When a car moves along a flat road the engine has to work to overcome two main resistances - air resistance and rolling resistance (the drag in tyres, wheel bearings etc). The top speed of the car is determined by the amount of engine power available and the size of these retarding forces. The maths to work out these equations for an actual vehicle are very simple. In order to calculate the top speed we need to work out the size of the retarding forces.
Defined as the force needed to just start a car rolling on flat ground this force is mainly a function of vehicle weight. You can measure it yourself fairly easily with a pair of bathroom scales or a spring balance. Just hold the scales vertical against the rear bumper and push until the car starts to move. You might find that once the car is rolling the force needed to keep it just moving falls slightly. This lower force is the number you are after.
For most cars the force in pounds can be estimated as follows:
Rolling resistance (lbs) = vehicle weight (lbs) x 0.012 to 0.015 (I usually take 0.013 as a good average)
Obviously if the tyres are flat or a wheel bearing is half seized this force can alter a fair bit but we will see later that it is air resistance that is the main obstacle to top speed so even a large error in the rolling resistance calculation won't matter much. Rolling resistance is taken to be a constant i.e. not varying with vehicle speed although this is really somewhat of a simplification. For an average car weighing 2500 lbs this force is therefore in the region of 33lbs.
This is a function of the frontal area (fA) of the car and its coefficient of drag (Cd). Often car magazine tests show these numbers and all manufacturers will have the data if they can be persuaded to release them. Most modern cars have drag coefficients between 0.3 and 0.4 with a few really streamlined ones as low as 0.28 or so. The Cd is a measure of how "slippery" a shape is as the air goes round it.
Frontal areas tend to lie between 19 and 23 square feet for european cars (we can exclude 4 wheel drive yank tanks and similar from this exercise because who cares how fast they go anyway?)
The drag in pounds goes up with the square of speed and can be calculated from the following formula:
Air resistance (lbs) = fA x Cd x 0.00256 x speed squared (speed in mph)
Average family cars have a top speed of 120 mph or so these days so let's have a look at the size of this force at that speed. We'll assume the car has a frontal area of 21 square feet and a Cd of 0.35
Air resistance (lbs) = 21 x 0.35 0.00256 x 120 x 120 = 271 lbs
As you can see this is a much larger force than the rolling resistance. In fact rolling resistance only makes a major difference to vehicle dynamics at very low speeds (under 60 mph or so) and means that heavy cars use more power and therefore have poor fuel consumption at low speeds. At higher speeds the air resistance becomes paramount and so even heavy cars can show good fuel consumption if they are well streamlined.
The final step is to relate the drag figures above to the power required to overcome them. If we add rolling resistance and air resistance together we get total drag in pounds. Power required is then calculated as:
Power (bhp) = Total drag x mph / 375
We could if required split the power into the amounts needed to overcome each drag separately. The equations would then become:
Power to overcome rolling resistance = weight x 0.013 x mph / 375
Power to overcome air drag = fA x Cd x 0.00256 x mph cubed / 375
Hopefully something of major importance should be clear from the above. We already know that it is air resistance that is the major element in this equation and we can see that we need to incorporate mph cubed in the power equation for air drag. As a simplification therefore we can say that power required is closely related to mph cubed - i.e. to double the speed of a vehicle we need 8 times the engine power. Alternatively we can express this as top speed is a function of the cube root of engine power. This means that engine modifications will have a much greater impact on acceleration (which is directly related to power) than top speed. Also that is why an old engine which is down on power might accelerate slowly but still have close to its original top speed. So next time your mate tells you in the pub that he put a K&N air filter in his car and the top speed went up by 10 mph you can explain exactly why that isn't going to be very likely.