Akash
Cheers for that info, Its a 2004 model so hopefully no problem's but we will see.
Right then I have slept on your formula and still think your sort of right but still wrong with it.
Yes the formula is correct and there are a great many forum's on the net debating this problem of increasing speed over air resistance however your start point for the calculation are wrong!
A car company produces a car by cost aswell as design, so it budgets parts of the total production cost to major parts ie brakes, engine, shell, interior which makes a limit for each department so top line cost. The engine in the S3 is pretty good in standard form and produce's a stated 265bhp out of the box (quite often a fair bit more) Once the car is designed and first produced for testing all the company comes together and nit picks and health and safety and marketing guys and so on! how do you sell a small hatch that only does 10mpg because it goes so fast etc so most company's will put limitations onto the product to keep running cost's down, euro speed agrements etc even down to the fact that they dont want higher end products being shown up by a possible cheaper part of the brand name.
So say they limit the output and speed by 20/30% to make the vehicle safe, cheap to run,appealing to the mass'es, cheap cost of parts, insurance friendly etc
The speed of the standard s3 is controled by the setting of the rev limit ie 6500rpm the rev limiter cuts in and drops engine power by cutting the fuel pump until rev's drop back down and then it lets the engine work again. This max theretical speed of the gearbox as you say is around 160/165mph however the standard car has not actualy run out of power and is quite happy to carry on going faster at that point as it has not run out of steam or "hit the wall" it has been made to slow down by limiting its fuel supply. At the point of the rev limit kicking in the car may possibly only be using 80% of its 265 bhp?
The stated formula is the correct way to work out how much extra power is needed to increase the top speed of the vehicle after a given point.
The s3 has "not hit the wall" at 160mph it is still going strong and if the rev limit was raised it would carry on using its 265bhp to continue accelerating for a few more mph (say 170/175)
the tuned s3 makes around 360bhp so 95 bhp over standard which as you say is about 35% more.
apply your formula with the intention of a 5 or 10 mph increase and then see how much closer the bhp figures are?
As I said your formula is correct but your start figures are wrong as they are asumptions as to the original top speed achieved by the engines 265bhp as the manufactures have put a mechanical limit to the engine therefore tampering with the figures.
So with that in mind guys and Paddy........ Yes the S3 was actualy made to drive and brake from that sort of speed it has just been toned down by the car company for many reasons known only to them.
Thanks for the debate though guy's its been interesting.
Gaz
