I want to settle an ongoing debate that has plagued some car forums I have been on for years.
Scenario:
- A Rear wheel drive car; 1996 M3 @210whp, against an AWD 60/40 transfer case ratio 2004 STi @220ish AWHP.
- 0-100mph race the STi wins (AWD duh)
- if started at 100-150mph the M3 wins (RWD duh)
- Drag coefficient of the STi is .29, M3 is .32 (advantage STi)
- Final Drive gearing is near the same
Basically those details above aren't really important; What I'm trying to prove to these guys is that an AWD car (with a set distribution of power [60rear/40front]) will encounter increased loss of wheel power as the speeds increase and the engine fights to put down power through all the gears and driveshafts. The RWD will suffer from the same losses, just not as much due to having less gears, less driveshafts, and less half shafts.
What I'm looking for is a theory, or equation that proves this. I know for a fact that a RWD car with less whp will be faster from this 100-150mph run than the AWD car with slightly more whp (how much more till the AWD car is the same speed [in time], I do not know).
For the record; I do my racing on the track (the 1996 M3 being my own). This is just to prove to some of the dyno whp brainwashed guys that think a whp number is the end all be all of real world performance figures.
Please don't include AWD super car examples that transfer upwards of 100% of the power to the rear wheels to take advantage of RWD superiority at speed. I already know this is why those manufactures do this and using this example to some of the simple minded folk on said forums doesn't go far.
Any help sorting these guys out will help a bunch, I already know I'm right, just lack the equations and terminology to prove such.
I'm trying to reason it out. Because you're talking about acceleration, I believe you have to take into consideration not just the horsepower available, but the torque being put on the wheels, and thus the actual force accelerating the car forward. This can also be complicated by different sizes in the front and rear tires when you consider the awd car.
For simplicity, let's consider the ideal case where both cars' engine output is (I will do this in metric for simplicity) 100kW (roughly 133 horsepower) and 100% of the power gets put to the wheels. I'm also going to assume that all driving wheels provide equal acceleration force with no slip. Each cars will also have an assumed mass of 1000kg (around 2200lb weight) I'm also going to admit that I don't know a whole lot other than the basics of how an AWD car works, so I'm going to calculate everything by the observable horsepower at each of the wheels. For simplicity's sake I'm also going to assume each wheel is equal in size and has a 1m diameter (large, but I don't think this will matter as long as it is uniform).
To start the calculations, I'll assume both cars are moving at a constant speed of 50m/s, or around 112 mph. Because v=r*w (v is velocity, r is wheel radius, w is angular speed), the angular speed of the wheels are v/r, or 50/(.5)=100 rad/s . Power, in watts, is equal to P = T*w or (power = torque * angular speed). Assuming equal torque spread between all driven wheels means that there are 2 driving wheels on the RWD and 4 on the AWD. So, the total power output of all the wheels on the RWD will be T*w*2, and for AWD will be T*w*4. However, because the transmission is 100% effecient and both cars produce 100kW power, the power in both cases has to be equal to 100kW. Therefore, each wheel on the idea AWD car only puts out half the torque of the wheels on a RWD car.
For numbers sake, for AWD:
P=T*w*4 or 100,000 W = T * 100 rad/s * 4, or T = 250 N-m.
For RWD:
100,000 W = T * 100 rad/s * 2, or T = 500 N-m.
What actually accelerates the car, however, will be the force, resulting from the torque of the wheels, on the ground. Torque is force*radius, so the force from the wheels will be the torque divided by the wheel radius.
Thus, for AWD:
F=T/r or 250/.5 = 500 N
For RWD:
F=500/.5 = 1000 N
The total force acting on the car will be the sum of each wheel's force on the road. In this simplified case it will simply be the individual wheel force multiplied by the number of wheels. In this example, this total for both cars is 2000 N. Both of these cars in the ideal case have the exact same force acting to accelerate them forward.
Now that I've analyzed the obvious, it is important to emphasize what this all means: There is no inherent advantage for the theoretical AWD or RWD car. Even changing the power distribution between the front and rear serves no real fundamental purpose for better acceleration. You're simply multiplying and dividing by the same fixed constant and arrive to the same answer, that the force being put down ends up being the same when you assume 100% efficiency. Even shifting 100% of the power at high speed to the rear wheels on a supercar doesn't magically change anything about the physics of the situation. I just want to make sure that is clear, you probably already know this.
What DOES make a difference is the aerodynamic drag, the transmission, and the additional components in the AWD vehicle. You simply cannot beat the fact that an AWD vehicle simply has more power loss between the engine and the wheels. You can't beat entropy. A supercar most likely shifts power to the rear wheels, additionally, to provide better handling and to counteract the tendency of the front end of the car to lift while accelerating. By shutting down the drivetrain between the engine and the front wheels, additionally, the supercar will not lose the power it would while in AWD mode.
In addition to loss in the drivetrain, the transmission components for the AWD car are more numerous and thus will also need to be accelerated (I don't know how much this actually matters in the long run, but the engine is having to spin up additional shafts, gears, and other components. Even if the power is provided hydraulically, there will be friction loss in the hydraulic power system). All the rotational mass of these components can have the same effect as trying to run with ankle weights. Sure, you can do it, but you can't move your legs as fast because of the additional momentum.
For acceleration from 0 to an arbitrary speed, the AWD car will most likely win because it has a better traction availability (less traction demand on each wheel means that the power is spread more evenly, so slippage and loss of traction is less likely). As soon as you get out of a limited traction situation, the car with the least transmission loss will win.
I cannot come up with some equation that says, yes, in this situation the AWD or RWD car will win without going through some complicated assumptions and equation gymnastics. Even then, the driver of the car is probably going to mess the nice clean numbers up.
Now, if you were driving the cars with electric power, the losses might make the difference between AWD and RWD insignificant, but with mechanical and hydraulic drivetrain components, I'm pretty sure RWD is going to win the high speed race, every time.