Delft Hull Series

I completed an important step towards the development of a prediction software for the hull resistance. The attached report contains a statistical analysis of the DSYHS database and a proposal for new regression parameters.
I would be happy if someone could read the paper and give me a feed back.
Any comments about the mathematical or physical methods or assumptions but also about suboptimal style and clarity are highly appreciated.
Uli

 

Well, it about time somebody had a serious go at reworking this data. I have expressed my dislike of the previous regression treatment in a couple earlier threads.

The take away for me is Fig 3. The reversal of so many proposed terms at Fr = .4.

You made the following comment just above the chart -

I would suggest you also look at another possibility. That terms which tend increase wetted area but decrease wave making (and vis versa) may also show a reversal due to the sudden increase in the residual drag compared to viscous drag. Basically, I think you need to do a parallel analysis on the viscous drag and inspect the results to see if a proposed term has a consistent effect on the total drag. You may have a situation with a term being quite strong and opposite in viscous and residual resistance, but is rather weak overall. I would ask that all terms in a regression formula that showed such a reversal have a solid theoretical underpinning - more than a "it would seem logical"

Some of your comments on colinearity might also benefit from this sort of thinking. You have done the work and your opinion what to make of the colinearity analysis is probably true, but presenting the colinearity info up front as you did, the reader pretty much has to take it on faith. You might want to leave it more as an open question in its current location, or shorten it and give the full blown version with conclusions at the end of the paper once the reader has seen the regression.

 

Thanks a lot Phil for your feed back!
You are quite right, my explanation of the sign-reversal in the correlation coefficient was just a guess and is not based on thorough analysis. It is quite possible that the change in wetted surface plays a role. The change in viscous resistance by the changing wave pattern along the hull and the wave making resistance are both contained in the residuary resistance. To separate these effects is only possible with extensive CFD-analysis, which is beyond my scope and my means. My simple boundary layer calculation assumes an undisturbed waterplane without waves. In this regard it is identical to the ITTC-method.

Yor second point is also helpful. I will most likely phrase the impact of collinearity more as an open question.
Thanks
Uli

 

There are two terms that I suspect are being overworked in the regression formula.

1. The prismatic coefficient. I think you should try to capture the actual curve of displacement with a three or four parameter function. Even if it is just two parameters, are for-and-aft prismatics the two that best distinguish the shapes for wave resistance? In effect, you are already using four parameters because you include a pair of angles as well. I just think a reference curve and four bump function parameters might do a better job.

2. LCF and LCB. Again, there is in reality a curve of LCF(z) for each waterline. This is usually a fairly simple looking curve and could be captured with three parameters fairly well. I would normalize the curve's z axis with Froude depth (and perhaps B/T) and normalize the x axis with LPP as you are doing and see what happens. The idea is that the shape of the curve near the surface is what is important. That is a bit awkward because the parameters for the same hull change with speed, but you are already doing that anyway.

So I would try to replace CP1, CP2, entrance angle, buttocks angle, LCF, and LCB with 7 different parameters which may better discriminate between the overall geometry of the hulls. No small task, but I suspect that grouping the terms like that would help with the theoretical side and make extrapolation a bit more stable. I'm guessing it would reduce colinearity somewhat as well.

<edit> so my suspicion is that these geometric functions are being underfitted. This isn't a critique of Uri's paper in any way. I'm curious if there are any other regression attempts that have taken a similar approach to the one I suggest. As far as parameterizing the displacement curve for use in a residuary resistance fit, what sort of parameterization would the rest of you use as a first attempt?

 

Longitunal metacentric height

Is the waterline length the best indicator as reference measure for describing a vessel's characteristics?

Since almost all the parameters are set in relation to the waterline length, we can ask if there is a better measurement to create dimensionless numbers.

I myself have wondered about if the longitudinal metacentric height provides a better indication to relate to. This measurement is affected by the shape above the waterline and should be better in relation to the wave length, thus forming resistance.

JS

 

If you had to pick just a single one: yes, pretty much.

 

Good point! I am planning something similar, the attenuation of the offsets with Froude depth. It will take some time to rewrite my program. As soon as I have results i will come back.

 

I have both parameters in my list, LWL and BM. I use dimensional analysis to reduce the number of variables. With this method it does not matter, which length is used in the denominator. The results for the resistance are identical, provided the functionality between the variables is correctly determined. This is an outcome of Buckingham's PI-theorem.
Uli

 

Earlier, I suggested -

- and you responded with -

That's not what I had in mind. You have a viscous drag calculation routine. Just run the exact same straight correlation on the viscous drag routine as you did on the residual data. Start by calculating the ratio of viscous drag to residual drag for each hull. Fit some std curve. Then sort the models into two or three bunches based on the Fn where the drag crosses over. So you have low speed, mid speed, and high speed boats bunched. You may want to eliminate boats with large trim conditions. For each bunch, run the correlation of Xi to Yi and Xi to Viscous resistance and see what shakes out.

 

It seems that we are misunderstanding each other. The calculated viscous coefficient is almost constant, the reason is explained in post#3. Between Fn=0.35 and Fn=0.55 where the sign reversal of the correlation for the residuary resistance occurs, the viscous resistance coefficient practically does not change. The ratio that you propose, would give exactly the same correlation as the residuary coefficient alone, because it only differs by a constant factor. The prediction parameters for the best fit that are chosen in the full search would be the same.

I have meanwhile investigated the impact of the attenuation of the offsets with Froude depth. The standard error of the prediction did not change, only the curtosis was reduced from 4.09 to 3.95. I do not think that this is worth the extra effort.
Uli

 

You would need to convert the viscous coefficient into resistance, and then apply the same nondimensionalization to it that you chose for Y in order to compare correlations directly to Y. Basically, it looks like it will be the term Area-wetted/(vol/L) that you would be testing the correlation against if you have chosen the viscous coefficient to be uniform across the entire sample set. The differing nondimensionalization was throwing us both off a bit, I think.

 

Revision available

A revised version is available at
http://www.remmlinger.com/Regression DSYHS.pdf
I cleaned up the Delft-point-files that define the geometry of the hulls and I added a new parameter for the volume, attenuated with depth.
The quality of the regression is improved compared to the initial version.

 

This is very interesting for me as a canoe designer. We race around Fn=0.4

Some small feedback:

top of page 8 "exit angle... independent of T/L1" did you mean T/L2?

In Figure 3. You refer to T/L2 but have not defined T. Is that draft at the max section or draft at the stern? Maybe it should be (Tx-Tstern)/L2 to capture the vertical exit angle of the keel? (recalling "yatch designed after the same rules")

at Fn=0.5, Peasons's for T/L2 is about 0.9, however you also show Pearson's for (T/L2)^2 is negative at the same Fn. (mathematically impossible?)

 

Thank you for reading my paper so carefully!

r for Tx/L1 is 0.88
r for Tx/L2 is 0.83
These are both high values and especially Tx/L1 is not related by definition to the exit angle, the correlation is mainly driven by aesthetic reasons.

In the text I have used Tx for the draft at the max area section. In excel-diagrams it is difficult to use subscripts, therefore the x is missing.

The regression tells me that an increase in (Tx/L2)^2 will decrease the resistance very slightly (r<0), the impact is almost zero. Whereas an increase of Tx/L2 will increase the resistance very definitely. This means that by squaring Tx/L2 the relevant information is lost and the quadratic term is not helpful in predicting the resistance at this FN.
Thanks for your efforts, appreciate it
Uli

 

A paper I bumped on..."A scaling law for form drag coeffcients in incompressible turbulent flows". Maybe a little off the topic, but casting light on the skin friction/viscous pressure/form drag issue.