Skin-Friction Formulas

[Leo Lazauskas]

I found an interesting comparison of some skin-friction formulas in Table 2.1, p. 23 of O.M. Faltinsen's "Hydrodynamics of High-Speed Marine Vehicles", 2005, Cambridge Press.

I have attached a spreadsheet that shows predictions of various old formulas in that table, as well as some new ones. The formulas of Katsui and Grigson are being currently being investigated by the ITTC as possible alternatives to its interim 1957 ITTC line. The LL08 line is my variant of Grigson's line.

Results are shown for Reynolds numbers from 10^6 (i.e. model scale) up to 10^10, which is typical of very large ships.

Faltinsen calls White's 1974 results "Exact", which is a bit slipshod: the columns labelled "Errors" should probably be referred to as "Differences".

The Hughes formula seems particularly bad, with errors ranging from -3.6% at model scale, to -15.9% at large scale.

Of course there is a lot more to viscous drag than what is given by simple equations for the turbulent friction on a smooth flat plate, but the range of differences is a bit of a worry.

I wouldn't be confident in extrapolating from small model scale (where the ITTC formula is over-predicting by 7.9%) to full-scale where the same formula under-predicts by 5.2%. Nor would I be all that confident of using the ITTC formula as is for small towing tank models or very small boats (e.g International One Metre class).

So, is anyone prepared to stick their necks out and defend or trash one or more of these formulas?

Does anyone use some other formula we should know about?

Leo.

[daiquiri]

I would like to reply with another question...

In an engineering field where performance is higly dependant on a very variable local weather phenomena such as waves, winds, turbulence and temperature, on hull surface fouling by marine growth, on imperfections due to construction methods, etc. - how important really is a difference of 2, 3 or 5% between various calculation methods?

Please take a look on some graphs (from page 3 on) taken from operational data of some commercial ships in service:
http://www.cleanhull.no/doc/PDF%20fi...-%20CASPER.pdf
It's a very first thing I've found through a search in internet, tens of other examples could be added to that one...

So I really wouldn't be too much worried by errors of less than 4-5%. This is not deep-space probes we are talking about, trying to get outputs with 6 decimal places (just to say a figure) is pretty much useless in this field (and in many other fields of mechanical engineering) and is a waste of your precious intellectual energies, imho...

[Guest625101138]

Originally Posted by Leo Lazauskas

....
I wouldn't be confident in extrapolating from small model scale (where the ITTC formula is over-predicting by 7.9%) to full-scale where the same formula under-predicts by 5.2%. Nor would I be all that confident of using the ITTC formula as is for small towing tank models or very small boats (e.g International One Metre class).

..
Leo.

Leo
I have done just a little testing with tow tests and glide tests on models but even side-by-side tow tests on a balance beam at model scale have not yielded much useful results for me.

The most extensive comparison testing I did was for the V8 boat. This ended up submerged buoyancy that had a scaled main hull of 250mm long compared with a 0.9m slender hull. Scaling was 8X to full scale but I was interested solely in the comparison thinking that the comparison would be valid for the both model and full-scale. The submerged buoyancy was better but when built I could not get the hull as deep as the model and still use it so it became a learning exercise about wave drag from a submerged hull.

I note the testers of small models refer to using a trip wire to get the laminar/turbulent transition on the model to agree with the full scale. I then wonder how the results are scaled given that the components of drag scale in different ways. So without separating the components how do you get to something meaningful.

Have you ever thought about validating tank tests? Lets say Michlet produces an exact result over a wide range. How do the standard tank testing and scaling methods stack up against it? What sort of errors are there for various hull forms in scaling at different speeds?

Have you done anything like this?

Rick W

[Leo Lazauskas]

Written off-line, so excuse no formatted quotes.

Thanks for the paper, Slavi.
I haven't had time to read it thoroughly, but I'll be interested to see if the rule-of-thumb "friction increases by about 0.1% for each day in the water" is a reasonable one. I don't think extra decimal places are very important in that equation!


Daiquiri wrote: "In an engineering field where performance is highly dependant on a very variable local weather phenomena such as waves, winds, turbulence and temperature, on hull surface fouling by marine growth, on imperfections due to construction methods, etc. - how important really is a difference of 2, 3 or 5% between various calculation methods?"

1. I agree that for those cases a few percent here and there can be lost in the muddy uncertainties surrounding other important practical considerations. However, I also agree with Grigson: "Every part of a prediction method ought to be as accurate and true to the physics as one can make it".

2. Those differences are important when it can lead to under-powered ships being delivered. Financial penalties for that can be very high. Skin-friction dominates the total drag for many classes of ships, so it is important to get that component accurately as it ultimately affects, for example, the choice and sizing of propellers etc.

If a non-physics-based method gets you the right answer then you are lucky, or experienced enough to know its limitations. That's the art of engineering, I guess.

3. Some of the friction lines in Faltinsen's table are used to discredit other skin-friction prediction methods, when they themselves are very dodgy scientifically.

4. The differences are also important for yachts and other high-performance applications.

In a discussion of Grigson's 1999 presentation to RINA, I.M.C. Cambell of the Wolfson Unit admitted anomalies with the ITTC line. He also wrote that "it should be borne in mind that yacht tests are conducted to discriminate differences of less than 1% between significantly different forms".

Prof. D. Faulkner, Vice-President of RINA wrote:
"...there is little doubt in my mind that the ITTC line is poor in powering... I find it difficult to understand the acceptance of the ITTC 1957 formula."

Of course, that is just me cherry-picking some arguments in favour of a position I happen to agree with!

There were other supporters and antagonists in the many discussers of Grigson's work presented to RINA. I should also note that several very experienced marine engineers (e.g Kracht) completely misunderstood the fluid dynamic equations and their implications.

The Proceedings of the latest ITTC and its Specialist Committees on Powering etc can be found at:
http://ittc.sname.org/proceedings.htm


Daiquiri wrote: "So I really wouldn't be too much worried by errors of less than 4-5%."

5. I'm guessing that you design a limited number of boats for a limited variety of missions, so I agree that a few percent here or there are probably not of great concern to you personally. That doesn't mean that it isn't important elsewhere. E.g. I doubt that you do many extrapolations from small models to full-size ships.

The ITTC line (and other lines) are also used for non-marine applications where the effects of weather, surface roughness etc are not important.


Daiquiri wrote: "This is not deep-space probes we are talking about, trying to get outputs with 6 decimal places (just to say a figure) is pretty much useless in this field (and in many other fields of mechanical engineering) and is a waste of your precious intellectual energies, imho..."

6. A bit patronising, but you are basically a nice bloke so I won't take it to heart.

I like a reasonable number of decimal places when I am solving boundary-layer equations. Engineers can choose for themselves how many are adequate for their particular applications. And for some boat-huggers science isn't an issue at all.

7. The ITTC line is actually used for some "space" applications, e.g. to predict the drag of re-entry vehicles, with compressibility and enormous heat effects added in to make it even more uncertain than a bit of "weather".

8. Why would you worry about skin-friction now anyway. Shouldn't you be more concerned with ice-breaking friction where you live?

9. So, yes, I think an accurate, physics-based, skin-friction line has a place in marine engineering, ship design, and many other fields. Sometimes differences of less than 4%-5% are important.

And also, yes, those same differences are not important in many, many cases.

We call that "having a bit each-way" in Australia

All the best,
Leo.

[Leo Lazauskas]

Originally Posted by Rick Willoughby

I note the testers of small models refer to using a trip wire to get the laminar/turbulent transition on the model to agree with the full scale. I then wonder how the results are scaled given that the components of drag scale in different ways. So without separating the components how do you get to something meaningful.

There are accepted standard procedures, but it requires great care and experience. I'm not sure that the required care is always taken. I mentioned in a previous post the large discrepancies that occur even when the method is used by professional tank operators and technicians.

Patrick Couser attached Ship Report 71 to one of his posts in another thread. He gives a good description of the technique he used with the placement of studs on his (small) models, and the scaling laws used in his experiments.

Originally Posted by Rick Willoughby

Have you ever thought about validating tank tests? Lets say Michlet produces an exact result over a wide range. How do the standard tank testing and scaling methods stack up against it? What sort of errors are there for various hull forms in scaling at different speeds?

Have you done anything like this?

I have done a little, others have done enormously more over a long time, but the ITTC and its members are the big players in this game. Their powering committee reports, and the International Collaboration (I often refer to) are the one's to keep up with if you want to stay informed. Not everyone has the unadulterated nerdiness and time for that sort of thing though

As to Michell's theory in prediction, it has been used for a very long time.

Without going into the gory mathematical details, the basis of form factor predictions involves a limit of thin-ship wave resistance as speed tends to zero. See, for example, Wehausen, "The Wave Resistance of Ships".

I also looked into including the effects of viscosity on that limit, but I'm still scratching my head over what it all means.

As I said once before, you are likely getting good estimates for your work using thin-ship theory and the ITTC line because you are not extrapolating too far, you tend to test in calm water and, most importantly, your Reynolds numbers are roughly in the region where there is little difference between the ITTC line's predictions and those of other methods. (See the table I attached previously). And your hulls are usually hydraulically smooth which is important.

Leo.

[Guest625101138]

Leo
Back on the Michlet thread I was quite surprised by how wide the error band was for friction factors based on a small measurement error.

Lets assume that the measurement error in scale testing could be eliminated. What would be interesting to determine is how wide the error band gets as results are scaled up from model tests to various sizes.

Lets say that Michlet with the ITTC line gives the exact answer. Using the other methods of determining friction and the normal scaling relationships for Froude and Reynolds how wide will be the error band to Michlet(ITTC) at various scales.

Has anyone involved in model testing actually done this?

Of course one of the great features of having a reliable physics based model of skin friction is that you are in a better position to work out how various factors impact it and some creative solutions for reducing it.

Rick W

[Leo Lazauskas]

Originally Posted by Rick Willoughby

Leo
Back on the Michlet thread I was quite surprised by how wide the error band was for friction factors based on a small measurement error.

Lets assume that the measurement error in scale testing could be eliminated. What would be interesting to determine is how wide the error band gets as results are scaled up from model tests to various sizes.

Lets say that Michlet with the ITTC line gives the exact answer. Using the other methods of determining friction and the normal scaling relationships for Froude and Reynolds how wide will be the error band to Michlet(ITTC) at various scales.

Has anyone involved in model testing actually done this?

Of course one of the great features of having a reliable physics based model of skin friction is that you are in a better position to work out how various factors impact it and some creative solutions for reducing it.

There are a couple of famous tests that tried, but the experimental difficulties are enormous.

Tests were made with the "Lucy Ashton" in 1953, but I haven't had a look at the results in detail. There have been some re-examinations of that data in the last 20 years, but again I haven't seen the papers.

The British Admiralty tested the HMS Penelope with props removed and found the resistance was 14% more than predicted from model tests and correlations. They also found that props were more efficient and powerful than predicted by model tests. Nice that it balanced out a bit!

There have been a few "Telfer tests" reported in the literature where several geosims are used in order to get an idea of Reynolds number effects on resistance, but these are very expensive. The Italian paper from FAST2003 I cited previously used three geosims and they found large discrepancies (4% - 14%) because of uncertainties with boundary layer trips.

So, no, I don't know of any tests at the same Froude number but at Reynolds numbers of, say, 10^6, 10^7,..., 10^10.

Yes, an accurate skin-friction method is a great asset for all manner of purposes, and in particular for the accurate determination of form factors.

Leo.

[kistinie]

I hope you will forgive my intrusion in this thread for specialist.

Do we know skins texture that are reducing frictions compare to a perfect flat surface ?

If yes, how can they be done ?

[Leo Lazauskas]

Originally Posted by kistinie

I hope you will forgive my intrusion in this thread for specialist.

Do we know skins texture that are reducing frictions compare to a perfect flat surface ?

If yes, how can they be done ?

Search for:
riblets
and
hydrophobic surfaces
and
shark skin

That should give you a good start.

[gonzo]

Are there any tanks using a lower viscosity liquid or viscosity modifiers?

[Leo Lazauskas]

Originally Posted by gonzo

Are there any tanks using a lower viscosity liquid or viscosity modifiers?

Not that I know of, although others have thought about it too. I don't think that there is a whole lot to be gained - the kinematic viscosities of liquids at room temperature don't vary by much, certainly not orders of magnitude.

Turbulent eddy viscosity in the ocean can affect wave decay and wave resistance. These eddy viscosities can vary by up to 6 orders of magnitude, e.g. from about 10^-6 to 1.0 depending on how thrashed the surface is due to wind, ambient waves and passing ships.

Most towing tanks allow the water to settle after each run. It would be interesting to thrash the surface before each test to see if that makes a difference, and whether it can simulate more closely the conditions in a real sea.

Leo.

[gonzo]

It seems that all the lower viscosity liquids are solvents or flamable. Unless you count liquid nitrogen and such.

[daiquiri]

Hello,
It was a bad day today and I feel soooo tired, but I'll give my best to try to reply...

Originally Posted by Leo Lazauskas

Skin-friction dominates the total drag for many classes of ships, so it is important to get that component accurately as it ultimately affects, for example, the choice and sizing of propellers etc.

I agree with you on that, as a principle. But I was referring to the fact that during full-scale tests and operation of a ship surrounding conditions are so variable and unpredictable, and the gathered data is so gross that smashing your head about 3% difference between various methods for calculation of the friction line might divert you from other issues.

We are living in a non-perfect world (thank God), where 2-3% is something in the laboratory conditions, but is nothing in a natural environment. Even viscosity, the base of Reynolds number calculations, is commonly measured with some 0.5-1.0% of accuracy... And also, what about the engine rated power, which nearly never have more than 3 significant digits...? And the propeller efficiency, which have 2, or at best 3 significant digits? The same for transmission drives (2-3 significant digits in lab conditions, God knows what it becomes if slightly disaligned) and so on...

But I do agree that a common idealized model is useful for comparing various design solutions. I also agree that it is rather important for racing yachts (AC for example) which are optimized for a narrow range of weather conditions. So when it happens that the weather or waves on the race day are different than what was assumed at the design stage, the yacht is no more the optimal one.
I think that, when operating in a practical environment, a 3-4% uncertainity about frictional drag between two hulls might easily be cancelled out by the additional drag due to fouling, unsteady motion, wave and wind action, engine and transmission issues and many other natural and mechanical variables. Hence my question about the practical usefulness of that level of precision.

There was time when I was reasoning in such strict and precize terms, it seems that with age I'm getting too flexible and am conceding too much to natural variables...

Originally Posted by Leo Lazauskas

I doubt that you do many extrapolations from small models to full-size ships.

Yes, it is true.
In this case it would be nice to hear what Ad Hoc had to say on the issue, since he is the one who makes his living with those extrapolations, but I don't believe he will jump in anymore.

Originally Posted by Leo Lazauskas

Daiquiri wrote:
"This is not deep-space probes we are talking about, trying to get outputs with 6 decimal places (just to say a figure) is pretty much useless in this field (and in many other fields of mechanical engineering) and is a waste of your precious intellectual energies, imho..."
A bit patronising, but you are basically a nice bloke so I won't take it to heart.

If it sounded patronizing, I beg for pardon. It wasn't intentional...

Originally Posted by Leo Lazauskas

I like a reasonable number of decimal places when I am solving boundary-layer equations. Engineers can choose for themselves how many are adequate for their particular applications. And for some boat-huggers science isn't an issue at all.

As long as your input data (viscosity, turbulence, temperature, speed etc.) have the necessary precision to support your output decimals, it is perfectly ok.

Originally Posted by Leo Lazauskas

The ITTC line is actually used for some "space" applications, e.g. to predict the drag of re-entry vehicles, with compressibility and enormous heat effects added in to make it even more uncertain than a bit of "weather".

Now this has really puzzled me. It is a news for me, because ITTC line is a correlation line created for extrapolation of ship scale-model data, obtained from towing tests, to real-size ships. It is not based on boundary layer theories, just a mathematical correlation line for experimental data on flat plates to ship hulls, in standard athmosferic conditions. I don't see where a high-speed, high temperature reentry vehicles might jump into that story.
I do admit though that it might be just my ignorance, so I would like to learn more about that, if you give me a hint on appropriate readings.

Going home now, need a good dinner and a glass of wine after a day like this, to gather myself...

All the best,
S.

[daiquiri]

Originally Posted by Rick Willoughby

Leo
Back on the Michlet thread I was quite surprised by how wide the error band was for friction factors based on a small measurement error.

Hello Rick,
The graph you are referring to is puzzling me. I think you should check out your calculations and the assumptions behind them. I have performed the analysis on Ct coefficient and have obtaind results in line with commonly accepted error estimates in the low-Fr range, which is around 25-30% for 1% equipment precision. It is still high but nothing like the enormity in your graph.
Apart that, your graph would imply (imho) that all the technical and academic people working at and around towing-tank facilities are all inepts, if they published data with such incredibly huge error bands. I just don't want to believe that possibility (but it's a big world out there and I might be very wrong about it).

S.

[jehardiman]

Originally Posted by Leo Lazauskas

So, is anyone prepared to stick their necks out and defend or trash one or more of these formulas?

Does anyone use some other formula we should know about?

Leo.

Leo, I think it is important to point out that those formulas for skin friction are a mix of smooth and turbulent, 2-D, 3-D, and pipe formulations. For example, the Hughes line is for smooth 2-D flow on polished steel plates. For a history of the ATTC and ITTC lines and the compromises knowlingly made and what to do about it, read PNA Chapter 5, section 3.

FWIW, if I really need to calculate a good friction drag, I do it in 3-D with flow and form corrections using Schoenherr's log-log mean line plus a little.

Additionally, I concur with daiquiri that because you are going to add 10-15% sea power reserve for fouling and seaway, is it really necessary to get down in the weeds. Of course, you may be doing an ACC, in which case you would perfer, like the Swiss, to sail in a bathtub...

Also notice in the Ct vs Fn graph the error is proportional to speed and tracks the wave making humps...so, when calculating Ct which "S" do you use? The still water line one? And which "V"; nominal, crest, or though?