# Need help with Equations

Discussion in 'Boat Design' started by ENG Student, Feb 14, 2010.

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### ENG StudentJunior Member

Hi all
I need some help with some equations for a university project i am undertaking, i am studying automotive engineering so i have knowledge of land vehicles but not marine vehicles
I hope u guys can help

1) Equation for calculating Drag - I know D = 1/2 p A v Cd (p - density, A - frontal area, v - velocity Cd - coefficient of drag) but how does this apply to a hull where only part of the hull is submersed in water

2) Calculating the position waterline at max load displacement

3) Calculating the Power required to achieve a speed of 15 knots

thanks

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### Leo LazauskasSenior Member

Hydrodynamic drag in the presence of a free-surface is much more complicated.

Start here and work your way through the maze
http://en.wikipedia.org/wiki/Ship_resistance_and_propulsion

Leo.

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### ENG StudentJunior Member

Thanks mate
ive done some research and some quick calculations from what ive found but something doesnt seem to be quite right for me

The boat in question is a catamaran - 30ft weighing approx. 1000kg
the resistance i have calculated is 24.1 lbs (107 N), which to me seems out...but again im not sure
can someone verify if this figure is roughly correct or should i double it for both the hulls?

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### PetrosSenior Member

drag force will change with speed, so what speed are you designing to, the 15 knots?

Or do you have a given amount of thrust (or power available) and want to determine the speed a given hull design can go? that is more common.

total gross weight divided by water weight will give you cubic feet of displacement, than you have to calculate volume of hull shape, and how much it changes as the WL changes. There is free software for down load that can do this, but you have to build up the 3-D shape of the hull(s) into the program to allow it calculate WL, if the hull is relatively simple shape you can approximate it pretty close with hand calcs of volume.

There are standard methods for determining drag, power required and max speed for various hull configurations. Search the archives of this forum and you will find links to pages with the standard equations, and even Excel spread sheets you can use.

Good luck.

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### sandeepSandeep

Hi,

Equation for calculating Drag - D = 1/2 p A v^2 Cd (p - density, A - submerged area, v - velocity Cd - coefficient of drag).

To Calculate the position waterline at max load displacement you should do the reverse calculation,Disp=L B T Cb where L=length B=bredth T=Ht of WL from keel Cb=Disp/(L B T Cb). BY changing the value of T you can find the Disp.After 3 or 4 iteration you can find the ht of WL.It is applicable when the wt is equally distributed.Otherwise you have to calculate LCG,TCG etc and find wt buoyancy distribution of that vessel, it is quiet complicated.

Resistance of the hull and other appendages determines the power of engine.Resistance of the hull mainly depends upon Reynolds and Froude number. And you have to consider various factors while propelling the vessel like Transmission efficiency,Hull efficiency,Rotational efficiency etc.

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