NUMBERS

Alright Lets talk supercharger (or turbocharger sizing) ...

First you have to think about just how much performance you want, what your engine can stand, head gasket, fuel delivery, etc... Just the basics to start so you have a basic

Lets assume we find a SC that will give us 15 PSI. Now we need to ensure it is a match for our engine needs. In other words does it give us enough air or not? To much is not a good thing, neither is to little.

To determine how much air will flow through the engine you have to start with engine displacement and an RPM point, then plug it into:

CFM for 4 stroke = Displacement in CI / 3456 * RPM * VE

Lets look at 1998cc (forgive me if I am off a little on the 924) this is 121.9 cubic inches so at 6000 RPM it will flow:

CFM = 121.9 / 3456 * 6000 * VE = 211.6 CFM * VE

VE is volumetric efficiency, which is a value indicating how much of the potential air flow volume actually makes it through the engine at a given RPM. If you throw in a guess-timate of about a 75% VE for the 924 @ 6000 RPM, you get:

CFM = 211.6 * 0.75 = 158.7 CFM

Now is this in or outside the compressor map into the surge area? If it’s outside that would be a cause for concern, however that’s not the end of things. Because this is only telling you what the engine can flow in a naturally aspirated mode at or near redline.

To determine what it will do under boost, you have to determine what density ratio the compressor and intercooling system you have will give you. To do that we need to take our boost point and determine how hot the compressor is going to make the air at a that boost:

Tout (in F) = (((Tin (in F) + 460) * (Pressure Ratio 0.283)) - 460)

So, let say you set the boost controller for 15psi of boost at sea level at an ambient temp of 85F (85F in this case so that our computed CFM ends up matching that of the compressor map). Most compressor maps are taken at 85F

Tout = (85 + 460) * 2.020.283 - 460 = 205F

This assumes an ideal, 100% efficient compressor. The round circles in the compressor map tell us how efficient the compressor is going to at a given pressure ratio and flow level. Lets assume that most of the map is at least 70% efficient or better, we'll use that figure, we will either be close or underestimating a little. But keep in mind that Roots superchargers SUCK when it comes to efficiency.

Our real outlet temperature is going to be:

delta T actual = delta T ideal / efficiency

For our example, the delta T ideal is 205F - 85F or 120F:

delta T actual = 120F / 0.70 = 171F

171F is how much the compressor is going to heat the air above the inlet temp, so the real outlet temp is 171 + 85, or 256F.

What happens when this air mass hits the IC?

Two things: first, a pressure drop and second, a temperature drop. The pressure drop is going to be about 0.5psi for a good side mount IC such as the GReddy, HKS or Spearco units and we will assume a 65% efficiency number which is reasonable for a good side mount IC:

T IC drop = (T IC in - T ambient) * IC efficiency

So we get:

T IC drop = (256 - 85) * 0.65 = 111F

Therefore the IC will drop the SC outlet temp by 111F, turning the 256F air into 145F air and dropping the pressure 0.5psi to 14.5psig. What does this do to our normally aspirated engine?

Well, the density of the air is increased by a ratio:

density ratio = ((Tin + 460) / (Tout + 460)) * (Pout / Pin)

For out example, we get:

density ratio = ((85+460)/(145+460))*(14.5+14.7)/14.7 = 1.79

This density ratio means that you will get 1.79 times as much air flowing through the engine with this compressor and intercooler combination at this pressure point and this ambient temperature than you would in normally aspirated mode.

Going back to our 158.7 CFM value, we multiply that by the density ratio to get 284.073 CFM

Now as I Said most compressor maps are taken at 85F (just look on it, you can tell by looking at the formula written on the map which has a temperature number like 545 and subtracting 460 from that number to convert it to Fahrenheit).

One cubic foot of air at 85F weighs 0.07282 pounds. So, at 85F, convert pounds per minute to CFM by multiplying by 13.73. Lets do the reverse to see what our pounds per minute is.

284.073/13.73 = 20.68 pounds per minute

Now is this inside the compressor’s map or not? Lets assume it is, so we have a reasonable value. If it weren't, you wouldn't be getting 15psi out of the compressor, the actual pressure would have dropped.

Now, are we in the compressor's maximum efficiency range? Lets say yes, so our manifold temperature will probably be a little lower than we calculated with our 75% efficiency value and our density ratio just a tad higher.

This means we are close enough to the money to make it work for our purposes. No real need to go back and try to get the value to be more accurate, since we are already guessing on a number of other things (such as VE) which is having a bigger impact on our actual flow.

Given what we have calculated, we can approximate how much horsepower we will produce. The basic crank HP formula is:

Crank HP = MAP (in absolute psi) * Compression ratio * CFM / 228.6

The compression ratio lets say is 7.5. So, we plug in the real numbers into our HP formula and get:

Crank HP = 29.2 * 7.5 * 284 / 228.6 = 272 HP

Throw in 20% drivetrain loss and you have 217 rwhp @ 6000RPM.


NOW for an NA STOCK MOTOR

Crank HP = 29.2 * 9.0 * 284 / 228.6 = 326 HP

Throw in 20% drivetrain loss and you have 260 rwhp @ 6000RPM.

So, what makes it a little tough to predict what you really are going to get is getting an idea of what the final VE of the system will be (which is not constant, but changes across the RPM/Manifold pressure range) since belt slippage, rotor condition and housing, air flow into the SC. Does the air filter restrict flow? What about the AFM? It is all going to have an effect on the VE map.

So lets say our stock housing and configuration is so restrictive that it drops the engine VE well below 75% at 6000 RPMs (also known as "choking" the engine).

One other item we should check since we have the numbers calculated is whether the compressor will not be forced into the surge line.

Surge is caused when the engine cannot ingest enough air to keep the compressor inside its map.

Now, let's assume that the turbine and turbine housing we will choose can power the compressor to reach 15psi by 3500RPMs. We keep the density ratio the same, but we have to re-compute the flow for the engine at 3500RPMs. The VE at this point should be better than at 6000, so we'll use a value of 85%. At 3500RPMs, the engine will be ingesting:

CFM = 121.9 / 3456 * 3500 * 0.85 = 104.9 CFM

That's in normally aspirated mode. Multiplying the density ratio, we get:

104 CFM * 1.79 = 186 CFM

Now if this is near the surge limit for this compressor, what can we do… granted the VE might be even better, but we could be off.

We could fix this problem on most SCs by modifying the housing to modify air flow which would slow down the spool time to bring the compressor up to this pressure ratio when the engine is reving a little faster and thus ingesting more air. That is on a Centrifugal Unit, on a Roots or Screw, you race port the inlet and outlet to reduce restriction(friction) and increase effeciency

In the case of a turbocharger, a larger AR also allows more exhaust to flow and thus improve VE to also increase air flow and move the system even farther into the compressor map away from the surge line. Bottom line, anything you can do to improve efficiency and increase or decrease air flow to match the engines needs is a good thing, more efficiency means less heat (delta) and cooler air means the capacity for more power.

Now having said all that Supercharger efficiency is one thing sizing is another, the most efficient SC isn't the best unless it fits your application.