I don't think I have ever seen a proper explanation of how to size a Rotrex for a specific engine anywhere on the entire internet - and I've been searching for a few years.
Sizing a positive displacement supercharger like an Eaton M62 or TVS1320 is simple: The volume of air on every revolution is known and it has to be stuffed into the cylinders. This gives CFM and boost versus engine RPM.
But for a Rotrex or other centrifugal supercharger it is not so simple and the relationship is highly non-linear. To my knowledge, nobody has ever given a clear explanation of how to make the calculation of estimated flowrate and boost versus RPM for a Rotrex.
The reason for this, I believe, is because "thought leaders" of supercharging theory have a bias against centrifugal superchargers, so therefore they have not bothered with any relevant analysis. And outside of a handful of these influential designers, nobody seems to have sufficient understanding of how to do it. You'd almost think it takes a PhD in Chemical Physics to solve these problems. Well maybe that's what it takes.
Here in this thread I will lift the veil, open the kimono, and perform the daring feat that has eluded so may for so long: the complete design calculation for a Rotrex, from soup to nuts, including boost curve versus RPM, and Torque and HP versus RPM estimates.
Let's start with the few basic things that almost anybody reading this should already know.
For most superchargers, including the Rotrex, the manufacturer publishes the compressor efficiency charts. For example, the following are the charts for the C38 family of Rotrex superchargers, the C38-71, C38-81, and C38-91. The C38-61 we won't bother with, it's just a toy.
![Image]()
NOTE: You can right-click on any image and select "view image" to get an exploded full-size view of the image.
The source for these charts is in the Rotrex Technical Datasheets.
Basically these charts give an description of the operational parameters of each supercharger. At any specific impeller RPM, the compressor is capable of producing a range of flowrate and pressure. This range is represented on the chart as the isocline for that RPM - these isoclines are the lines labeled 90k, 80k, 70k, et cetera. The trick is how to narrow this range to a specific point for each RPM when the compressor is matched to the engine. And how to go from there to get the boost curve and the flow rate curve for every engine RPM. This leads to the torque curve and the HP curve versus RPM. Which is exactly what we would like to know when we are designing a system.
To answer these questions we start with something very basic. What is the relation of the supercharger impeller RPM to the engine RPM, or in other words what is the engine RPM that corresponds to each isocline. Very easy, this is derived from the pulley sizes for the supercharger and for the crankshaft, in combination with the supercharger's internal drive ratio that relates is external pulley RPM to its internal impeller RPM.
RPM (engine) = RPM (impeller) x P.D. (SC) / ( P.D. (crank) x Drive Ratio (SC) )
The pulley diameter (P.D.) for the 2GR crank is 142mm. The drive ratio for the C38 series is 7.5. So for a given Rotrex pulley diameter, we can produce a table of engine RPM's that corresponds to the Rotrex isoclines. Here we show this for two different pulley diameter, 95mm and 85mm.
![Image]()
The next step is to answer the question: How much air does the engine draw at any given RPM and boost level? This is simple and not-so-simple. The mass of air drawn by a cylinder on its downstroke is:
Mass (air) = Density (air) x V(cylinder) x (Pressure ratio) x (Volumetric Efficiency)
Therefore the air drawn by the engine over time is 1/2 times this - when talking about a four-stroke engine) - times the RPM.
Mass Flow Rate (air) = Air Density x Displacement x PR x VE X RPM / 2.
Quick discussion: The pressure ratio is derived directly from boost.
PR = Pressure Ratio = 1 + Boost (psi) /14.7
The displacement is 3500 cc or 3.5 liters.
Note the air density is referenced at atmospheric pressure (14.7 psia) and corrected by the pressure ratio to give the mass of air occupying a volume under pressure. This is an outcome of the ideal gas law PV=nRT.
What about the volumetric efficiency? The volumetric efficiency is a non-linear function of flowrate which depends on RPM. For the 2GR-FE engine, the V.E. as a function of RPM can be deduced from dyno measurements. Thanks to Marc aka Gouky we have estimates of the V.E. and the flowrate as a function of RPM - these are derived from dyno measurements:
![Image]()
The volumetric efficiency depends on RPM and flowrate.Taking this into account would make the problem that we are seeking to solve non-linear, requiring an iterative solution. This is entirely do-able. However, for a first-pass solution, we will rely on a simplifying linearizing assumption that the volumetric efficiency is an invariate constant. Arbitrarily, we choose 90% as the value of the volumetric efficiency over the entire range of RPM and flowrate.
So now with these explanations and assumptions it becomes simple to calculate the the flowrate as a function of boost or pressure ratio for a given RPM. Let's start with the engine RPM 8028 that corresponds to the impeller speed 90000RPM with compressor pulley 95mm. It's easy to calculate the engine's flowrate at various levels of boost. Here is the calculation in tabular format:
![Image]()
And here the same table is represented as a chart of Pressure Ratio versus Air Flow in kg/s units for engine RPM equal to 8028:
![Image]()
What happens if we take this chart of the engine's Pressure Ratio versus Air Flow at the given RPM 8028 and superimpose it (with proper scaling of course) on the Rotrex compressor chart? Recall that the engine RPM 8028 with pulley size 95mm corresponds to an impeller RPM of 90000. And the engine pressure ratio vs. flow rate line for engine RPM=8028 intersects the compressor's isocline of pressure ratio vs. flow rate for impeller speed 90000 at a unique point [this happens to be a fundamental principle of Euclidean geometry]. This unique intersection point is in fact the predicted operating point of the turbine mounted to the engine spinning at 8028RPM with pulley size 95mm. Meaning that the predicted values of pressure ratio and flowrate of the turbine at this RPM can be read directly off the chart from this intersection point.
![Image]()
So, reading off the coordinates for the 8028 engine RPM and 90000 compressor RPM intersection point, using the red cursor lines, the values are Pressure Ratio = 2.110, Flow Rate = 0.545. This gives us our first operating point.
Now we repeat this for each of the engine RPM's that were tabulated previously, with compressor pulley diameter 95mm, corresponding to isoclines of constant impeller RPM on the compressor chart. And let's do this for all three compressors, the 71, 81, and 91. The 95mm compressor pulley matches an engine max rpm of 8028RPM to the max impeller speed of 90KRPM.
![Image]()
Next we repeat this with the 85mm pulley. This pulley matches a max engine RPM of 7183RPM to the max impeller speed of 90KRPM.
![Image]()
Keep in mind this very important point: For each engine RPM line (the colored fan lines), the only point that matters is where it intersects the impeller RPM isocline that corresponds to that engine RPM with the pulley size being used - these intersection points are the dots of the same color as each line. Each of these intersection points is the predicted operating point for pressure ratio and flowrate at that RPM with that pulley. By reading off the intersection point for each RPM, and tabulating them then charting them, we get the operating charts of boost versus RPM and flowrate versus RPM from which torque and power versus RPM can be derived.
This will be shown next...
Sizing a positive displacement supercharger like an Eaton M62 or TVS1320 is simple: The volume of air on every revolution is known and it has to be stuffed into the cylinders. This gives CFM and boost versus engine RPM.
But for a Rotrex or other centrifugal supercharger it is not so simple and the relationship is highly non-linear. To my knowledge, nobody has ever given a clear explanation of how to make the calculation of estimated flowrate and boost versus RPM for a Rotrex.
The reason for this, I believe, is because "thought leaders" of supercharging theory have a bias against centrifugal superchargers, so therefore they have not bothered with any relevant analysis. And outside of a handful of these influential designers, nobody seems to have sufficient understanding of how to do it. You'd almost think it takes a PhD in Chemical Physics to solve these problems. Well maybe that's what it takes.
Here in this thread I will lift the veil, open the kimono, and perform the daring feat that has eluded so may for so long: the complete design calculation for a Rotrex, from soup to nuts, including boost curve versus RPM, and Torque and HP versus RPM estimates.
Let's start with the few basic things that almost anybody reading this should already know.
For most superchargers, including the Rotrex, the manufacturer publishes the compressor efficiency charts. For example, the following are the charts for the C38 family of Rotrex superchargers, the C38-71, C38-81, and C38-91. The C38-61 we won't bother with, it's just a toy.
NOTE: You can right-click on any image and select "view image" to get an exploded full-size view of the image.
The source for these charts is in the Rotrex Technical Datasheets.
Basically these charts give an description of the operational parameters of each supercharger. At any specific impeller RPM, the compressor is capable of producing a range of flowrate and pressure. This range is represented on the chart as the isocline for that RPM - these isoclines are the lines labeled 90k, 80k, 70k, et cetera. The trick is how to narrow this range to a specific point for each RPM when the compressor is matched to the engine. And how to go from there to get the boost curve and the flow rate curve for every engine RPM. This leads to the torque curve and the HP curve versus RPM. Which is exactly what we would like to know when we are designing a system.
To answer these questions we start with something very basic. What is the relation of the supercharger impeller RPM to the engine RPM, or in other words what is the engine RPM that corresponds to each isocline. Very easy, this is derived from the pulley sizes for the supercharger and for the crankshaft, in combination with the supercharger's internal drive ratio that relates is external pulley RPM to its internal impeller RPM.
RPM (engine) = RPM (impeller) x P.D. (SC) / ( P.D. (crank) x Drive Ratio (SC) )
The pulley diameter (P.D.) for the 2GR crank is 142mm. The drive ratio for the C38 series is 7.5. So for a given Rotrex pulley diameter, we can produce a table of engine RPM's that corresponds to the Rotrex isoclines. Here we show this for two different pulley diameter, 95mm and 85mm.
The next step is to answer the question: How much air does the engine draw at any given RPM and boost level? This is simple and not-so-simple. The mass of air drawn by a cylinder on its downstroke is:
Mass (air) = Density (air) x V(cylinder) x (Pressure ratio) x (Volumetric Efficiency)
Therefore the air drawn by the engine over time is 1/2 times this - when talking about a four-stroke engine) - times the RPM.
Mass Flow Rate (air) = Air Density x Displacement x PR x VE X RPM / 2.
Quick discussion: The pressure ratio is derived directly from boost.
PR = Pressure Ratio = 1 + Boost (psi) /14.7
The displacement is 3500 cc or 3.5 liters.
Note the air density is referenced at atmospheric pressure (14.7 psia) and corrected by the pressure ratio to give the mass of air occupying a volume under pressure. This is an outcome of the ideal gas law PV=nRT.
What about the volumetric efficiency? The volumetric efficiency is a non-linear function of flowrate which depends on RPM. For the 2GR-FE engine, the V.E. as a function of RPM can be deduced from dyno measurements. Thanks to Marc aka Gouky we have estimates of the V.E. and the flowrate as a function of RPM - these are derived from dyno measurements:
The volumetric efficiency depends on RPM and flowrate.Taking this into account would make the problem that we are seeking to solve non-linear, requiring an iterative solution. This is entirely do-able. However, for a first-pass solution, we will rely on a simplifying linearizing assumption that the volumetric efficiency is an invariate constant. Arbitrarily, we choose 90% as the value of the volumetric efficiency over the entire range of RPM and flowrate.
So now with these explanations and assumptions it becomes simple to calculate the the flowrate as a function of boost or pressure ratio for a given RPM. Let's start with the engine RPM 8028 that corresponds to the impeller speed 90000RPM with compressor pulley 95mm. It's easy to calculate the engine's flowrate at various levels of boost. Here is the calculation in tabular format:
And here the same table is represented as a chart of Pressure Ratio versus Air Flow in kg/s units for engine RPM equal to 8028:
What happens if we take this chart of the engine's Pressure Ratio versus Air Flow at the given RPM 8028 and superimpose it (with proper scaling of course) on the Rotrex compressor chart? Recall that the engine RPM 8028 with pulley size 95mm corresponds to an impeller RPM of 90000. And the engine pressure ratio vs. flow rate line for engine RPM=8028 intersects the compressor's isocline of pressure ratio vs. flow rate for impeller speed 90000 at a unique point [this happens to be a fundamental principle of Euclidean geometry]. This unique intersection point is in fact the predicted operating point of the turbine mounted to the engine spinning at 8028RPM with pulley size 95mm. Meaning that the predicted values of pressure ratio and flowrate of the turbine at this RPM can be read directly off the chart from this intersection point.
So, reading off the coordinates for the 8028 engine RPM and 90000 compressor RPM intersection point, using the red cursor lines, the values are Pressure Ratio = 2.110, Flow Rate = 0.545. This gives us our first operating point.
Now we repeat this for each of the engine RPM's that were tabulated previously, with compressor pulley diameter 95mm, corresponding to isoclines of constant impeller RPM on the compressor chart. And let's do this for all three compressors, the 71, 81, and 91. The 95mm compressor pulley matches an engine max rpm of 8028RPM to the max impeller speed of 90KRPM.
Next we repeat this with the 85mm pulley. This pulley matches a max engine RPM of 7183RPM to the max impeller speed of 90KRPM.
Keep in mind this very important point: For each engine RPM line (the colored fan lines), the only point that matters is where it intersects the impeller RPM isocline that corresponds to that engine RPM with the pulley size being used - these intersection points are the dots of the same color as each line. Each of these intersection points is the predicted operating point for pressure ratio and flowrate at that RPM with that pulley. By reading off the intersection point for each RPM, and tabulating them then charting them, we get the operating charts of boost versus RPM and flowrate versus RPM from which torque and power versus RPM can be derived.
This will be shown next...
