RPM / Altitude / Power Equation - for Fixed Pitch Prop

[OpenCirrus619]

I don't know if anyone can help on this - I'm looking for someone practical who also knows the theory (Genghis??).

I am looking for a (relatively) simple formula that gives the relationship between RPM, Power and Altitude for a fixed pitch propellor - but have had no luck so far :ugh:

The aim of the exercise is to be able to produce a table giving RPM required for various power settings at various altitudes. The input data being a full throttle run at a know density altitude - giving a reference power (100%), altitude (from the altimeter) and RPM (from tacho).

I have so far managed to find a formula giving the relationship between Power and RPM (assuming the same altitude) at: How To Determine The Part-Throttle RPM of a Fixed Pitch Propeller At a Given Horsepower (http://www.eaa62.org/technotes/prop.htm)
HP2 = HP1 (RPM2 /RPM1 )^3
where
HP2 = part-throttle hp
HP1 = full throttle hp
RPM2= part-throttle rpm
RPM1 = full throttle rpm
- though I'm prepared to be convinced that this is not correct (it doesn't seem to accurately fit a POH I've tried to test it against).

Any help on this one would be appreciated :ok:

OC619

P.S. I do have a maths/engineering based degree - but it's a couple of decades since I really had to use it (so please be gentle with me) :\

[Genghis the Engineer]

In a nutshell, there isn't one. That's why the POH of every VP/complex aeroplane I've ever flown (and doubtless many I haven't) has a set of lookup tables in the performance section.

The nearest to an attempt at simple relationships I've ever found was those in John Lowry's book "Performance of Light Aircraft", which is very clever, but gave me a bit of a headache working through the maths - so best of luck.

If you want something reasonably simple for your own use in a particular aeroplane, then plot graphs or create "subset tables" at your prefered cruising conditions from the tables in the POH. That's certainly what I did when doing a lot of Arrow flying (which I've stopped doing on budgetary grounds).

If you want something generic - I really don't think it can exist, there are too many variables, and enough of them are design specific to make that impossible.

G

[IO540]

As you found, the power absorbed by a fixed pitch prop (and thus the thrust too, more or less) is proportional to the rpm cubed.

This will be true for small changes e.g. a 1% increase in the rpm will increase the thrust by 3% (on the basis of the standard bit of calculus of small changes e.g. 1.01 ^ 3 is very close to 1.03).

For large charges, a lot of other stuff will come into it. A while ago I was reading something on propeller drag and saved this article (http://www.peter2000.co.uk/aviation/misc/prop.pdf) but while I was going to post the original URL I noticed that the original is now gone offline. Anyway this may give you some pointers showing that this stuff is significantly empirical.

There is a lot of stuff online e.g. this (http://www.pilotfriend.com/training/flight_training/fxd_wing/props.htm).

I haven't got a clue how altitude affects efficiency but obviously it is an aerofoil "like any other" so thinner air will affect it. It has got to produce less thrust (and will be absorbing less power) in thinner air; that much is obvious if you consider the extreme case of no air at all. So in thinner air the AoA should be greater for the same effect, which brings us to the VP prop whose AoA is governed to (essentially) absorb a constant engine power output.

What are you trying to achieve?

[bbrunton]

Try

HP = RPM x MP x K

K = a constant that can be calculated using max values for MP and RPM for each engine.

Bill

[IO540]

The OP asked about a fixed pitch prop so using MP is unlikely to work.

He prob99 hasn't got an MP gauge.

With a VP prop, MP (at constant RPM) is roughly proportional to torque i.e. HP i.e. thrust.... which is basically what you are saying...

[mm_flynn]

At a slightly simplistic level the propeller is a wing airfoil. However, even though it is a fixed pitch, the angle of attack varies with the true airspeed and RPM.

The thrust produced is basically the same angle of attach *True speed (in this case it is the sum of the speed due to rotation and forward advance)*density relationship as a wing, but with an additional variable. The efficiency is dependent on the difference between the inflow and outflow airspeed (which is why static thrust is lower than one might expect).

The power is then this rather complicated thrust * True Airspeed.

I suspect it is much easier to take some values from the POH and draw curves fitting the datapoints.

[24Carrot]

For propellers, googling "propeller advance ratio" provides an introduction to their complexities.

For the engine efficiency, I think density altitude alone is not enough, you need to consider both density and pressure. This old pprune thread is an interesting introduction:
Piston engine power at altitude [Archive] - PPRuNe Forums (http://www.pprune.org/archive/index.php/t-126079.html)

One more thought: all the Flight Sims have modeled it somehow, you could try looking there.

As others have said, it isn't simple, especially in real life!

[mm_flynn]

One more thought: all the Flight Sims have modeled it somehow, you could try looking there.
My understanding of MSFS in particular is that the aircraft models are built on performance tables rather than engineering pricniples (X-Plane's flight model is derived from the engineering data, but I believe the X-Plane poweplant model is an idealised (probably table driven) model and not that accurate).

[Pilot DAR]

Would this calculator provide the information you seek?

Side 1

http://i381.photobucket.com/albums/oo252/PilotDAR/IMG_2230.jpg

Side 2


http://i381.photobucket.com/albums/oo252/PilotDAR/IMG_2231.jpg

[24Carrot]

Assuming I made no mistakes going into metric and back again, the Power / Thrust part of the calculator assumes (with consistent units):
Thrust = 0.83 x HorsePower / Speed

which is fine as far the physics goes, but I suspect the 0.83 efficiency factor might not be a universal constant!:)

[mikehallam]

Nice slide gauges.

Using a scrap of paper to change/correct the slide position I could compare some findings with my own actuals on the 66" dia.WD Rans S6-116 and all (max. 80) h.p.

Tip speed at 550 ft/min is a comfortable 50% mach 1 at sea level.
Pitch actual is 14 1/2 deg achieved by trial & eeror., whilst slider suggest 13 1/4, for input 1,940 rpm and 90 mph. [I have to accept that some pundits do recommend 13 1/2 or so.]
Thrust comes out ~100lb for a solo weight of ~725 lb, which appears uncommonly close to the glide ratio ?

Just for fun you know.

mike.

[mikehallam]

Oh, Just noticed.

Pitch off slider probably at 3/4 prop dia,
WD call for tip pitch angle.
So 14 1/2 at tip is x less at 3/4 dia.

[OpenCirrus619]

All,

Thanks for your input on this.

I was hoping to do one 100% power test run and derive power settings at various altitudes.

The aircraft is a PA18-150 - the POH only gives a figure for 75% (and that is a speed to fly, not RPM).

The slide rule looks interesting - I'm going to have a play with that :ok:

Thanks again

OC619