Aerodynamics, Horsepower, and Speed

- Double The Speed, Need Four Times The Power -
Frank Hartung
By: Frank Hartung, March 1998


My hope is to shed some, if not a lot of light in the simplest terms, how aerodynamics and horsepower affects speed. I'll also cover briefly the areas covering temperature, humidity, wind, weight, and their effects on speed.

I will make some assumptions that will carry throughout, except where noted. This is all approximate, so don't hold me to this.

1. Bike is a Zx-11 C - model.
2. The Zx-11 motor is producing *160 crank horsepower.
3. There will be no mechanical or frictional losses accounted for.
4. There is no "Wind".
5. Conditions are the "Standard" - Sea Level, 59' F, and 29.92" of Mercury.
6. With the above in mind. this Zx-11's Top Speed is 176 Mph.

* Zx-11 produces 149 crank hp at 10,500 rpm. With ram air this will increase it to the said 160 hp. The losses in the driveline for simplicity reasons, ( #3.) will be said to be the same percentage as the power is increased.(in real life this might not be the case).

What effect does Aerodynamics have on Horsepower requirements?

To double the speed, the engine needs to produce four times more power.

At 22 mph, engine needs to produce 2.5 Hp
At 44 mph, engine needs to produce 10 Hp
At 88 mph, engine needs to produce 40 Hp
At 176 mph, engine needs to produce 160 Hp
At 352 mph, engine needs to produce 640 Hp

If top speed and horsepower numbers are known, calculate the percentage increase in speed wanted. Square this percentage and add to the known horsepower

Example:

Everyone has gone 180 Mph! So how much power is the engine making?
176 plus 2.3% = 180, So, 1.023 x 1.023 = 1.0465 or 4.65%.
160(hp) + 4.65% = 167 hp. needed

Everyone wants to go 200 miles per hour.
176 + 13.7% = 200, So 1.137 x 1.137 = 1.293 or 29.3%
160(hp) + 29.3% = 207 hp. needed

Mr. Turbo's 1992 Zx-11 C - Model top speed of 215 mph.
176 + 22.2% = 215, So 1.222 x 1.222 = 1.493 or 49.3%
160(hp) + 49.3% = 239 hp needed

Mr. Turbo's 1993 Zx-11 D - Model top speed of 231 mph.
(note: does not take aerodynamical differences of the D-model into account)
176 + 31.3% = 231, So 1.313 x 1.313 = 1.724 or 72.4%
160(hp) + 72.4% = 275.8 hp needed

In summary:

88 mph requires 40 hp
176 mph requires 160 hp
180 mph requires 167 hp
185 mph requires 177 hp
190 mph requires 186 hp
195 mph requires 196.5 hp
200 mph requires 207 hp

Temperature: How does it effect Horsepower?

For every 11 degrees Fahrenheit or 6 degrees Celsius change at the carburetors, a 1 percents change in horsepower can be realize if jetting is also corrected for that temperature. Cooler air is more dense and therefore has more oxygen per cubic foot than warmer air. More oxygen allows for more fuel to be burnt, and therefore more power to be produced.

Example:

If the air ingested by the engine is 66 degrees Fahrenheit cooler than the surrounding air, (engine heat!?!) then a 6 percent increase in power can be realized with proper jetting.

Aerodynamics and Horsepower: How does Ram-air fit in?

Atmosphere pressure is 14.7 pounds per square inch. This is equal to 29.92 inches of Mercury. At 170 miles per hour, the pressure created at the front of an object that is moving through clean air, and causes that air to stop or become stagnant, will increase the pressure by 0.5 pounds per square inch.(in that immediate area) This translates into an increase of 3.2 percent in air pressure. Hence, a 3.2 percent increase in Horsepower.
Again, there is a square root effect that comes into play. At 100 miles per hour, the increase in pressure is only 0.17 pounds per inch or 1.2 percent.

front d6

Air that is moving from the front towards the side is less stagnant air and will lose some of this effect. It's pressure will be closer to atmosphere pressure as it speeds up.
Air that is moving along side of the fairing will be at surrounding atmospheric pressure.
The air passing at right angles by the fairing may actually cause it to create a vacuum by the carburetors / airbox. A pressure drop at the carburetors will cause a loss of power.

Humidity: How does it effect Horsepower?

Humidity is the amount of water vapor in the air. Relative humidity is the amount of water vapor in the air compared with the amount of vapor needed to make the air saturated at the air's current temperature.
The dewpoint temperature gives a much better estimate of the amount of moisture actually present in the air, which is very important in determining precipitation amounts and even how comfortable you feel. Very cold, 10 degrees Fahrenheit air with a relative humidity of 100% with 72-degree tropical air, also with 100% relative humidity. In both cases, the relative humidity is 100%, but the cold air's dewpoint is 10 degrees and the warm air's dewpoint is 72 degrees. The higher the dewpoint temperature, the more moisture in the air.
As the temperature goes up, so does the ability of the air to hold more Water vapour before it reaches 100 percent humidity.
At 32 degrees Fahrenheit and 100 percent humidity, the water content is approximately 1 percent (this is not the correct percentage. I am still trying to find the correct number. For demonstration purpose, I have used 1%. This is in the ball park. If anyone knows the exact figure, e-mail me) So there will be 1 percent less air available to the engine.
At 100 degrees Fahrenheit and 100 percent humidity, the water content is approximately 6 percent. So to make better sense of it, at 32 degrees with 100 percent humidity, power loss will be 1 percent at that temperature. While at 100 degrees with 100 percent humidity, power loss will be 6 percent at that temperature.
This is on top of the power loss or gain due to temperature change.

Air temperature in degrees FAmount of water vapor air can hold at this temperature
(100 percent relative humidity)
86 degrees30 grams of water per cubic meter of air
68 degrees17 grams of water per cubic meter of air
50 degrees9 grams of water per cubic meter of air

To some it all up. Humidity is less of a factor in cooler weather than in warmer weather. If the air temperature is around 40-50 degrees Fahrenheit, its 100 percent humidity (raining), and you experience power loss or poor throttle response, chances are you are suffering from Carburetor Icing.

Weight: How does it effect Horsepower and Speed?

These rules assume there are no Aerodynamic forces (drag) coming into play.

Rule #1 : If you double the weight, it will require double the power to accelerate a weight at the same speed.
Example:
It takes a known amount of power and time to accelerate 500 lbs to 50 mph. If this weight is increased to 1000 lbs, it will take twice as long to accelerate to 50 mph, or the power will have to be doubled to maintain the same time.

Rule #2 : If the Power to Weight ratio is known, then removing that amount of weight will accelerate the bike as if the engine has gain 1 Horsepower. (that's why the bike is more fun with an empty fuel tank). Adding weight is like losing power.
Example:
Bike weighs 550lbs. plus 200 lbs. rider total = 750 lbs.
Horsepower is 150. Power / Weight ratio is 5 / 1.
Remove 5 lbs is same as 1 Hp increase.

Wind: How does it effect Horsepower requirements and Speed?

The Zx-11 needs 160 horsepower to achieve 176 mph in still wind conditions. With a 20 mph tail wind, the Zx-11 would / could theoretically obtain 187 mph. This is due to the fact that at 176 mph the Zx-11 is actually moving through the air at 156 mph. This leaves 40 extra horsepower to accelerate the Zx-11 to the 187 mph.
With a dreaded 20 mph head wind, the Zx-11 would only be able to theoretically obtain amazingly enough, 163 mph. Because at that speed, the bike would be moving though the air at 176 mph. And we know that it takes 160 horsepower to go that fast. The only difference is that the bike would be in top of 5th gear instead of 6th because the ground speed is 163 mph. With a 42 tooth rear sprocket and a 17 tooth front, plus a 35 mile per hour tailwind, the bike would go a true 200 mph!

Brakes: How weight and speed effects them!

At any speed:
Double the weight, need double the braking power
Double the speed, need quadruple the braking power
Double the weight and the speed, need Eight Times the braking power!

Frank's bike

In Conclusion:

The most important piece of equipment on a bike is ..... the brakes! If anyone out there has ever reached for the lever only to have it go to the bars, knows what I mean! The biggest diaper will not be enough!
Temperature, ram-air, humidity, weight, all play a part in how much horsepower an engine will ultimately produce. But, aerodynamics and wind direction play a major (understatement) role in what the top speed of any bike is. Magazine's that do two way averaging is not an accurate way of measuring the top speed. So is the CBR-1100 the World's Fastest Production bike. Maybe. It has less weight to accelerate and therefore will most likely get to top speed quicker. For true comparison, it must be tested at the same time with no wind, (zero) a standard day, (29.92, 59 degrees, 0 % humidity) and identical riders (twins). Then the truth shall be known!.

By Frank Hartung