Its been posted before but might mak for interesting reading.
To work out drag you need the Cdp and the frontal area and the top speed car car attains and how much HP the car makes when the cars flat out .
Take for example a car with a Cdp of 0.3 and a frontal area of 3m squared (32.3 feet squared)
It has a equivalent frontal drag of 32.3 x 0.3 = 9.69ft squared.
This figure is what you need when calculating drag at a particular speed. What the figure is meant to represent is the cars equivalent flat plate drag ie what would the car be equal to in terms of a flat piece of material striagt on to the oncoming air.
To find out the drag multiply this equivalent frontal drag by the dynamic air pressure at the speed since the faster you go the more the more the drag this dynamic air pressure isn't constant.
At 57.5mph = 10
At 115mph = 33
At 138mph = 50
At 172.5mph = 75
At 230mph = 140
(See this and this for a spreadsheet graph to get accurate value for the dynamic pressure over a bigger range)
So to find out the air drag of the vahicle multiply the above figure by the equivalent flat plate drag area.
So assume our car of 9.69ft maxes out at 138mph then the drag from the car (tyre drag not included) is 9.69 x 50 = 484.5lb drag so assuming that the was no tyre drag and the car had a long enough road the car with a 484.5lb thrust turbo jet would reach 138mph dead although it might take a lifetime to get there.
To convert this lb drag to an equivalent hp you multiply it by the speed in MPH and by 1.467. Then divide this figure by 550.
So for our example 484.5 x 1.468 x 138 = 98085
Then 98085 / 550 = 178hp.
So out car has 178hp at the ground (assuming its flat out and it isn't at the rev limiter).
Then we ned to add a few hp to the car to account for the drag the tyres generate so 10hp isn't a bad guess.
Therefore at whatever rpm gave the flat our speed the engine has 188hp.
This above calcs arn't totally accurate since air pressure varies not just with speed but also altitude and temp along with constistance but its accurate enough for most people. Also other facts ie ram effect on the intake (ie the Ferrari 550 uses its ugly scoop) will have an effeect on engine power since more air is going into the engine.
Another example is a 172 Clio it has a Cdp of 0.36 and a frontal area of 2.01m squared (multiply by 10.76 to get ft squared so 21.64 square feet)
We will assume it will achieve 138mph which is about right Evo manged on the speedbowl so its not to bad a guess.
Therefore: fronal area x Cdp x dynamic air pressure at the speed x 1.468 x speed in MPH / 550 = HP at ground at that RPM
21.64 x 0.36 x 50 x 1.468 x 138 / 550 = 143hp at 6.9k (assume 20mph per thousand RPM)
Assume an extra 10hp from the drag of the tyres then a 172 has 153hp before the gearbox which is quite accurate since I havn't fiddled the figures to fit.
Another example is a 1.4 Clio it has a Cdp of 0.36 and a frontal area of 1.89m squared (multiply by 10.76 to get ft squared so 20.3 square feet)
We will assume it will achieve 115mph.
Therefore: fronal area x Cdp x dynamic air pressure at the speed x 1.468 x speed in MPH / 550 = HP at ground at that RPM
20.3 x 0.36 x 33 x 1.468 x 115 / 550 = 74hp at 5.75k (assume 20mph per thousand RPM)
Assume an extra 5~10hp from the drag of the tyres (there smaller than 172 etc ones) so a 1.4 has 79~84hp before the gearbox which is not bad, it shows that a 1.2 won't get to a real 115mph without a reduction in drag or a hill (which gives the car more energy which means more power).
An interesting thing is using these equations you can work out what sort of power you'd need to do 200mph in a Clio (aassuming you have a long enough ratio box)
fronal area x Cdp x dynamic air pressure at the speed x 1.468 x speed in MPH / 550 = hp required
20.3 x 0.36 x 110 x 1.468 x 200 / 550 = 429hp
A normal shell is less draggy so this is what we would use. but we need 429hp to get there and even if we have a diesel box giving us 35mph/thousand rpm the engine need to make 429hp at 5.7k.
429hp is expensive (2 x 172 engine with N20 or throttle bodies maybe, or a highly tunned turbo engine) but if you go back to the equuation all you need is
fronal area x Cdp x dynamic air pressure at the speed = lb thrust turbo jet engine
20.3 x 0.36 x 110 = 803.88 lb thrust which is a very low poer turbo jet. A l-29 last generation engine makes 1850lb thrust for £5k.
Since the L-29's turbo jet engine will make 1850 or so power how fast would a Clio with this engine go?
Well for 230mph it needs
Fronal area x Cdp x dynamic air pressure at the speed = lb thrust turbo jet engine
20.3 x 0.36 x 140 = 1023lb
For 345mph it needs
Fronal area x Cdp x dynamic air pressure at the speed = lb thrust turbo jet engine
20.3 x 0.36 x 300 = 2192.4lb
But to get to 345mph in a normal engined Clio we'd need
fronal area x Cdp x dynamic air pressure at the speed x 1.468 x speed in MPH / 550 = hp required
20.3 x 0.36 x 300 x 1.468 x 345 / 550 = 2019hp
To work out drag you need the Cdp and the frontal area and the top speed car car attains and how much HP the car makes when the cars flat out .
Take for example a car with a Cdp of 0.3 and a frontal area of 3m squared (32.3 feet squared)
It has a equivalent frontal drag of 32.3 x 0.3 = 9.69ft squared.
This figure is what you need when calculating drag at a particular speed. What the figure is meant to represent is the cars equivalent flat plate drag ie what would the car be equal to in terms of a flat piece of material striagt on to the oncoming air.
To find out the drag multiply this equivalent frontal drag by the dynamic air pressure at the speed since the faster you go the more the more the drag this dynamic air pressure isn't constant.
At 57.5mph = 10
At 115mph = 33
At 138mph = 50
At 172.5mph = 75
At 230mph = 140
(See this and this for a spreadsheet graph to get accurate value for the dynamic pressure over a bigger range)
So to find out the air drag of the vahicle multiply the above figure by the equivalent flat plate drag area.
So assume our car of 9.69ft maxes out at 138mph then the drag from the car (tyre drag not included) is 9.69 x 50 = 484.5lb drag so assuming that the was no tyre drag and the car had a long enough road the car with a 484.5lb thrust turbo jet would reach 138mph dead although it might take a lifetime to get there.
To convert this lb drag to an equivalent hp you multiply it by the speed in MPH and by 1.467. Then divide this figure by 550.
So for our example 484.5 x 1.468 x 138 = 98085
Then 98085 / 550 = 178hp.
So out car has 178hp at the ground (assuming its flat out and it isn't at the rev limiter).
Then we ned to add a few hp to the car to account for the drag the tyres generate so 10hp isn't a bad guess.
Therefore at whatever rpm gave the flat our speed the engine has 188hp.
This above calcs arn't totally accurate since air pressure varies not just with speed but also altitude and temp along with constistance but its accurate enough for most people. Also other facts ie ram effect on the intake (ie the Ferrari 550 uses its ugly scoop) will have an effeect on engine power since more air is going into the engine.
Another example is a 172 Clio it has a Cdp of 0.36 and a frontal area of 2.01m squared (multiply by 10.76 to get ft squared so 21.64 square feet)
We will assume it will achieve 138mph which is about right Evo manged on the speedbowl so its not to bad a guess.
Therefore: fronal area x Cdp x dynamic air pressure at the speed x 1.468 x speed in MPH / 550 = HP at ground at that RPM
21.64 x 0.36 x 50 x 1.468 x 138 / 550 = 143hp at 6.9k (assume 20mph per thousand RPM)
Assume an extra 10hp from the drag of the tyres then a 172 has 153hp before the gearbox which is quite accurate since I havn't fiddled the figures to fit.
Another example is a 1.4 Clio it has a Cdp of 0.36 and a frontal area of 1.89m squared (multiply by 10.76 to get ft squared so 20.3 square feet)
We will assume it will achieve 115mph.
Therefore: fronal area x Cdp x dynamic air pressure at the speed x 1.468 x speed in MPH / 550 = HP at ground at that RPM
20.3 x 0.36 x 33 x 1.468 x 115 / 550 = 74hp at 5.75k (assume 20mph per thousand RPM)
Assume an extra 5~10hp from the drag of the tyres (there smaller than 172 etc ones) so a 1.4 has 79~84hp before the gearbox which is not bad, it shows that a 1.2 won't get to a real 115mph without a reduction in drag or a hill (which gives the car more energy which means more power).
An interesting thing is using these equations you can work out what sort of power you'd need to do 200mph in a Clio (aassuming you have a long enough ratio box)
fronal area x Cdp x dynamic air pressure at the speed x 1.468 x speed in MPH / 550 = hp required
20.3 x 0.36 x 110 x 1.468 x 200 / 550 = 429hp
A normal shell is less draggy so this is what we would use. but we need 429hp to get there and even if we have a diesel box giving us 35mph/thousand rpm the engine need to make 429hp at 5.7k.
429hp is expensive (2 x 172 engine with N20 or throttle bodies maybe, or a highly tunned turbo engine) but if you go back to the equuation all you need is
fronal area x Cdp x dynamic air pressure at the speed = lb thrust turbo jet engine
20.3 x 0.36 x 110 = 803.88 lb thrust which is a very low poer turbo jet. A l-29 last generation engine makes 1850lb thrust for £5k.
Since the L-29's turbo jet engine will make 1850 or so power how fast would a Clio with this engine go?
Well for 230mph it needs
Fronal area x Cdp x dynamic air pressure at the speed = lb thrust turbo jet engine
20.3 x 0.36 x 140 = 1023lb
For 345mph it needs
Fronal area x Cdp x dynamic air pressure at the speed = lb thrust turbo jet engine
20.3 x 0.36 x 300 = 2192.4lb
But to get to 345mph in a normal engined Clio we'd need
fronal area x Cdp x dynamic air pressure at the speed x 1.468 x speed in MPH / 550 = hp required
20.3 x 0.36 x 300 x 1.468 x 345 / 550 = 2019hp
