In jet engines, I read that thrust is related to the fuel flow rate, whereas in turboprop engines power produced is related to the fuel flow rate. What is the reason and brief math behind this?

up vote 28 down vote accepted

Ultimately what you want from all three types of engines is quantification of thrust available to push an airplane through the sky. The turbofan/jet engines are self contained and produce thrust directly but a turboprop engine requires the addition of a propeller, which may have differing characteristics based on the installation.

Since thrust is not known for a turboprop until its installation has been determined, manufacturers instead quantify the power available to drive a prop. This allows engines to be compared so that an airframe manufacturer can make the proper selection.

Fuel flow is then related to either thrust or power as a measure of efficiency, depending on type of engine. There is generally no published mathematical relationship between power and thrust for a given engine. It is not needed for turbofans/jets and not possible to determine at time of manufacture for turboprops.

  • 6
    This is the only post that directly answers the stated question. – Ralph J Nov 4 at 21:12

Jet engines directly produce thrust by exhausting gas (and in a modern turbo fan also moving a lot of air around them), so fuel flow rate is directly related to the thrust that is generated.

In a turbo prop the engine produces power which, via a gear box spins a propeller that generates the thrust. Since most turbo props have the ability to adjust the propeller pitch the engines power output is not always directly related to the thrust generated at a given time.

  • why you wrote that turboprop engines generate power, whereas while writing for jet engines you wrote that they generate thrust. This was my actual question? I understand mechanics of both, but why is it intentionally written different? Am I missing something? – user5349 Nov 4 at 9:57
  • @user5349 Turboprop engines generate shaft power: P = 2*piMn via a low pressure turbine which connects to a shaft. The shaft drives a propeller through a gearbox. – jjack Nov 4 at 17:06

To expand on what Dave said, the term Power is used for turboprops because the thrust produced by the prop is a function of horsepower applied to the prop, that is, torque @ RPM.

The gas generator of a turboprop - the jet engine part - has its output indicated as a percentage of maximum torque it can apply to the propeller gearbox, whereas a pure jet engine, who's push results from the mass airflow accelerating through the engine, has its output indicated by Engine Pressure Ratio, the difference between the air pressure going in vs the air pressure going out.

Turbofans are kind of in the middle of the two, being sort of a turboprop with a fixed pitch many bladed propeller. Because the fan is fixed pitch and has no constant speed regulating ability, you don't need to know the torque being applied to it and it's sufficient to go by just fan RPM (N1, indicated as percent of max). Turbofans also show core engine RPM (N2), but the fan speed N1 is the primary power setting measurement.

For turbofans vs turboprops, its similar to how piston airplanes with fixed pitch props just measure RPM, like a turbofan, whereas piston planes with constant speed props need to show RPM and manifold pressure (MP being more or less equivalent to torque in a turboprop).

Not sure what you mean by the math part.

  • 1. In turboprop engine, Is it that this torque produced by gas generator is constant ? the ultimate thrust generated by the power plant will be depending on the propeller pitch ? Which is a variable ? – user5349 Nov 4 at 10:08
  • No the torque that acts on the propeller varies with gas generator speed. Think of a turboprop as a pure jet engine where you point the tail pipe at a windmill to make it spin. You could call the jet engine part a "gas generator". The windmill getting blown on is connected to a huge fan by a gearbox. The air blowing on the windmill generates torque to make it spin, driving the fan. You speed up the jet engine itself to increase the torque on the power turbine (the windmill). Move the windmill to inside the jet engine to just behind the compressor's turbine, and there's your tubroprop. – John K Nov 4 at 20:52
  • @John K Your opinion please. Thrust produced by the prop (propulsion force) is determined by pitch and rpm of prop. Power to turn prop = DRAG of prop. Would not Power to turn prop be THRUST of pistons no matter how it was geared? Would not the Propulsion force actually be the LIFT of the propeller. Just being academic, but it is interesting to consider in light of the trend towards efficiency in jets (fans are getting bigger and slower). – Robert DiGiovanni yesterday
  • I would say that difference is due to the fact that the thrust of the jet pretty much all is from the air that is forced to accelerate out the convergent tailpipe nozzle, whereas the thrust of the propeller is a secondary result of torque applied the propeller. So, the go lever in a jet just controls how fast the air comes out, whereas the go lever in a TP controls the torque to the gearbox, and torque x RPM = HP, so POWER is a more appropriate term. With turbofans you have a kind of half TP and half jet, but there is no measurement of torque vs RPM for the fan so thrust lever does the job. – John K yesterday

The real reason is that, by definition, a jet engine does not output any kind of power but outputs the thrust force instead. Turbopropeller engines do not output a thrust force but rather output a mechanical power through a shaft and gearbox supplied by said power by either a power turbine or the gas core itself.

That arrangement has to do more with how the FAA and other governing bodies defined these engines, not so much based on physics. I am aware that both engines are, in fact, generating energy and power, it’s just we don’t typically quantify energy output from jet engines that way.

Ironically many turbopropeller engines are often rated in equivalent shaft horsepower (ESHP) this is a sum of both the mechanical power delivered by the driveshaft and the reaction thrust created by the engines exhaust gases.

This also has regulatory impacts as well. Pilots of jet aircraft do not require neither a complex nor high performance endorsement in their logbooks to log PIC time in a jet, but it is required if your aircraft is powered by either a reciprocating or turbopropeller power plant.

  • Agree 100%. This appears to be a matter of convention, a little like saying, ok, from now on we're going metric. Nope, not happening. Maybe, in the future... – Robert DiGiovanni Nov 10 at 19:54
  • Definitely not ironic for turboprops to rated ESHP as mechanical power + engine exhaust thrust. This is in fact correct. Shaft horsepower is torque at a given rpm, which for piston engines is the AVERAGE thrust (cylinders firing per minute x Lever Arm of crankshaft divided by diameter of drive shaft x any other gearing ratio). At constant rpm this = DRAG of prop (thrust = drag) and produces a forward force WRT aircraft. Thanks for allowing my opinions to be aired. I will try to learn the conventions. – Robert DiGiovanni Nov 10 at 20:10

Oau, a lot of answers and almost nobody touching on the real issue.

Propellers will produce a thrust that decreases with increased speed. Since power= thrust x speed, this means the engines will produce (more or less) an (almost) constant power throughout the speed range of the aircraft. Given a specific fuel flow, it will produce a specific (calculatable) power, which will translate to a varying thrust depending on the current speed. Therefore fuel gives you power.

Jet engines will produce a constant thrust (almost) regardless of current aircraft speed. This means “power” is not really a usefull measurement in jet (all of them are thrust-rated, not power-rated), as you can just double the current speed and the jet is now producing twice the power, even though you have not changed the fuel flow. A specific fuel flow to the jet engine will produce a specific (calculatable) thrust, but it can produce any amount of power depending on the current velocity of the aircraft. Therefore fuel gives you thrust

You wrote in a comment on Dave's answer:

why you wrote that turboprop engines generate power, whereas while writing for jet engines you wrote that they generate thrust. This was my actual question? I understand mechanics of both, but why is it intentionally written different? Am I missing something?

So it sounds like the main question you're trying to ask is: what is the difference between power and thrust?

Power and thrust are two different measures of the output of an engine (just like how height and weight are two different measures of the size of a person). All engines generate power, and all engines generate thrust, but they're two different numbers with two different meanings.

Thrust is a bit easier to describe. Thrust is often measured in pounds or newtons. If an engine is producing 500 pounds of thrust, then it's pushing on the aircraft with the same amount of force that a 500-pound weight would push on it. The difference is that the engine pushes forwards while the weight pushes downwards.

Output power is a bit harder to describe. Power is often measured in horsepower or kilowatts.

For rocket engines, the formula for output power is simple:

$$\text{output power} = \text{thrust} \times \text{exhaust speed}.$$

Unfortunately, most airplanes aren't powered by rocket engines, so this simple formula no longer applies, though. But the basic principles are the same:

  • As an engine produces more thrust, it will also produce more power.
  • Even if an engine is producing a constant amount of thrust, as the airplane flies faster, the engine will end up producing more power.

Power production is directly related to power consumption. If you make an engine produce more power, then it will consume more fuel.

  • I see that this answer has gotten a downvote. As far as I know, there's nothing wrong with it; it seems correct and useful. – Tanner Swett Nov 6 at 3:51
  • I was not the downvote, but it might be because of the ‘power= thrust x exhaust’. For any thrust, , force x velocity (of that force) will produce power – Radu094 Nov 11 at 18:05
  • @Radu094 Does that contradict what I said? If it does, I don't see how. – Tanner Swett Nov 12 at 1:43
  • Not contradicting, just unclear I’d guess. A sitting (fixed/bolted) rocket spweing exhaust at high speed produces a nice display and a lot of thrust, but 0 power. Not really related to the asked question, I know, but it caught my eye and someone prob downvoted because of it – Radu094 Nov 12 at 1:52
  • @Radu094 That's a good point. I want to say that the rocket still is producing a lot of power, but all of it is going into the exhaust. But I don't know how the "output power" of an engine is usually defined. – Tanner Swett Nov 12 at 13:11

Finding a conversion factor for thrust and horsepower may at not be impossible when one looks at the original definition of horsepower and how its meaning, and math, became garbled over time.

First thrust: Is a force = mass x acceleration (gravity). Units of expression: kg meters/second squared or simply weight in pounds F = kg × G

Now horsepower: based on a horse pulling a rope attached to a weight across a pulley. Horse walks forward a 1 meter in 1 second of time lifting the 75 kg weight. Work W = weight x distance

Formula P = W/t = Fd/t = Ma x d/t = Ma x v!

Checking the units we have kg meters/second squared x meters/second = kg meters squared/second cubed.

What is going on here? Is this a steady state, or is it an accelerating system? Looking at the accelerated case provides the link between thrust and horsepower, and cleans up the math quite nicely.

To qualify as a horse, you have to lift the weight, but why include distance over time? Because a clever pony could put in a compound pulley attached to the weight and lift it half the height in the same distance walked forward. But this is where the true meaning of "horse power" was lost.

No mechanical advantage allowed! The draft horse, being stronger, simply walks forward and lifts the weight. Looking closer, the horse velocity is 0 and accelerates to walking speed. The act of lifting the weight 1 meter in one second not only matches gravitational force, but accelerates the weight upwards. Two draft horses will either accelerate it faster or lift double the weight in the same time: 2 horsepower! Since force vectors can be added, the math cleans up to:

Force = kg G + kg v/t = kg (G + a) kg meters/second squared

Naturally the horse does not continue to accelerate to a gallop, but how it is useful in the 18th century? If the horses are taking longer to reach walk speed, they are getting tired and need to rest!

In modern times, horsepower is fuel consumed, so is thrust! The explosion pushes the piston, the rest are torque forces. It is thrust. How to compare it? Have any engine (rocket, piston engine/prop, husky team etc.) accelerate the weight without mechanical advantage. Call it what you will. It is Force.

Power = Force/time. Notice d does NOT belong in the equation! In steady state flight, there is NO consideration for distance in force vectors! Power is Thrust/time even if you are not moving!

d comes into torque as F x d = torque

This is the source of "horse power" confusion.

But the usage in our language, 120 years past "horsedrawn days", remains in many forms.

  • 1
    This doesn't even remotely begin to answer the stated question. – Ralph J Nov 6 at 23:51
  • You see a piece of wood, I see a sculpture. Don't know what else to say. The question invokes a comparison of fuel consumption to 2 different definitions, I try to show a similarity. I hope you remotely understand this. Thanks for your comment. – Robert DiGiovanni Nov 7 at 0:50
  • Or, in other words, "Horse power" may be a misunderstood and archaic definition. As you can see, the original meaning was lifting weight and accelerating it upwards (from mineshafts). Others said turning a wheel. What resulted was confusion. If there is any question about the writing post it, and I will make every effort to explain. But please read it carefully. – Robert DiGiovanni Nov 7 at 1:09
  • So the effort is to separate thrust (force) from torque. Better to have the Belgian drafter under the hood on a hill, or you need more gears, ok? – Robert DiGiovanni Nov 7 at 8:29

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