Propeller Calculator, Crouch's Calculator

Optimizing the performance of Boston Whaler boats
jimh
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Propeller Calculator, Crouch's Calculator

Postby jimh » Sat Oct 17, 2015 9:52 am

The two very useful performance-related calculators, the Propeller Calculator and Crouch's Calculator, are at this moment no longer available due to the move of the website to a new host. I am particularly fond of both of those calculators and will be making an effort to get them working again. While there are many alternative calculators available for the propeller calculations, the Crouch's Calculator was unique.

jimh
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Joined: Fri Oct 09, 2015 12:25 pm
Location: Michigan, Lower Peninsula
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Re: Propeller Calculator, Crouch's Calculator

Postby jimh » Mon Mar 28, 2016 7:09 pm

I have not yet been able to restore the old Propeller Calculator that was available for years here on CONTINUOUSWAVE.COM. For an alternative propeller calculator, I recommend the very nice propeller calculator implemented at:

http://www.rbbi.com/folders/prop/propcalc.htm

The above calculator is very versatile and the presentation is excellent. I recommend using this calculator until I can get our old one working again.

jimh
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Joined: Fri Oct 09, 2015 12:25 pm
Location: Michigan, Lower Peninsula
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Re: Propeller Calculator, Crouch's Calculator

Postby jimh » Sun Oct 23, 2016 8:36 am

Crouch's method came to my attention in a book, PROPELLER HANDBOOK, written by naval architect Dave Geer. The original speed predictions and hull constants were for boat speeds in nautical-miles-per-hour, but I preferred to use statute miles per hour, and emended the formulas to give the predictions in that speed unit. I created an on-line interactive calculator that was quite unusual and was the first known implementation of Crouch's method in an on-line calculator. Unfortunately, a change in the website hosting arrangement caused the calculator to go offline due to the particular underlying software used in its design.

An alternative to the Crouch's Calculator that was available here has been found at

http://www.go-fast.com/boat_speed_predictions.htm

Although the above linked page attributes this analysis to Mercury Marine, the method is identical to Crouch's analysis. The basis for Crouch's Calculator was the observation that boat speed is proportional to the power-to-weight ratio to the 0.5 exponent times a constant that was scaled for the type of moderate v-hull planing boat being analyzed. For a typical Boston Whaler hull the hull factor of 180 can be used to get a reasonable estimate of hull speed potential in MPH.

jimh
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Re: Propeller Calculator, Crouch's Calculator

Postby jimh » Wed Apr 22, 2020 4:43 pm

Propeller Calculators use the relationship between RPM, RATIO, PITCH, (BOAT) SPEED, and SLIP as described below to calculate one parameter from the other four.

  • RPM, a positive number; the crankcase speed in revolutions-per-minute
  • RATIO, a positive number; lower unit gear reduction ratio; the number of revolutions of the crankshaft to produce one revolution of the prop shaft.
  • PITCH, a positive number; blade pitch of propeller in inches.
  • SLIP, a percentage, 0.1 to 99.9; index of propeller performance.
  • SPEED, a positive number; the boat speed in various units of measurement
  • C a constant to convert inches-per-minute of revolution to boat speed;
    for miles-per-hour, 1056; for nautical-miles-per-hour, 1215.2; for kilometers-per-hour, 656. (See below for derivation.)
The basic calculation is to find SPEED, which by definition is described in (1) below; the other elements can also be calculated as shown:

Defining relationship
RPM PITCH
(1) SPEED = ----- × ----- × [ 1- (SLIP/100) ]
RATIO C

SPEED × RATIO × C
(2) SLIP = 100 × [ 1 - (-------------------) ]
RPM × PITCH


SPEED × RATIO × C
(3) PITCH = ( -------------------------- )
RPM × [ 1 - (SLIP/100) ]



RPM × PITCH × [ 1 - (SLIP/100) ]
(4) RATIO = ( ---------------------------------- )
SPEED × C


SPEED × RATIO × C
(5) RPM = ( ---------------------------- )
PITCH × [ 1 - (SLIP/100) ]


The constant C is derived from the analysis of the dimensions involved in the calculations. The propeller advance is generally given in INCHES/REVOLUTION and the speed of the propeller rotation is generally given in REVOLUTIONS/MINUTE. The speed of advance (or how far the screw propeller would move if in a solid) would then be calculated in units of INCHES/MINUTE, an unusual dimension which needs to be converted into something more commonly used for boat speed.

The most common conversion is to MILES/HOUR (MPH), which is derived below:

1 HOUR     12 INCH    5280 FOOT    1056 HOUR INCH     
------- × ------- × --------- = --------------
60 MIN 1 FOOT 1 MILE 1 MIN MILE


Similarly, if the results are desired in NAUTICAL MILES/HOUR (NMPH):

1 HOUR     12 INCH   6076 FOOT      1215.2 HOUR INCH     
------- × ------- × ----------- = -----------------
60 MIN 1 FOOT 1 NAUT-MILE 1 MIN NAUT-MILE


And if results are desired in KILOMETERS/HOUR (KPH):

1 HOUR   12 INCH     3.28 FOOT   1000 M   656 HOUR INCH     
------- × ------- × --------- × ------ = --------------
60 MIN 1 FOOT 1 METER 1 KM 1 MIN KM

jimh
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Re: Propeller Calculator, Crouch's Calculator

Postby jimh » Thu Apr 23, 2020 9:43 am

An example of calculating SLIP from RPM, RATIO, and PITCH from real data for boat speed in MPH:

An engine with a 1.85:1 gear ratio accelerates to 4,340-RPM turning a 17-pitch propeller. The boat speed in MPH is 32.5. Find the propeller slip.

SLIP is calculated from RPM, RATIO, PITCH, and SPEED using the relationship in (2) above:

SLIP = 100 × [ 1 - ( 32.5 × 1.85 × 1056) / ( 4340 × 17 ) ]
SLIP = 100 × [ 1 - (63492/73780)]
SLIP = 100 × [ 1 - 0.86 ]
SLIP =100 × 0.139
SLIP = 13.9 percent