§ How it works

At steady speed on a level road the engine fights two forces: the air it has to shove aside, and the tires flexing as they roll.

Aerodynamic drag

F_d = \tfrac{1}{2}\, \rho\, C_d\, A\, v^{2}

$\rho$ : air density, 1.225 kg/m³ at sea level and 15 °C.
$C_d$ : drag coefficient, a measure of shape. $A$ : frontal area. Their product $C_d A$ is what the air actually "sees".
$v$ : speed through the air in m/s. Drag force grows with its square.

Rolling resistance

F_{rr} = C_{rr}\, m\, g

Roughly constant with speed, so it dominates in town and fades into the background on the motorway.

Power demand

Power is force times speed, which adds one more factor of $v$ :

P = \left( F_d + F_{rr} \right) v = \tfrac{1}{2}\, \rho\, C_d A\, v^{3} + C_{rr}\, m\, g\, v

That cubic term is why top speed is so expensive. Going 10 % faster needs about 33 % more power; doubling top speed needs roughly eight times as much. Top speed is found where the demand curve crosses the power the car can put to the road.

References

Modern Drag Equation — NASA Glenn Research Centerthe D = ½·Cd·ρ·V²·A form used above

§ How it works

At steady speed on a level road the engine fights two forces: the air it has to shove aside, and the tires flexing as they roll.

Aerodynamic drag

F_d = \tfrac{1}{2}\, \rho\, C_d\, A\, v^{2}

$\rho$ : air density, 1.225 kg/m³ at sea level and 15 °C.
$C_d$ : drag coefficient, a measure of shape. $A$ : frontal area. Their product $C_d A$ is what the air actually "sees".
$v$ : speed through the air in m/s. Drag force grows with its square.

Rolling resistance

F_{rr} = C_{rr}\, m\, g

Roughly constant with speed, so it dominates in town and fades into the background on the motorway.

Power demand

Power is force times speed, which adds one more factor of $v$ :

P = \left( F_d + F_{rr} \right) v = \tfrac{1}{2}\, \rho\, C_d A\, v^{3} + C_{rr}\, m\, g\, v

References

Modern Drag Equation — NASA Glenn Research Centerthe D = ½·Cd·ρ·V²·A form used above

Aero Drag & Top Speed

Inputsdrag · tap · type

Fig. 16Airflow and power demand

§ How it works

Aerodynamic drag

Rolling resistance

Power demand

References

Aero Drag & Top Speed

Inputsdrag · tap · type

Fig. 16Airflow and power demand

§ How it works

Aerodynamic drag

Rolling resistance

Power demand

References