Residuary resistance with Matlab

Discussion in 'Hydrodynamics and Aerodynamics' started by HarryS, Dec 20, 2012.

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HarrySNew Member

Hi,

I have started to learing Matlab just for fun and I have written some useful functions with it.
Today I tried to solve the residuary resistance given by Fabio Fossati in Aero-hydrodynamics and the Performance of Sailing Yachts (page 24)

I have now written the Fn as a vector Fn_V=[0.15 0.20 ...0.70]
and the coefficients by the table as

coef=[ -0.0005 -0.0003 -0.0002 -0.0009 -0.0026 -0.0064 -0.0218 -0.0388 -0.0347 -0.0361 0.0008 0.0108 0.1023
0.0023 0.0059 -0.0156 0.0016 -0.0567 -0.4034 -0.5261 -0.5986 -0.4764 0.0037 0.3728 -0.1238 0.7726
-0.0086 -0.0064 0.0031 0.0337 0.0446 -0.1250 -0.2945 -0.3038 -0.2361 -0.2960 -0.3667 -0.2026 0.5040
-0.0015 0.0070 -0.0021 -0.0285 -0.1091 0.0273 0.2485 0.6033 0.8762 0.9661 1.3957 1.1282 1.7867
0.0061 0.0014 -0.0070 -0.0367 -0.0707 -0.1341 -0.2428 -0.0430 0.4219 0.6123 1.0343 1.1836 2.1934
0.0010 0.0013 0.0148 0.0218 0.0914 0.3578 0.6293 0.8332 0.8990 0.7534 0.3230 0.4973 -1.5479
0.0001 0.0005 0.0010 0.0015 0.0021 0.0045 0.0081 0.0106 0.0096 0.0100 0.0072 0.0038 -0.0115
0.0052 -0.0020 -0.0043 -0.0172 -0.0078 0.1115 0.2086 0.1336 -0.2272 -0.3352 -0.4632 -0.4477 -0.0977];

I also have all the indata ready like LWL=9.88 and so on. Im just unsure how solve this in. Any help will be appreciated!

Thanks

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jehardimanSenior Member

It's a curve fit, for given volumetric Froude numbers just like the Mercier and Savitsky did for Fn_V 1.0- 2.0 in thier 1973 paper. Just plug and chug for the bounding Fn's and then interpolate.

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DCockeySenior Member

Harry, are asking how the equation works, or how to program it into Matlab?

Froude number is not used explicitly in the calculation; it is implicitly specified by which row of coefficients are used in the calculation.

I'm not a Matlab user but I've done more than a little bit of matrix math. Set up a vector of the terms calculated from the hull parameters. The first term in the vector is 1, second is LCB/LWL * Del^1/3/LWL, third is Cp * LCB/LWL * Del^1/3/LWL, etc. Multiply the matrix of coefficients by the vector of terms and the result is a vector of Rw / (Del * rho * g) with each term being the value for the Fn corresponding the row of the matrix of coefficients.

An alternative formulation would be to divide both sides of the equation by Del^1/3/LWL which would make the first term in the vector of terms 1 / (Del^1/3/LWL), second is LCB/LWL, third is Cp * LCB/LWL, etc.

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HarrySNew Member

Thank you very much! Everything works well now!
i just had a typo in my code.

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