The faster you go, the more dense the air becomes.
Hate to disagree with you, but although it may feel like that when you stick your hand out of the window, air does not change density.
The reason that so much more power is needed to go just a bit faster is because the drag experienced on a body in a fluid (like a car in air) is a square law with respect to speed. Going from 20mph to 40mph is a doubling of speed, but a factor of 4 in the power required. Same is true at higher speeds. Go from 50mph to 100mph and it's another factor of 4 needed. This is borne out in power and top speed figures. A 100hp car that makes 100mph would need 400hp to achieve 200mph.*
*ish. Unfortunately Cd for a car is not constant over that range of speed. Manufacturers quoted Cd is always the lowest Cd measured, not the average. In general, higher speeds induce higher Cd as the airflow will start to detatch from some surfaces, causing eddying and more drag.
Sorry, my brief explanation was erroneous... what I was implying was;
All figures for explanation reasons only;
If you are stood still, and there is 1000mb Air Pressure, you then accelerate to 100MPH. This will result in the air in front of the you becoming compressed, therefore increasing its density (not on a molecular level) you are simply hitting more molecules at any given time-frame (pre second, per minute etc). Essentially, as you compress it (make it smaller) it will take up less space (volume) allowing more molecules into a given area (1 cm3 / 1m3 etc) Boyles Law states this.
Charles' law would also play a trivial part, in that the action of compressing 'air' would cause heat.... I dont think enough of a rise in temperature could be calculated in MPH as it would have almost no 'practical' influence in this type of instance.
Then take into consideration Newtons law of motion, we can assume the reduced air pressure at the rear of the car is equal to the increased pressure at the font of the car. Of course, to put all of this theory into actual workable figures, we'd have to place a car (probably an Omega) into a Wind Tunnel and get some boffin with a Casio Calculator to do the math.
I am no expert of Physics, just remember the basics from my education..... so, if I'm talking complete balls, just tell me to go away!
