# Savitsky Method

Discussion in 'Software' started by Joakim, Jan 12, 2007.

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### JoakimSenior Member

I'm trying to learn the Savitsky Method as a hobby. I have read the original 1964 paper and the new paper from 2006 wich deals with whisker spray and aerodynamic resistance (http://hudson.dl.stevens-tech.edu/personal/mdelorme/Whisker Spray/Whisker Spray 2-28.pdf). I have played with the Dingo's Excel as well.

I tried to model my old "racing" boat which is 3.8 m long and has a displacement of about 250 kg (including driver, motor etc.). With 40 hp it reached 48 kn and had a very short and narrow wetted area. I used Dingo Excel, but it gave higher power demands at that speed. In real life I think well over 50 kn would have been possible with a more optimized propeller and much smoother bottom with much sharper edges. The boat was made using an existing boat as a male mold, thus the bottom was far from perfect.

It seems that the aerodynamic drag was very much overpredicted (seems to have a Cd of 1.2 inside the Exce)l, but even correcting that didn't really help. Then I realized, that the model assumes the bottom to be wetted for the whole beam at the transom, which can not be the case, since draught is under 5 cm according to the Dingo Excel at 48 kn.

A couple of things are not quite clear to me.

What should be done at very high Fn, when the chines are completely of the water? Should B be reduced until draught/sin(deadrise) equals B/2? Or should B jump to the spray rail at some point? Both these would need another iteration loop, since draught (and drag, trim etc) depend on B. If B would be in the middle of the bottom (not on chine or spray rail), then the whisker spray resistance would need to be calculated differently. I guess whisker spray resistance is quite important with this boat.

What would be a reasonable aerodynamic Cd for a racing boat with a rather long and sharp bow? Certainly 1.2 is not reasonable. Maybe 0.5 or even less?

How important are the vertical forces and moments caused by a cleaver propeller? How to calculate them? How should the location and angle of the propeller shaft be given? Giving the actual propeller axis is not adequate, since only about 40% of the propeller touches water.

Will aerodynamic lift of the hull be important at these speeds and with a V-bottom? How to approximate the lift coefficient?

I'm planning to write my own C-language program for this as I have already done for sailing boats (Delft series based VPP), since I really don't like Excel.

Joakim

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### RANCHI OTTONaval Architect

Reasonable Cd for your boat is 0.45/0.5 if the deck is open not more.

For an high speed boat of 14/15 m with superstructure, I calculate the wind resistance with a Cd of 0.5.

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### Tim BSenior Member

Joakim,

I've been planning to do the same thing myself. I'd suggest going back to Savitsky's original paper and starting from there.

Tim B.

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### JoakimSenior Member

I have my C-program now quite ready. It includes the original 1964 model, my own aerodynamic model and the whisker spray model from 2006 paper.

There are some details missing in the 1964 paper and the results in 2006 paper are a bit confusing.

I was able to reproduce the results in 1964 with quite good accuracy, but not exactly (1-5% differences in some variables). The same was true for the 2006 paper results. The trim predicted was within 0.1 degrees, but not exactly the same. Lk and Lc where 1-2% too high with the same trim. The bare hull resistance was within 1%. There were bigger differences (~10%) in the aerodynamic model, since I used a different approach, which takes into account the draught and trim to the frontal area and a lower Cd.

The whisker spray resistance was clearly different (up to 100%), but the reason seems to be only in the friction coefficient, which is defined for model scale in the paper. I guess the reason for this is to compare with the (wrong) old full scale prediction and thus the reported whisker spray resistances are wrong in the paper.

The detailed comparison with the reported results is very difficult, since there are values missing (e.g. viscosity and density of water) and there seems to be some errors as well (e.g. the reported beam in table 2 is 31.1 ft and LOA 41 ft).

Are the porpoising stability curves in the 1964 paper still the most accurate ones or are there better sources?

Why is the standard roughness allowance of 0.0004 in Cf used? I included a Cf computed based on the actual roughness of the boat. The actual roughness (in um) equaling delta Cf of 0.0004 varies quite much depending on the the size and speed of the boat, thus I think it is a very poor approximation for planning hulls.

Joakim

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### Tim BSenior Member

Cf of .0004 is really just a factor to take into account some typical roughness. For the moment, stick to what savitsky uses, otherwise you'll never get correllation of the results.

Are you using floats or doubles in your C code? you may find that using doubles improves the accuracy considerably. Use the "%lf" formatter to read/write them.

Do you have a copy of Savitsky's 1964 paper?

Tim B.

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### PI DesignSenior Member

Hi Joakim, I can't answer any of your questions I'm afraid. It's been a long time since I've looked at Savitsky closely, but I do remeber that the Centre of Pressure equation, Cp = 0.75 - 1/((5.21Cv^2/Lamda^2)+2.39)
should actually read Cp = 0.75 - 1/((5.236Cv^2/Lamda^2)+2.40)

where lamda is length/breadth ratio and Cv is the beamwise Froude number.

This could be one source of error in your model.

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### JoakimSenior Member

I think Cf correction of 0.0004 is stupid, thus I don't use it and I also had the Cf model already from my VPP. When comparing the results, I can adjust the roughness to give the same Cf, thus it's not a problem.

As an example of this: A rather normal roughness value for an antifouling is 50 um. With this roughness the "roughness allowance" at 30 kn would be ~0.0014 for my race boat, ~0.0007 for a 70-footer in Savitsky 2006 paper and ~0.0004 for 1000 foot ship. In order to have 0.0004 "roughness allowance" for my boat the roughness needs to be about 10 um.

I think 0.0004 allowance is only reasonable for displacement speeds.

I always use doubles, since there's no penalty from them in modern computers. I have the 1964 paper. Reading the paper it seems, that the example results are taken from the figures and thus not computed and not that accurate. In 2006 paper many details are left unmentioned from the example results. The values of a, f, c and VCG are not given. Maybe it is assumed, that a,f and c are zero and thus VCG is unimportant?

Joakim

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### Tim BSenior Member

Out of interest, are you developing under Windows or Linux? and which C compiler are you using?

Cheers,

Tim B.

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### JoakimSenior Member

I'm developing on cygwin or Linux with gcc. Just basic C without any graphics or other system dependent stuff. Maybe I add gtk GUI some day, but I'm more used to work with shell based programs. Can easily be compiled to run on W32 without cygwin.

Where does the correction to Cp formula come from? Is that the one used in the 2006 paper?

Joakim

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### PI DesignSenior Member

The correction is simply due to having a calculator these days! If you follow through the original working out, you should end up with the Cp equation I posted, not the one in the paper. There is no modification to the underlying theory, just the accuracy of the calculation.

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### JoakimSenior Member

I don't think that is the reason. You seem to assume, that the 33% value in the paper is actually 1/3 (33,3333333%). You have to remember that all this is based on the approximate for center locations and also the lift equation is only accurate to 2 numbers. Calculating more digits to Cp equation doesn't improve accuracy, but gives slightly different results.

Joakim

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### PI DesignSenior Member

Yes, you are right - the 'revised' formula is not necessarily more accurate, just different. If your code solves these equations from the beginning, rather than inputting the Cp equation given directly, then it will calculate Cp for the revised formula. If you then compare it to the Cp value from the original paper, you will get a source of difference (but not, as you say, error).

I just thought that might be one possible explanation for your slightly different results.

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### JoakimSenior Member

That may be. I have used the actual formula (with 2.39 etc.). I have no idea what Savitsky has done in his program. I have asked him for more detailed results for the examples in 2006 paper.

It is a bit annoying to get a somewhat different results. There might always be a bad error, that just doesn't show in these examples.

Joakim

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### DingoJunior Member

Slightly Different Method

I have posted this request in a different thread, but I will repeat it here. There is a paper on the Small Craft CD by SNAME written by Richard A. Royce entitled "A Rational Prismatic Hull Approach for Planing Boat Analysis". Has anyone used this method?

By the way, I have debugged a trim tab error on my spreadsheet and reposted it.

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### CGNSenior Member

Hi Dingo thanks for your spreadsheet and update, i have a question about lewandowski "dynamic roll prediction", basically what is? and what are you actually seeing on the results?, where do you use this results or result?

thanks

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