Propeller Efficiency Help

[Stoney]

Gents,

Ok, for the last few months, I've been working on a master spreadsheet that catalogs a large number of aerodynamic characteristics for most of the Aces High plane-set, minus stuff like the C-47, for example.  Anyway, so far, I've included both the zero-lift and induced drag coefficients, but have yet to include any correction for compressibility drag (that's planned for later).  I've put all of this information together so that I can do some quick analysis whenever I want.  I started testing out my propeller efficiency formulas and have hit a snag, as I don't really trust the numbers.

For example:

F6F-5 at 25% fuel = 11358 lbs
Wing Area = 334
Clean stall = 96 mph IAS (tested in game)
dynamic pressure = 23.57
Cdi =.1363
Cdoi =.0272

Drag = Cd * 1/2pv^2(dynamic pressure) * Area

Induced Drag @ stall = (.1363)*(23.57)*(334) = 1073.2 lbs
Zero-Lift Drag @ stall = (.0272)*(23.57)*(334) = 214.1 lbs
Total Drag = 1287.3 lbs

Thrust = Drag

Thrust at stall = 1287.3 lbs (not including exhaust thrust)
Power at stall = 550*2000bhp = 1100000
Velocity = 96mph*1.467 = 140.8 ft/sec

Prop Effi = Thrust*Velocity / Power
Prop Effi(stall) = .1648 ~ 16.5%

Now, I know propeller efficiency starts getting wonky when velocity drops off, so I wasn't really sweating this one.  But when I plug everything in for max speed, my efficiency number looks pretty whacky.  Can the exhaust thrust make a big enough difference to throw the number off this much?

~Max speed at Sea Level = 320

Dynamic pressure = 261.9
Cdi = .0011
Cdo = .0272
Induced Drag = 96.6 lbs
Zero Lift Drag = 2379.3 lbs
Total Drag = 2745.9 lbs

Thrust = 2745.9 lbs
Power = 1100000
Velocity = 469.4 ft/sec
Prop Effi = 1.17 ~ 117% <-------I know that is way wrong.  Where did this get screwed up?

[Badboy]

Prop Effi = 1.17 ~ 117% <-------I know that is way wrong.  Where did this get screwed up?

Yep, your Cdo value is too large.

Badboy

[Stoney]

Hmm, that number came out of Dean, but I suppose he could have been mistaken.  I found another number of .0211.  I plug that one in and get:

Prop Effi @ stall:  15.8%

Prop Effi @ 320:  83%

Still seems like the full speed number may be a bit high, but certainly closer to what it should be.  Anyone know a good correction for exhaust thrust?

Thanks for the correction...

[hitech]

Exhaust  thrust can be as high at 200lb on some planes.

HiTech

[Stoney]

Found this on the NASA reports server:  http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20090014842_2009014224.pdf

Looks like they got ~4.5% of total thrust at 325 mph from the experimental data, with the collector ring and nozzle.  I'm not sure if the in-service nozzles were as efficient as the test nozzle.  Would this be a conservative correction for thrust or is it too different to be used as a valid approximation?

[TimRas]

Anyone know a good correction for exhaust thrust?

Hoerner gives a rule of thumb formula for exhaust thrust:
T [lb]= (0.11 to 0.13)*P [hp]

This does not apply with turbocharged engines, where (I think) you can assume the exhaust thrust as zero.

[Stoney]

Hoerner gives a rule of thumb formula for exhaust thrust:
T [lb]= (0.11 to 0.13)*P [hp]

This does not apply with turbocharged engines, where (I think) you can assume the exhaust thrust as zero.

Is that theoretical max or max realized? 

[Stoney]

Ok, another problem I'm having is that the efficiency, if extrapolated beyond Vmax, just keeps increasing to beyond 100%.  This doesn't follow most prop efficiency curves I've ever seen.  It should be decreasing as it approaches Vmax, right?

[Stoney]

I have assembled this which turned out as I expected it would.  Vmindrag is = to Vy, correct?

[Brooke]

I'd be suspicious of any prop efficiency that comes out lower than about 0.5 or so for an airplane in flight.

Here's a way to estimate prop efficiency using advance ratio and power coefficient, which are calculated from aircraft velocity, prop diameter, prop RPM, and engine HP.  See the "Thrust Equations" section of this document:

http://electraforge.com/brooke/flightsims/aces_high/stallSpeedMath/turningMath.html

[TimRas]

Is that theoretical max or max realized? 

Neither. I said "Rule of thumb".
IMO that means "You can use this for calculations if you don't have any better data".
I have seen exhaust thrust charts for BMW801 and Jumo 213.

Brookes' formulas seem to be "rule of thumb" -sort also. They don't take account of the blade numbers, blade width, blade airfoil etc.
The equation 2.2 seems to need some iterative calculation.

[Brooke]

Neither. I said "Rule of thumb".
IMO that means "You can use this for calculations if you don't have any better data".
I have seen exhaust thrust charts for BMW801 and Jumo 213.

Brookes' formulas seem to be "rule of thumb" -sort also. They don't take account of the blade numbers, blade width, blade airfoil etc.
The equation 2.2 seems to need some iterative calculation.

Yep, there are more-complicated eta calculations, but the equation will get in the ballpark.

Equation 2.2 isn't iterative, but requires solving a nonlinear (cubic) equation, or using numerical methods or just graphing it (Figure 3-17).

[chewie86]

I have assembled this which turned out as I expected it would.  Vmindrag is = to Vy, correct?

Did you mean: at Vmindrag you are climbing at Vymax? If so I would say yes.

For a C47 would be fun to estimate the max angle of climb (very close to stall's angle) if someone wants to sneak a base placed on a steep hill eheh..

[Stoney]

Here's a way to estimate prop efficiency using advance ratio and power coefficient

Using advance ratio is typically only used for determining static thrust.  The method I used is normally used for approximating thrust in the normal flight regime.  Most designer interpolate the transition area between takeoff and stall by drawing a curve between the two.  At least, that's what Dan Raymer says in Aircraft Design:  A Conceptual Approach

Now, that being said, I may have made a mistake in calculation, so if you see one, feel free to point it out.  Regardless, thanks for the help.

[Stoney]

Neither. I said "Rule of thumb".
IMO that means "You can use this for calculations if you don't have any better data".
I have seen exhaust thrust charts for BMW801 and Jumo 213.

Brookes' formulas seem to be "rule of thumb" -sort also. They don't take account of the blade numbers, blade width, blade airfoil etc.
The equation 2.2 seems to need some iterative calculation.

Well, you're certainly getting that from a "bible", but I was simply curious as to how the exhaust configuration would change that number.  For example, a collector ring and pipes (such as on a radial) versus the paired exhausts of the Merlins.