300 mph: The Aerodynamics of Drag and Power
Aviation people distinguish air resistance as parasitic and induced drag, but the critical thing to understand is that drag increases as the square of speed. That is, while power increases in a linear fashion, drag increases exponentially with speed, in a parabolic function. For example (neglecting the effect of rolling resistance), if 100 horsepower would push a certain vehicle 100 miles per hour through the air, doubling the speed to 200 would require two-squared or 400 horsepower to overcome air resistance, while 300 miles per hour would require 900 horsepower.
Components of the following formulae which can be used to compute power required to achieve a certain speed in a vehicle:
Power = 8.702 x 10**(-6) x Cd x A x V**3
where Cd = coefficient of drag (look it up for your vehicle)
A = square feet of frontal area of the vehicle
V = Velocity, in miles per hour
The 8.702 x 10**(-6) section of the equation is a slightly-fudged correction factor made up by me to account for air density, gravity, rolling resistance, etc. Bell uses 6.7 x 10**(-6) x Cd x A x mph**3 and adjusts for actual rolling resistance, where
Rolling Power = 4.0 x 10**(-5) x weight x mph
Cd is adjusted to include rolling resistance (a relatively flat function), and air density is assumed to be standard Temp. and pressure at sea level. Intuitively, power required to achieve a certain speed is dependent on how good a shape the vehicle has (coefficient of drag), how big the shape is (frontal area), and how dense the air is.
Working through an example, Bill Gordon’s Norwood Autocraft 8.2L 288-GTO 308 conversion, assuming a Cd of .33, a frontal area of 20.5 square feet, and assuming a target speed is 200 mph. Therefore,
Required Power = (8.702 x 10**(-6) x.33 x 20.5 x 200**3
Required Power = 0.000008702 x .33 x 20.5 x 8,000,000
Required Power = 472
Observed results when Norwood was running the car with a super-high-output naturally-aspirated 302-inch Chevrolet small-block engine were that the estimated 550-600 plus crankshaft horsepower took the car to 199 mph. Norwood says experience indicates it takes almost 600 crankshaft horsepower to break 200mph, a rule of thumb born-out yet again when a Norwood Toyota MR2-turbo set a record in the 1.5-liter blown modified sports class after it attained 207 mph on 465 chassis dyno rear-wheel horsepower, an estimated 585 at the crank.
Another formula computes power required to increase to a new higher speed:
New Required Power = Old Power (New Speed/Old Speed)**3, where Old Power is total available rear-wheel power.
For the 288-GTO to attain 300 miles per hour,
New Power = 472 x (300/200)**3
New Power = 1593
In another example, lets consider the same car with the frontal area reduced by decreasing the height by one inch (which can often effectively be achieved by lowering the car). In round numbers, assume frontal area is decreased by .5 square feet. This reduces power required to break 200 in the GTO to 460 at the wheels, meaning crankshaft horsepower required to break 300 is reduced by about 55.
Lowering the entire car has a direct effect on the frontal area multiplier, and is why you see speed record cars virtually scraping the ground. Lowering the GTO even one inch reduces frontal area roughly .5 square feet, reducing the frontal area multiplier to 20 square feet, which reduces required horsepower to hit 200 to 460, or 12 rwhp less. The point is, the effect of reducing drag pays far greater dividends on top speed than adding horsepower. It is standard practice to remove the side-view mirrors from “unmodified” cars before top speed runs.
The above equations assume that a vehicle’s the torque and power curves are optimized for the application—that is, that the powerplant is mated to a gearbox that enables the vehicle to be at or very near its peak power at the target potential top speed. Naturally, the vehicle's cooling system must keep up with thermal loading at wide open throttle long enough to reach the target speed, the tires must maintain their integrity, and so on.
Of course, most enthusiasts are more interested in road-racing-type performance than top speed, in which case the large down-forces needed to hold the car to the road on high-speed turns becomes essential and a necessary tradeoff against the added drag of the down-force wings. Good rear wings and frontal splitters and canards can add thousands of pounds of down-force at speeds over 100 mph, but they also add hugely to drag. You've heard it before, but there's no free lunch in aerodynamics either.