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The pressure drop in the venturi is proportional to air density and the fuel is at ambient pressure in the float chamber, so I would expect the fuel flow to reduce proportionally with density, and that response to preserve the fuel-air ratio over changing altitude.

But in practice that does not seem to be the case. Proper response to altitude requires additional modification that most carburetors don't have, so the pilot usually has to lean out the engine as they climb. What am I missing here?

(Update) More specifically, I would expect that at the same RPM, the volume flow rate will be the same—because the engine pulls in its displacement per revolution. Now velocity in the venturi $v$ is just

$$ v = \frac{\dot V}{A} $$

Where $\dot V$ is the volume flow rate and $A$ is the cross-section of the venturi. So it will also be the same independent of altitude. Since dynamic pressure

$$ p_d = \frac 1 2 \rho v^2 $$

And that is also the pressure that pulls in the fuel (when the float chamber is open to ambient pressure). Substituting mass flow

$$ \dot m = \rho v $$ $$ p_d = \dot m \frac 1 2 v $$

and as long as $v$ is mostly constant,

$$ p_d \sim \dot m $$

This still leaves open the dependence of fuel flow on $p_d$. If the relation is reasonably close to linear, it should mean the venturi mixes properly by mass. I can see a reason why higher pressure should cause less than linear increase in fuel flow, but not much why it should cause more than linear increase in fuel flow—but that is what the actual behaviour would need.

Note: Did you notice the extra $v$ conspicuously missing from the last equation? That suggests the mixture should become richer with throttle opening—which is actually the reason there are extra fuel jets after the throttle that pull in extra fuel when the throttle is at idle and slightly above. It might also explan what is going on here, but would require explaining why the speed should increase when the density is lower.

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  • $\begingroup$ The fuel could be going through an engine driven fuel pump. Then the fuel might not be at ambient pressure. $\endgroup$ – Jan Jan 23 at 7:20
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    $\begingroup$ @Jan is on right track, fuel orifice is designed to add excess fuel even below sea level. Fuel lean control valve pinches off fuel flow VOLUME, to maintain proper mixture at all altitudes. Air density changes with altitude, fuel density does not. It has to be adjusted. $\endgroup$ – Robert DiGiovanni Jan 23 at 14:30
  • $\begingroup$ Possible duplicate question: aviation.stackexchange.com/questions/24097/… $\endgroup$ – Mike Sowsun Jan 23 at 14:57
  • $\begingroup$ @MikeSowsun, no, that is not a duplicate. The question asks about what the mixture should be. $\endgroup$ – Jan Hudec Jan 23 at 19:15
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The simple reason is that high altitude changes the density of air, but not the density of fuel.

Most simple carburetors use a simple venturi design that mixes air and fuel by VOLUME.

But, the correct air/fuel mixture must be based on MASS, not Volume.

If the air/fuel Volume is correct at sea level, it will be too rich at altitude. This is because a given volume of air will have less Mass at high altitude, while a given volume of fuel will have the same Mass at high altitude.

Aircraft carburetors have a mixture control to "lean" the volume of fuel to the volume of air, and are then able to maintain the correct air/fuel ratio at all altitudes.

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    $\begingroup$ But why does it mix by volume? As the same volume of air flows by (if rpm stays the same, it should), it generates less pressure difference (because that is proportional to density) and therefore pulls in less fuel—by both volume and mass, because density of that didn't change. But it pulls less, proportionally by density of the air, therefore mixing properly by mass, not by volume. I understand there is an error in that reasoning, because it does not match the reality—but I am asking where specifically. $\endgroup$ – Jan Hudec Jan 23 at 19:40
  • $\begingroup$ It must be simple physics. I guess the venturI effect is more dependent on the velocity of the air rather than the mass of the air. $\endgroup$ – Mike Sowsun Jan 23 at 21:06
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    $\begingroup$ It is probably simple physics, but not exactly obvious. In either case, the Venturi effect is simply the kinetic term of Bernoulli's equation, so density and square of velocity, but I don't see a reason for the velocity to be higher (piston engines are constant volume, which suggests it should be the same). $\endgroup$ – Jan Hudec Jan 23 at 21:17
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Leaning is not done to counter carburetors that do not "preserve the fuel-air ratio over changing altitude".

The [operationally] ideal stoichiometry (air:fuel ratio) is not fixed, it depends on what is being sought. Leaning is done because it provides better fuel consumption when less than full power is needed (see graph below), which coincides with cruise.

enter image description here

Rich mixtures also burn cooler, so leaning becomes practicable and easier on the engine in the colder air of the cruise altitudes.

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  • $\begingroup$ But do carburetors preserve the fuel-air ratio over changing altitude? At least the simulator thinks they definitely don't. $\endgroup$ – Jan Hudec Jan 23 at 21:33
  • $\begingroup$ @JanHudec - My understanding is that main metering circuits "provide a constant fuel–air ratio at any engine speed and condition above the engine’s idle speed". $\endgroup$ – ymb1 Jan 23 at 21:51
  • $\begingroup$ It certainly would make sense. Because, after all, the pressure difference does depend on density. $\endgroup$ – Jan Hudec Jan 23 at 22:02
  • $\begingroup$ @JanHudec - That's the way I see it too. If the differential pressure were to be fixed at high altitude, then the fuel mass would come into play, but I don't see how. $\endgroup$ – ymb1 Jan 23 at 22:18
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    $\begingroup$ @Jan Hudec Pondered a little more. Your points regarding the carburetor are very good and, once again, got me thinking. Exhaust and prop were considered. It may be we "lean" for altitude in a fixed pitch aspirated carb engine because less power is required to spin the prop at a given rpm. Notice rpm is limiting. This may also play into service ceiling for these types of air craft. The rpm limit. Look forward to more comments. Great site! $\endgroup$ – Robert DiGiovanni Jan 24 at 1:04
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It's not pressure that forces fuel into the venturi as much as the vacuum pressure sucking it out. Fuel is pumped or gravity fed to the carb, but then it's metered into the bowl by the float. Fuel sits in the bowl before getting pulled into the jets and then into the venturi. There is air in the bowl, sure, and as that air pressure decreases with altitude there is a bit of a decrease in the pressure behind the fuel, however the part you may be missing is that air can mix with a much higher ratio of fuel than what is ideal for an engine. Airplane engine carbs are generally tuned so at sea level they deliver slightly over the ideal ratio, this is done by restricting the fuel flow. If it wasn't restricted the engine would run rich on the ground.

As density altitude increases the amount of air going through the venturi decreases, but the air still can hold more fuel so the mixture richens even though there's less pressure.

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  • $\begingroup$ What amount of fuel the air “can” hold is not really relevant. The amount it pulls in is. The amount it pulls in depends on the pressure drop in the venturi. But this pressure drop decreases linearly with the density of that air. So why does the amount of fuel pulled in not decrease the same way? $\endgroup$ – Jan Hudec Jan 23 at 19:43
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First the float chamber. Fuel flow into the float chamber and out into the carburetor venturi functions exactly like a toilet bowl irrespective of whether the fuel is pumped or gravity fed. As fuel level drops the float opens a valve to allow more fuel into the chamber.

The explanation of fuel/air mixture relative to altitude is explained in "Flight Mechanic" as follows: fuel draw into the venturi is dependent on airstream velocity. There for, as air density decreases with altitude, the fuel air mixture reaching the cylinder through the intake manifold will be richer. This is why fuel mixture is "leaned" with altitude.

Post Script: ymb1 may be closest here. It may be we do not lean for high altitude, we richen for lower altitude. This is because more power (Fuel burn) is required for take-off or go-around. Full Rich is selected to avoid overheating the engine. At cruise power demands are less, therefor more economical lean can be selected. Although gas is wasted at full rich, it does serve a critical function of keeping engine cooler at max power output.

There for, the carburetor fuel aspirator oriface is designed to give a rich fuel mixture, that can be leaned (pinched) by the pilot with the fuel mixture control.

Addendum to Post Script: The crux seems to be "at constant (cylinder) volume, RPM, throttle, and rich control settings, does fuel/air mixture change with altitude (ambient pressure). This could be easily tested in a room where "altitude" can be adjusted (CO meters please). Lower ambient pressure should result in lower fuel intake, as Jan Hudec suggests, due to lower pressure differential, but other factors may be at work here. Rate of fuel evaporation will increase at lower pressures significantly, which may account for richening of mixture. Also, positioning of fuel oriface in the carburetor (why not after the venturi where vacuum is greater?) could be tested as well.

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    $\begingroup$ Sorry, but that is missing a huge step in the derivation. The fuel drawn into the venturi is dependent on the airstream velocity—which I believe should stay roughly the same—*and the density*. Therefore, as air density decreases, the expectation would be that the flow decreases accordingly. $\endgroup$ – Jan Hudec Jan 23 at 19:47
  • $\begingroup$ @Jan Hudec The best way is to pull apart a carburetor. The fuel drawn into the carburetor is limited by the fuel intake needle valve. It is not dependent solely on Air flow. I would not ponder too much on these types of carburetors, they are primitive and inefficient compared with supercharging and fuel injection for 2 reasons: drawing vacuum must costs the engine power and vacuum aspiration of fuel risks icing of carb. Notice all kinds of screws and air vents are added to try perfect it, but their purely mechanical simplicity does have appeal. $\endgroup$ – Robert DiGiovanni Jan 23 at 23:40
  • $\begingroup$ Actually, the fuel drawn into the carburetor is dependent solely on the air flow. The needle valve is just a typical pressure reduction valve that lets in as much fuel as was drawn out by the injector while keeping it at the reference, ambient, pressure. $\endgroup$ – Jan Hudec Jan 24 at 6:20
  • $\begingroup$ Ok, the (terminology) fuel drawn into the intake manifold (sorry) is limited by the fuel rich knob. It is not dependent solely on Air flow. We must also realize gasoline will combust in a wide range of fuel/air mixtures. 🙄 It will also "boil" faster at lower pressures too! Will continue to tease out the important factors. It looks like "leaning for altitude" is more like "leaning for economy at lower power setting where overheating is less of an issue". Thanks. $\endgroup$ – Robert DiGiovanni Jan 24 at 9:04

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