Maximum possible speed

Symbol Input Unit Value
c drag coefficient 0.34
D density of air $(kg/m^3)$ 1.25
w width of 205 Si $(m)$ 1.570
h height of 205 Si $(m)$ 1.375
A projected area $(w \cdot h)$ $(m^2)$ 2.159
P power $(W)$ 65,000
v velocity relative to air $(m/s)$
$$\begin{eqnarray} F_{drag} &=& \frac{1}{2} \cdot c \cdot D \cdot A \cdot v^2 \\ \\ P &=& F \cdot v \\ &=&\frac{1}{2} \cdot c \cdot D \cdot A \cdot v^3 \\ \\ v &=& \left(\frac{2 \cdot P }{c \cdot D \cdot A}\right)^{\frac{1}{3}} \\ &=& \left(\frac{2 \cdot 65000 }{ 0.34 \cdot 1.25 \cdot 2.159}\right)^{\frac{1}{3}} \\ &=& 52.13\,m/s \\ &=& 187.67\,km/h \\ \end{eqnarray}$$
  • does not account for drag from rolling resistace; at maximum speed, air resistance dominates
  • does not account for drivetrain losses (power at the wheels)
  • something closer to 175 km/h is probably a more realistic estimate of maximum speed (assuming the above factors are equivalent to a 20% drop in power)