Thread: Wind resistance Formula

I recall reading many years ago that the power (power is the rate of expending energy) required increases with the cube of the speed.

That is, if you double the speed of an object, say from 100km/h to 200km/h, you need 2^3 = 2x2x2 = 8 times the horsepower or kW to overcome air resistance.

Happy to be corrected if not right.

Originally Posted by Leo109

I recall reading many years ago that the power (power is the rate of expending energy) required increases with the cube of the speed.

That is, if you double the speed of an object, say from 100km/h to 200km/h, you need 2^3 = 2x2x2 = 8 times the horsepower or kW to overcome air resistance.

Happy to be corrected if not right.

Sounds about right. I recall reading something similar about the power needed to achieve the results VW needed to make the Bugatti Veyron live up to the promises. People should genuflect in awe at that car. It is a stupendous achievement. Pity only spoilt brat sons of Sheiks can afford one.

Yes. Resistance is proportional to the square of the speed, so power will be proportional to the cube of the speed.

In real life, it may not be quite that simple, as the airflow may well change as speed changes. And of course when you get close to Mach 1 it will certainly change.

John

I'm only thinking legal QLD speeds John,,

Originally Posted by Pedro_The_Swift

I'm only thinking legal QLD speeds John,,

In Qld everything's legal as long as you don't get caught. ( With apologies to Bob Dylan )

Air Resistance Formula
Air resistance is a force that affects objects that move through the air. Often physics problems used in teaching ignore it, but it is very important for understanding the motion of fast-moving objects like airplanes. It depends on the density of the air, the area of the object, the velocity it is moving, and a "drag coefficient" that accounts for other properties of the object like the surface roughness, and turbulence. Air resistance is also called "drag", and the unit for this force is Newtons (N).


F = force due to air resistance, or drag (N)
k = a constant that collects the effects of density, drag, and area (kg/m)
v = the velocity of the moving object (m/s)
ρ = the density of the air the object moves through (kg/m3)
CD = the drag coefficient, includes hard-to-measure effects (unitless)
A = the area of the object the air presses on (m2)

Air Resistance Formula

The aforementioned was of course 'cut and paste'. There was a time when I might have understood all that, but that time is long past.

Actually fairly simple derivation of the basic formula if you consider that effectively you are accelerating the air in front of the vehicle to the speed you travelling (the volume of air is the frontal area multiplied by the distance travelled for CD=1).

John