Draft Calculations for Design Stage

Hi there,

I was wondering how ship designers would calculate things such as draft and different coefficients of form (such as block coefficient) during the design stage, before the ship would be set in the water. Does anyone know what formulas would be used?

Thanks.

 

Designing a ship requires its design weight equal to its displacement of water. The volume of displacement of a certain hull shape is a function of draft.
For a start look at this:
Simpson's rules (ship stability) - Wikipedia https://en.wikipedia.org/wiki/Simpson%27s_rules_(ship_stability)

(Nowadays naturally it is done by software.)

 

thanks for this. After determining the internal volume and weight of the ship, how would the draft then be calculated?

 

Calculate the total weight of the boat in as much detail as possible. Once that is done, check at what draft the weight of the displaced water is equal to the weight of the boat.

 

Thanks for the input. Would the block coefficient come into play with checking for the correct weight and if so how would that be calculated?

 

The displacement is the sum of everything. It includes hull, decks, machinery, fuel, water, supplies, cargo, passengers, etc. The block coefficient is useful for resistance calculations, and can give you a rough idea of speed and power necessary. Also, you need to calculate the center of gravity (CG) to find out the trim of the ship. It should float on her lines. That is, not listing or squatting. However, the submerged volume will be the same whether she floats on her lines or not. I am not sure what you mean by the correct weight though. The weight is a function of the needs and function of a ship.

 

The block coefficient is a number that relates to the immersed part of the hull. So for calculating the block coefficient you have to know first the draft.

First you have to determinate the volume of water displaced by the hull at different grades of immersion by numerical integration.

Define an appropriate horizontal plane under the hull parallel to the design waterline of the boat so the deepest point of hull will just touch that plane (base plane). Define a lot of stations equal spaced along the longitudinal axis of the hull. Find the cross sections of the hull with a perpendicular plane at each station. Calculate the immersed area of the cross section at each station depending of a certain draft, measured starting with zero at the base plane. For the immersed volume you will have to multiply the average immersed area of all stations with the lenght of the hull.
Check the result. Displacement volume times water density has to be equal to the weight of ship. If displacement is to small, calculate again with an increased draft. Vice versa. And so on until you will meet the weight. The is no real formula it is done by iteration.

Software does it in a similar way: https://www.bootsphysik.de/boot25m.php
(Button English top right)

 

The block coefficient, Cb, is the quotient between the displacement (m3) and the product of waterline length, waterline beam, and draft, all in meters. (Other units can be used).
The Cb cannot give an idea of the speed of a ship. With a certain power, a certain Cb and many other things, much more complicated to calculate, a forecast of the ship's speed can be made, in certain conditions of the sea, wind, etc. While it is true that, for a given displacement and a given power, and other conditions being equal, a lower Cb facilitates a higher speed, there is no way to have an idea of what that speed will be.

 

Hold on, you have to have some requirements ( a SoR...Statement of Requirements) in order to begin the design process. For draft as an example, a 1950's trans-Atlantic liner has twice the draft of a modern cruise liner, even though they superficially appear to have the same size, shape, and function. It is because the weather and route requirements are different.

Start with a volume (displacement) to length curve for the speed-length ratio you want/are given (these can be looked up in a good NA text). This gives a the station areas and a midship section within beam and draft restrictions based upon standard types (cargo, combatant, passenger, speedboat, sail boat, etc.). You seem to have some of these already, so work them all up.

The LWL to speed places the midship location, then put in a few waterlines, diagonals (and or bilge radii) and a profile to cover the "cargo" block buildup (ie container hold stacks, cargo holds, staterooms, weapons, engine room and machinery spaces, etc.).

Then the cross-checking of stations/waterlines/diagonals to the displacement-length curve goes through a few cycles as you put in some control points (design waterline, deck edge, turn of the bilge, etc) for each station and begin your weights. Cycle and repeat until structure, decks, weights, powering, and prime mover are pretty settled. Then finalize the shell and do a clean lines plan. After the lines plan is finished and all the limits (tonnage, length, beam, etc) are met, then pull the offsets off.

Of course, a lot of that work today depends on how you are developing the drawing, by hand to be digitized or directly on the computer. Sometimes you need to work with (or around) any drafting program you are using. FWIW, I have not yet found a CAD program I like for developing a lines plan from scratch.

 

AyJayO,
One of our members did this.

https://ericwsponberg.com/wp-content/uploads/2021/09/THE-DESIGN-RATIOS.pdf
https://ericwsponberg.com/