<science>
How much power does it take to accelerate a given mass to a given velocity?
P=W/t
W=Fd
F=ma
d=.5at^2
a=v/t
P=W/t=Fd/t=mad/t=(m(v/t)(.5(v/t)t^2)/t=(.5m(v^2/t^2)*t^2)/t=.5mv^2/t
thus:
P=.5mv^2/t where P is watts, m is in kg, v is in m/s, and t is in seconds.
P85D weight 0-60: (.5*2238.93*(26.8224**2))/3.1 = 259,802 Watts.
Of course in HP that's ~350 HP.
Show me a 5000lbs car with 350 HP, electric or ice, that will hit 0-60 in 3.1 seconds... Of course not, getting the nameplate horsepower actually output in a useful way is some ridiculous fantasy.
For those of you about to complain about drag, go ahead do the calculation, you should find it's nearly insignificant compared to the amount of energy used to accelerate the mass when you've only been moving for 3.1 seconds.
Stick that in your pipes and smoke it....
</science>
OK, you like numbers. So do I. Here's a correction for you: the 350hp figure you calculated is correct as an average. It is actually completely useless though in the case of determining peak hp required for a car.
Instantaneous power can be calculated like this: P=E/t=f*d/t=f*v=
m*a*v. Where v is current speed (m/s).
As you can see, the above formula means that if you hold mass and acceleration constant, power rises linearly with speed (which is basically what you see on the power meter on the dash board). Or put it another way: if you double your speed, you'll get half the acceleration (holding power constant). This has nothing to do with gearing or loses.
Assuming constant acceleration: a=v/t=26.822/3.1=8.6522m/s/s (~0.882g)
Right at 60mph, it takes the following power to accelerate at 0.822g (aka the avg rate):
P=E/t=f*d/t=m*a*v=2238.92(kg)*8.6522(m/s/s)*26.822(m/s)=519,586W=
693whp.
This does
not mean that you need 693whp to get to 60mph in 3.1s. It only means that accelerating at ~0.882g while going 60mph requires this power output.
For example: to get an average of 0.882g, you could accelerate at 1.1g for 1.55s and at 0.664g for the next 1.55s. This would only require a peak power of
520whp (390kW) @ 60mph. Note that due to tire grip limits + electronics current limits and transient response, you really can't accelerate at more than ~1.3g(max) regardless of power available.
Here is a nice graph from DragTimes that demonstrates this acceleration profile. You can calculate peak whp using m*a*v from that graph if you want, but the numbers are a bit off.