are on a highway and the whole road turns to the left the right side of the road will be higher than the left side, causing the whole road to tilt from right to left. This is done because as you take your turn the car has a natural tendency to drift towards the outside of the curve. This can be dangerous, especially on icy or rainy roads, as you can lose traction and spin out. The banking of the roads fights against this inclination, making you less like to slip.

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).