Boost Calculations for M52B28 Motor and SC14 Supercharger
Here I will try to show the calculations and formulas used to get an rough estimation of expected boost from an Supercharger. The Formula can be applied to other setups and superchargers as well,
For this example We will be using the BMW 2800cc M52B28 engine as the basis the amount of boost expected from using the SC14 + 103mm Holden Pulley, To read more about pulley options for the SC14 please go read About the SC14 Supercharger Category.
And please skip to the bottom of the page if all the math below makes you dizzy, I originally modified and used this formula courtesy of the datsun1200 forums.
Note: This has served in conjunction with the FAQ section of the old site since 2015, now that we have our dedicated FAQ Section, its time to retire this as a simple post back on the blog. Last Updated – 4/29/2017
First we need to calculate:
How much air you engine needs to run.
Then how much air is needed to run at a set boost level
The volume of air the selected Supercharger makes.
What Boost Level you want to run.
The size of the PULLEY need to make that Boost level etc.
Calculating Engine Liters/min @ 0 Psi
Formula: Liters x RPM / 2 = Liter of Air/Min at 0 psi (N/A Motor)
Multiply engine capacity (in liters) times maximum engine Rpm.
2.8 liters x 7000 rpm = 19600 liters/minute.
Divide this figure by 2 as engine only fills every second stroke.
19600 / 2 = 9800 liter of air/min on a naturally aspired M52B28.
Calculating Boost Ratio
Add the boost pressure desired (5 Psi) for the engine to 14.7 Psi (atmospheric pressure).
5 psi +14.7 psi = 19.7 psi
Divide this answer by 14.7 and this gives the boost pressure ratio. (21.7/14.7=1.476) This is the boost pressure ratio above atmospheric pressure.
19.7 psi / 14.7 = 1.34
Calculating Actual Air Requirements at Desired Boost
Multiply the boost ratio by the liters/minute obtained for 0 Psi and you get the actual air requirements in Liters/min for the engine at that boost. In our example this is
9800 liters/min X 1.34 = 13132 liters/min
Often the question arises if the SC14 is adequate for the 2.8L or even 3L M3’s, They flow more air(1.4L) vs the Eaton M62(1L), and we will be doing some calculations to decide on the correct size of supercharger for your car, you need to know:-
1. The swept volume per revolution of the supercharger. (Eaton M62 1 litre/rev, SC14 from a 1G-GZE 1.4 litres/rev)
2. The maximum continuous safe operating speed for the supercharger. (Eaton M62 14000 rpm continuous, Toyota SC14 12000 rpm??)
3. The maximum pressure that can be safely produced by the supercharger continuously. eg. Eaton M62 = 12 psi, Toyota SC14 = 10Psi(? Beyond that Teflon on rotors melts?)
Calculating Supercharger Rotor Speed
Divide the desired air flow (13132L/min) by the swept volume of the supercharger (SC14 from the 1G-GZE is 1.42 litres per revolution). This will tell you the maximum speed the supercharger rotors must be run at to produce the volume required.
13132 / 1.42 = 9248
Calculating Pulley Size Ratio
Divide the rotor Rpm by maximum desired engine rpm to get the drive ratio of the pulleys. For an SC14 on a 2800cc @ 5psi boost the desired supercharger pulley ratio is
9248 / 7000 rpm = 1.32 Pulley Size Ratio
With an 4″ (103mm) Pulley on the supercharger the size of the crank pulley for this ratio would be
1.32x 4 = 5.28”
Note: M52B28 Crankshaft Pulley is around 6” or 152mm, the SC14 differs between 115mm and 125mm, We are using a 103mm pulley.)
Pulley Size Ratio –> 6″ (crank pulley) / 4″ (SC14 pulley) = 1.5
Max SC14 RPM –> 1.5 (Pulley Size Ratio) x 7000 (Max Engine RPM) = 10500 RPM
Air output with 6″ Crank Pulley –> 1.42(SC14 Displacement) x 10500(Max SC14 RPM) = 14910cc
Boost Ratio –> 14910 / 9800 = 1.52
Max PSI Boost –> 1.52 x 14.7 = 22.34 – 14.7 = 7.6 PSI at 7000RPM or 5PSI at 6000RPM – both using the 4” (103mm) Pulley.
Therefore we can theoretically come to the conclusion the SC14 is more then enough for the M52/M50 engines, You can expect a total of 70HP – 120HP gained at the crank depending on 1. Pulley size used, (Stock SC14 vs Modified & Aftermarket Pulleys, Larger the Crank Pulley, More Power it will make, Smaller the SC Pulley more power you make). 2. Gearshift points, 3. Expect Increase if using accommodating modifications as M50 Intake Manifold, Exhaust Headers, LSD etc). Also Take Note, I always recommend a tune, although I have seen many people running under 5PSI just fine on the Factory ECU, a Tune always helps and gives you even more power = more fun. Also those with the M3’s, take into consideration that the S50B30/B32 Engines have a higher rev range, this from my backyard science tells me you will essentially stress the SC14 Charger out a lot more and most definitely require a tune to remap your air fuel ratios so your engine doesn’t choke.