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## Air- and roll resistanceRoll resistance is calculated as follows:
F with
C
So the roll resistance of an 8 series is 0.015 × 1900 kg × 9.81 m/sec That number, as you can see, does not depend on the speed but on the car's weight only. So it will become more and more insignificant the faster the car will be. Nevertheless the engine always has to overcome a force of 280 N = 28.5 kg to keep the 8 moving. Next comes the formula for air resistance:
F with
A being the frontal area of the car in m
Now speed comes into the equation. As many values become constants if the formula is applied to one car only, we will now simplify this:
The BMW 8 series has a frontal area of 2.07 m
Now half of the air resistance area has to be multiplied by the density of our atmosphere:
(0.6 m
The force of the air resistance can now be calculates very easily: F
That's an interesting table but it doesn't help much. What is missing is the power in Watts that is necessary to achieve those speeds. It is calculated the following way:
Here you can see that the needed power rises to the power of three which means eight times as much power for twice the speed and 27 times the power for triple speed!
From 250 kph / 160 mph on the required power rises very quickly. Now it becomes clear why Bugatti needs 1000 hp in its 16.4 Veyron in order to pass 400 kph / 250 mph as planned. But remember, those values in the tables here are valid only for the BMW 8 series or cars with identical aerodynamics. Still we are not finished because the calculated horsepower must be at the wheels, not at the engine! That means the engine power has to be even higher in order to compensate the energy loss of gearbox and drivetrain. This loss is about 17% with rear wheel driven and 15% with front wheel driven cars. So for the RWD 8 series you end up with the following values:
The factors for drivetrain loss are guessed - somewhat. It seemed to be a reasonable average when looking up this data on the internet and although it seems to be a bit on the high side, the power and top speed of the Alpina B12 5.7 coupé as well as my personal experience seem to confirm the choice. It goes without saying that the transmission must be carefully chosen/developed so that the top speed will be achieved at the engine's power peak. The 380 hp of a stock 850CSi will never get you near 300 kph because the engine develops them at 5300 rpm and 250 kph. Beyond that power drohp off again and reduces top speed. So if you keep the standard gearbox you will need some engine tuning to get a higher top speed. Which brings us to the next point.
Because of the power of three in our equation, the engine has to undergo extensive surgery to provide a noticeable change in top speed. To be
only ten percent faster requires a third more engine power (1.1 But now again the generic formula which calculates the reqired engine power at a given speed:
P with
A: being the frontal area in m With all the values that are constant for the 8 series you get:
P |
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