Added Resistance in Wave

Hi guys,

I know the forum is mainly for small craft designers but I am currently working on big merchant ships and kinda stucking at some calculation methods, hope someone may help me out on this problem...

It is the calculation of Added resistance in Wave, Raw.

I have looked at the ITTC 7.5-02 07-02.1 & 7.5-02 07-02.2, but could not actually work out...

I have attached the formula that we should follow.

Thank you very much and hope to see your ideas soon.

 

Not so. Anything that floats

Below are draft and i do stress draft guidelines relating to the new IMO rules on the forthcoming EEDI. So, whilst these may still be draft, the calculations for added resistance to establish the EEDI may be of help. Excerpt taken for your ref:

 

Thanks Ad Hoc, so glad to see your reply because this is also what I am doing, but I am dealing with the MEPC 65, ANNEX 5, the new rule adopted last month, about Determining the Propulsion Power for Adverse Condition.

I have been away from university for quite a while, so it is a little hard for me to deal with these formulas.

I have been looking through many papers on internet for ref, but still cannot understand how to put all the formulas into use properly...

Thats why I am looking for some more detailed explanation, if anyone can help.

 

This sample calculation shall help then

 

Thanks Ad Hoc, I will try to get through it...

If you have any other related papers, please show me if you dont mind.

And if you have time to look at the MEPC 65 - ANNEX 5, please let me know your ideas.

Thanks alot.

 

Hi PHQ:
As far as I remember, the key around that formula is arriving to a good value of the term Raw for each wave into the studied spectrum.
Once got, things become easier and just an addition of each spectral term effect.

Im digging in my archieves looking for some more information.

Regards

 

Hi Crownest,

Thanks for your advice, I am still working on it, spending hours for reading papers in relation... But still no clue...

As I found in the ITTC 7.5-02 07-02.1 & 7.5-02 07-02.2, there is the formula for the wave spectrum S(omega), which I think we can calculate it. But I still dont understand the whole thing in the Resistance (Raw) formula.

If anyone can explain me in more details for each elements of the formula, and how to calculate them, It would be very much appreciated...

I have attached the formula again and the ITTC documents, just let me know how you feel.

Thank you and have a nice day.

 

Looks like Ad Hoc's post #4 contains all the info you need, regarding the calculations.
The only thing that is missing is the explanation of the term I1 (modified Bessel's function of the first kind of the order 1), but remember - Google is your friend: http://mathworld.wolfram.com/ModifiedBesselFunctionoftheFirstKind.html - check the equation 5. Or even at http://www.efunda.com/math/bessel/modifiedbessel.cfm
Cheers

 

The formula assumes you have the added resistance for a particular speed and wave frequency. That's the function Rw(Vs, omega) in the integrand. The rest of the formula is the integration of the added resistance function over the wave spectrum to get the total added resistance.

The hard part is getting Rw(Vs, omega). This can be calculated by a sea-keeping code like SMP.

 

Hi daiquiri,

Yes you are right, the guideline Ad Hoc posted is very useful and I am following it now.

To be honest, I have never seen the Bessel's function before, I didnt learn it in university for some reasons... thats pretty odd... But I am trying to go through it now, thanks for the webs daiquiri.

If someone can explain it in a more in-person-way with examples and how we can apply it into calculations, that would be rather brilliant...

Thank you & nice day.

 

Hi tspeer,

Thats also what I am concerning...

The wave spectrum function S(omega) I can calculate according to the ITTC, but the Raw(Vs,omega) I have no idea what to do with it.

The formula Raw I posted is given out for the calculation method to base on, so I am quite struggling with the method Ad Hoc posted (because it is for different calculation guideline, not mine..) , not sure if I can apply it or not, even though I know its also the correct one.

 

Hi Everybody,

Thanks for this smart topic, I apologize in advance if the following question is a bit candid, if not stupid:

Is it relevant to apply these formulas for 16 feet to 25 feet beach cat's hulls,
adjusting H,T and other parameters for bay chop ?

Best Regards

EK

 

Hi,

I just came across this thread, and I am not sure it is still relevant. But as I have been lately working on this subject, I have decided to post an answer. I hope it can still be of some help.

As said, I have been lately working on the calculation of added resistance in waves for sailing yachts. I have made available a calculation template online where you can also find a short video showing how to use it: Added resistance in waves knowing yacht’s radius of gyration (calculation) https://navalapp.com/articles/added-resistance-in-waves-knowing-yacht-radius-of-gyration-calculation/

The calculation of added resistance in waves for merchant ships and small craft follows, in fact, the same process:

• First, we represent mathematically the surface, i.e., the waves, of the particular sea where we assume the vessel is sailing. In other words, we model the sea surface.
• Second, we mathematically model the vessel's response to waves of different frequencies and heights.
• Finally, we put both together, i.e., how the vessel responds to different waves of different frequencies and heights and the model of the sea surface where the ship is in, to estimate the added resistance in waves.

In the equation you attached, S(w) represents the sea surface model as a function of the wave frequency. The modeling is often done by applying single-modal spectra models to real sea surface data to obtain a mathematical description of the sea state. Among them, the more extended spectra models are the Bretschneider spectrum which is the one recommended by the ITTC (International Towing Tank Congress) for fully developed seas, and the JONSWAP (Joint North Sea Wave Project) spectrum recommended by the ITTC for fetch-limited situations. Regarding this subject, you may find interesting the following post: Sea state and wave forecasting https://navalapp.com/articles/sea-state-and-wave-forecasting/. You can also obtain Bretschneider and JONSWAP spectra at: Wave spectral density (calculation) https://navalapp.com/articles/wave-spectral-density/

The other part, RAW/Wave_Amplitude^2, represents the model of the vessel as a function of the wave frequency and vessel's speed. It is, in fact, a transfer function, also known as the Response Amplitude Operator (RAO), and models how the boat responds to waves of different heights and frequencies. It can be calculated analytically or by analyzing the results obtained in towing tanks tests specifically carried out for this matter. As the boat's speed affects the frequency at which the vessel encounters the sea waves, different RAOs are obtained for different boat speeds. This is the meaning of the dependency on Vs shown by Raw/Wave_amplitud^2: you have a different RAO for a different boat speed. I have made also available an online calculation template for RAO of sailing boats: Added resistance in waves: Response Amplitude Operator (calculation) https://navalapp.com/articles/added-resistance-in-waves-response-amplitude-operator-calculation/

Finally, as shown by the equation, once the RAO and Sea State models are available, we multiply the value given by each model at a particular wave frequency for the whole wave frequency range, integrate the result, and multiply by 2 to obtain the added resistance in waves. By multiplying RAO and the Sea State, we obtain the boat's response to that particular sea state (note that the multiplication result is just "0" for frequencies where there is no overlapping between both models). By integrating, we obtain the value of the area enclosed by the RAO x Sea State curve and the x-axis. The "2" of the equation does not have any physical meaning. It is due to the maths involved when creating the models. The units are:

• RAO units: N/m^2 (as a function of wave frequency in rad/s);
• Sea State units: m^2 s / rad (as a function of wave frequency in rad/s);
• RAO x Sea State units: N s / rad
• Integration for w (rad/s) of RAO x Sea State units: N (Newtons!)

I hope this helps!