The EatonM45 supercharger (typically salvaged from a MiniCooperS or available new from Eaton) is a popular addition to many smaller four piston engines, and the 1800cc BMW 16V M42 engine is no exception. In fact, due to the reasonably high volumetric efficiency of this 16V engine, the M42 is an ideal candidate for the M45 supercharger.
Before we consider how the BMW M42 engine will respond to the fitment of an Eaton M45 roots pump, you need to be aware of a few basic facts: The mechanical work output (power output, typically measured in units of horsepower or kilowatts) of any engine is a direct function of the mass of air inducted into the engine and, as one would expect, the mass of fuel combusted with the inducted air. Now, the mass of fuel that may be combusted (oxidised) successfully during the combustion process is entirely dependant upon the mass of air inducted into the combustion chamber. Thus, to increase the power output of an engine it is necessary, first and foremost, to increase the mass of air inducted into an engine, before contemplating increasing the mass of fuel to be combusted with the increased mass of air. One of the most popular techniques employed to increase the mass of air inducted into an engine is to afix an air pump of some description (such as a supercharger or turbocharger) to the engine. Another (less popular) technique is to induct Nitrous-Oxide (laughing gas) which, upon heating, liberates copious quantities of oxygen to the combustion reaction as the Nitrous-Oxide decomposes into Nitrogen and Oxygen.
Thus, to estimate the power output of a forced induction engine you first and foremost need to determine how much air the engine will forcibly induct as a function of engine speed. To aid us in this task manufacturers of turbochargers and superchargers supply flow maps for their compressors. Below is the flow map for the Eaton M45 supercharger, supplied by Eaton.
Figure 1: Eaton M45 roots pump flow map.
However, before we can successfully use this rather formidable looking graph we need to understand what it tells us. Ignoring (for the moment) the blue circles, figure 1 shows us the ratio of the compressor outlet to inlet air pressure (on the Y-axis) as a function of the volume of air flowed through the compressor (X-axis) at a particular compressor speed (the pale green dotted lines).
For example, looking closely at figure 1, we see that if we were to rotate the compressor input shaft at a speed of 8000rpm (see the dotted pale green line marked ”a8000”a) such that we induct 300 cubic meters of air per hour through the compressor, the air pressure at the outlet of the M45 roots pump will be roughly 1.35 times greater than at the inlet. Thus, if you are fortunate enough to live at a sea level with a daily barometric air pressure of 1bar, you would expect to measure an absolute pressure of 1.35bar at the compressor outlet. However, since your typical boost gauge measures gauge (relative) pressure (not absolute pressure) you would read this as 0.35bar or 5.1psi of boost. That is to say, an outlet pressure 0.35bar greater than the inlet pressure.
Now, a few facts about roots pumps to help you better understand figure 1. Roots pumps, due to the way they work, pump a roughly constant volume of air for each rotation of the compressor input shaft. The Eaton M45 is stated by Eaton to pump 0.75 litres (that’s 0.00075 cubic meters) of air per each revolution of the input shaft. Thus, at a shaft speed of say 10000rpm we would expect the EatonM45 to pump
regardless of the inlet to outlet pressure ratio.
A quick review of figure 1 indicates that this is not the case, and for very good reason. In fact, at a pressure ratio of 1 (with both the inlet and outlet open to atmospheric pressure) the Eaton M45 roots pump is only capable of pumping roughly 410 cubic meters of air per hour (40 cubic meters per hour less than our calculated value of 450 cubic meters per hour). Furthermore, as the pressure ratio is increased the flow rate is observed to drop. This is due to the fact that roots pumps are notorious for the fact that the blades of the compressor rotors do not form a perfect seal against each other or against the rotor housing, and thus they leak air. If they formed a perfect seal, each of the dotted pale green lines in figure 1 would rise vertically up the graph. However, because the roots pump rotors leak a small amount of air, the volume of air pumped past the rotors decreases marginally (for a given shaft speed) as the pressure ratio is increased. This explains the tendency of the dotted green lines or ”aisospeeds”a as they are termed, (since the dotted green lines represent the performance of the pump at constant rotational speed), to peel off backwards as the pressure ratio rises.
Finally, we see that figure 1 includes a number of concentric circles ranging in colour from dark blue (inner circle) to pale blue (outermost circle), and that the perimeter of each circle has a number on it. These circles indicate zones of efficiency and provide the user with an indication of what fraction of the power required to turn the compressor input shaft is actually put to useful work pumping air. Armed with this knowledge you will no doubt conclude that in order to get the most out of your Eaton M45 roots pump you would do best to operate it in the zone of maximum efficiency, that is to say, within the dark blue centre circle at an efficiency (from the number along the side) of roughly 67%. Outside of this circle we can see the efficiency of the pump progressively falls.
So, if we put 1kW of work into driving a compressor that is only 67% efficient, what happens to the remaining 33% that isn’t being used to compress the air inducted through the compressor rotors? The simple answer is that it is turned to heat. That is to say, 330W of the 1kW power input to the compressor shaft heats the pump rotors and the pump housing. And it doesn’t end here. Since the air passing through the compressor is cooler than the compressor, this heat is transferred to the air that is ultimately inducted into your engine. Although it is true to say that some of this heat is radiated away from the pump body into the engine bay, the great majority is transferred to the pumped air.
Since roots pumps are generally the most inefficient of the forced induction pumps, they have a reputation for transferring the most heat to the air inducted into the engine. However, as with any forced induction pump, this can be dealt with by means of a water-to-air or air-to-air intercooler mounted after the pump.
Now, you may ask, why is it necessary to cool the air leaving the pump? After all, your typical engine runs fairly hot and it’s not as if a bit of hot air down the inlet manifold is going to hurt the engine ”“ is it? There are actually two reasons why the air should be cooled before entering the engine. The first, and most important, is due to the fact that the power output of an engine has very little to do with the pressure to which the pump pumps the inlet manifold. It has, more specifically (as stated in the third paragraph of this post) to do with the mass of air, inducted into the engine, and the relationship between the mass of air inducted into and engine and the pressure at which is inducted, depends upon, you guessed it, the temperature of the air. Point of fact, regardless of the pressure at which you pump air into your engine, the cooler the air, the greater the mass of air you will induct into your engine and thus the greater the power your engine will be able to deliver (with the right amount of fuel combined, obviously). This is why I find the habit of quoting the value to which various engines have been boosted so damn ridiculous. I couldn’t actually care to what pressure you have boosted your engine, I care more about the mass of air you are flowing into your engine. Put another way, to say that one engine produces 200hp at 5000rpm and 1bar boost does not mean that another identical engine will produce 200hp at 5000rpm and 1bar boost when the two identical engines have different methods of forced induction and entirely different capacity intercoolers. They could, quite easily (and in fact most likely) be inducting entirely different masses of air, albeit at the same pressure.
The second reason for wanting to keep the air cool is the occurrence of detonation. Detonation is a phenomenon that occurs in the combustion chamber (in place of combustion) when the fuel and air are combined under conditions of high pressure and/or high temperature. I won’t go into the physics of exactly what constitutes a detonation here, but a detonation is, as you have probably guessed, a violent explosion of the fuel rather than a progressive burn. Needless to say, sustained detonation of the fuel in the combustion chamber is not a good thing due to the likelihood of damage to the engine. Aside from the benefit of inducting the maximum mass of air into the engine, keeping the temperature of the air as cool as possible is one mechanism to avoid detonation when operating the engine at high pressure (such as in the case of a high air-pump pressure of high compression ratio).
In my next post I will explain how to calculate the mass of air inducted into the combustion chambers using some basic facts about the M42 engine. We will then look at how to interpret this data to estimate the engines power output at various engine rpm.
