Indeed turbofan engines and piston-props are quite common, however, there's one key difference: the fan is an integral part of the "turbofan" engine. When we say "Cessna 172 has a 180 SHP engine", we are talking specifically about the Lycoming IO-360-L2A engine. If we were to talk about the engine prop combo, it is more appropriate to talk about their thrust; shaft power is no longer the useful metric that it used to be.

Likewise, when considering generator units like LM9000, SHP is useful. But when talking about the GE90 (which includes the fan), SHP is not as useful as thrust.

@RobertDiGiovanni To make the difference more pronounced, I thought it would be more appropriate to consider two drastically different propeller choices, and so I compared the Osprey with the Thunderscreech. I made this graph which compares the thrust and efficiency of the two propellers. Ofcourse it is not to scale, it's just a rough graph I made to illustrate a point.

What we see here is that - for a given SHP, Osprey prop produces more thrust than Thunderscreech prop when the speed is low. but beyond a particular speed, the Thunderscreech prop produces more thrust. There are certain speeds at which, while Thunderscreech prop still manages to produce a positive thrust, the Osprey propeller doesn't, or infact produces drag. (at those speeds, Osprey prop is no longer able to accelerate the air particles backwards, or even manages to accelerate them forwards!)

Similar to a jet engine, the Thunderscreech prop has poor efficiency at low speeds. Also similar to the jet engine, it has good efficiency at higher speeds.

(the point of my first two paras is that while the core of GE90 produces shaft power, the combination of the core and the fan produces thrust power. Since "thrust power" is practically useless for the operator, thrust is what we use instead.)

@AdityaSharma excellent graphs! Yet you still are graphing Power. Why? To me (just my opinion) drag increases so much with speed the thrust curve is an impossibility. But the relationship between Osprey and ThunderScreetch is very accurately portrayed.

Now back to basics. Power increases quadraticly because DISTANCE TRAVELLED increases as such. Remember velocity is linear to acceleration, distance is quadratic. This does not apply to equilibrium physics, it does apply to accelerating a mass

But then there is drag. I honestly believe Power is archaic, born of a misunderstanding (and insistance) that Power "carries through" a piston engine moving and object.

My work has shown that pistons produce force. Now if we simply combust fuel in a cylinder, we have a (very inefficient) pulse jet. (The tuned exhaust pipe makes it a bit better).

Well, I'm not graphic power, my graph is a thrust-velocity curve graph for a given power; it is indeed a thrust curve.

But very inefficient. So we close the cylinder and extract MECHANICAL ENERGY to turn a propeller. And the turbine in a jet does what? To turn what? And what? Really the same.

But please keep your good work going. Excellent reading. I find I am mostly in agreement. Bob

OK. Now PLEASE graph thrust for a given Velocity. But understanding the difference means they will both be the same.

Thrust for a given velocity varies linearly with power.

But is power constant as velocity increases?

Or does it increase quadraticly because distance traveled increases as such.

Thrust for a given velocity varies linearly with power. OK!!!

Because of drag, thrust must increase to increase velocity

Therefor, if we increase thrust, the new steady state will increase velocity by the square root of thrust increase

Yea, at double the velocity, the thrust required is 4 times greater

This is why power only increases that way with speed, not because thrust is any less (Unless efficiency changes).

and it requires 8 times greater thrust power to produce that 4 times greater thrust at 2 times greater speed

Well, studies continue. TSFC numbers seem to be helping. I will check those for ThunderScreetch

Alright :)

(Just a reminder: TSFC numbers on their own might be misleading, since they do not account for speed. For instance 10 units of TSFC might be a great value at high speeds, but it may be a terrible value at low speeds.

Ideally, if we were to replace η with something else, thrust-power-specific-fuel-consumption would be the most appropriate candidate, since it does account for speed @RobertDiGiovanni

Well, it's only inefficient because it is not moving so fast. Give it some time.

Yes, but the Osprey propeller running at same SHP is producing more thrust and is therefore more efficient at that particular speed.

I see with props as mass movers, as speed increases V2-V1 decreases. But, as an airfoil, at lower speeds, efficiency can be maintained by adjusting AOA. But only to a certain point. Around Mach 0.5

it no longer functions as a "wing".

I guess that starts to get into "specific impulse" why the lowly rocket can carry on.

But, in all fairness, TSFC considered as Thrust x velocity should be evaluated at steady state. Of course, sitting there with brakes locked is not very efficient Powerwise.

Sure. Good day!

@AdityaSharma they do talk about TSFC at take-off and cruise speeds. A good idea.