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Rotax engines have no mixture control, yet they don't seem to have any more problems than other engines at altitude. How do they handle the lower air density in order to not get a too rich a mixture?

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According to this owners manual

4.5 High altitude compensator (H.A.C. kit)

H.A.C. is a high altitude compensator developed by ROTAX which adjusts the air/ fuel mixture automatically from sea level to 6500 m altitude using a special BING carburetor.

This page has information on how the Bing carburetor works (with pictures!):

Here's how it works

Did you ever wonder what makes fuel flow up the jets, from the carburetor float bowl, enroute to the engine? Is it vacuum at the venturi? That's not quite descriptive enough. It is better defined as a differential pressure between the float bowl and the venturi. What's the pressure in the float bowl? Here is an important hint, the bowl is vented to outside atmosphere. So, it should be the same atmosphere, or ambient pressure, that's feeding the airfilter. If it is not, the differential between the venturi and float bowl is going to change and so will the mixture...Maybe richer, maybe leaner. Just think of that for a second. If fuel air mixture can be thrown off, accidentally by improperly venting the the float bowls, why not control the venting to effectively control mixture? That's exactly what your Bing 54 can do, automatically, when a High Altitude Compensator is added. If pressure in the float bowl is reduced, relative to the venturi, less fuel makes its way up the jets, and consequently, mixture is leaner.

The HAC unit has two chambers separated by a diaphragm. One chamber is completely sealed (except during calibration) and air density within remains constant. The other has airfilter, float bowl, and venturi connections, so air density on this side is variable. It is in this chamber, that ambient pressure can be reduced by feeding it to the venturi via a connection on late model carburetors. The amount of ambient reduction is controlled by a tapered needle which changes position with deflection of the diaphragm. Think of the diaphragm as a flexible wall between two chambers that allows the sealed side to expand or contract as changes in ambient pressure occur on the other side. The reduced (from ambient) pressure gets routed to the float bowl(s) via their vent lines with a resulting leaning affect.. If that supply of low pressure is shut off, float bowl pressure returns to ambient, and the mixture goes as rich as the jets will allow. With HAC installations, standard jetting starts out several steps richer. This is why we say the default, or failure mode is typically toward the rich side.

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The simple answer to this, is that Rotax employs Constant Depression carburetors, which is a type of Variable-Venturi carburetor. In essence the fuel/air ratio is adjusted automatically based on air pressure.

The fuel jet opening is varied by a tapered needles that slides inside the fuel jet and is controlled by a vacuum operated piston.

enter image description here

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