Spindash64
Airman
- 88
- Oct 21, 2021
From what I can tell, a centrifugal supercharger essentially "multiplies" the input air pressure to a new, output air pressure, by increasing density along with some increase in air temperature. The relationship of this pressure ratio with speed eludes me, but with most aircraft engines of WWII using constant rpm props (thus making unintended fluctuations in rpm rare) and with these engines developing their best power and efficiency in a relatively narrow band, this shouldn't introduce TOO much variability.
Also, supposedly ambient air pressure drops by roughly 1"HG per 1,000ft, and it appears to be relatively linear for the altitudes aircraft can actually fly at
If this understanding is correct, then:
An R-2800-8, with only the main blower active (thus I don't need to worry about multi stages yet, although there may be some after-cooling I'm not aware of), can generate 2,000hp at 2,700rpm at the first critical altitude (so no throttling losses) of around 1,000ft (I assume this is without ram), when using 53"Hg (I don't have a way to double check the manifold pressure, but I'm confident it's within 10% of that). Ambient air pressure at this altitude should be around 29" (30 - 1). If this is the case, the main blower should be able to put out a maximum pressure ratio of 53/29 = 1.83.
Additionally, if this math is correct, climbing to 10,000ft without engaging the aux blower (and still at engine rpm of 2,700) should take the ambient air pressure of 30-10 = 20", and multiply it by 1.83, giving 36.5" Hg. I can't just do a direct multiplier to the crit Alt 1 engine power to see what the resulting power is at this Alt (or at least I don't believe I can, since that wouldn't account for the power being used to drive the supercharger), but if I did, we would have less than 1,400hp.
Because this is just a pressure RATIO, if we run the aircraft at some lower manifold pressure (but the same rpm), the critical altitude will actually increase, as we simply don't NEED as much extra air for this lower power setting, and it can thus be held to a higher altitude. ie, we can hold 40" even when ambient pressure is 22", at 8000ft
Attempting to run this 1.83 pressure ratio at exactly sea level, and/or with significant ram air effect, would result in a slight overboost (slight in this case because the critical altitude I used is so incredibly low. But it's the best data I could find in my crappy, quarter built data sheets for a single stage crit Alt and a known map). Because of this, the engine must be throttled slightly, which actually results in losing not just the power of the extra boost, but an additional loss due to lowered efficiency of a throttled compresser. I don't know how much these throttling losses work out to, unfortunately, but they appear to be VERY roughly between 1 half and 1 quarter the slope of power loss for increasing altitude: ie. going 1,000ft below critical pressure altitude appears to result in the same general power reduction as going somewhere between 250ft and 500ft above critical pressure altitude.
I know that Multi-stage supercharging has greater efficiency than single stage, and I believe that inter and after cooling also have direct effects on the end pressure ratio for a given "system setting" of supercharger speeds, in addition to the charge cooling allowing a higher maximum safe map. I unfortunately don't know how MUCH that affects things. I also don't know how to determine the needed "drive power" for a given compression ratio. Since compressor rpm is usually directly proportional to engine rpm, it seems like it could be expressed as what fraction of gross torque is needed, but that might just make things more confusing. I know MUCH of this will depend on the specific engine and specific supercharger and their respective mechanical efficiency, but it seems safe to assume that the majority of the power required is being used to compress the air rather than overcome mechanical friction
Also, supposedly ambient air pressure drops by roughly 1"HG per 1,000ft, and it appears to be relatively linear for the altitudes aircraft can actually fly at
If this understanding is correct, then:
An R-2800-8, with only the main blower active (thus I don't need to worry about multi stages yet, although there may be some after-cooling I'm not aware of), can generate 2,000hp at 2,700rpm at the first critical altitude (so no throttling losses) of around 1,000ft (I assume this is without ram), when using 53"Hg (I don't have a way to double check the manifold pressure, but I'm confident it's within 10% of that). Ambient air pressure at this altitude should be around 29" (30 - 1). If this is the case, the main blower should be able to put out a maximum pressure ratio of 53/29 = 1.83.
Additionally, if this math is correct, climbing to 10,000ft without engaging the aux blower (and still at engine rpm of 2,700) should take the ambient air pressure of 30-10 = 20", and multiply it by 1.83, giving 36.5" Hg. I can't just do a direct multiplier to the crit Alt 1 engine power to see what the resulting power is at this Alt (or at least I don't believe I can, since that wouldn't account for the power being used to drive the supercharger), but if I did, we would have less than 1,400hp.
Because this is just a pressure RATIO, if we run the aircraft at some lower manifold pressure (but the same rpm), the critical altitude will actually increase, as we simply don't NEED as much extra air for this lower power setting, and it can thus be held to a higher altitude. ie, we can hold 40" even when ambient pressure is 22", at 8000ft
Attempting to run this 1.83 pressure ratio at exactly sea level, and/or with significant ram air effect, would result in a slight overboost (slight in this case because the critical altitude I used is so incredibly low. But it's the best data I could find in my crappy, quarter built data sheets for a single stage crit Alt and a known map). Because of this, the engine must be throttled slightly, which actually results in losing not just the power of the extra boost, but an additional loss due to lowered efficiency of a throttled compresser. I don't know how much these throttling losses work out to, unfortunately, but they appear to be VERY roughly between 1 half and 1 quarter the slope of power loss for increasing altitude: ie. going 1,000ft below critical pressure altitude appears to result in the same general power reduction as going somewhere between 250ft and 500ft above critical pressure altitude.
I know that Multi-stage supercharging has greater efficiency than single stage, and I believe that inter and after cooling also have direct effects on the end pressure ratio for a given "system setting" of supercharger speeds, in addition to the charge cooling allowing a higher maximum safe map. I unfortunately don't know how MUCH that affects things. I also don't know how to determine the needed "drive power" for a given compression ratio. Since compressor rpm is usually directly proportional to engine rpm, it seems like it could be expressed as what fraction of gross torque is needed, but that might just make things more confusing. I know MUCH of this will depend on the specific engine and specific supercharger and their respective mechanical efficiency, but it seems safe to assume that the majority of the power required is being used to compress the air rather than overcome mechanical friction
