Dynamics of a Car Think what happens when you press the gas (acceleration) pedal: –push the pedal and the car accelerates –after a time speed becomes constant –to keep the speed you must keep the pedal pushed –when the pedal is released the car slows down
Dynamics of a Car Forces acting here: –Engine drive –Aerodynamic Resistance (Drag) –Rolling Resistance FEFE R air R rolling
Aerodynamic Drag V 2 – square of velocity of the car – mass density of the air S p – projected frontal area C d – drag coefficient 0.29 < Cd < 0.4 – sports cars 0.4 < Cd < 0.5 – normal cars & pickups 0.6 < Cd < 0.9 – large tracks, tractors
Aerodynamic Drag Aerodynamic Drag is directly proportional to the square of velocity This is why it is so difficult to get a really fast car Aerodynamic Drag is directly proportional to the Frontal Area and Drag Coefficient This is why the profile of sports cars is so important
Aerodynamic Drag Cannon Balls also subject to Aerodynamic Drag Ballistic Demo Revisited...
Rolling Resistance friction between tyres and the road C r – coefficient of rolling resistance typical value for a single car tyre: 0.015 w – weight of the car
Dynamics of a Car Air resistance quickly increases with speed The faster is the car, the higher are the resistances For the given engine drive F E, the speed is maximal if: FEFE R air R rolling
Dynamics of a Car FEFE R air R rolling this formula shows the maximum speed for the given engine drive force
Dynamics of a Car FEFE R air R rolling Rolling Resistance is a constant component (providing road conditions and tyres don’t change) Brakes make another resistance force making the speed decreasing with almost uniform delay (or negative acceleration) R brakes
Turn the Steering Wheel a Side Force is generated friction between the tyre and the road heading towards the centre of the curve
Centripedal Force is what keeps the car turning Centrifugal Force is an inertial force Both are of equal value, opposite direction High velocity or tight curve radius increase the forces If tyre-road friction exceeded – skid!