Supercharging info/ratios/speeds

[Silent1]

Right, i've seen a few threads asking about the Cooper S supercharger ratios / speeds

I've managed to source all the info for the stock pulley and for the Eaton M45 so here goes:

The stock crank pulley size is stated by MINI as 140mm
The stock supercharger pulley is stated by EATON as 65.5mm
This gives a ratio of 2.13 meaning at 6,750 rpm the supercharger is spinning at 14,427 RPM

Eaton state the maximum RPM for the M45 is 16,000rpm
So to stay within their tolerances when getting a smaller supercharger puller, the smallest you could get would be ~59mm
So that would equate to approximately a 10% pulley

For boost pressure i've had to base it on 4 degrees of overlap as i can't find any other info:
So with standard pulleys the supercharger produces 14.63 PSI
With a 15% pulley the supercharger produces 19.87 PSI
With a 17% pulley the supercharger produces 20.84 PSI
With a 19% pulley the supercharger produces 21.66 PSI

All of these are based on theory, they don't take into account thermal inefficienies due to going over the max RPM

If anyone wants to look at the excel spreadsheet i've created to work these out, PM me

[tirlibibi]

I got probs to understand
So you mean, with a 15% pulley, it is already out of tolerances ?

'cause i doubt JCW will go out of tolerance, on the GP it is 14.xx pulley and 7250rpm !

If you can explain me please

And all Cooper S Tech docs said 11,60PSI (0,8bar) with the orginal pulley !

[Rigsey]

A 17% pulley is more like 17psi

[Silent1]

Ok, the equation i used for the pressure from the supercharger is as follows:

Pulley Stock
S/C CC/rev 750
Engine CC 1600
Pulley Ratio 2.13
Atmospheric Pressure 14.7
Valve Overlap 4

(((750/(1600/2)*2.13*14.7)-14.7)-((4/10)*0.05) = 14.6340625

Boost 14.6340625

Do point out anything you think is amiss from it, i'm going to see if i can remember any other equations, and if i can find the info for the valve overlap on a standard cam (the 4 degrees is a shrick fast road cam)

[MINI-Morgan]

Maybe the equation doesnt count for inefficiencies. As the speed goes up the pressure doesnt go up the same amount

17% is 18psi max.

[Silent1]

Indeed, that's what i said up there somewhere, it doesn't take into account thermal inefficiences

[k-huevo]

Silent1, I’ll add tolerance stacking and differences in volumetric efficiency as other variables. On my vehicle with head/valves & exhaust manifold improvements, the highest pressure documented was 17psi, on a 101 F day with a 19%. Stock head, cat back, and 15%, saw 16psi on a very hot day, both attained on a dyno. I know this is an exercise and thank you for the effort.

tirlibibi, the JCW pulley is 58 mm OD. If you use the Eaton OD stock measurement it would be ~11.5% smaller. I’ve measured more than a few of both pulleys and have not seen anything smaller than ~10.9% reduction in comparison.

[Silent1]

Quote: Originally Posted by k-huevo (original)

Silent1, I’ll add tolerance stacking and differences in volumetric efficiency as other variables. On my vehicle with head/valves & exhaust manifold improvements, the highest pressure documented was 17psi, on a 101 F day with a 19%. Stock head, cat back, and 15%, saw 16psi on a very hot day, both attained on a dyno. I know this is an exercise and thank you for the effort.

tirlibibi, the JCW pulley is 58 mm OD. If you use the Eaton OD stock measurement it would be ~11.5% smaller. I’ve measured more than a few of both pulleys and have not seen anything smaller than ~10.9% reduction in comparison.

Thanks for that K-Huevo, i'll sit down and work some more 'real world' results out tonight

[MINIMANIAUK]

and dont forget the supercharger power comsumption from crank is non linear and rpm dependent.and the effect of turbulence within charger,and altered clearances between rotor/case, and altitude -give up yet

[k-huevo]

Here is something else to consider, boost is formed in the intake manifold, not the Roots SC. Eaton’s supercharger is not a compressor, it moves air into the IM faster than it can be consumed, and air stacks behind the intake valves creating pressure above atmospheric. This is the reason changes downstream of the supercharger (VE improvements, valve overlap/cam profile, etc.) can affect boost and why best case pressure calculations are not valid in all situations; although, good for SC rpm comparisons.

[MINI-Morgan]

You mean pressure build up anywhere after the SC outlet

[Freedo]

Just out of interest what is 20psi in bar?

[Jaw_F430]

Quote: Originally Posted by Freedo (original)

Just out of interest what is 20psi in bar?

1.37895146 bar

[Lucky Dave]

I get 19.5 psi with a 17% using a calibrated gauge.

[Silent1]

Quote: Originally Posted by MINIMANIAUK (original)

and dont forget the supercharger power comsumption from crank is non linear and rpm dependent.and the effect of turbulence within charger,and altered clearances between rotor/case, and altitude -give up yet

It's not rocket science, if i can understand quantam physics then this isn't exactly taxing, the best thing is, at some point i'll get some gauges on the car and provide a proper cooper s specific equation