Alright… am not sure if this is the right place to ask… but im sure u have have a better idea abt cars than i do.
I need to calculate the performance of a imaginary car… driving on a small engine… i have calculated the gear ratio, power, torque, dist travelled per rev of wheel etc etc… i jus cant seem to figure a way to calculate the max speed of the car, which need to be calculated on flat groung, 10% and 20% slope.
Well, in reality, everything plays a factor. Power, weight, drag, gear ratio, rolling resistance. Lots of variables. It usually takes 30-40 hp to go at a steady 100 km/h (60 mph). It takes 1000 hp to go 250 mph;)
download the program from the link above, cartest. You can input all your data into the DOS version, which is freeware, and it will give you top speed, acceleration, mpg, etc. It’s fairly accurate too.
Weight plays a very minor role in top speed, provided you have a long enough straight to accelerate on. The only thing weight would affect is rolling resistance, and that’s a minor contributor to total drag power.
To answer the original question, assuming you’re not undergeared, a car’s top speed comes when the power required to overcome the drag equals the maximum power output of the engine. Here are the equations (I’m using SI units, but just remember to be consistent):
Rolling resistance is nearly constant with speed, or near enough that for your purposes you can treat it as such. If you want accuracy, you’ll need some accurate tire data, otherwise, you can just use an empirical approximation:
Frr (rolling resistance force) (N) = vehicle weight (kg) x 0.012 X g (9.81)
For now, don’t worry too much about the accuracy of this coefficient assumption: for a 1500kg vehicle, the rolling resistance is only 176N. The aero drag will be much greater, as you will see:
Fd (aero drag force) (N) = 0.5 * Ï * v^2 * A * Cd
Ï = air density = 1.168 kg/m3 (at STP)
v = speed in m/s
A = frontal area, in m^2
Cd = drag coefficient
Drag Power = (Frr + Fd) * v
So let’s do a case study. Here’s the data for an Audi A4 1.8T Quattro, grabbed at random off the web:
Cd = .31
A = 2.14 m^2
m = 1475kg (this is unladen, so add 100kg for driver and a little fuel, or 1575kg)
Engine power = 140kW (probably not wheel power, so we need a transmission loss figure. It’s AWD, so let’s assume 20%. That gives a wheel power value of 112kW)
Running these figures through the equations above gives a top speed of approx. 229km/h, which compares well (2% error) with the published top speed of 234km/h. Not bad considering we took a few wild ass guesses (our transmission loss figure is probably a little high).
As an aside, using our original figures, doubling the weight would reduce the top speed by only about 9km/h, or 4%. And of course, the rolling resistance contribution to the total drag decreases proportionally with the square of speed. If you doubled the power, doubling the weight would only reduce the top speed by about 7km/h, or 2%