# ORC added resistance

Discussion in 'Hydrodynamics and Aerodynamics' started by vicbauwens, Oct 11, 2014.

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### vicbauwensJunior Member

Good day to all,

I am trying to get my head around the added resistance formula as given in the ORC VPP Documentation 2013. This formula is found on p69 with reference [74]

The general build-up of the formula is quite clear, with a rather serious exception: I can't see how they end up with a result that has units of Force [N] since analysis of the units in the formula leads me to [N/m2].

Essentially the formula says rho x g x L , multiplied by a string of dimensionless parameters. This gives me kg/m3 x m/s2 x m, which in turn yields N/m2

Under the safe assumption that the good people of ORC know what they are doing, I conclude that I must be missing something, or there could be a typo in the formula as printed? It must be noted that [72] also has lettersetting issues, with the accolade brackets overprinting important info.

Your help is much appreciated,
best regards, vic

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### TANSLSenior Member

I just do not understand.

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### vicbauwensJunior Member

Hi Tansl
N = kg.m/s2 following from basic Newtonian formula F=m.a
Thx, vic

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### JoakimSenior Member

I haven't looked in detail this ORC formula, but in my own VPP the added resistance is modelled with C * rho * L * h^2. It has a problem with units as well, but I think g is hidden in the constant (not constant, but dimensionless function of many things). h is the wave height, which is derived from wind speed in my VPP.

So it would seem likely that f(Vt) returns actually h^2 or that m^2 term is on some other function.

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### TANSLSenior Member

Sorry, had interpreted the following : kg/m3 x m/s2 x m = kg/(m x s2)

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### vicbauwensJunior Member

Hi Joakim,

Thank you for your thoughts, I think you have set me on a path to better understanding:

f(Vt) does not give the answer though. It is a dimensionless factor (seastate factor) which used to be just windspeed, untill replaced by a more intricate formula to address handicapping issues in light wind conditions. Technically it has a very messy unit (kts^kts^3.5 !!) but it is clearly used as a factor only an dthe ORC documentation is relatively clear on this (p68 fig 34)

What I have understood meantime, is that the Raw value as calculated in [74] is only part of the work. This formula merely calculates the Response Amplitude Operators (RawRAO), which must still be multiplied by the "wave energy spectrum". Your suggestion of multiplying Raw by waveheight squared is actually a very interesting as it is a simple and straightforward way of modelling the kinetic energy of the waves. In absence of more precise wave spectrum information, I will follow that lead and relate windspeed to a certain waveheight, see where that takes me.

On your remark that your formulation also has issues with units; Could it be that your VPP uses imperial units in origin? In that case there is a good chance that your rho would be calculated with lbf instead of slugs (believe it or not the slug is the unit of mass in the imperial system...) and lbf already has gravitational acceleration built-in... Imperial notation is sometimes lacking hygiene in that department.

Cheers, vic

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### JoakimSenior Member

I made the model my VPP has based on papers I found about 10 years ago. I think I have just hidden g into the constant. I'm not that interested in cases where g is not the one we have at the surface of the earth. I never use imperial units nor the papers I used. This paper shows rho * g * LWL * h^2 function for resistance: http://www.boatdesign.net/forums/at...nce-waves-2006-mdy-added-resistance-waves.pdf

In my model wind speed is used to derive wave height and wave period. The resistance coefficient is calculated from (wave period)/sqrt(g/L), which defines how badly the boats pitching resonates with wave period.

In ORC model the f(Vt) is the only function with wind speed and thus it must be the one giving wave energy/height etc.

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### vicbauwensJunior Member

Hi Joakim,

Thanks for the paper, it has been most helpful as I am also in the process of programming a VPP. Believe to be at over 90% currently. Once finished, I will post a beta on this forum for commenting.

best rgds, vic

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### Ben GJunior Member

"kg/m3 x m/s2 x m, which in turn yields N/m2"

No, it doesn't, it gives you kg.m/s2, making the answer in Newtons.. surely. Unless you're missing a few brackets

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### HumbertoJunior Member

""Ben G "kg/m3 x m/s2 x m, which in turn yields N/m2"

No, it doesn't, it gives you kg.m/s2, making the answer in Newtons.. surely. Unless you're missing a few brackets"

Nop. I do not remember th ORC equation, but this precise equation [rho x g x L] is kg/m3 x m/s2 x m, reorganised to (kg x m x m) / (m3 x s2), reduces to kg/(m x s2), which is neither Newtons nor N/m2. Please, recheck both derivations and correct me if I am wrong
Best

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### vicbauwensJunior Member

Hi guys,
Sorry to contradict here, I may be a hobbyist in this field, but I'm a seasoned master in civil engineering Calculations are my daily bread and i invite you to please have another good look at the formula as it well and truly gives N/m2. I concurr with the opinion that this cannot be understood as pressure, but it takes these units.
The Madrid paper referred to by Joakim provides excellent further reading on the wave spectrum energy the RAO is to be multiplied with.

Humberto, I regularly make use of the free version of your fine program. Given that my interest in yacht design is purely a hobby, I did not purchase the professional version but I appreciate the availability of a free version for educational purposes very much. Thank you for that.

Best rgds, vic

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### HumbertoJunior Member

Yes, you are right, it has units of N/m2. This is one of the few ORC equations that I have not checked in my VPP.

BTW thank you for using my program. It is always good to know there is somebody using it!! Stay tunned, I will be releasing a new improved version soon.

Humberto

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### Pablo SopelanaJunior Member

Hi,

In equation [73] in ORC VPP Documentation 2013, or (6.57) in ORC VPP Documentation 2020, the RAW/Wave_Amplitude^2 term is the Response Amplitude Operator (RAO), and S(w) is the wave spectral density.

Equations [74] in ORC VPP Documentation 2013, and (6.58) ORC VPP Documentation 2020 calculate the RAO.

The units are:
• RAO: N/m^2
• Wave spectral density: m^2 s / rad
• RAO x Wave spectral density: N s / rad
• Integration for w (rad/s) of RAO x Wave spectral density: N (Newtons!)

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