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Roll resistance is calculated as follows:

F_Roll = C_r × m × g

with

C_r being some coefficient which is about 0.015 in our case,
m being the vehicle's mass, including passengers (about 1900 kg for the 8 series),
and g being the earth's gravitational acceleration (9.81 m/sec²).

So the roll resistance of an 8 series is 0.015 × 1900 kg × 9.81 m/sec² = 280 N

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_Air = A/2 × C_d × D × v²

with

A being the frontal area of the car in m²,
C_d being the drag coefficient,
D being the density of air (1.29 kg/m³) and
v being the velocity in m/sec.

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 m². This is compensated by the very low drag coefficient (C_d) of 0.29 which leaves us with an air resistance area of 2.07 m² × 0.29 = 0.6 m². Here you can see how C_d influences the 'size' (from the point of view of the airflow) of the car. The lower C_d the easier it is for the air to pass the obstacle. The car becomes more streamlined. The 850CSi's C_d is 0.31 but it has a different frontal area (unknown to me - lowered chassis, different mirrors).

Now half of the air resistance area has to be multiplied by the density of our atmosphere: (0.6 m² × 1.29 kg/m³) / 2 = 0.387 kg/m.

The force of the air resistance can now be calculates very easily: F_Air = 0.387 kg/m × v². Because speed is squared in the equation, extreme forces can be expected at high velocities.

0 kph	0 N =	0 kg
50 kph	75 N =	8 kg	+ roll resistance (280 N) =	37 kg
100 kph	299 N =	30 kg	+ roll resistance (280 N) =	59 kg
150 kph	672 N =	69 kg	+ roll resistance (280 N) =	98 kg
200 kph	1194 N =	122 kg	+ roll resistance (280 N) =	151 kg
250 kph	1866 N =	190 kg	+ roll resistance (280 N) =	219 kg
300 kph	2688 N =	274 kg	+ roll resistance (280 N) =	303 kg
350 kph	3658 N =	373 kg	+ roll resistance (280 N) =	402 kg
400 kph	4778 N =	488 kg	+ roll resistance (280 N) =	517 kg

0 mph	0 N =	0 kg
35 mph	94 N =	10 kg	+ roll resistance (280 N) =	38 kg
60 mph	278 N =	28 kg	+ roll resistance (280 N) =	57 kg
80 mph	495 N =	50 kg	+ roll resistance (280 N) =	79 kg
100 mph	773 N =	79 kg	+ roll resistance (280 N) =	107 kg
120 mph	1113 N =	113 kg	+ roll resistance (280 N) =	142 kg
140 mph	1515 N =	154 kg	+ roll resistance (280 N) =	183 kg
160 mph	1979 N =	202 kg	+ roll resistance (280 N) =	230 kg
180 mph	2505 N =	255 kg	+ roll resistance (280 N) =	284 kg
200 mph	3092 N =	315 kg	+ roll resistance (280 N) =	344 kg
220 mph	3742 N =	381 kg	+ roll resistance (280 N) =	410 kg
250 mph	4832 N =	493 kg	+ roll resistance (280 N) =	521 kg

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:

P =	(FRoll + FAir) × v
=	(Cr × m × g + A/2 × Cd × D × v2) × v
=	Cr × m × g × v + A/2 × Cd × D × v3

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!

Speed	Total resistance	Required power
50 kph	355 N	5 kW =	7 hp
100 kph	579 N	6 kW =	22 hp
150 kph	952 N	40 kW =	54 hp
200 kph	1474 N	82 kW =	111 hp
250 kph	2146 N	149 kW =	202 hp
300 kph	2968 N	247 kW =	336 hp
350 kph	3938 N	383 kW =	520 hp
400 kph	5058 N	562 kW =	764 hp

Speed	Total resistance	Required power
35 mph	374 N	6 kW =	8 hp
60 mph	558 N	15 kW =	20 hp
80 mph	775 N	28 kW =	38 hp
100 mph	1053 N	47 kW =	64 hp
120 mph	1393 N	75 kW =	102 hp
140 mph	1795 N	112 kW =	152 hp
160 mph	2259 N	162 kW =	220 hp
180 mph	2785 N	224 kW =	304 hp
200 mph	3372 N	301 kW =	409 hp
220 mph	4022 N	395 kW =	537 hp
250 mph	5112 N	571 kW =	776 hp

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:

Speed	Power at the wheels	Power at the engine
50 kph	7 hp	8 hp
100 kph	22 hp	25 hp
150 kph	54 hp	64 hp
200 kph	111 hp	130 hp
250 kph	202 hp	237 hp
260 kph	226 hp	264 hp
270 kph	250 hp	293 hp
280 kph	277 hp	324 hp
290 kph	306 hp	358 hp
300 kph	336 hp	393 hp
310 kph	368 hp	431 hp
350 kph	520 hp	609 hp
400 kph	764 hp	893 hp

Speed	Power at the wheels	Power at the engine
35 mph	8 hp	9 hp
60 mph	20 hp	23 hp
80 mph	38 hp	44 hp
100 mph	64 hp	75 hp
120 mph	102 hp	119 hp
140 mph	152 hp	178 hp
160 mph	220 hp	257 hp
180 mph	304 hp	356 hp
200 mph	409 hp	479 hp
220 mph	537 hp	628 hp
250 mph	776 hp	908 hp

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 (1.1³ = 1.33), and with the maximum of 10% power increase that common tuning chips for normally aspirated engines provide, only a 3% higher top speed is possible (cubic root of 1.1). With previously possible 290 kph it will bring you very close to the magic 300, but weaker cars will get from, let's say 160 kph before to only 165 kph afterwards which isn't even worth mentionning.

But now again the generic formula which calculates the reqired engine power at a given speed:

P_Engine = ((A/2 × C_d × D × v³) + (C_r × m × g × v)) × 1.17

with

A: being the frontal area in m²
C_d: being the drag coefficient (0.29 for the 8 series)
D: Density of the air (1.29 kg/m³)
C_r: roll resistance coefficient (about 0.015)
m: Mass of the car in kilograms (about 1900 kg for an 8 series)
g: The earth's gravitational acceleration (9.81 m/sec²)
v: Velocity in m/sec (= kph / 3.6 or mph / 2.2374)
1.17: Factor to compensate the energy loss in the drivetrain (1.15 for front wheel drive)
P_Engine: Engine power in W (divide by 736 to get hp)

With all the values that are constant for the 8 series you get:

P_Engine = (0.387 kg/m × v³ + 280 N × v) × 1.17