starsmith
Go Kart Champion
- Location
- Shakytown, CA
- Car(s)
- 2019 Urano Grey GTI
OK so since yall speculated on where I'm getting these numbers, and I think this is valuable to discussions about when a given amount of power is useful or not, here is a detailed derivation of the absolute maximum power that a FWD car can put down at a given speed. This makes some simplifying assumptions, but is valid at the low (~45mph) speeds we have been discussing, where both drag and downforce are too weak to be important in any road car.
Assume the power of the car is P. Power is the rate at which mechanical work is done, and work is the product of force and distance. Since velocity is the rate at which distance increases, the rate at which work is done is the product of force and velocity, F * v, so P = F v and hence
F = P / v (Eq 1)
Assume now your car is at the absolute limit of its front wheel grip - the force of friction is F = μ F_N, where μ is the coefficient of friction and F_N is the force with which the tire is pushing against the surface. In this case, we assume F_N is equal to the fraction of the vehicle's weight on the front wheels, around f = 60% of the weight for a GTI. So the forward thrust provided at the wheels is
F = μ f m g (Eq 2)
Here m is the mass of the car and g is the acceleration due to gravity, 9.8 m/s^2. μ will be ~1.2-1.3 for the absolute best road tire in existence on the absolute nicest unprepped track surface in existence, whereas you can get more like ~2 in drag conditions. We are neglecting weight transfer here because we want a best-case scenario - in practice the car will lift off its front wheels, reducing f. This is what suspension setup can help with somewhat.
OK now equate F from Eqs. 1 and 2. We have
P / v = μ f m g
Solving for P, the maximum power you can put down is
P = μ v f m g
Plugging in μ=1.3, f=0.6, m=3300lb, g = 9.8m/s^2, and v = 45mph, we obtain a maximum power that can be put down of about 300hp. Remember, this is assuming 0 wheel hop, 0 weight transfer, and absolute top-shelf sticky meaty rubber on clean asphalt, so in practice it will be less. That's why tuned GTIs like to spin if you mash the throttle from a 40 roll in 3rd.
Assume the power of the car is P. Power is the rate at which mechanical work is done, and work is the product of force and distance. Since velocity is the rate at which distance increases, the rate at which work is done is the product of force and velocity, F * v, so P = F v and hence
F = P / v (Eq 1)
Assume now your car is at the absolute limit of its front wheel grip - the force of friction is F = μ F_N, where μ is the coefficient of friction and F_N is the force with which the tire is pushing against the surface. In this case, we assume F_N is equal to the fraction of the vehicle's weight on the front wheels, around f = 60% of the weight for a GTI. So the forward thrust provided at the wheels is
F = μ f m g (Eq 2)
Here m is the mass of the car and g is the acceleration due to gravity, 9.8 m/s^2. μ will be ~1.2-1.3 for the absolute best road tire in existence on the absolute nicest unprepped track surface in existence, whereas you can get more like ~2 in drag conditions. We are neglecting weight transfer here because we want a best-case scenario - in practice the car will lift off its front wheels, reducing f. This is what suspension setup can help with somewhat.
OK now equate F from Eqs. 1 and 2. We have
P / v = μ f m g
Solving for P, the maximum power you can put down is
P = μ v f m g
Plugging in μ=1.3, f=0.6, m=3300lb, g = 9.8m/s^2, and v = 45mph, we obtain a maximum power that can be put down of about 300hp. Remember, this is assuming 0 wheel hop, 0 weight transfer, and absolute top-shelf sticky meaty rubber on clean asphalt, so in practice it will be less. That's why tuned GTIs like to spin if you mash the throttle from a 40 roll in 3rd.
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