PROPELLER PERFORMANCE -

A Computer Program

0.30 028

By Don Hewes (EAA 32101) 12 Meadow Dr. Newport News, VA 23606 HE PROGRAM COVERED in this article calculates to a reasonable degree of accuracy the operating performance of a family of propellers applicable to small airplanes. The diameter, pitch and number of blades can be varied as desired as well as the ranges of airspeed, propeller rpm and altitude. The results are given in terms of the thrust and power coefficients, thrust, advance ratio, efficiency, power required and tip mach number as functions of either airspeed or propeller rpm.

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The program is based on a few simple equations and a

single set of data which describes the aerodynamic characteristics of the propeller. These data were derived from some early NACA tests of & family of propellers obtained in some of the wind tunnels at NACA around 1930 to 1940. A typical set of data is shown in Figure 1. Several years ago, I developed some equations to reduce these relatively complex data to the data shown in Figure 2 so that the data could be handled in a more compact form. The equations were based on the simplifying assumption that the thrust and torque of the propellers were produced by forces (PD and PL) acting solely at the 75% station along the blade radius. (Shortly after completing this work, I found that many years ago famed Fred Weick and then some British researchers had made somewhat the same simplifying assumption and obtained essentially the same results as shown in Figure 2. However, there were no apparent attempts to use this approach in subsequent work as far as I have determined.) It can be seen that all the data of Figure 1 tend to fall on a set of just two curves depicted in Figure 2 by the dashed lines. In fact, these two curves have somewhat the same appearance or shapes as those of the familiar lift and drag coefficient curves for conventional airfoils, however, the terms used are not directly equivalent. There are some small departures of the data points from the two curves of Figure 2, however, these generally occur in the portions of the curves that tend to be outside the normal operating ranges of most lightplane propellers. The assumption that these two curves represent the operating characteristics of the particular family of propellers leads to relatively small errors of 5% or less for most practical purposes. The propellers used on homebuilt airplanes vary most significantly in diameter, pitch, blade shape and, in a few cases, the number of blades. The shape or planform of the propeller is represented in engineering circles by the term "activity factor" which is a mathematical way of representing the distribution of blade chord or area along the blade radius insofar as the absorption of power and development of thrust are concerned. It is true that there are a few other factors or parameters which influence the

propeller performance, such as Reynolds Number, blade airfoil section, pitch distribution and tip Mach number

and tip shape. But for purposes of this program, these factors were considered as secondary and represented to

reasonable degree by the specific features of the NACA propeller family employed. Most of the tests were made with blades using the Clark-Y airfoil section with an activity factor of about 90. Some NACA tests were made

002 O

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2

Fig-

V/r»0

IG

2.O

Fig. 2

It should be noted that the standard method for measuring blade angle or pitch is to refer to the chord line at the 75% blade station. Some propeller makers may use different references, such as the flat bottom of the airfoil and the propeller tip. In these cases, the blade angle and pitch measurement must be corrected to correspond to the standard method before using this program. If activity factor for a particular propeller is unknown,

it can be determined by measuring the chord or blade width from the 20% radius station to the 100% or tip station of the propeller in 10% increments. The resulting values are entered in the special subprogram in the se-

quence called for and the resulting activity factor is calculated.

with blades of different activity factors and it was possible

DEFINITION OF TERMS AND SYMBOLS

to develop correction factors based on those test results to account for activity-factor differences in this program. The practical range for activity factor values is from about

this program. For the most part, these follow standard

70 for a very thin bladed propeller to about 150 for a broad bladed propeller. 44 AUGUST 1984

The following are definitions of the various terms in NACA/NASA definitions, however, in writing a computer

program it is sometimes necessary to use other terms or symbols to represent a given factor.

AF

Activity factor. Sit tut

AB t BT

Reference blade angle of attack at 751 radiui station of bladi Nuiber of propeller bladii Blade pitch angle at 75! radiui station 2 5

CP

Po«r coefficient, Po«r/R0 x N i O 2

CT

Thrust coefficient. Thrust/RO x N x O

D ET J HP N PO

Propeller diaieter, Ft Propeller efficiency. CT x U CP (Also referred to as ETA) Advance ratio, V/N x D Horsepooer, Poner/550 ft-lbi/iec Propeller speed, Revs/Sec Apparent drag at 751 radius station

PL fi P HT

Apparent lift • • • Torque, ft-lbs Potter, 8 x N ft-lbs/sec Altitude, thousands of ft

HACK

(tach nuiber, Prop tip speed/VS 3

RC

Air density, slugs/ft ( 0.00238 for Sealevel, standard teip. )

TT TR

Propeller total thrust, Lbs Air teeperature, Degs. Rankin

V

Flight velocity, Ft/Sec

VS

Sonic velocity, Ft/Sec

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In the program, the numbers 1 and 2 are used to denote the minimum and maximum values for parameters V and N. Also the letter D is used to denote the incremental change in these two parameters. DISCUSSION OF PROGRAM

The program is written in Microsoft Basic (MBasic) as used on a Heathkit 89 computer with a Magnolia GPM operating system. The program itself requires about 6K bytes and the Basic program will require an additional 24K bytes to operate. Persons using this program may find it necessary to alter the program slightly to work properly on their particular system. The printer commands (LPRINT) to obtain printed copies of the calculations have not been included to reduce the length for publications. The program is provided with a standard set of operating parameters which are displayed in a menu format. The values of these are given in line 30 of the program and are displayed automatically in the menu which is generated in lines 190 to 230. These values can be changed easily from the menu by following the instructions that appear at the bottom of the menu (lines 240 to 250). The standard values can be changed permanently by altering the terms in line 30.

The values used in the menu are the more or less conventional dimension of rpm, mph and so forth, however, note that altitude is given in "thousands" of feet. For convenience, propeller pitch is shown in terms of the advance distance normally used to define pitch but the program uses the angular value in the calculations. Consequently, the angular value is calculated and shown. A special subprogram is used to calculate the activity factor of some specific propeller if the width or chord of the blade at various radial stations can be determined. This program is entered by typing item number 11 at the bottom of the menu (line 240). This directs you to enter any activity factor value you desire or to type the number 1 which then calls up the subprogram written in lines 650

to 700. When all dimensions are entered, the program calculates the activity factor and returns to the menu with

the new value displayed as item 11.

In line 290, the values are converted to the proper

dimensions to match the equations used and mathematical operations of MBasic. These values are subsequently reconverted in line 640 where the program loops back to the menu. Bear in mind these dimensional changes when

checking your version of the program. Due to this conver-

sion process, the maximum velocity or rpm calculation may not be printed. If this happens and you want that particular condition, merely increase the range of that parameter in the menu to the next larger value. Line 300 is used to calculate the effects of altitude on air density and temperature. Sonic velocity at altitude is also determined. Lines 310 to 330 let you select the type of step calculations to be performed. You can hold the airspeed constant and let the airspeed step through from minimum to maximum or vice versa. Lines 340 to 410 take care of formatting and printing the headings for the tabular results on the screen. If a permanent copy of the results is desired, add the appropriate LPRINT commands here. Lines 420 to 630 perform the step by step calculations and printing of the results. Line 430 calculates the reference blade angle of attack for the particular set of operating conditions. Tip velocity and mach number are calculated in line 440. Lines 450 and 460 are used to limit the blade angle to values greater than -3.5 degrees where the thrust is essentially zero and below which the calculations would be in error. Lines 470 to 500 look up the propeller data stored in the G-array and interpolate to determine the PL and PD values for the specific blade angle. These values are then converted to the standard propeller coefficients in lines 510 to 540 and then to thrust and power values in lines 550 to 560. The data is formatted and printed in lines 570 to 600. Add LPRINT commands here if desired. Line 630 is used to stop the computer for display and permit recycling to the menu when desired. A sample of the results for a particular run is shown in Figure 3. The operating conditions used in this case correspond approximately to those for the Dragonfly airplane which has a recommended 52 diameter x 42 pitch propeller. The activity value corresponds to the particular propeller I am currently using. It is made by Bob Amar of Glenwood, Maryland.

Fig. 3

PERFOSHANCE CALCULATIONS ALTITUDE - 0 FT DENSITY = .00238 SLU6/CU.FT. PROP OIAH = 52 IN. NO. BLADES - 2 BLADE PITCH = 42 IN. OR 19 DES. ACTIVITY FACTOR - 98 KPfl AB CT CP THRUST J ETA HP 2500 -.1 .029 .031 45 .81 .85 14.3 2600 .6 .036 .033 57 .84 .78 18.1 2700 1.2 .04 .036 69 .75 .83 22.2 .039 2800 1.9 .044 82 .72 .82 26.6 2900 2.4 .048 95 .7 .042 .81 31.4 3000 2.9 .044 .052 110 .67 36.4 .8 .045 3100 3.4 .056 125 41.8 .65 .8 3200 .059 .047 3.9 141 .79 47.4 .63 .048 3300 4.3 157 .062 .61 53.5 .78 3400 4.7 .049 .064 174 .59 .77 59.9 VEL= 100 HPH

CLOSING COMMENT

This program can be used to study the effects of the various propeller parameters on its performance and may

help in solving different propeller questions you may have.

Bear in mind that the propeller modeled in this program may not match exactly the propeller that you have but the results should be fairly close. If there are any questions on programming problems, you should consult anyone who is fairly familiar with

current home computer systems. There are many stores

that might be able to answer some questions, but don't expect a lot of help. Your best source of help will be someone in the many computer clubs that are springing up all over the country or perhaps someone who teaches at the

local high school or community college. Unfortunately, I'm afraid I'm not of much help along this line because I have very little experience and no knowledge of the other systems. However, I will try to answer some questions, especially if they relate to the Heath-Zenith systems.

(PROGRAM ON NEXT PAGE)

SPORT AVIATION 45

I

10 REN - PURPOSE IS TO CALCULATE PERFORHANCE OF A PROPELLER 20 CLEAR 30 H[=0:V]=50:DV'10:V2=170:Nl=2400:DN=100:N2=38oO:D»52:8«2:P'42:AF=98 40 FOR R*0 10 9:REAO 6IR,0).6lR,ll,6lR.2):NE»l 50 DATA -4.0,.001 60 DAIA 0..0285..0015 70 DAIA 4..055,.0035 8 0 DATA 8..08..006

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90 DATA 10..091..008 100 DATA 12..099,.012 110 DATA 14.,104..016 120 DAIA 16.. 106,.022 _____________________ 130 DATA 18..11..028 • •-.'• . • 140 DAIA 20..11.,u35 150 FOR R=l 10 K;PRINI:NE»i:PRINri»MllllllllinilltMIIHtlllllllIHIUIIIIIIIIIHIIIIIIIIIIMIIHMIIIMHH|.. . , . 160 PRINI" 1H1S IS 'PROP' PROIiRAH - APR In, 1984' 170 PRINT' BV lion He«5, EAA 32101 X

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180 FOR n=0 TO 76:PR1NI'»'::NEIII H

HO PRINT:PR1NT IAfli26):11FLIBHI LONDIT10NS':PRIN1:PR1NI'1 ALI1IUDE - ":HT:' IHOUSANB FT.':TABl40):"2 HIN. AIRSPEED - ":V1:" hPH'iP RlNTiPRINT'3 SPEED 1NCREHENI -'iOV:IAB(40)"4 HAI AIRSPEED - "iV2:FUR R* 1 10 /SsPWNl'-'llNtJI RI 200 PRiNl IABl26):'EN61NE CONDJUONS':PRINI:PhlNI'b MIN ENGINE RPtl - ":Nl:IABi4oi:"6 RPN INCRENENi - ":DN:PR!NI:PfiINI - 7 HAX EN6IN t RPH - "!N2

210 BT=INTl573IAINlP/iD»2.356)))/10

220 FOR R=l 10 78:PRINT'-"::NE»T RiPRINT TA6i26):"PROP CONDilIONS":PHINI:PRlN!'8 PROP DIAHE1ER IN INCHES - ":D:TAB 140):"9 NOHbER O F BLADES - ':B 230 PRINTsPRlNPlO PIICH - ":P:N IN. OR ":BT:' DEBs. ":IAB140):"11 ACIIVITY FACTOR - ':AF:FOR H«l TO 78:PR]NI 10 CALCULAIE FACIOR OR 10 ENIER AN* VALUE.'.»Y:IF n=l IHEN Vy>0:60TO 650 PRIN1:1NPUPENIER DESIRED VALOE.'-.I IF i«l IHEN Hl>/ ELSE IF 1=2 THEN Vl=i ELSE IF r=3 IHEN W-l ELSE IF (=4 IHEN V2=/ ELSE IF >=5 IHEN Nl=2 ELSE IF 1=6 IHEN DN=Z E IF 1=7 IHEN N2«Z IF y=8 IHEN 1)»Z ELSE IF W IHEN B'/ ELSE IF »=)0 IHEN P«i ELSE IF r=ll IHEN AF=Z

60TO 180 Vl'Vlll.47:DV=DVH.47:V2=V2«1.47:D=0/12:flI=Bl/57.3:HI=HII100o:Nl=Nl/60:DN=DN/60:N2=N2/60 TE=ll-6.89E-06»HT):S6=IE"4.25:RO=S6J,oo238:KH=lSG-UI-S6)/7,55i):IR=1.8»l2BB.15-.00198IHT):VS'SUR\2403iyRl PRINhPRINI'fyPE '1' 10 VARy RPH «T CONSTANI A1RSPEE0."::1NPUI"'.VN

320 IF VNOl IHEN PRINMPRINI'ftlRSPEEd MILL VHRr FROH ":INh.b*Vl/1.4/i: M TO •:1NU.5»V2/1.47):'. ENTER DESIRED RP« VALUE.";:INPUT"'

:N:N=N/6o:60TO 34o

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330 PRINT:INPUT'ENIER DESIRED 'V VALOE.•!V:V«lNTl.5*V»14.;)/10:VD=l

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340 PRINI:PR1NI:PR1NI lABlJOli'PERFORHANCE LALLULAllONb'

350 360 370 380

IF VN=I THEN PRINI:PRiNI"VEL= ':iNTl.5»V/l,47):' HPH': IF VN01 THEN PR1NT:PR1NI-RPH= •:1NU.5AB';rA6l20)iICI":fAB(26l:'CP':TAB(36):"rHRUST':IABi4B):'J":rAfli56l:1ETAiiTAB(64i:"HP':TABi72)"HALH' 420 IF VN=1 IHEN FOR N=N1 10 N2 SIEP DN ELSE FOR V=VI 10 V2 S1EH UV 430 J=V/lNIO):FI=ATNt.424IJ):A8=BI-FI:AB=ABI57.3 440 VI=(V2*t3.14INtD)"2) '.5:I1ACH=VI/VS 450 IF VN=I THEN IF Afl\-3.5 IHEN N=N*DN:BOTO 430 46(1 IF VNUl IHEN IF AB1 THEN PRINT INII.5+V/1.47I: 600 PRINT IABUOl!AflirAbll8)!CI:TAfll26l:CP:lAH36i: (l!l«Bi46)!J:lHB(55):ET:IABi6i)!HP:IABl7D:HHCH 610 IF VNul IHEN NEll V 620 IF VN=1 IHEN NEXI N

630 PRINI:INPUI"PRESS RETURN) 10 CON1INOE,'.X:PR1N1:PRINI:PRINI:PRIN1 640 PA=l:HI=1.47:Vl=INTIVl/HI):DV=lNT(DV/HI):V2=INnV2/Hll:RP=60:Nl=NltRP:DN=DN«RP:N2=N2IRP:BT=INltBTI5730)/100:DMNIlD»12):HI=HI/10

00:6010 180 650 660 HEN 670

PRINTiFOR R=2 10 10 :PR1NT'EN1ER CHORD AT 'iRIIO:' PERCENT SIA110N IN INCHES. > !!lNPUT".CHiR):PRlNliNEXT PRlNhPRINT'ENTER SlAlION PERCENI 10 CORRECI EKROR. ":PR1NI IA6(20i"OIHER»lSE PRESS