Talk:Hull speed

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[edit] Concerned and Curious

I would like to know the references for the formulas and theories presented here.

Jmvolc 00:31, 18 May 2006 (UTC)

http://www.antrimdesign.com/articles/hullspeed.html
http://www.frontrower.com/hullspeedchart.htm
http://www.dynagen.co.za/eugene/hulls/
...and that's just from the first page of hits of a Google search on "hull speed". As I recall, the formula was devised by naval architect William Froude--that article has a picture of the scale models he used in towing tests to come up with the formula and conversion factor. scot 14:46, 18 May 2006 (UTC)


William Froude takes credit for the Froude number which bears his name. It was originally defined by Froude in his 'Law of Comparison' in 1868 in dimensional terms as Speed-Length ratio

Speed-Length Ratio = V / ( L )^0.5

where:

v = speed in knots
L = LWL in feet

The Naval Constructor Reech put forward the concept in 1832 but had not demonstrated how it could be applied to practical problems in ship resistance.


Fn was later refined to the non-dimensional :

Fn = v / ( g L )^0.5

where:

v = speed in m/s
g = gravity in m/s2
L = LWL in m

The term 'Hull Speed' is loosely used by yacht designers and sailors but has no basis in science. It is unclerly defined as being a Speed-Length ratio between 1.34 and 1.5. This corresponds to a point where the wave making resistance of a hull form increases dramatically in some forms.

It should be defined as such.

Jmvolc 00:38, 19 May 2006 (UTC)

I'll admit that the formula is a rule of thumb, and I have changed the article to reflect that. However,I object to the "no basis in science" statement; the scale effects of hull speed were experimentally determined, and exerimentation is part of the scientific method. Hull speed is also demonstrably related to wave drag, which can be mathematically described, and it's not just coincidence that the hull speed formula looks a lot like the simple harmonic motion formula. Having, for example a rule of thumb to pick the length of arm and mass for a clock pendulum (I'm just making this up, based on calculations done in physics class) doesn't have "no basis in science" just because it ignores the mass of the arm, it's just a first order approximation that knowingly ignores the minor conributions to the system. The hull speed formula is the same thing--it might not tell you exactly fast you boat will really go, but it does give you a good idea of what kind of change you can expect by adding a couple of feet to the waterline length. scot 16:43, 19 May 2006 (UTC)

If we use the example of a Tornado Cat, it has a very low wetted area and a very low displacement for its length. Note that it does not have a shape that can generate any dynamic lift (planing) so it always stays in a displacement mode. At high speeds (Fn>=1.0) the wave making resistance varies approximately as the square of the displacement. Due to it's very light displacement it generates a very small wave train allowing it to power well beyond its "Hull Speed".

At 30knots the Fn for a Tornado (LWL=6.10m) is Fn = 30 x 0.5144 / (9.81 x 6.10)^0.5

    Fn = 1.99

The "Hull Speed" is around 6knots, so is clearly not a good first estimate of what the form is capable of. As the science of Naval Architecture progressed from carving half-models to computational fluid dynamics more and more vessels became capable of going 2 or 3 times their 'Hull Speed'. It really does not provide any real useful design information as it is dependent on many interrelated parameters.

The relationship between wave motion and hull speed is new to me. I have reviewed my references and cannot find any such link. Can you provide some insight? Jmvolc 00:50, 20 May 2006 (UTC)

The hull speed rule of thumb takes into account wave drag and wave drag only; since the wave size varies with the displacement, the wave drag also varies with the displacement. An infinitely thin hull will displace nothing, and so will be subject only to skin drag. Catamarans, or better the original proas they descend from, have far longer, thinner hulls than any traditional ballasted ship carrying the same amount of sails. Because of this, they have an order of magnitude (or more) less wave drag than a similar length hull. Since the width of the multihull allows far more sail to be carried, they can push much, much farther up the exponential slope than traditional displacement hulls. The same applies to modern ultralight displacement boats, which, even when not designed to plane, will plane to some extent if pushed hard.
Since hull speed is based only on wave drag, hull speed is linked to the wave speed. Deep water waves (where the water depth is greater than half the wavelength[1]) propagate at a speed of sqrt((gravity * wavelength) / (2 pi)). At hull speed and below, the boat's hull spans at least one wavelength. Push the speed beyond that, and the stern drops, the bow lifts, and you're effectively sailing uphill. This is where the real increase in wave drag starts to appear.
Does that make any sense? The only reference book I personally have is Marchaj's "Sail Performance", and I'm not sure how much it has in it on hull issues--it's mostly concerned with the sails, but I can go track it down and see if it has anything related to hull speed. scot 20:05, 20 May 2006 (UTC)

[edit] More concerned and curious

I'd like to know why you insist on claiming that hull speed "has no basis in science" without actually providing any argument or references to support that claim. If you are correct, then you should be able to provide verifiable references that state that hull speed is unrelated to wave drag, or that wave drag is unrelated to wave propogation speeds, or something. If you can't prove your claims, or disprove the claims of the existing article, then I'm going to have to insist that you are just making biased changes to the article to support your opinion. scot 14:02, 22 May 2006 (UTC)


Providing a reference is problematic. The books that I have on Hydrodynamics and Naval Architecture make no reference to Hull Speed. "The Oxford Companion To Ships And The Sea" edited by Peter Kemp does not have the term "Hull Speed" either and it is meant to be of general interest as opposed to a technical reference. However, it does talk about a "theoretical maximum speed" in the entry on "Wave Line Theory". "Hydrodynamics In Ship Design" by Harold E. Saunders was my last hope as it was written in 1957. No luck there either. So that would be 14 text books and a bookshelf full of technical transactions.

Books I have on yacht design such as "Elements of Yach Design" by Norman L. Skeene, "Basic Naval Architecture" by Kenneth C. Barnaby discuss how the wave making resistance increases at or around a Speed Length Ratio of 1.34 but I did not find the term "Hull SPeed" defined in clear terms. Even "The Common Sense of Yacht Design" by L. Francis Herreshoff published first in 1946 (?) (a great read and not very technical) does not mention the term "Hull Speed".

So how am I to provide a reference that that says something doesn't exist when the references that I have don't even acknowledge the term?

I am not going to enter into an "editting war" over this. I leave it to you to replace the text as I have entered it. I cannot add a reference to the term Hull Speed as I have none other than magazines and other popular literature.

It is my intention to clarify a few terms dealing specifically with Naval Architecture. If anyone has a reference that is in conflict with what I have changed or added, I would be very interested in reviewing it.

Jmvolc 15:05, 22 May 2006 (UTC)

Ah, it all becomes clear now. Books I have on yacht design "Elements of Yach Design" by Norman L. Skeene, "Basic Naval Architecture" by Kenneth C. Barnaby discuss how the wave making resistance increases at or around a Speed Length Ratio of 1.34.. It looks like the issue here is one of semantics, not one of science. What a scientist or an engineer calls "Speed Length Ratio" is what the lay world calls "hull speed", and plugs in an empirically determined constant of 1.34 or so. Here are some references that show that the "speed length ratio" and "hull speed" are basically synonymous:
I'd like to come up with an article we can both agree on, and I think that, if you'll agree that our differences are primarily semantic, we can add information on speed/length ratio and make the same article address both; at that point, I see "hull speed" being a just a note that it's a common rule of thumb based on the speed/length ratio, and the rest of the article can concentrate on the physics behind the wave drag (unless you think that information should go in the existing wave drag article, which is currently entirely aircraft oriented). You've certainly got me beat as far as available hydrodynamic reference materials goes, so I'd like to have your input on the physics behind wave drag. Does that sound like an acceptable compromise? scot 15:34, 22 May 2006 (UTC)


I'm very much in favor of having an article that represents a collective agreement. As I understand it - that is the essence of Wiki. Wave drag in Naval Architecture is usually termed Wave Resistance and really doesn't belong in this article - it may not belong in Wikipedia at all as it is extremely technical. Your statement "I see "hull speed" being a just a note that it's a common rule of thumb based on the speed/length ratio" is very encouraging and absolutely correct. This should be the central theme for this article. It must also be noted that the term is not used within the commercial or military sectors of ship design, only in the yacht design sector (and not much there anymore either). This is what I had meant by the term "no basis in science" ... the industry does not accept the notion of a "Hull Speed". I feel strongly that this should be brought to light. I can assure you that everything in the article I put forward is verifiable - I am also willing to concede that it could be re-structured or re-worded to make it more appealing to a general audience. Please feel free to make any changes along those lines. I'm afraid I object to the section currently termed "The physics of hull speed" as it is mis-leading in that it introduces Hull Speed as a central term that can be demonstrated within the analysis of wave making resistance.

Jmvolc 15:47, 22 May 2006 (UTC)

I'm glad we've agreed to agree--edit conflicts are always so stressful. On that note, let me start a new section titled...

[edit] Proposed new format

I did some quick Google searches, just to get some idea of the usage frequency of various terms and combinations of terms:

  • 7,230 for "hull speed
  • 241 for "speed length ratio" (same for "speed/length ratio", and other punctuation)
  • 49 for "length speed ratio" (same for "length/speed ratio", and other punctiation)
  • 3 for "length to speed ratio"
  • 62 for "speed to length ratio"
  • 80 for "speed length ratio" "hull speed"
  • 24 for "speed to length ratio" "hull speed"
  • 0 for "length speed ratio" "hull speed"
  • 0 for "length to speed ratio" "hull speed"

This shows that "hull speed" is the dominant term on the web, and that 1/2 to 1/3 of the articles on "speed length ratio" or "length speed ratio" also use the term "hull speed". Based on this admittedly shaky statistical basis, "hull speed" is probably going to be the most likely path through which a user will find the article (since by the nature of Wikipedia it's going to attract users who are not domain experts--you for example, are apparently a domain expert, but you're an editor in this area, not a user). So hull speed needs to show up in the first paragraph or two, and be in bold. I'd say a good intro paragraph might be of the form:

Speed/length ratio is (breif definition). Speed/length ratio is commonly used in the form of a rule of thumb called hull speed, used to provide a quick approximation of the speed potential of a given displacement hull, such as a sailboat or rowboat.

From there I think there should be discussions of the history of the speed/length ratio, a discussion of the physics of wave drag, and a note on hull speed and the range of constants used for hull speed calculation. I'm not sure there's an internally logical way to order those sections, and if not, I'd say go with the hull speed paragraph first as it's likely to be of interest to the greatest number of readers. Then history, and leave the physics last, since it would appeal to the smallest audience.

The article could also be moved to "speed/length ratio", as that would be the main focus of the new article, and "hull speed", "speed to length ratio", "length to speed ratio", "speed/length ratio", etc. could be created as redirects to the new "speed/length ratio" page. Or, we can leave it where it is and redirect everything here--that would have the slight advantage of leaving the existing links to "hull speed" direct to the article, and not double links through a redirect.

Any additions, deletions, or changes you think should be made? scot 16:15, 22 May 2006 (UTC)


A very curious approach to re-defining the article ... entirely different than I would have used but it certainly has merit! I agree to your proposal as long as the article does two primary things:

1) Defines Hull Speed as a specific Speed Length Ratio (i.e: approx 1.34)

2) Notes that it is a term that is not used in the industry as it can not be quantified.

I would caution against delving into the physics of wave making resistance beyond noting that it is the phenomena that drives Hull Speed. This would prove to be a real Pandora's Box (take my word for this) and would argue against your intent of making the article more relevent for the general public. The history or origins section should reference Froude number as Speed Length Ratio is already covered there and I do not believe there is any verifiable origin to the term "Hull Speed".

I look forward to the article's next evolution. Jmvolc 17:00, 22 May 2006 (UTC)

I can certainly agree to both conditions. As far as physics goes, there's not really any useful information in wave propagation or wave drag to indicate to anyone why the waves speed would have any relationship with the length of the hull. Admittedly a full analysis of the wave resistance would be out of scope, but I think the derivation of the simple harmonic motion formula to show the math behind deep wave propagation speed would be reasonable; it's simple algebra, so many readers will be able to follow it. I think the true "Pandora's Box", as you put it, is the issue of wave amplitude--as I understand it (and I am an amateur at this) that's the bit that requires the intense computational analysis.
It may be a day or two before I can grab a big enough chunk of time for the rewrite; I'm tracking down an interprocess communications bug that's very dependent on synchronization (a.k.a. a Heisenbug) and those can take a while. scot 17:31, 22 May 2006 (UTC)


Please consider adding any text concerning the wave making reistance ( I'm going to stick with this term as your ref Wave drag is a aerodynamic term not a hydrodynamic term ) should go in Froude number where you will already find text along those lines. The wave making resistance of ships is infinitely more complex than the math behind deep wave propagation. This is due to vicous effects, eddy making, virtual lengthening of the hull, etc. Jmvolc 19:02, 22 May 2006 (UTC)


[edit] Still astray of the subject, I fear

The article is Hull Speed. The introductory text on Speed Length Ratio is redundant as it is addressed in the referenced Froude number article. This is also true for the History section - I think you would agree that the history of Hull Speed is what should be addressed here not the history of Speed Length Ratio. I have no reference for the history of Hull Speed and would suggest deleting the section in its entirety. The "Physics" section is somewhat misleading ... as discussed at length above, the physics of wave making resistance is incredibly complex and the "Physics of Hull Speed" is something that is at best, misrepresented in the present article. Currently the attached graph adds nothing to the article as the "Hull Speed" point (i.e. Speed Length Ratio = 1.34) has no distinguishing characteristic at all. This, I'm afraid, is the point that I have been trying to make ... Hull Speed is not a real thing at all.

I’m afraid my opinion is still that the present article does not describe the subject “Hull Speed” well and still has a significant amount of text that is not relevant.

At the risk of raising your ire, would you consider re-introducing the text I had put forward and enhancing the appeal to a general reader while still maintaining the technical validity? Jmvolc 02:08, 27 May 2006 (UTC)

[edit] Layman's Comment

Since the term is no more than a rule of thumb, we should not expect it to be applicable to all cases, merely those resembling historically familiar ship hulls. As I see it, these issues are unlikely to be settled until somebody presents, say Mitchell's slender ship theory, in a form which is accessible to the intelligent layman. I wish you good luck in the venture. It is easy enough to regurgitate the text book, but this level of explanation requires a depth of understanding of the subject which is indeed rare. There is quite a sufficient wardrobe of emperor's new clothes amongst the more technical articles, were authors appear to have neither the communication skills nor good manners to consider their audience adequately.

All that is really missing is the explicit statement that the speed is that of a surface wave having wavelength equal to the ship length (or is it twice?). An appeal to the familiar lifting of the bow at high speed, and a picture of a ship superimposed on the wave, is all that is required. Perhaps some cross sections of rounded bilge displacement hulls, and hard chine speedboats would serve to illustrate the how the hull shape must change with the onset of planing.

Gordon Vigurs 08:22, 28 May 2006 (UTC)

The speed/length ratio of 1.34 gives you the wavelength equal to the hull length. As for diagrams of the hull climbing the bow wave, I can certainly come up with some of those. I'm not sure round bilge vs. hard chine hulls really belongs here; that's covered in the articles on hull (watercraft) and chine (boating), and planing is covered in planing (sailing). scot 20:08, 30 May 2006 (UTC)

I tend to agree ... there is way too much text here that talks around the subject and the real information is lost in the technical details. Jmvolc 21:51, 29 May 2006 (UTC)

I'm having trouble understanding what you think "the real information" is. You maintain that hull speed is a fiction because it is in essence an arbitrary spot chosen on an exponential curve. I agree that the number is somewhat arbitrary, in that there is no inflection point on the graph at the speed/length ratio of 1.34, though 1.34 does happen to be otherwise significant as it gives you the wake speed, and it is the most commonly encountered speed/length ratio.
While the article resides at "hull speed", the article is now more an article on "speed/length ratio", and if you look that up this is where you'll land. I merely kept the article physically present at "hull speed" because that is where the article "evloved" into this state, so it contains the history and discussion. I beleive an admin could move the article and preserve the history, but I think that's beyond the power of an ordinary editor. scot 20:08, 30 May 2006 (UTC)

[edit] Another Layman's Comment

After reading the article (admiditly not very closely) I still do not have a clear idea of how the physics produces the effect. I do have a physics background, with a family background in sailing, so I have heard the term "hull speed" before - understanding it to be an emperical result - the top speed of a displacement hull set solely by the waterline length of that hull. After reading the article it does not seem completely clear why 1.34 is the magic number. Maybe we need a slightly stronger link between the "physics" section and the "hull speed" section? Is this a correct understanding: (a) The wavelength of the bow-wave is set by the waterline length. (b) The propagation speed of a wave is set by the wavelength. (c) The "hull speed" is the propagation speed of the bow-wave, since traveling faster than the bow-wave is really hard to do in a displacement hull. If this understanding is correct - should we have some wording to that effect in the article, or does the article already make it clear? j-beda 12:19, 8 July 2006 (UTC)

Yep, that's right. Basically, when you hit a speed/length ratio of 1.34, the hull speed, you have to basically climb out of the hole created by your wake. The Savitsky paper I've been working from has some really good diagrams of this, and I'll try to re-generate them and get them in the article. scot 21:52, 13 September 2006 (UTC)

[edit] References

I was curious about the lack of references that used the term, so I did a quick scan and found a couple:

Edmond Bruce in Design for Fast Sailing 1976 p199

Frank Bethwaite in High Performance Sailing 1996 p267

There is good discussion of the speed barrier in Marchaj's Aero-Hydrodynamics of Sailing (with a graph showing the performance limit of various hull types) and in Larsson & Eliassons' Principles of Yacht Design (note that they give the multiplier in metric units as 1.25, not 2.5, because they use m/s as the unit of speed. knots is hardly metric!). These references make it clear that the phenomenon is real but neither of them use the term hull speed as far as I can see.

Dave Howorth 2006-08-24


Dave, I immediately checked out Marchaj after reading your discussion. You are absolutely right. On page 76, Marchaj states "In practice, heavy-displacement yachts can only attain Vs about 1.5 Sqrt(L) (called sometimes 'hull-speed limit') in the most favorable reaching conditions." Additionally, on page 50 is a fine graph that shows a number of other hull types exceeding their 'Hull-Speed' quite handily. I have been singularly unsuccessful in explaining that 'Hull-Speed' is not a universal phenomena, nor is it a term that is accepted in industry, however, it is certainly a term that is used and needs to be clearly explained as Marchaj did. I would be most pleased if someone was successful in re-building this article without incurring the wrath of the original author. Much of the text that remains in the article is more-or-less correct and does provide a description of Speed-Length Ratio. One has to question why the re-direct for Speed-Length Ratio is to Hull Speed and not to Froude Number (any way to fix that??). Should this aritcle not focus on Hull-Speed and have all the text on Speed-Length Ratio moved someplace else?

Jmvolc 13:49, 30 August 2006 (UTC)

I had Dave scan in the relevant sections and e-mail them to me, and I've had a chance to look them over. I've also found an interestin paper by Daniel Savitsky, Professor Emeritus, Davidson Laboratory, Stevens Institute of Technology, presented to the Greek Section Of the Society Of Naval Architects and Marine Engineers[2]. It covers the hypothetical development of a 12k ton payload, 50 knot cargo vessel. The first section deals with speed/length ratios of displacement, semi-displacement, and planing hulls, and I think it's got a lot of good information in it, at a fairly accessable level. While the term "hull speed" doesn't ever appear in the paper, he does say:
Figure 3 is a plot of total resistance coefficient versus speed/length ratio. It clearly demonstrates this “wall of resistance” at a speed-length ratio equal to 1.34. Figure 4 is a typical plot of the resistance/weight ratio vs. SLR for a displacement hull. The very sharp increase in resistance at SLR > 1.25 is most obvious.
He then goes on to choses a 1480 ft. hull for his hypothetical ship, because 50 = 1.3 * sqrt(1480), and going any faster would require moving to a semi-displacement mode and require 10x the power, significantly reducing the cargo capacity. Page 5 also covers the varying effects of s/l ratios from 0 to 3 in the semi-displacement hull, which also explains why most commercial vessels operate at s/l ratios of under 0.9.
What I think I'm going to do is start by drawing a sketch of Fig 4 that I can attach to the article, since it is the best illustration so far I've seen of what hull speed really means, and also explains why catamarans so easily break the barrier (being semi-displacemnt hulls) and also shows the limit that they will hit at s/l ratios of 3 or so. I think that will give me enough data to pull the speed/length ratio discussion out, but I'll probably leave in the wave propogation stuff, since that isn't really relevant to the speed/length ratio, but does play into the hull speed.
I will also take a look at Froude number and see about pointing speed/length ratio there; it may take a bit of modification to make the article appropriate for both subjects. Sound like a workable plan? scot 16:04, 13 September 2006 (UTC)
OK, I've made some significant changes and moved a lot of data around. I created a wave making resistance aritcle, moved stuff out of hull speed and into that and Froude number, and re-created Fig. 4 in Savitisky's paper. I probably left a lot of loose ends dangling during all this, but it won't do me any good to look at it any more right now, as I'll see what I intended to be there, not what really is. I'll come back later and see if there's anything needing cleaning up. scot 21:49, 13 September 2006 (UTC)

[edit] Hull speed drives me nuts

I wish the term hull speed would go away. It is the most misunderstood and misused term among amateur boat users.

Hull speed is a special case of a speed-length ratio
These are just two different terms for the same idea applied for the specific case of a vessel when the waterline length equals the wavelength of a transverse bow wave.
Hull speed is not empirical
The hull speed equation has been derived by Froude based on a simple assumption - set the wavelength of a transverse bow wave equal to the waterline length of a vessel. The reason is to determine the speed-length ratio where the two are the same.
This is explained in Marchaj's Sailing Theory and Practice (pp 245-257). I've put this derivation on my wiki at Hull speed.
Hull speed is not a speed limit
It is an arbitrary point where the wavelength of a transverse bow wave is equal to the waterline length of the vessel. It just happens that this point, when viewing a graph of speed versus resistance, corresponds to a point where the resistance increases a lot for a relatively small change is speed. There is no "kink" or visual indicator of this point in graphs of typical hulls in towing tests. Many vessels can routinely operate at speeds much higher than hull speed without planing.
Hull speed does not result because you have to "climb the bow wave"
You can no more climb the bow wave than pick yourself up by your bootstraps. You can't climb a wave you are making. The force increase is because you're pushing a lot of water around and the incremental increase at that speed is significant.
Hull speed does not mean your bow rises sharply and stern sinks significantly
For some vessels, you'd have a hard time noting any apparent change of trim due to the bow/stern position. ICF flatwater racing kayaks come to mind. The pitching of the kayak due to the paddler's effort is way greater than any trim difference (such kayaks/paddlers win races around a speed-length ratio of 2.2). In other craft, you can see a difference.
Moving faster than hull speed does not result in planing
Planing requires an appropriately shaped hull. Lacking that hull shape, the hull will continue to displace water in order to support its weight.

I really wish the term would go away. Michael Daly 22:57, 31 August 2007 (UTC)


I couldn't agree with you more. I would like to suggest that everything after USE be deleted and replaced with a reference to Froude Number. This will provide a link for those folks looking for a definition of Hull Speed but will not let them believe that it is the correct term to 'compare different hull forms'. Jmvolc 12:02, 24 October 2007 (UTC)


[edit] Would it help to clarify the derivation?

I also hate the confusion caused by this term. It seems to me that the article should make it clearer that Hull Speed is misused when taken as a performance indicator. However, since people insist on using it I think it might be helpful to be more explicit about the derivation. The constants 1.34 for knots and feet, 1.25 for meters per second and meters and 2.43 for knots and meters relate to a specific construct. That is the purely theoretical two dimensional condition where a wave created by a point moving through the water at a specific speed will have a length equal to a "load water line". Thus:

In deep water the speed of a water wave is:

V = \sqrt { \frac {g \lambda}{2 \pi}} .

Where the boat is traveling at the same speed as the wave it creates by substitution we get:

V = \sqrt{ \frac {g * L_{WL}} {2 \pi}} . This is hull speed. If we quit here there are no approximations.

Replacing the constants for gravity and pi with decimal approximations and moving them out of the root we get:

V \approx 1.34\sqrt{L_{WL}} when using feet and knots and V \approx 1.25 \sqrt{L_{WL}} when using meters and meters per second.


I think the approximation implies an empirical relation that doesn't exist. The theoretical implication is that there is a scale relationship between V and \sqrt{L_{WL}}. This leads to the use of Speed to length ratios and the dimensionless Fn. As far as I know that is the only useful "use" of hull speed. The construct says nothing about "speed limits" or "digging in" and so forth. In short, I agree with Michael. Could we change the use section to "illustrative only"? The entire use section really deals with some kinds of ill-defined (maximumish?) speed/length rations and not hull speed.

I also wonder what "semi-displacement" proa the author was thinking about. The great majority of proas are displacement boats. Tsmwebb (talk) 06:31, 28 November 2007 (UTC)


I'm not sure that more mathematics would resolve the problems with this article. There seems to be a fundamental disagreement between two camps:

Hull-speed is a readily definable point with scientific significance, and;
Hull-speed is a special speed-length ratio that only has historical significance.

Until these two widely differing points of view can come to some agreement, I don't think any math will help. Unless there is a massive uproar to the contrary, I will attempt a re-write in the New-Year. Jmvolc (talk) 03:59, 31 December 2007 (UTC)