How to calculate displacement of newly designed ship

by Charles Roring

Naval architects when designing a ship often face many difficulties in determining the displacement due to the lack of data for the weights of hull components, propulsion machinery, wood and outfit, equipment and etc.
Displacement of a ship is the volume of water that it displaces when floating at sea or river. The volume is calculated in cubic meter. If it is multiplied with the sea water density (1.025 metric ton/cubic meter) then we can get the displacement which equals to the ship weight.

On page 4 of Ship Design and Performance for Masters and Mates, Dr. C.B. Barrass gave a simple formula for calculating the displacement of newly designed ships. The formula is called deadweight coefficient.
C_D = dwt/W
The following table is the typical deadweight coefficient for various types of merchant ships

DWT Coefficients of Merchant Ships

The deadweight coefficient varies from one ship to another depending on its type and is calculated up to SLWL or Summer Load Water Line. It is the condition where a ship is fully loaded.

Worked Example:

For a new design, the deadweight of the ship is determined to be 12,000 metric tons. Information from previously built similar ships suggests C_D to be 0.6. Estimate or calculate the fully loaded displacement (W) and the lightweight of the new ship:

W = dwt/C_D

W = 12,000/ 0.6 = 20,000 metric tons.
Lwt = displacement - deadweight
= W - dwt
= 20,000 - 12,000 = 8,000 metric tons This is only for preliminary design calculation.
If we see on the table above, the ship is a container ship.

When the lines-plan of a ship is available, the calculation of her displacement can be done by integrating the areas of waterlines usually from WL 0 to Summer Load Waterline. Similar calculation of ship displacement can also be carried out by integrating the areas of stations from the stern to the forward end of the ship. Hydrostatic and Bonjean curves provide a lot of information which sailors or ship designers can use to analyze the hydrostatic and hydrodinamic properties of the ship.

Recommended Book
There is a good book for naval architects or anybody who is interested in learning about this topic. Its title is Ship Design: Methodologies of Preliminary Design, written by Apostolos Papanikolaou.
You could order this book to learn more about the determination of hull form, the main dimensions and the basic characteristics of different types of ships. I highly recommend this book for you to read it.

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Ship's Displacement Calculation Using Simpson's Rules