# Improving fuel economy for the 1991 200q 20v

Dan Cordon cord4530 at uidaho.edu
Fri Mar 11 12:47:40 EST 2005

```For those who have extra time on their hands, here's the general
equation for road load on a vehicle. This is shown as a power prediction
vs. vehicle speed.

Power = [Cr*w*cos(theta) + w*sin(theta) + 1/2*rho*Cd*Af*V^2]*V

Where:
Cr = coefficient of rolling resistance
w = weight
theta = angle of incline (pos) or decline (neg) - not grade
rho = density of air
Cd = coefficient of drag
Af = frontal area of vehicle
V = velocity

For a first draft of modeling our cars, consider Cr ~ 0.015, Cd ~0.35,
Af ~ 2.5 m^2, and rho ~1.2 kg/m^3

These values give:
27 hp @ 65 mph
79 hp @ 100 mph
234 hp @ 150 mph
526 hp @ 200 mph
600 hp @ 208 mph (Talladega Audi 5000CS)

In reality, this is a pretty crude model. For instance, Cd isn't
constant, but rather a function of velocity, the weight chances as
aerodynamic forces add or subtract weight on the wheels, and Cr can be
slightly sensitive to weight (which is sensitive to velocity). But for
ball-park approximations, it's amazingly close!

<break>

I just threw together an Excel workbook of this. It can be downloaded
directly here:

You can input the road load parameters of your choice and see the
results. On the first page, you can see total power for a given speed,
and the % contribution of each term (rolling, weight, and aero) to the
total load. One graph shows power all the way to 200+ mph, and the
second chart only goes to 90 mph. It's interesting to note that for our
cars, the rolling resistance is the dominating one until ~45 mph.

Also, plug in a 5% grade and see how that changes things. The weight
term (completely absent on flat ground) is usually dominant all the time.

--
Dan Cordon
Mechanical Engineer
University of Idaho - Engine Research Facility

Enzeder wrote:

> Alright - on a tangent.
> am I right to assume then that:
> If it takes 100hp to push a car through the air at 100mph, it'll take
> 800hp to push it through the air at 200mph, and 2700hp to run 300mph.
> (assuming someone was foolish enough to leave all other things equal).
>
> Sometime in the late 80's or early90's I remember reading about a Camaro
> (late 60's model) that crossed the finish line of the Silver State
> Classic at 211mph.  It was supposed to have about 800hp and looked about
> as aerodynamic as a brick.  I think it was owned by a father and son
> team named Gotleib.

```