Horsepower Versus Thrust

[Ivan]

Hello Aleatorylamp,

I had originally intended to post this in your Turbo Prop thread before it was closed.
Hopefully posting a new thread to do this won't get anyone upset at me. I didn't want to leave the last thread where it stopped because it sounded like you might have been interpreting my questions as criticism while I had intended them to get you to think about what was really happening with Manifold Pressure and its meaning.

This is not intended to start any arguments but only to present what I believe to be a fairly "reasonable" approach.

Your first post in the Turbo Prop thread had me a bit concerned.
A simple constant multiplier to convert Shaft Horse Power to Thrust is not a reasonable solution.

First of all, one has to understand the meaning of Thrust and of Power and how they are different.

Thrust is pretty simple: It is the amount of force your engine generates to push the aeroplane forward.
For a Jet or Rocket, it is the only force you have to worry about.

So far no disagreements, right?

As for Power, it is Force * Speed. A typical unit such as 1 Horsepower is defined as 550 Feet * Pounds / Second.
Lets move those units around a bit without changing their meaning so that they have the appropriate context here.
550 pounds * feet/second.

So..... How about our typical Piston Engine with 1000 HP?
How much Thrust does it generate?

Well, it depends on HOW FAST the aeroplane is going.
At 200 MPH or 293 Feet/Second we have:

1000 HP * 550 ft-lb/sec divided by 293 ft/sec == 1877 Pounds of Thrust

At 300 MPH or 440 Feet/Second we have:

1000 HP * 550 ft-lb/sec divided by 440 ft/sec == 1250 Pounds of Thrust

.....

This calculation has neglected one very important thing: How do we convert Engine Power to Thrust?
The calculations above would be correct if the Engine were turning a pulley that was hauling the aeroplane forward without any slippage or power losses but most folks use a Propeller of some kind because there aren't a lot of places to attach the other end of the rope in the sky.

A typical Propeller only converts about 75% to 80% of the supplied power into actual thrust. A really good propeller gets around 80% under ideal conditions.
Use whatever number you believe to be appropriate. I am going to use 75% for these calculations.

This business about Propeller Efficiency and how that changes with Propeller Pitch and how the Pitch Angle is selected is what Records 511 and 512 are all about.

.....

Now back to the Turboprop.
The Allison T56 engine on the P-3 Orion is listed as making 4910 SHP.
It is also putting out some amount of Jet Exhaust as Thrust.
The HP equivalents I have seen go all over the place, typically in the 6000-6500 HP range.
The number listed by Aleatorylamp was 6400 HP, so let's use that for now.

Keep in mind that we are using a few assumptions for Propeller Efficiency here, so if you vary that a bit, the numbers can change by quite a lot.

4910 HP actual + Some amount of Thrust HP == 6400 HP.

Thrust HP = 1490 HP

If we go back to the calculation method used above, we find that:

886 pounds * 694 ft/sec / 550 / 0.75 = 1490 HP

473 MPH, the Maximum Speed of the Orion is 694 ft/sec.
550 is the conversion from ft-lb/sec to HP
0.75 is the assumed Propeller Efficiency.

Is this number correct? Maybe.... Maybe Not.
Wikipedia says the typical Jet Thrust is only 750 pounds, so you decide.
750 pounds gives an equivalent power of 6171 HP.

-------

I will leave it here for now in case this discussion upsets anyone.

- Ivan.

[Motormouse]

All plausible but ... Jet thrust on a turboprop is deemed of negligible benefit (it basically counters the drag of the inlet)
and try 90% for prop efficiency

https://www.grc.nasa.gov/WWW/K-12/ai...e%20propeller.

ttfn

Pete

[Ivan]

Hello Motormouse,

The "negligible" benefit of the jet exhaust depends on very much on the speed of the aircraft.
At low speeds, the jet exhaust thrust doesn't have much effect but that low effect becomes proportionally greater as the thrust from the propeller becomes less.

Regarding the drag of the nacelle / inlet: That drag will be present regardless of whether the jet exhaust is present or not.
The fact that SOMETHING is counteracting that drag is a good thing.
Also, if the inlet drag is proportional to dynamic pressure (1/2 Rho*V^2) then it isn't going to be a constant number.
Exhaust thrust isn't really a constant number either because the velocity matters also, but for the purposes of the primitive calculations we are doing here, we can treat them as a constant.

Regarding the benefit of exhaust thrust, one can look back on the WW2 era fighters. Just about everyone considered exhaust thrust useful. As a case in point, one can compare the very similar A6M3 Model 32 and the A6M5 Model 52 Type Zero Fighter.
With the same engine and wing area and very nearly the same contours, the A6M5 with ejector stacks was 5-10 MPH faster.

Just out of curiosity, which aero propeller that you know of has 90% efficiency and under what conditions?
What is its efficiency under maximum speed conditions say around 400 Knots or so?

One should work out the numbers of what a fairly larger propeller such as that of the P-3 Orion is actually doing when the aeroplane hits it maximum speed of 473 MPH or 411 Knots at 15,000 feet. RPM can't be too high or the tips will go supersonic and efficiency gets pretty bad, so blade angle is probably pretty coarse and that isn't going to do much for efficiency.
I would say 75% efficiency is being pretty generous.

- Ivan.

[Ivan]

Hello Aleatorylamp,

You made a comment implying that Turboprops had superior altitude performance to supercharged Piston Engines.
Perhaps some do, but the two examples that we seem to be working with here are examples to the contrary.

The Lockheed P-3 Orion with its Allison T56 engines has a fairly low critical altitude and service ceiling.
Maximum Speed is 473 MPH at 15,000 Feet
Service Ceiling is 28,300 Feet.

This is fairly average performance for a Single Stage Engine Driven Supercharger as seen early in WW2.

The Dornier Seastar with its P&W Canada PT6A engines has even less altitude performance.
Service Ceiling is 15,000 Feet.

This is pretty typical performance for an Naturally Aspirated Piston Engine or a very heavily loaded bomber type.
Power to Weight ratio isn't too bad with 1300+ HP on a maximum Take-Off weight of 10,000 pounds which is better than a typical bomber, so this probably means that engine power falls off pretty quickly with altitude.

For this exercise, I used the Dornier Seastar, which has 2 x 650 shp P&W Canada PT6A-135A), with a top speed of 180 Kt, and a turbine thrust of 1802 flb quoted on the factory´s engine certificate.

Using the formula Flb Torque = (HP * 5252 / Prop. RPM), and we get 1796 flb turbine thrust, which is quite accurate.

I suspect that you might have been misreading the specifications on the factory engine certificate in this case.
From what I have been able to find (not that I have looked that hard) it does not seem that this engine generates much exhaust thrust at all. It might be due to the unusual arrangement of the "hot section" of this engine near the propeller to make maintenance easier and in the case of the Seastar, it is so slow that (as Motormouse pointed out), the exhaust thrust isn't all that effective anyway.

The other thing to note here is that your calculation is actually for Torque or Twisting Moment rather than Linear Force as you would want to determine Thrust. That the numbers match the specification might just be a truism in that the specifications list Horsepower and the RPM and Torque readings to get that output and you are confirming their calculations are correct.

Hope this makes sense.

- Ivan.

[aleatorylamp]

Hello Ivan,

There are two interesting points you are making here, one about the basic conversion formula from Horsepower to Foot-pounds Thrust, which has been bothering me for years now, and one the formula which I was using because it worked so much better on the sim, which now turns out to be a Torque formula, not a Linear Thrust one.

I was using the 650 Hp PT6A-135A engine as it also quoted with a 1802 flb thrust,which now turns out to be Torque, not Linear Thrust.

This engine can maintain an altitude of 30000 ft, although the Dornier Seastar has a ceiling of 15000 ft as it lacks a pressurized cabin.

Anyway, I decided to conduct some experiments to see what would happen with the formula you mention.

According the 300 mph section of this formula, a 650 Hp engine would give 1230 flb thrust, so I adjusted the .air file. Top speed was fine at 180 kt, but accelleration was poor and initial RoC (at 1000-2000 ft) was 700 fpm instead of 1079 fpm, even with the low-speed power increase in the Jet Power Curve Record #601.

Then I used my habitual 2.5xHp=Flb Thrust formula, with which the 650 Hp engine would yield 1625 Flb Thrust, and I adjusted the .air file again.

This time accelleratioin was better, and initial RoC improved considerably to 1030 fpm, but was not quite up to par, and some more power compensation was required.

With my previous entry of 1802 and the power increase in the Jet Power Curve, RoC was a bit high, at 1250 fpm. Of course, without the Record #601 adjustment, it was fine.

My next trial was with 1700 flb Thrust, and the Record #601 adjustment, and performance matched specifications, so in conclusion, it seems that some extra power compensation is needed to make turboprop performance more realistic in the sim.

Cheers,
Aleatorylamp

[Motormouse]

Figures according to chart on wiki for ESHP and SHP for the small block PT6A-135

PT6A-135

787 eshp

750 shp

ttfn


Pete

[aleatorylamp]

Hello Motormouse,
Thank you for the data, but I´m afraid the Dornier Seastar has its
P&W Canada PT6A-135A engines flat rated to 650 shp, so the data in
your post just now would not apply to the specific testing situation.

Hello Ivan,
The information you provide as regards conversion formulae etc. is all
very well in theory, but unfortunately provides no improvements when
applied to the simulator, so I have no alternative but to stick to what
I´ve been doing.

Anyway, I will no longer be experimenting along these lines, so my
present post concludes my intervention on this thread and subject.

Cheers,
Aleatorylamp

[Ivan]

Hello Aleatorylamp,

The fact that the PT6A can be run at 30,000 Feet does not necessarily mean that it will maintain Sea Level Power to that altitude.
The Allison T56 that is installed in the P-3 Orion is operable to 55,000 Feet but with standard aircraft, its service ceiling is much lower at 28,300 Feet. A specially configured P-3 did set an altitude record for the class at 46,000 Feet though.

Perhaps the Dornier Seastar has better altitude capability. I don't know. That is up to you to determine.

Regarding the HP to Thrust conversion, your end result should simply be Pounds of Thrust, not Foot-Pounds.
As for the conversion value, You need to determine the Propeller Efficiency under the particular conditions.
Whether you want to go any further with this idea is entirely up to you.
We all do things a bit differently and there is nothing to say that my idea is better than yours.


Hello Motormouse,

I made an assertion about the efficiency of the Propeller of the P-3 Orion being fairly low under maximum speed conditions.
Here are some numbers to put that assertion into perspective:
At N1=100%, the Propeller is spinning at 1105 RPM.
The Propeller is a 13 Foot 6 inch Diameter Hamilton Standard.

The Speed at Advance Ratio J=1.0 is 169.6 MPH.
At the Orion's maximum speed of 473 MPH, the Advance Ratio would be approximately 2.8.
Keep in mind that a typical propeller with a Pitch of 45 Degrees is unable to provide ANY propulsion an Advance Ratio of about 2.6.
Its relative AoA to the airstream is Zero.

The typical maximum efficiency of a propeller is generally achieved somewhere between 30 degrees and 45 degrees pitch and coarser pitch means significantly worse efficiency.

Another thing to note is that the critical altitude of the P-3 Orion may actually be due to transonic effects on its propeller.
The C-130 Hercules achieves its maximum speed at 20,000 Feet with fairly similar engines but is going about 100 MPH slower.

At 15,000 Feet, the Speed of Sound is only 721 MPH under standard conditions.
This works out to 1057 Feet/Second.

The Tip Velocity of the Orion's Propeller when the forward velocity is taken into account works out to 1045 Feet/Second which doesn't leave a lot of margin before going supersonic.

- Ivan.