On a highway, why are sharp turns banked more steeply than gentle turns?
I will be happy to critique your thinking.
Sharp turns are banked more steeply because when turning the vertical component does not matter, however it is the horizontal component should be balanced otherwise the car skids on in the horizontal direction??
On a banked curve, the force of gravity tends to make the car slide downward (into the curve). This provides some of the force necessary to make the car turn inward, friction on the tires doing the rest. Turning inward is necessary if the car is to move along the curved road.
You want the weight component down the slope to exactly result in mass times centripetal acceleration component down the slope.
Call bank angle up from horizontal road = T
then m g sin T = m (v^2/r)cos T
tan T = (v^2/rg)
for a given v, as r goes down (tighter turn), tan T and therefore T goes up.
On a highway, sharp turns are banked or curved more steeply than gentle turns to optimize the safety and comfort for drivers. This banking helps to prevent vehicles from sliding off the road or losing control during the turn. The steeper banking provides several important benefits:
1. Friction: When a vehicle takes a turn, centrifugal force pushes it outward, creating a sideways force. This force needs to be counteracted by the friction between the tires and the road to maintain control. In a sharp turn, the sideways force is greater, so a steeper banking angle is required to provide the necessary friction to keep the vehicle on the road.
2. Speed: Sharp turns usually require lower speeds due to their tight radius. The steeper banking angle helps to facilitate these turns at higher speeds by compensating for the higher centrifugal forces. It effectively reduces the lateral forces on the vehicle, allowing it to maintain stability and control even at a higher speed.
To understand the exact angles and calculations for banking on a highway, engineers use mathematical formulas and principles. They consider factors such as the radius of the curve, the speed limit, and the type of vehicles expected to travel on the road. By applying these calculations, engineers can determine the ideal banking angle for a specific sharp turn.
Overall, the steeper banking in sharp turns on a highway is designed to ensure that drivers can safely navigate the turns while maintaining control of their vehicles, reducing the risk of accidents and enhancing the overall driving experience.