Superchargers and turbochargers are essentially pumps that force air into another air pump equivalent to the engine. All else being equal, two superchargers that are equally efficient at compressing air at a given RPM and consume the same amount of power to turn will make identical power on a given engine. There's no x-factor when it comes to supercharger sizing; it's all a matter of balancing variables and choosing a supercharger size and design that will operate best at the intended RPM.
Calculate your engine's theoretical non-supercharged air intake in cubic feet per minute (CFM). Theoretical CFM is simple to calculate: multiply the engine displacement in cubic inches by the target RPM and divide by the constant 3,456. For example, a 350 cubic-inch engine theoretically will inhale 607 CFM at 6,000 RPM (350 x 6,000 / 3456 = 607) and 202 CFM at 2,000 RPM.
Adjust the theoretical RPM by multiplying by volumetric efficiency (VE). An engine is an imperfect air pump because while it can pump with 100-percent efficiency within a certain RPM range, it usually doesn't. VE is generally about 95 to 105 percent at the engine's torque peak, and tends to taper down to about 70 percent just past the engine's horsepower peak. The 350 in our example has a theoretical 100 percent VE at its 2,500 RPM torque peak, so it uses 240 CFM at 2,500 (350 x 2,500 x 0.95 / 3456 = 240).
Calculate the airflow values adjusted for VE within your target RPM range. We'll say the target RPM range for our 350 engine is from just below its torque peak to just above its horsepower peak at 6,000 RPM. We know from the calculation in step two that the engine uses 240 CFM at its torque peak, and assuming a 70-percent VE at 6,000 RPM gives us 425 CFM (350 x 6,000 x 0.70 / 3456 = 425.9). We now have an airflow range of 240 to 425 CFM.
Determine the desired horsepower level as a gain over your naturally aspirated (non-supercharged) levels. For example, our 350 engine makes 300 horsepower without a supercharger, and we want 500 horsepower. One pound of boost is generally worth about a seven- to nine-percent increase in power. Divide the target horsepower by current horsepower, subtract one, multiply by 100 and divide by between seven and nine (depending on the supercharger type and its efficiency). For our example, we'll use a conservative seven percent to arrive at a 9.5 psi of boost (500/300 = 1.66, minus one and multiplied by 100 equals 66.6, which divided by 7 equals 9.5).
Add your target boost to 14.7 psi (the air pressure at sea level), and divide that figure by 14.7 to arrive at the pressure ratio. In our example, this works out to a 1.6-to-1 pressure ratio (14.7 + 9.5 / 14.7 = 1.6). Now that you have the desired pressure ratio and CFM range, you can size the supercharger. You may need to convert the flow rates from CFM to metric (meters-squared per second, or M3/s) by multiplying the CFM by 0.00047.
Multiply the non-supercharged airflow requirements by the desired pressure ratio to determine how much air your supercharger will need to flow to feed the engine. In this case, our pressure-adjusted airflow range is 384 to 680.
Compare your airflow range and target pressure ratio to a supercharger compressor map. A compressor map looks like a series of concentric ovals; the vertical part of the chart indicates the pressure ratio and the horizontal aspect the airflow in CFM or M3/s. The center-most oval indicates the supercharger's peak efficiency range of pressure ratio relative to airflow; each oval further out indicates a drop in efficiency. We would want to utilize a supercharger with a center oval that spans from 384 to 680 CFM along at the 1.6 marking on the vertical pressure ratio line.
