# Find The Output Power Po Use V 2 R Formula Supercharger Calculators Explained

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## Supercharger Calculators Explained

The basics of supercharger calculators…

Supercharger calculators are based on several fundamental equations that govern performance and the physical laws that bind superchargers. At the very heart of the matter, superchargers operate on the ideal gas law where PV = NRT pressure x volume = number of gas molecules X a constant X temperature. What superchargers do is, they feed the engine with more air molecules by forcing air into the engine. This air enters the engine because the supercharger blows more air into the engine inlet than the engine can normally breathe on its own. The result of this ‘forced induction’ can be seen and measured in one of two ways: pressure or temperature. In an ideal world, with a supercharger at full adiabatic efficiency, we would be able to feed twice as many air molecules (to double the horsepower figure) to the engine by doubling the inlet air pressure (to 2.0 atmospheres or what we call 15 pounds). boost per square inch (PSI). In the real world, superchargers are not 100% efficient, and so it is possible that doubling the inlet boost pressure will give us less than double the horsepower because:

P*V=n*R*T Pressure increases by a factor of 2 Volume is fixed Number of gas molecules is 80% (or a factor of 1.8) Temperature increases by 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 increase in pressure is equaled by the combined effect of the increase in airflow. and the increase in temperature).

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

Assuming an inlet temperature of 80*F, we find the supercharger outlet temperature to be T2 = 309*F. Something to consider here is an intercooler or aftercooler….after the cooler are the radiators that remove heat from the compressed air. leaves the supercharger. The ideal intercooler cools the air temperature dramatically by disrupting the airflow path and with minimal pressure drop. An intercooler increases horsepower in three ways:

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

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

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

With a good intercooler, we are able to lower the air intake charge temperature to within 30 degrees of the ambient air temperature. At the same time an intercooler will have a marginal 0.5 to 1.0 psi pressure drop in the core. Given these figures, combining a supercharger with an efficient intercooler gives us a system with adiabatic efficiency very close to 100%, and means we are able to make nearly double the horsepower of our original engine’s 18psi. boost (instead of 27 without an intercooler, and instead of 15 for the ‘ideal’ supercharger) if you care to go into the math behind this scenario.

Once you have your pressure ratio, your density ratio, your intercooler outlet temperature and your overall horsepower and flow numbers, most supercharger calculators are able to give you more detailed specs for your car’s build (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 be correct. This is great information to know, as many people choose to sell pumps that use water drainage pumps and use them on boats as ‘electric’ superchargers for small displacement engines. It has been shown many times by attaching a boost gauge to the inlet of any ‘electrically supercharged’ engine that these bilge pumps have no flow or block off pressure capability to increase the boost pressure of the inlet mixture by any measurable amount. . Pressure (as we already explained) is not the only indication of forced induction… but without any pressure increase, it means that the ‘electric’ supercharger has 0% efficiency, which means that it will only be good. Heat the inlet air and no excess air flow will be shown.

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