Banked Turns

  • Allow vehicles to go around a circuit faster than unbanked curves
  • Reduces the reliance on tyre friction, since gravity provides some of that force
  • Sum of forces is equal to the centripetal force

Design Speed

  • At the design speed, the centripetal force is entirely made up of the normal reaction and the weight force
  • At the design speed, the bank angle is optimal.
  • Frictional forces are not applied

vector banked curves

Effect of Friction

If v < v optimal, then the friction force works parallel to and up the slope to prevent the car from slipping

firction up slope

If v > v optimal, then the friction force works parallel to and down the slope to prevent the car from going up
friction down slope

To quantify the effects of friction, you need to calculate the x and y components of the frictional force.

Equations:

Vertical Motion: there is no vertical acceleration

vertical component banked curves

Horizontal Motion

horizontal component banked curves

Optimum design angle:

optimum design angle

 

 

 

 

 

 

 

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