Atmospheric factors affecting the power of a reciprocating engine

[deputc26]

I am currently a flight instructor and I have seen numerous performance charts that show the performance (max horsepower) of a reciprocating engine decreasing more rapidly than the density of the air. Air density (to my mind) should be the ONLY factor affecting recip output as it should be directly proportional to oxygen available.

apparently I am missing something...

 

[reallyscrued]

Maybe it is proportional, but exponentially and not linearly like you imagine.

<talking out of my ass.

 

[eLiu]

If you make all of the idealizing assumptions, the power output of an internal combustion (otto cycle) engine is: Cp*(T3-T4)*mdot (per cylinder) where Cp is the specific heat of air at const pressure, mdot is the mass flow rate of air through the device, T3 is the air temp as the piston begins down-stroke, and T4 is the air temp at the end of the down-stroke.

Density goes down exponentially with altitude, so if T3 and T4 were constant, the power would indeed scale with density. But T3 and T4 won't be the same at all altitudes. First, for ideal gas & isentropic process (so everything is ideal and happy), T4 and T3 are related--if I know one I can find the other. So T3 is reached by burning fuel. The relation for this is qdot = Cv*(T3-T2)*mdot, where Cv is the specific heat of air at const volume, T2 is the air temp as the piston reaches the top of its stroke (like right before the spark fires), and qdot is the heat/time generated by burning fuel. To raise qdot, you'd want more airflow and more fuel. So as the amount of airflow drops b/c density is falling, you will also get less energy from each 4stroke cycle.

So basically I think the underlying reason for what you're observing is that at altitude, you also generate less energy per cycle in addition to simply having less mass flow.

But horsepower isn't it. Owing to the reduced density, prop performance and lift will similarly be reduced meaning the plane's performance will be worse across the board.

 

[reallyscrued]

^ That's what I meant.

 

[gsellis]

Add to this that the envelope for fuel to air for gasoline is very small. You cannot rich the mixture to compensate for the reduced air density. With alcohol you could, but it has less energy. And adding fuel just reduces range even further. And still, alcohol just reduces the effects of the inevitable. You run out of O2.

 

[deputc26]

eLiu it seems like you understand this well but I still don't understand this statement (or the answer to my question)

So basically I think the underlying reason for what you're observing is that at altitude, you also generate less energy per cycle in addition to simply having less mass flow.

How is generating less energy per cycle separate from reduced mass flow? isn't the former simply a product of the latter? Are you saying that thermal efficiency goes down as a result of the less energetic combustion? or that delta T (between T3 and T4) can change (significantly) independent of compression ratio?

But horsepower isn't it. Owing to the reduced density, prop performance and lift will similarly be reduced meaning the plane's performance will be worse across the board.

This is not really true unless your prop is fixed pitch and thus rpm limited, aerodynamic performance generally increases with altitude because aircraft will fly at a constant q given constant power (neglecting compressibility effects) of course to achieve the same q at lower density you must increase V resulting in a greater true airspeed per unit power. But in the normally aspirated aircraft that I'm talking about power does not remain constant... actually now that I think about it this isn't relative to my original discussion because the observation that surprised me was greater than expected decrease in published power not performance.

for the record I understand that density does not decrease linearly with altitude, I believe that reallyscrued is saying that relative to density, power decreases exponentially rather than in a linear fashion. Could this be because frictional losses remain constant at a given rpm instead of decreasing with power output resulting in an increasing percentage of power going to fight friction instead of doing useful work?

Thanks again you guys, there's not many places you can find truly knowledgeable people willing to answer questions like these.

 

[PlasmaBomb]

You already know that as altitude increases air density decreases.

Also -
Altitude decreases the fuels resistance to detonation. So engine timing will need to be altered, sacrificing power.
The composition of the air changes, not only is there less air, there is less oxygen in the air that is there!
The humidity of the air at varying altitudes will be different
The volumetric efficiency of the engine can take a massive hit -

A 200 m change on the altitude of the engine, corresponding to a change in atmosphere pressure of about 3000 Pa, may lead to change fuel consumption and volumetric efficiency up to 40%.

 

[KIAman]

BUT... consider that higher altitude has lower density of air which allows reduces the friction on the airplane thus leading to an increased perception of power. I think in the OP's example, there is no typical norm, rather this is specific to the type of aircraft and engine.

 

[deputc26]

Thanks PLasma Bob I didn't know altitude decreased the fuels resistance to combustion. The composition of the air does not however change significantly with increasing altitude.

 

[skyking]

Originally posted by: PlasmaBomb
You already know that as altitude increases air density decreases.

Also -
Altitude decreases the fuels resistance to detonation. So engine timing will need to be altered, sacrificing power.
The composition of the air changes, not only is there less air, there is less oxygen in the air that is there!
The humidity of the air at varying altitudes will be different
The volumetric efficiency of the engine can take a massive hit -

A 200 m change on the altitude of the engine, corresponding to a change in atmosphere pressure of about 3000 Pa, may lead to change fuel consumption and volumetric efficiency up to 40%.

The typical general aviation engine has fixed timing. The newer FADEC designs may incorporate variable ignition timing but those are the exception in the market.

 

[deputc26]

Originally posted by: skyking

Originally posted by: PlasmaBomb
You already know that as altitude increases air density decreases.

Also -
Altitude decreases the fuels resistance to detonation. So engine timing will need to be altered, sacrificing power.
The composition of the air changes, not only is there less air, there is less oxygen in the air that is there!
The humidity of the air at varying altitudes will be different
The volumetric efficiency of the engine can take a massive hit -

A 200 m change on the altitude of the engine, corresponding to a change in atmosphere pressure of about 3000 Pa, may lead to change fuel consumption and volumetric efficiency up to 40%.

The typical general aviation engine has fixed timing. The newer FADEC designs may incorporate variable ignition timing but those are the exception in the market.

How does timing interact with decreased density to further decrease power.

Re: FADEC -To bad Thielert went belly up, their engines had almost exactly twice the efficiency of an io-360!