# At what Mach number does a fan jet become more efficient than a turboprop?

Dynamic pressure is based on air density and the true airspeed of an aircraft. As one climbs, indicated airspeed can remain constant as true airspeed climbs, resulting in only minor changes in Reynolds number (therefor performance) until critical Mach number is approached.

This was shown in 1937, when a biplane flew to over 50,000 feet.

However, a propeller must spin faster and increase its pitch as True airspeed increases and air density decreases. Fans are already supersonic and seem to suffer less by increasing RPM.

Although turboprops are clearly more efficient lower and slower, is there a "cross-over" point where it is more fuel efficient to have a fan jet engine in terms of thrust per gallons of fuel consumed/second?

At what Mach and altitude would this be?

• That's an interesting topic. I want to know the answer too. I'm also curious how that 1937 biplane flew so high. I thought piston engine can't do that.
– crow
Commented Jun 30, 2022 at 17:40
• @crow, power of both piston and turbine engines declines with density altitude in approximately the same way, so reaching a high altitude is a matter of installing a sufficiently powerful engine so enough power is left even with the low air density up high (often then you are not allowed to open the throttle or fuel valves to full down low, because the engine isn't designed to handle the torque or temperature it would produce in the dense air). Commented Jul 3, 2022 at 19:19
• @Jan Hudec, Thanks man. So my "understanding" of how piston engine works is actually just how it normally worked with common airplanes.
– crow
Commented Jul 5, 2022 at 3:12
• @JanHudec But you also need dense enoug air for a propeller. There must be some air for the propeller to use, not just for the engine to work, otherwise the aircraft couldn't fly. The Caproni was close to the altitude limit for piston-driven props. The altitude record for a manned piston prop is the Grob Strato 2C's 60,900 ft. Commented Jul 5, 2022 at 8:42
• @HiddenUser, both a propeller and the ducted fan of a turbofan or even a turbojet need the air to produce thrust. The jet has a bit of advantage in being able to generate higher delta-V, but since that reduces the propulsive efficiency, and the shortage of air limits the power, it does not help all that much. Commented Jul 6, 2022 at 13:17

From Torenbeek, Synthesis of Subsonic Airplane Design. The graph compares Thrust Specific Fuel Consumption of jet engines with [quote from the book]:

C$$_P \cdot$$V / $$\eta_{prop}$$, where V is the flying speed, C$$_P$$ the specific fuel consumption related to the shaft horsepower and $$\eta_{prop}$$ the efficiency of the propeller.

This is a 1980's graph for Mach and altitude at cruise condition, comparing aeroplanes optimised for their missions with existing technology. It reveals the following:

• Propeller aircraft are the most fuel efficient, until compressibility effects around the tips cause large losses. The graph is a generalised one, propellers designed for high sped with swept tips hold their fuel efficiency advantage over a larger speed range.
• Turbine engines are slightly less fuel efficient than piston engines, however they scale up better, have lower weight and burn kerosene, not aviation gasoline.
• At higher subsonic speeds the bypass engine (the turbofan) is the most fuel efficient. Depending on the bypass ratio, $$\lambda$$ of > 10 is no exception nowadays.

So comparing conventional props with conventional turbofans, the cross-over point for fuel economy is between 0.4M and 0.55M. It can be seen that the open propeller is much more efficient than the shrouded fan before the compressibility starts to play a role, and therefore there has been over half a century of research into propfans.

The pic above (from the wiki entry for propfans) shows an open dual-disked fan, each with 8 swept blades in order to delay compressibility effects. Which will shift the crossover fuel efficiency point to higher Mach numbers.

However, a propeller must spin faster and increase its pitch as True airspeed increases and air density decreases.

Not for constant-speed propellers, which only change their pitch when true airspeed varies.

• Much lower crossover than I thought! Could enclosing the fan in a duct (possibly lowering incoming airstream velocity and increasing pressure as a ram) be helping the fanjet? (as compared to a prop spinning in the freestream). Commented Jul 5, 2022 at 14:31
• There has been over a half centurt research in unducted fans, but the noise remained the main problem. The research kept on trying because of the increased fuel efficiency of unducted fans. Commented Jul 5, 2022 at 23:04
• The graph indicates that standard props are better at lower Mach numbers, until the compressibility effects start playing a role. Change the shape of the prop, and the compressibility effects are delayed to a higher M. Commented Jul 6, 2022 at 6:40

Safran is showing an updated version of 'Propfan', 'UnDucted Fan', UDF, they call it 'Open Rotor', see image.

Attached chart is from book by Hovey 'Ducted fans for light aircraft and homebuilt'. The concept of propulsion enclosed in a duct is having interest today. Blessings +

• Can you confirm the "propfan" set up is contra rotating? Also, we aren't looking low end airspeeds, and somehow $ducted$ $fans$ do very well at higher Mach. I suspect that the back prop may be doing a higher percentage of "pushing" at speed, the front blades may be sending a pulse of more compressed air into them. I am wondering if the duct acts as a ram, with the same effect, at higher Mach. Essentially, pre-compression may give the prop (or fan) more to "bite" into. Commented Jul 7, 2022 at 11:23
• Thanks for your interest. Let them talk about me, even if it's badly. Sorry, I have no more info, even if SAE member, I'm not engineer, but videos about PropFan show it is contrarotating. Blessings + Commented Jul 7, 2022 at 13:37