# Two different values of source strength in Michell’s thin ship theory

Discussion in 'Boat Design' started by Anum, Oct 30, 2013.

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### AnumJunior Member

I want to calculate wave making resistance with Michell’s thin ship theory.
I noticed two different values of source strength, one in the report entitled “Sea Wave Pattern Evaluation-Part 3 Report: Near-FieldWaves” and another in a thesis entitled “wave resistance calculation using michell’s thin ship theory”.

1. According to Report: Sea Wave Pattern Evaluation-Part 3 Report: Near-FieldWaves (Page 3, Line 10)
Michell says that for a monohull thin ship with offsets y = +Y(x; z), the source strength is proportional to the longitudinal slope i.e.
m(ξ;ς)=2UYξ(ξ; ς)

2. According to thesis on wave resistance calculation
From to linearized thin ship theory, the body boundary condition will be satisfied by the center plane distribution of sources with local strength equal to UYx /(2*pi). The detailed derivation is given below
The linearized body boundary condition is

UYx(x,z)= φy(x,0,z) ……………………………(1)
The distribution of sources on the central plane S0 of the ship
dm=σdxdz
Where σ (x,z) is surface density. Now the flux out of dxdz is 4πσdxdz and for half hull 2πσdxdz. On the other hand the flux out of one side of ship hull is dxdzφy(x,0,z)
So
2πσdxdz= dxdzφy(x,0,z) .. π=pi
σ= (1/2π)φy(x,0,z)
from (1)
σ= (U/2π) Yx(x,0,z)

Can someone please explain the reason for the difference in the source strength values?

Waiting for a kind response

#### Attached Files:

• ###### SEA WAVE PATTERN EVALUATION (SWPE )Part 3 Report-Near-Field Waves.pdf
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### Leo LazauskasSenior Member

I could not find the thesis you mentioned on Google.

Many authors leave out factors of 2*pi or 4*pi in the definition of
the source strength, and then include the factors in final calculations.

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### AnumJunior Member

Dear Leo Lazauskas Sir;
The thesis i mentioned is not available online. The theoritical formulation of Mitchell's thin ship theory for wave resistance calculation,used in the above mentioned thesis, is given in attached file.

#### Attached Files:

• ###### Linear Wave Resistance Theory.pdf
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### Leo LazauskasSenior Member

Who is the author of the thesis? And where was it published?
"Hydrodynamics and Aerodynamics" forum, not in the "Design" forum).

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### AnumJunior Member

Dear Leo Lazauskas Sir;
I agree with you, since my question was related to hydrodynamics, i should have posted my question in "Hydrodynamics and Aerodynamics" forum. I will be more careful in future about this. Sorry for inconvience.
The thesis work was done by a masters student at Harbin Engineering University.
Sir i want to calculate the trim and sinkage along with wave resistance. While calculating sinkage and trim, can i use the body boundary condition satisfied by the center plane distribution of sources with local strength equal to UYx /(2*pi)?
then i will use the following formula for the net upward force acting on the ship’s hull due to ﬂuid pressure.
F=2∫∫p(x,0,z)Yz(x,z)dxdz
And for the stern-up moment about the origin due to the ﬂuid pressure
M=2∫∫xp(x,0,z)Yz(x,z)dxdz.

Waiting for kind response

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