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## Crouch's Calculator

Horsepower Pounds Hull Factor Boat Speed

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

This useful calculator computes an estimate of boat speed for a modern planing monohull using inputs of the power at the propeller shaft, the total boat weight, and a coefficient called the hull factor. The calculator can also compute any one parameter from the other three parameters—a most useful feature.

The hull factor for predicting speed in units of statute-miles-per-hour for a typical modern planing monohull is about 180 to 190. A value of 190 works well with classic Boston Whaler boats. Hulls with Whaler Drives may be more like 180. Long and narrower hulls with with flatter running surfaces may have a higher hull factor coefficient, perhaps 200 or higher.

Actual measured values for power, weight, and speed can be used to compute a hull factor coefficient. The hull factor coefficient can then be used to calculate other values not yet observed. For example if the known data about a boat's performance is used to calculate a hull factor when the speed unit was MPH, then the calculator can be used to predict new boat speeds in MPH with changes in horsepower or weight using that value for the hull factor. Similarly, with an assumption of a proper hull factor value, data about speed and horsepower can estimate boat weight.

The units for the boat speed calculation are dependent on the hull factor coefficient used. If the hull factor is being calcuated from a boat speed measured in a particular unit, then the hull factor calculated will be appropriate for that speed unit and can be used to predict speeds in that unit.

The fundamental concept embodied in the calculator is that boat speed is in proportion to a hull factor coefficient times the square-root of the power-to-weight ratio. The effect of this relationship means to double the speed would require four times the power with no change in weight.

If calculating a new boat speed based on past observations and power is increased. then the weight should be similarly changed to reflect any change in boat weight due to the engine change.

### Foundation

The calculator uses known inputs of propeller shaft horsepower (HP) and total boat weight (LBS), and an estimated hull factor coefficient (C), and from these three parameters the boat speed (SPEED) is calculated The relationship is expressed mathematically:

```          HP
SPEED = ( --- )^0.5 × C
LBS

```

With algebra any of the other three parameters can also be calculated:

```          SPEED
HP = ( ----- )^2 × LBS
C

```
```         SPEED
C = ----------
(HP/LBS)^0.5

```
```           HP
LBS = ----------
(SPEED/C)^2

```

As already mentioned, the hull factor coefficient, C, must be chosen with respect to the speed units desired. A reasonable starting point for a typical monohull planing boat for speed units in statute miles-per-hour (MPH) is to use C=180. The equivalent for speed units in nautical-miles-per-hour is 156. For other values for C with speed in nautical-miles-per-hour, see Gerr's Propeller Handbook, mentioned below.

Another assumption made in the calculation is the propeller being used has reasonable efficiency. The propeller efficiency is assummed to be in the range of 50 to 60-percent. Propeller efficiency is not a parameter in the calculator, nor do most recreational boaters have any method to measure or know propeller efficiency. A more complex speed prediction formula is offered by Gerr in his Propeller Handbook, mentioned below.

### Acknowledgements

The basis for the calculations embodied in the calculator comes from the work of naval architect George Crouch, as described by author Davd Gerr in his book "Propeller Handbook" (published by International Marine) in Chapter 2, pages 15 and 16 where it is referred to as Crouch's Planing Speed Formula. Therein some values are given for hull factors for calculating speeds in nautical-miles-per-hour for various hull types.

This calculator is a revised version of an earlier calculator created at continuouswave.com that introduced the Crouch speed predicting method more than ten years ago and was the first of its kind on-line. The revised calculator is an entirely new implementation with a different code base.

Similar calculators which work in an identical fashion and attribute the method to a particular engine manufacturer would appear to be overlooking the original work of naval architect George Crouch.

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Author: James W. Hebert