(#291) Boost Calculations When Using A Centrifugal Supercharger

The output provided by a centrifugal supercharger increases with the square of the speed of the impeller. As a consequence, this means that it generates very little output at low impeller speeds.

To illustrate this definition, let's examine a Vortech V-7 YSi supercharger that has a maximum output capacity of 1600 cfm at a max impeller speed of 65,000 rpm.

At 90% of 65,000 rpm (58,500 rpm) the supercharger will deliver 90% x 90% or 81% of the YSi's maximum capacity. This works out to 1600 cfm x 81% or 1296 cfm.

From the above information we can develop a table showing air delivery at various percentages of maximum impeller speed.

90% x 90% = 81% of 1600 cfm = 1296 cfm
80% x 80% = 64% of 1600 cfm = 1024 cfm
70% x 70% = 49% of 1600 cfm = 784 cfm
60% x 60% = 36% of 1600 cfm = 576 cfm
50% x 50% = 25% of 1600 cfm = 400 cfm
40% x 40% = 16% of 1600 cfm = 192 cfm
30% x 30% = 9% of 1600 cfm = 108 cfm
20% x 20% = 4% of 1600 cfm = 48 cfm
10% x 10% = 1% of 1600 cfm = 12 cfm

You can see how a centrifugal supercharger's output is disproportionately low at low impeller speeds.

Using the data from the above table we can take the first step in calculating the supercharger boost of any given engine at any rpm.

Theoretical boost can be calculated by taking supercharger output and dividing it by the engine's demand for air. If we had a supercharger supply of 1000 cfm and an engine demand of 500 cfm then we end up doubling the normal atmospheric air pressure.

Atmospheric pressure at sea level is 14.7 lbs/sq. in. Doubling that = 29.4 lbs/sq. in. How much of that total pressure is boost? To calculate that we need to subtract normal atmospheric pressure and the remainder is our boost - in theory, at least.

So, in the above example, we have generated 2 atmospheres (or "bars" as they are also known) and subtracting 1 atmosphere leaves us with 1 atmosphere. One atmosphere = 14.7 lbs so we generated 14.7 lbs of boost.

If we changed the above scenario to a supercharger supply 1500 cfm then we would have tripled the normal atmospheric pressure. Three atmospheres minus 1 atmosphere leaves 2 atmospheres or 14.7 x 2 = 29.4 lbs of boost.

The formula to this point is:
Supercharger air supply divided by engine demand = total atmospheres.
Total atmospheres minus 1 atmosphere x 14.7 = boost.

We'll leave supercharger output calculations now and go to calculating engine demand for air.

To calculate engine demand in cfm, we first need to calculate engine displacement in cubic feet. To do this we take the displacement in cu. and divide it by 1728. In the case of my engine which has a displacement of 371 c.i. the calculation is:

371 cu. in divided by 1728 = .2147 cu. ft.

Next, we need to multiply the displacement by engine rpm. Using 1000 rpm as an example, the calculation is:

.2147 x 1000 = 214.7 cu. ft.

Next, we need to remember that we have a 4 stroke motor which only intakes air every second stroke so we need to divide by two. The calculation is:

214.7 divided by 2 = 107.35

Now we have a number for engine demand per 1000 rpm. It is, obviously, easy to make the calculation for any other engine rpm.

However, there is an additional variable that we need to consider in order to refine our engine demand numbers.

There is a variable known as "Volumetric Efficiency". It is a measure of how efficiently a cylinder fills on the intake stroke. This figure will vary considerably from engine to engine and their various rpm levels. For the purposes of this article I am picking a V.E. of 90%. This level is not uncommon in modern high performance engines. In fact, on very high performance engines, a V.E. of 100% is not uncommon at peak torque.


This is a simple chart up for my engine's demand in cfm at various rpms.

1000 rpm = 107 cfm x .9 = 96.3
2000 rpm = 214 cfm x .9 = 192.6
3000 rpm = 321 cfm x .9 = 288.9
4000 rpm = 428 cfm x .9 = 385.2
5000 rpm = 535 cfm x .9 = 481.5
6000 rpm = 642 cfm x .9 = 577.8
7000 rpm = 749 cfm x .9 = 674.1
7500 rpm = 805 cfm x .9 = 724.6

It is important to remember that the 90% V.E. used in the above example is purely for the sake of convenience. In reality, Volumetric Efficiency varies a lot depending on the rpm. In some motors the V.E. will be higher at lower rpms and on some motors it will be higher at higher rpms. Some motors are designed for tow trucks and some motors are designed for racing.

Now we need to go back and calculate supercharger output at these specific rpms.

We will start with the highest rpm and descend with each rpm level as a percentage of 7500 where our supercharger is geared for the maximum output of 1600 cfm

7500 rpm = 100.0% x 100.0% = 100% = 1600 cfm
7000 rpm = 97.23% x 97.23% = 87% = 1392 cfm
6000 rpm = 80.00% x 80.00% = 64% = 1024 cfm
5000 rpm = 67.67% x 66.67% = 44% = 704 cfm
4000 rpm = 53.33% x 53.33% = 28% = 448 cfm
3000 rpm = 40.00% x 40.00% = 16% = 256 cfm
2000 rpm = 26.67% x 26.67% = 7% = 112 cfm
1000 rpm = 13.33% x 13.33% = 2% = 32 cfm

We can now calculate our boost numbers.

Formula = supply divided by demand

Therefore:

At 7500 rpm, boost = 1600 divided by 724.6 = 2.21 atmospheres - 1 atmosphere = 1.21 x 14.7 lbs per atmosphere = 17.79 lbs (This is my baseline for peak boost).

The rest of the numbers without showing the calculations look like this:

7500 = 17.79 lbs
7000 = 15.66 lbs
6000 = 11.39 lbs
5000 = 6.82 lbs
4000 = 2.41 lbs
3000 = 0 lbs

These are uncorrected numbers because there is a another variable to consider.

I'm sure you are surprised by how low the boost numbers are up to 4000 rpm but remember this, these are numbers that are uncorrected for the heat generated by compressing the air in the supercharger. These numbers will be quite a bit higher in practice. Finally, there are other variables which will affect boost levels i.e. ambient temperatures and restrictions in the tubing connecting the blower to the intake. Hot days and restrictions in the connecting tubes cause the air volume to increase and this will raise the air pressure within the tubing which, in turn, raise boost levels. However, all of these increased boost levels, due to heat expansion, do not add to horsepower levels since the number of air/fuel molecules in the charge do not change.

For the purposes of knowing how much boost I am going to have to contend with for detonation considerations my rule of thumb is to add up 5 lbs to my calculations to cover the heat of compression and other small variables but I do not use this additional boost to forecast horsepower.

To examine connecting tube issues clic here