Typical ship drag coefficients

I'm a student of mechanical engineering but with no specialization in maritime applications. I hope you can clarify something for me.

I'm in the process of determining the approximate forces that would affect a ship-sized vessel positioned by anchor or mooring and I reckon that would include wind, wave and current forces.

In estimating the forces I am using the drag equation which depends on the drag coefficient. Different sources claim the drag coefficient of a flat faced box to be 2.1 which I reckon would be a good estimate for the drag coefficient of a barge, as it resembles a box.

However, for the drag coefficient of a ship hull I am confused. Page 7 of this paper shows drag coefficients for a ship hull between 0.0027 and 0.0032, while the figure on the Wikipedia page shows that for an optimally streamlined body, the coefficient is 0.04.

The streamlined body is optimised for minimum drag, so I don't see how a ship hull could have even less drag.

Can you provide me with ballpark figures for the combined viscous and friction drag coefficient of typical ship hulls? I realize it varies a lot between different ship hulls but all I need is a rough estimate.

 

The difference in values of drag coefficients are probably due to different reference areas used for their calculation. In ship hydrodynamics, the reference area is usually the wetted surface area (the underwater part of the hull surface), while in aerodynamics the reference area is either the cross-section area or (in case of airplanes) the wing area.

The values given by the Wikipedia page are probably referenced to the cross-section area and that gives them a much higher values (because for streamlined bodies the wetted surface is an order of magnitude higher than the cross-sectional area). The values from that pdf-paper are more common.

As for your question about fundamentals of ship resistance and propulsion, I suggest you to download and read this nice manual about ship propulsion from MAN (producer of marine diesel engines): http://mandieselturbo.com/1005405/P...sion-Basic-Principles-of-Ship-Propulsion.html I think that you'll find all the answers you need for your task.

Cheers

 

What you’re trying to do is a dynamic nature and terribly complex. You can “estimate” from more empirical equations. But to calculate the forces direction, mathematically, is no day at the beach.

To begin with you need to establish the ROA (Response Amplitude Operator)….simplistically this defines an input, (a wave) of certain frequency and amplitude and an output, the vessels response, to said external force. Without knowing this, your task is made next to impossible.

To go into more depth about ROAs would take significantly longer too….and if you’re unaware of this, then I’m afraid it is a long haul to the answer, not a 5 min job.

As a starting point for your problem though, I would suggest you read:

"Low-Frequency Dynamics of Moored Vessels” by Oppenheim BW and Wilson PA, published in Marine Technology, by SNAME, January 1982.