Calculating Speed of a Boat for Dumbo - Help Needed

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To estimate the speed of the catamaran hull, the drag force must be considered, which varies with speed. The power output of the bilge pumps can be related to speed using the equation P = 1/2 ρ v^3 LW Cd, where ρ is the water density, v is speed, LW is the wetted surface area, and Cd is the drag coefficient. The drag coefficient should account for various types of drag, including viscous and wave drag. Given the hull dimensions and weight, the combined output of the pumps (84 liters per minute) will influence the achievable speed. Calculating these factors will provide a rough estimate of the boat's speed in either kph or mph.
Tai
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Hi everyone,

I'm hoping for some help in calculating the speed of a boat I am planning to build, I'm not looking for a precise speed just an indication of what it is likely to be to ensure the pumps I would like to use are powerfull enough.

The boat is a catamaran hull with the hull dimensions 150mmx100mmx620mm (per hull), the remainder of the boat will be above the water line. Overall the weight will be 8.5 Kilos, the propulsion system I would like to use is made up of two bilge pumps, each bigle pump is capable of moving 42 litres a minute so combined 84 litres per minute. The pump output pipe is 19mm in diameter, which i guess fits into the equation somewhere...

Is someone able to tell me an approximate speed in either kph or mph? I don't even have a clue where to begin :blushing:

Thanks in advance,

Tai
 
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You need to determine how the drag varies with speed. Then for a first approximation, you relate that to the power output of your engines:

P = \frac{1}{2} \rho v^3 LW Cd

Bear in mind that your drag coefficient would have to include viscous, wave and profile drag terms.
 

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