Akash, You are sort of correct. The S3 gearbox and wheel rolling ratio may be 165mph at the factory redline but dont forget the chipped redline is 1500rpm more so the top speed rises mate as the limiting factor of revolutions of the wheels has been raised quite a bit. Thats simple mechanics.
Gaz
I also mentioned the fact that
air resistance increases by the square of velocity and the amount of power to overcome that drag is proportional to the cube of cube of velocity, so simply gearing up and adding only 80-90 bhp would not get an S3 to over 180 mph. Thats only a power increase of 30-35 of percent to increase the speed by 16% ( 1.16) , but the power needed to overcome the drag is increased by 1.57 (1.16 cubed) times a constant. So already without taking the constants into account ( drag, frontal area and air density) your already looking at more then a 50% power increase to get to 180mph.
Using the following equation for Power needed to overcome drag force, you can calculate the percentage power increase it would take to get an S3 to 180 mph using the following equation:
Power = F ( of drag) X Velocity = 1/2 pV cubed X drag coefficent x frontal area.
p= air density, this can be taken as 1.2 kgm-cubed at 20c.
Cod for the S3 = 0.335
Frontal area is 2.06m squared
So if Force = factor increase +1.34 , Velocity = factor increase x+1.16 then the proportional increase in power needed to go 180 mph = 1/2 1.2 X 1.56 x 0.335 x 2.06 = + 0.65 increase in power needed to go 1.16 times faster.
http://en.wikipedia.org/wiki/Drag_(physics) calculate for yourself if you want
265 bhp X 0.65 =172 BHP. 265 + 172 bhp =
437 bhp
This does not however take into account the increas in rolling resistance onyl air resistance, but air drag is quite a lot greater, and assumes power train loss is the same.
So you'd need at least 437 bhp to get an 8p Audi S3 to 180mph at 20 degrees celcius , whch proves what I said that circa 360 bhp would not be enough to get an s3 to that speed.
Drag would increase at lower temperatures, but so would power the max power needed wouild be about the same.
that equation is all over the net so u can find it yourself, I'm a dentist but did A2 level physics and am still pretty handy with the old applied physics.
To reiterate, the air is very thick and you can't add a piddly amount of power and expect a huge gain in top speed!
the Veyron only needs 270 bhp to go 155 mph, but 720 bhp EXTRA to go 253mph!
So there you go.