# Supercharger Calculators Explained

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The basics of supercharger calculators…

Supercharger calculators are based on several basic equations that govern the performance and the physical rules that bind superchargers. At the very heart of the matter, superchargers work on the Ideal Gas Law where PV = NRT Pressure x Volume = Number of gas molecules X a constant X temperature. What superchargers do, is that they feed the engine with more air molecules, by over feeding the engine with forced air. This air is forced into the engine due to the supercharger blowing more air into the engine inlet, than the engine would normally breathe under its own device. The result of this ‘forced induction’ can be observed and measured in one of two aspects: Pressure or Temperature. In an ideal world, with a supercharger that has perfect adiabatic efficiency, we are able to feed the engine twice as many air molecules (to double the horsepower figure), by doubling the inlet air pressure (to 2.0 atmosphere or what we call 15 pounds per square inch (PSI) of boost). In the real world, superchargers are not 100% efficient, and so it is possible that doubling the inlet boost pressure gives us less than double the horsepower due to the following:

P*V=n*R*T Pressure increases by a factor of 2 Volume is fixed Number of gas molecules increases by 80% (or a factor of 1.8) Temperature increases by a factor 11% (or a factor of 1.11) If we look at our equation above we can see: 2*P*V = 1.8*N*R* 1.11T The equation is balanced as 2.0X1 = 1.8 * 1.11 (the rise in pressure is equaled by the combined effect of the rise in airflow and the rise in temperature).

From here, we can also see that even at the same ‘boost’ level, that a more efficient supercharger can make more horsepower because more of the supercharger energy is translated into compression and airflow rather than in thermal rise… So, how do we bring these equations into the ‘real world’ in terms of horsepower and boost ? Let’s start with a 2.0 liter (volume), 140hp (air molecules) engine. Say we have a target of 280 horsepower. Our flow ratio will be related to the ratio of our target horsepower to our current horsepower…. Density ratio = 280/140 = 2.0 Density = mass / volume and since the volume of the engine is fixed at 2.0 liters, then we need to fit 2.0 times the air mass into the same volume. This means that we need to fit twice as many air molecules into the engine. Now let’s assume we have a supercharger that is 70% efficient. This means that to reach a density ratio of 2.0 , we need a pressure ratio: P = 2.0 / 0.70 = 2.85 A pressure ratio of 2.85 is equivalent 27 psi. If we look instead at the temperature rise… then T2/T1 = Pressure ratio / Density Ratio So the supercharger outlet temperatures T2 = Pressure ratio (P) / Density Ratio * T1 (where the temperature is in degrees Kelvin).

Assuming an inlet temperature of 80*F , we find the supercharger outlet temperature to be T2 = 309*F On thing to think about here is intercoolers or aftercoolers…. After coolers are radiators that wick heat away from the compressed air after it leaves the supercharger. The ideal intercooler dramatically cools the air temperature without drastically impeding the air flow path and so with having a minimal pressure drop. The intercooler increases horsepower in three ways:

1 – By cooling the air charge, the mixture’s density ratio increases at the same pressure ratio.

2 – The final temperature of the air fuel mixture entering the engine drops, which gives a more power efficient combustion process (as the output power of the combustion event is directly proportional to the difference between intake mixture temperatures and exhaust mixture temperatures).

3 – Lowering the final octane requirements of the mixture, allowing us to add more timing advance or more boost pressure, and make more horsepower within the same octane limitations.

With a good intercooler, we are able to lower the temperature of the air intake charge to within 30 degrees of the ambient air temperatures. At the same time an intercooler will only have a marginal 0.5 to 1.0 psi pressure drop across the core. Having these figures in mind, the combination of a Supercharger with an efficient intercooler gives us a system that has an adiabatic efficiency much closer to 100%, and this means that we are able to make double the horsepower of our original engine at around 18psi of boost (instead of 27 without the intercooler, and instead of 15 for an ‘ideal’ supercharger) if you care to go through the math behind this scenario.

Once you have your pressure ratio, your density ratio, your intercooler outlet temperatures and your overall horsepower and flow numbers, most supercharger calculators are then able to give you more detailed specs for your car’s buildup (such as exact supercharger gearing figures, and required intake and exhaust dimensions, as well as fuel pressure or fuel flow upgrade requirements). But at the heart of any supercharged or turbocharged vehicle, PV = nRT will always hold true. This is great information to know, because several people have chosen to try and sell water evacuation pumps typically used on boats as ‘electric’ superchargers for small displacement engines. It has been shown many times that by hooking up a boost gauge to the inlet of any of these ‘electrically supercharged’ engines that these bilge pumps do not have the flow or block off pressure capability to raise the inlet mixture’s boost pressure by any measurable amount. Pressure (as we’ve explained earlier) is not the only indication of forced induction… but with NO pressure rise at all, that means that the ‘electric’ supercharger has a 0% efficiency, which means that at best it will just heat up the inlet air and no excess air flow will be observed.

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