I intend to stay out of the discussion of single vs. dual propellers. It is one of those topics that can be argued either way depending on the relative importance you attach to the various factors influencing ship propulsion. However the matter of propeller specification is much more deterministic. You can optimize a propeller for efficiency, size, drag under sail, noise and vibration, etc. It is all a matter of hydrodynamics. You can't optimize everything at once, however. Propeller specification requires considerable compromise. Here is a program, written in elementary BASIC, for calculating the proper propeller for displacement boats. I posted it to the TWL some time ago. It also performs a horsepower calculation necessary to achieve hull speeds and indicates the efficiency of various propeller pitches, diameters, and rpms. This program works better than the one used by Michigan Wheel or Federal Propeller. This bare bones program will run on any computer which supports the BASIC programming language, even palmtops. All PCs can run it from the TRS 80 or Commodore Pet to the iMac. I use it on an old HP200 LX palmtop running a copy of Radio Shack BASIC for the PC. No provision is made for printing. I assume that you have a pencil and pad handy to record the results. If you have a BASIC interpreter, simply copy the text file starting at line 10. Most BASIC programs are able to interpret text files. What, you don't have a BASIC interpreter on your computer? You can download a BASIC interpreter from www.chipbasic.com. The site has them for just about any computer and all free. Several other sites also have BASIC interpreters. Just do a Google search for BASIC programming. Less than 10 years ago all computers came with a built in BASIC program. Programming was even taught in high school. Alas - today everyone buys packaged programs and programming is relegated to the Microsoft nerds. -------------------------------- BASIC PROPELLER CALCULATION FOR DISPLACEMENT HULLS - L. R. Zeitlin This program is designed to give a quick estimate of propeller specifications for typical displacement hulls such as sailboats and trawlers. I must caution that propeller specification is an arcane art full of compromises and approximations. It is rare good fortune if you get it right the first time. This program will get you in the ballpark, about + or - 10% of the right value. From there on it is experimental trial and error. The program has very limited error checking. If you enter absurd prop or power specifications for a given hull, you will get an absurd result. From a theoretical point of view pure displacement hulls work best with large, slow turning props. Generally the diameter is determined by hull clearances. The pitch is the main variable under your control. Fortunately the pitch of most bronze propellers can be adjusted a couple of inches either way at relatively low cost. While the program is designed to give you the most efficient prop for a given engine speed, reduction ratio and hull speed, most of us can live with, and even enjoy boats that dont squeeze the last mile from a tank of fuel. The logic of the program is simple. After entering hull and engine characteristics, hull speed is calculated using the standard formula KT = 1.34 x ?WL. An estimate of power required to reach hull speed is obtained using Keiths formula (line 90). This usually works out to about 1 HP per 500lbs displacement. A slip estimate is made using Gerrs formula for displacement hulls (line 110). Given power, slip and shaft RPM, propeller pitch and diameter are calculated using Crouchs method. This should get you in the ballpark. The more accurate and complex Bp method of propeller specification is used as a check on the simpler approach. Va is estimated (lines 347, 348) and Bp is calculated (line 350). Lines 350 through 410 provide estimates of Delta, P/D ratio and efficiency based on the Taylor Bp charts. The calculation is made to provide optimum efficiency at a given Bp. If you don't know what these terms mean, look them up in a marine engineering text or in Gerr's Handbook. In both cases, engine power is derated 5% to account for gearbox and shaft losses. Small modifications in propeller specification (up to 15%) are usually acceptable if pitch is increased 2 for every 1 decrease in diameter. Bear in mind that diameter and pitch are related for maximum efficiency. If you increase the diameter too much, friction losses will consume a disproportionate amount of power. The limiting cases are props with very large diameter and very small pitch and props with very small diameter and very great pitch. Neither will move the boat very well. The theoretical limit for propeller efficiency is about 75% but a prop that exceeds 50% efficiency is far above average. Of course you may not want the most efficient propeller for a sailboat or motorsailer. Efficient propellers tend to be big and have a lot of blade area. This translates into unacceptable drag when sailing. In that case, play around with the prop RPM and the diameter until you find one that suits. If you have comments or questions, contact me at: LRZeitlin@aol.com -------------------------------------- 10 PRINT "Propeller calculation program" 20 PRINT "Copyright 1997: L. Zeitlin" 27 FOR x = 1 TO 30000!: NEXT x 29 PRINT: PRINT "CROUCH'S METHOD FOR OPTIMUM HULL SPEED PROPELLER CALCULATION." 30 INPUT "Waterline length in ft."; L 40 INPUT "Displacement in lbs.";D 50 INPUT "Engine rated HP"; HP 52 HP=HP*.95 'assume 5% HP loss in power line. 55 INPUT "Engine RPM at rated HP"; RPM 57 INPUT "Percent RPM used for calculations";PRPM 58 DRPM=PRPM*RPM/100 'desired RPM 59 HPREV=HP/RPM 'horsepower per revolution. 60 INPUT "Gearbox reduction ratio"; RG 70 HS= L^.5 * 1.34 'hull speed calculation. 80 PRINT "Hull speed ="; INT(HS *100)/100;"KT" 90 RHP = D * ((HS/(11.963 * L^.5))^3) ' Keith's formula, required HP for hull speed. 100 PRINT "Required HP ="; INT(RHP *100)/100 105 IF RHP > HPREV*DRPM THEN GOTO 900 110 SLIP = 1.4/(HS^.57) 'estimate of slip, Gerr's formula 120 HSRPM = DRPM/RG 'desired shaft RPM at hull speed. 130 PITCH = (HS*1215.6/(1-SLIP))/HSRPM 140 DIAMETER = (632.7 * ((HPREV*DRPM)^.2))/HSRPM^.6 150 PRINT:PRINT "Three bladed propeller:" 160 PRINT "Diameter ="; INT(DIAMETER * 10)/10; "inches." 170 PRINT "Pitch =" INT(PITCH * 10)/10; "inches." 180 PRINT:PRINT "Two bladed propeller:" 190 PRINT "Diameter ="; INT(DIAMETER * 10.5)/10; "inches." 200 PRINT "Pitch =" INT(PITCH * 10.1)/10; "inches." 205 PRINT "Slip estimate=";INT(SLIP*100)/100;"percent. 210 Thrust = 62.72 *((HP*PRPM/100*DIAMETER/12)^.67) 220 PRINT: PRINT "Static thrust =";INT(Thrust * 10)/10;"pounds." 225 PRINT:INPUT "Would you like to try another calculation using Crouch's method (Yes=1, No=2)";Q 226 CLS 227 IF Q=1 THEN GOTO 30 230 PRINT:INPUT "Would you like to try the Bp method of optimum propeller calculation (Yes=1, No=2)"; Q 240 IF Q=2 THEN GOTO 500 250 CLS 260 PRINT "Bp METHOD OF OPTIMUM PROPELLER CALCULATION." 263 INPUT "Choose method: (1) Calculate block coefficient. (2) Use average block coefficient."; Q 264 IF Q=2 THEN GOTO 300 270 INPUT "Waterline beam in ft. =";WLB 280 INPUT "Hull draft, excluding keel or skeg, in ft. ="; DFT 290 Cb = D/(L*WLB*DFT*64) 295 PRINT "Block coefficient ="; INT(Cb * 100)/100 296 GOTO 303 300 Cb = .53 303 INPUT "Desired engine RPM"; DRPM: DHP = DRPM * HPREV 306 PRINT "Available shaft HP at desired RPM ="; INT(DHP *10)/10 310 INPUT "Desired speed in Kt."; HS 313 RHP = D * ((HS/(11.916 * L^.5))^3) 'required HP for desired speed. 316 IF RHP > HPREV*DRPM THEN GOTO 1000 318 PRINT "Required HP for desired speed ="; INT(RHP *10)/10 320 SRPM = DRPM /RG 'shaft RPM. 330 SHP = DHP 'available HP at desired RPM 335 DX=0 347 Wf = 1.11 -(.6*Cb) 348 Va = HS * Wf 349 PRINT "Va="; INT(Va*100)/100 350 BP = (SRPM * SHP^.5)/Va^2.5 355 PRINT "BP"; INT(BP *10)/10 360 DELTA = 103.143 + (4.73 * BP) -(.034 * BP^2) + ((1.57/10000) * BP^3) - ((2.964/10^7)* BP^4) 361 IF DELTA <0 THEN PRINT "Entered values out of range. Try again." 362 IF DELTA <0 GOTO GOTO 303 365 DIAFT = (Va*DELTA)/SRPM 367 PRATIO = 1.014 - (.014 * BP) + ((1.72/10000) * BP^2) - ((9.873/10^7) * BP^3) + ((2.047/10^9) * BP^4) 370 PRINT "DELTA"; INT(DELTA *10)/10 375 PRINT "DIAFT"; INT(DIAFT *100)/100 380 DIAIN = DIAFT * 12 395 PRINT"P/D RATIO"; INT(PRATIO *100)/100 397 PITCH = PRATIO*DIAFT 398 SLIP = 1-(HS*101.3/(PITCH*SRPM)) 410 EFF = .742 - (.006 * BP) + ((5.086/10^5) * BP^2) - ((2.209/10^7) * BP^3) + ((3.835/10^10) * BP^4) 420 PRINT "Three blade prop diameter ="; INT(DIAIN *100)/100;"inches." 425 PRINT "Two blade prop diameter =" INT(DIAIN * 105)/100;"inches." 430 PRINT "Pitch ="; INT(PRATIO * DIAIN*100)/100;"inches." 440 PRINT "Slip ="; INT(SLIP*100)/100;"percent." 450 PRINT "Efficiency ="; INT((EFF-(DX/2))*100)/100; "percent." 451 Thrust = 62.72 *((RHP*DIAFT)^.67) 452 PRINT "Static thrust =";INT(Thrust * 10)/10;"pounds." 455 PRINT: INPUT "Do you wish to modify engine and speed variables (Yes=1, No=2)";Q 456 IF Q=1 THEN GOTO 303 457 INPUT "Do you wish to change recommended propeller diameter (Yes=1, No=2)";Q 458 IF Q=1 THEN GOSUB 2000 460 PRINT:INPUT "Another propeller calculation? (Yes=1, No=2)"; Q 465 IF Q=1 THEN CLS: GOTO 29 470 'IF Q=1 THEN GOTO 30 500 PRINT "GOODBYE" 505 FOR x = 1 TO 10000: NEXT x 510 END 900 PRINT "The engine does not have enough power to reach indicated speed." 902 INPUT "Do you wish to modify initial variables (Yes=1, N=2)";Q 903 IF Q=1 THEN GOTO 30 904 IF Q=2 THEN GOTO 500 905 RETURN 1000 PRINT "The engine does not have enough power to reach indicated speed." 1002 INPUT "Do you wish to modify initial variables (Yes=1, N=2)";Q 1003 IF Q=1 THEN GOTO 303 1004 IF Q=2 THEN GOTO 500 1005 RETURN 2000 INPUT "Desired diameter in inches"; DDIAIN 2005 DX = 1-(DDIAIN/DIAIN) 2010 DIAFT =DDIAIN/12 2020 DELTA = (SRPM * DIAFT)/Va 2025 PRATIO = (3.28) -(.03*DELTA)+((1.231/10000)*DELTA^2)-((1.719/10000000#)*DELTA^3) 2027 2030 GOTO 370 2040 RETURN