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Propeller Calculator: MPH

ENGINE PROPELLER BOAT
RPM RATIO PITCH SLIP MPH

The calculated value is indicated by the shaded heading in the table.

This useful calculator computes the speed-of-advance of a propeller based on:

The potential boat speed is then calculated from the speed-of-advance using SLIP, a percentage of lost speed, and unit conversion to boat speed in statute-miles-per-hour.

Instructions

The calculator always needs four inputs to calculate the fifth parameter. After input of any four parameters, click on the button for the unspecified parameter you want to be calculated. The calculated boat speed is units of statute-miles-per-hour. If you want to calculate boat speeds in nautical-miles-per-hour or KNOTS, a separate calculator is available.

Data Input

A value for RPM is typically input as a known parameter. Modern engines now have high-resolution data on engine speed and are very accurate. Older analogue dial-pointer tachometers are notoriously inaccurate. Use the manufacturer's recommended highest permitted engine speed to calculate highest possible boat speed estimates.

A value for RATIO is typically input as a known parameter. The manufacturer's data should be used. If the manufacturer specifies the reduction ratio as a single decimal number between 0 and 0.999, use the reciprocal of that number. For example, 0.542 becomes 1/0.542 or 1.845.

A value for PITCH is typically a known parameter, and should be taken from the propeller markings or the manufacturer part number. Calculating a value for PITCH is useful if the four other parameters are known with certainty.

A value for SLIP is typically a calculated value deduced from known or observed data for the other four parameters. Calculating SLIP gives a metric for how well the propeller is performing. Generally the calculated SLIP will tend to reduce to the range of 5 to 10 only when the propeller is working to push the boat to its highest boat speed range. At lower boat speeds SLIP will often be much higher, in the range of 10 to 30. If SLIP is to be an entered parameter, a reasonable guess at its value is 10.

Foundation

The underlying basis for all calculations is explanined below.

If a propeller were a helix screw advancing in a solid, then for each revolution it would advance a distance equal to the pitch of the blades, called the speed of advance. The boat speed would then be the speed of advance. However, a propeller operating in water will tend to advance less (for rather complicated reasons that won't be explained here), and the difference between actual advance and theoretical advance is expressed as a percentage factor called SLIP. The calculated boat speed is thus the theoretical speed of advance reduced by the SLIP. The relationship is expressed mathematically:

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

Where:

By manipulating the elements using algebra, any of them can be computed if the others are known. Hence:

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


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



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


               SPEED X RATIO × C
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 the boat 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 statute 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 (KNOT):

  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

Acknowledgements

A calculator that was recursive in its design and could calculate any one of several factors in a fixed relationship was first noticed by me in financial calculators. This method is a good approach to the problem of propeller calculators as it allows use of the calculator in many ways and to calculate any one of five factors used in the relationships. There are many similar propeller calculators now available on-line, but this one is unique in that it completely explains all of the relationships between the parameters and the formulas used to calculate them. Its use of HTML style sheets in presentation of the data is also rather unusual and seldom seen. This calculator was written in php using code created by the author. No Javascript is used.

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Author: James W. Hebert

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