I found the freefall motion equation which describes terminal velocity of a falling body, but I can't find a similar equation for a vehicle subject to constant traction force, so I tried determining it by myself, but resulting equation is not plausible, as it shows dozens of seconds needed for a 1600 kg vehicle to go from 0 to 60 mph, so there must be something wrong. I'm using this equation: $$v(x) = v_f \cdot \tanh\left(\frac F {mv_f} \cdot x \right) = v_f \cdot\tanh\left(\frac {T/w } {m v_f} \cdot x \right)$$
- $v_f$ = terminal velocity = $\sqrt {\frac F c} = \sqrt {\frac {T} {wc}}$
- $c = \frac 1 2 \rho C_d A$
- $\rho$ = air density = 1.225 $\frac {kg} {m^3}$
- $C_d$ = air drag coefficient = 0.32
- A = frontal area = 2.19 m$^2$
- T = given torque = 220 Nm
- w = wheel radius = 0.25 m
- m = vehicle mass = 1762.5 kg
Freefall motion equation is:
$$ v(x) = v_f \tanh\left( {x\sqrt{\frac{gc}{m}}}\right)$$
with $v_f=\sqrt{\frac{mg}c}$
With above data for the car, I should get around 10s time for 0-60 mph, but I get 63 seconds!
What am I doing wrong?
With above data(1) for the car, I know (2) I should get around 10s time for 0-60 mph, but I get 63 seconds!
What am I doing wrong?
Other literature data:
- Fiat Stilo - 255 Nm, 1488 kg, 11.2 s
- BMW M3 - 400 Nm, 1885 kg, 5.3 s
- Citroen C3 - 133 Nm, 1126 kg, 14.5 s
Literature data for electric cars:
- kg W Nm sec-to-60mph
- Chevrolet Volt 1715 63 130 9,0
- smart fortwo electric drive 900 55 130 12,9
- Mitsubishi i-MiEV 1185 47 180 13,5
- Citroen zEro 1185 49 180 13,5
- Peugeot iOn 1185 47 180 13,5
- Toyota Prius Plug-in 1500 60 207 10,7
- Renault Zoe 1392 65 220 8,0
- Renault Fluence Z.E. 1543 70 226 9,9
- Nissan leaf 1595 80 280 11,9
- Toyota RAV4 EV (US only) 1560 115 296 8,0
(1) "Evaluation of 20000 km driven with a battery electric vehicle" - I.J.M. Besselink, J.A.J. Hereijgers, P.F. van Oorschot, H. Nijmeijer
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