I am fascinated by Paul's prop design
and attempting to fully understand the rational behind
it.
I refined my QB program a bit further.
I also found a serious error as I was not
multiplying the lift function by the lift coef.
I also corrected the thrust for the thrust
in the direction of travel and not perpendicular
to the blade cord. That made a huge difference
in the thrust developed near the root of the blade
due to the unfavorable blade angle despite the seven
inch cord width. I also added
torque increment loads for each blade segment and totaled
them up. I got a ridiculous low over all torque load
for the blade of six foot pounds so there could
be a mistake in there some place. Also I may have
underestimated the operating lift coef. at only .5
and consequently also the drag coef. at only .01.
As the lift coef. is increased the drag coef. increases
faster.
Paul, what do you figure the lift coef. is?
Another possibility is the blade tip vortex torque load
which is CsubL squared divided by the aspect ratio
of the blade times pi times the length of the blade.
Could be considerable. In fact I think Paul mentioned that.
Hopefully some one on here will see the error of my ways.
Never the less this simple program is approaching usefulness.
Also sorts of trade offs can be tried such as wider blades
running at a lower pitch or lift coef..
BTW the prop torque generated by the rotary through the 2.85:1
PSRU is on the order of 430 foot pounds so I am way
off.
RPM = 2700 MPH = 200 Lift Coef. = .5 Drag Coef. = .01 Air density =
.0026
Radius Tan V Angle Cord V Cord Seg Area Seg Thrust Seg Torque
Inches MPH Deg MPH Inch Sq. feet pounds pounds
3.00 48.2 76.5 206 7.20 0.150 1.93 0.04
6.00 96.3 64.3 222 6.60 0.138 3.82 0.09
9.00 144.5 54.1 247 6.00 0.125 5.79 0.15
12.00 192.7 46.1 278 5.40 0.112 7.83 0.23
15.00 240.9 39.7 313 4.80 0.100 9.80 0.32
18.00 289.0 34.7 351 4.20 0.087 11.56 0.42
21.00 337.2 30.7 392 3.60 0.075 12.89 0.52
24.00 385.4 27.4 434 3.00 0.063 13.59 0.61
27.00 433.5 24.8 477 2.40 0.050 13.45 0.67
30.00 481.7 22.5 522 2.40 0.050 16.33 0.88
33.00 529.9 20.7 566 1.80 0.038 14.63 0.86
36.00 578.0 19.1 612 1.20 0.025 11.49 0.73
Total Thrust Pounds = 123 Total Torque Foot Pounds = 6
OPEN "C:\qb\props\pitch200.dat" FOR OUTPUT AS #1
CLS
DIM Cord(25)
Thrust = 0
Torque = 0
AirDen = .0026
MPH = 200
CsubL = .5
CsubD = .01
RPM = 2700
PRINT #1, "RPM ="; RPM;
PRINT #1, " MPH ="; MPH;
PRINT #1, " Lift Coef. ="; CsubL;
PRINT #1, " Drag Coef. ="; CsubD;
PRINT #1, " Air density ="; AirDen
PRINT #1,
PRINT #1, "Radius Tan V Angle Cord V Cord Seg Area Seg Thrust Seg
Torque"
PRINT #1, "Inches MPH Deg MPH Inch Sq. feet pounds
pounds"
FOR radius = .25 TO 3 STEP .25
RadiusInch = radius * 12
PRINT #1, USING "##.##"; RadiusInch;
TangVelFPS = (6.28 * radius * RPM) / 60
TangVelMPH = (TangVelFPS * 60) / 88
PRINT #1, USING "#####.#"; TangVelMPH;
tan1 = MPH / TangVelMPH
angleRAD = ATN(tan1)
angleDeg = (angleRAD * 57.295)
PRINT #1, USING "######.#"; angleDeg;
CordVel = (TangVelMPH ^ 2 + MPH ^ 2) ^ .5
PRINT #1, USING "######"; CordVel;
READ Cord
PRINT #1, USING "####.##"; Cord * 12;
SegArea = .25 * Cord
PRINT #1, USING "#####.###"; SegArea;
ThrustInc = CsubL * SegArea * (CordVel) ^ 2 * AirDen
'sin=opp/hyp
angle2Deg = 90 - angleDeg
angle2RAD = angle2Deg / 57.295
Thrust2 = SIN(angle2RAD) * ThrustInc
PRINT #1, USING "########.##"; Thrust2;
dragInc = SegArea * CsubD * CordVel ^ 2 * AirDen
TorqInc = dragInc * radius 'foot pounds
PRINT #1, USING "########.##"; TorqInc
Thrust = Thrust + Thrust2
Torque = Torque + TorqInc
NEXT
DATA .6,.55,.5,.45,.4, .35, .3, .25, .2,.2,.15,.1
PRINT #1,
PRINT #1, "Total Thrust Pounds =";
PRINT #1, USING "#####"; Thrust;
PRINT #1, " Total Torque Foot Pounds =";
PRINT #1, USING "#####"; Torque
CLOSE
SHELL "more < pitch200.dat"
END
If your interested in understanding prop design I would strongly recommend
getting Contact Magazine Issue #77 and read Paul Lipps' article. The design
of props is all about air flowing across a rotating wing. I don't have the
article in front of me but I believe Paul Lipps dismisses the concept of
prop pitch. Props are not like rotating screws. The resulting airflow is
influenced by airspeed, the rotational velocity of the prop (which varies
along each segment of the prop), inflow velocity (movement of the air toward
the prop ie. the fan affect) and swirl velocity ( the rotating effect of
inflow air). Prop modeling programs use successive approximation techniques
to estimate inflow and swirl velocities and combine them with the aircraft
airspeed and the rotational velocity in order to predict thrust and torque.
You can't use a single lift coefficient and drag coefficients. Lift
coefficients will vary from negative values to values exceeding 1.2.
depending on whether the plane is standing still or flying at Vne speeds.
Drag coefficients go up exponentially as the lift coefficient increases. A
prop cannot be fully optimized unless the prop can be twisted (not turned as
in constant speed props) at varies air speeds. The Angle of Attack of the
prop tip only needs to change a small amount and the root section of the
prop needs to change a lot to optimize it for all aircraft speeds. There is
Quick Basic Program by Peter Talbot in Martin Hollmann's book: 'Modern
Propeller and Duct Design'. The program is difficult to use because, to
change parameters, you have to change them in the code statements. I have
re-written this program in Visual C++ (for Windows operating system) but it
is still work in progress. The output of Peter's program and mine will show
the thrust and associated torque requirements at each increment in airspeed.
It will also show the prop section efficiencies.
To determine the 'ideal' prop you need to know how much thrust is required
for takeoff, climb and cruise along with the desired rates of climb. You
also need to model the engine's torque or horsepower performance. Or you
can take Paul Lipps approach and mount a prop with a known profile onto the
engine and go fly the plane, accumulate performance data and plug the
results into computer models to predict the aircraft thrust requirements for
different flight profiles. I am using John T. Lowry (Ph.D)'s Bootstrap
Approach to Aircraft Performance - Part two spreadsheet to predict the
trust, drag and climb performance for the Glastar. Dr. Lowry's spreadsheets
can be found at
http://www.avweb.com/news/airman/182410-1.html. I was able
to get then Part II spreadsheet of performance data for Chris Lowery's
Glastar (see Attached spreadsheet). With the aircraft performance data, the
prop thrust data from the C++ program and engine HP data, I can predict top
speed, excess thrust and climb rate potential and HP requirements at cruise
(and fuel burn). Of course the results are only as good as the data that
goes into the models.
There are two other programs out there that you might want to look at. The
propeller sizing spreadsheet that was part of the March 2004 issue of Sport
Aviation is available at
http://www.eaa.org/benefits/sportaviation/S407-PropDesign.xls. In Paul
Lipps' Contact magazine article he mentioned that props designed with
laminar flow airfoils have much lower drag coefficients than the standard
Clark airfoils typically used for prop designs. There is a program
available at
http://web.mit.edu/drela/Public/web/xfoil/ that will predict
Lift and Drag coefficients for various angle of attacks. The C++ program
enhancements that I am working on will use the Xfoil program to examine prop
performance and will plug that information into the prop performance
program. The user need only select airfoil profiles for the different
sections of the prop. The program will then work with Xfoil, feeding it the
Reynolds numbers (affected by airspeed) to acquire the lift and drag
coefficients at different angle of attack at different airspeeds and rpm
settings.
I have a question for Paul Lipps. The Xfoil program will graphically
portray the pressure distribution forces across the airfoil. The pressure
distributions forces are used to predict lift and lift is used to predict
thrust. However, if the summation vector of pressure forces is different
than the lift force vector it would seem to be more accurate to predict the
thrust directly from the summation force vector (the vector resulting from
the summation of all of the discrete pressure forces). I don't believe the
conventional prop modeling programs do this. Is the coefficient of moment
(Cm) related to this? Can Cm be used to predict airfoils that would be more
favorable for converting engine power to thrust?
Thanks,
Del Johnson
The ultimate would be 3D CFD (Computational Fluid Dynamics) but
I doubt I will be able to afford that anytime soon.
Paul Lamar
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