center of flotation calculation and implications?

[TeddyDiver]

Originally Posted by Leo Lazauskas

At low speeds (technically low Froude numbers) a displacement hull will sink down into the water slightly, and this might increase its wetted area a little. (At some low Froude numbers it can also rise slightly above its at-rest level).
Confusing? You betcha!

Could it be estimated somewhat of how many bow wave's there's on the length of the waterline.. like if there's one crest and two troughs boat sinks, and when it's 2/2 then not (depends how the volume of the hull is distributed?).. believe the opposite, having more crests than troughs is impossible bcs there's allways a trough first.

[Leo Lazauskas]

Originally Posted by TeddyDiver

Could it be estimated somewhat of how many bow wave's there's on the length of the waterline.

I doubt it. Among many other things, the first bow wave is usually much higher than other crests and troughs along the hull.

For very small models, surface tension complicates the problem further, e.g. how does one take into account the meniscus sticking to a hull that is not perfectly smooth?

So many fun problems, so little time
Leo.

[Eric Sponberg]

Originally Posted by mcollins07

Eric,
If we have two boats of close designs, i.e. same displacement, Lwl, and similar hull shape, there primary difference is the Cp values, then ….
Is it correct to say that less energy is required to get the boat with Cp = 0.7 to a speed/length ratio of 2.0 is less than energy required to get the boat with Cp= 0.61 to that same speed?

Where as, for two similar boats with Cp = 0.7 and Cp= 0.9 it will require nearly identical amounts of energy to get each boat to speed/length ratio of 3.0?
~ Michael

and

This graph might be helpful.

The data that Eric supplied us for Speed/length ratios correlated to optimum Cp values was plotted, Cp vs Speed/Length.

Just looking at the numbers, I think one would tend to see a linear correlation. A linear fit would lead one to think that a Cp value above 0.7 would be optimum for a Speed/Length ratio in the range of 2.0 to 3.0.

A non-linear fit to the data shows a much better fit (or correlation coefficient), thus the correlation is not linear. We should avoid our tuition to extrapolate linearly into the range of Speed/length ratios of 2.0 or above.

~ Michael

and

From Ancient Kayaker:

I agree a curve fits better than a straight line but it is unlikely to have a maximum or even be asymptotic. Both imply hull forms with Cp greater than about 0.7 either do not exist or do not have a solution for speed/length ratio.
I have trouble understanding this whole discussion of the impact of Cp on SLR. Surely length/beam ratio has far more impact? Or am I trying to make sense of a purely theoretical discussion?

and

From Fanie

Hi Ancient,

I have the same queery. I have drawed yet another hull. It seems the hull is more blunt if the Cp is around 0.7 than when it is 0.6.

The draft to carry the same weight between the two is about 100mm, so in the case of the Cp at 0.7 the draft is 400mm for 2300kg's and the draft for the Cp at 0.6 is 500mm also for about 2300kg.

This means the hull with a Cp of 0.7 has less water friction, the wetted area is smaller. The sharper hull with Cp of 0.6 and more draft has a larger wetted area.

Now the question is -

If speed increase, does the wetted area drag increase as well ?

How much ??? this will be drag per sq area and speed then ??

Good questions all. Michael's first question: Will a hull of Cp = 0.7 require less energy to reach S/L = 2.0 than a hull of Cp = 0.61, provided they are similar in hullform, displacement, and Lwl? We can't say for sure--we don't know the resistance curves of the hulls on the way up to S/L = 2.0. It may or may not. We can say that AT S/L = 2.0, the hull with Cp = 0.7 will likely have less resistance than the hull with Cp = 0.61. As you have probably deduced and as Fanie has found, the primary difference in the vessels is draft and wetted surface. There could also likely be differences in beam, all of which play a part in total resistance.

Fanie has drawn two hulls, one with Cp 0.7 and smaller wetted surface, and one with Cp = 0.6 and deeper draft and larger wetted surface. His question is if speed increases, does wetted drag increase? Of course it does. Cp has little effect on wetted surface (frictional) drag other than the fact that two different hulls inadvertantly have different wetted surfaces. Cp effect relates to wave-making resistance, and this is important at speeds close to hull speed, S/L = 1.34.

This effect of Cp is on wave-making resistance only, so if when you are changing hull characteristics that also change wetted surface, you are also affecting frictional resistance which has a primary effect at low speeds where waves are minimal.

And about Michael's second statement, two hulls of Cp = 0.7 and Cp = 0.9 requiring the same energy to reach S/L = 3.0? No, I don't think you can say that definitively. That is too much of an intuitive extrapolation. That is a huge difference in Cp, so for the same hull length I doubt that you would have the same displacement. Or, if they did, then the shapes of the hulls are vastly different and you end up with different 3D flow effects occurring which would affect resistance. Also, at S/L = 3.0, you are definitely in a planing regime where the whole Cp relationship with resistance disappears, as we discussed before.

I suggest that you all re-read Larsson/Eliasson's "Principles of Yacht Design", pages 71-84 in the Third Edition, which is in the chapter on hull design, a bit of the history of the Delft model series, and a discussion of wave resistance and the effect of Cp on it.

Remember, Cp does not tell you what speed the hull is going to attain. All hulls can achieve any speed given enough power. Cp has an effect on wave-making resistance which is important in the region of hull speed. And if your hull is going to be operating primarily at a speed close to hull speed (and most hulls do), it is worthwhile to have a Cp that is optimum (least wave-making resistance) for that speed.

Eric

[mcollins07]

Eric,
Thank you for your thoughtful response.


( deleted that question because it is closely related to a quesiton Eric has already answered, and the difference it not relevant to most practical designs. Better to move on. )

[capt vimes]

Originally Posted by eric sponberg

Remember, Cp does not tell you what speed the hull is going to attain. All hulls can achieve any speed given enough power. Cp has an effect on wave-making resistance which is important in the region of hull speed. And if your hull is going to be operating primarily at a speed close to hull speed (and most hulls do), it is worthwhile to have a Cp that is optimum (least wave-making resistance) for that speed.

now THAT sums it up perfectly for me... thank's yet again eric!

[TeddyDiver]

Originally Posted by Eric Sponberg

re-read Larsson/Eliasson's "Principles of Yacht Design", pages 71-84 in the Third Edition

Some symbols used are not included in the list in the book..
Tc is the draft of the canoe body and
Delta c is the displacement volume

ITTC symbols

[Fanie]

Great Eric !!

from me too, thank you for your thoughtful response.



Does any one have a curve to show what happens beyond hull speed ? It would be interesting to see what happens when you apply more power like when the wind is up and you let loose all those horses.

In the case of the hull's I drawed you require 240N to reach 7kn, and it seems 290 to reach 8kn, so it's not linear. There is a hump though beyond which the curve should change.


Btw, I drove in the car yesterday thinking about 20km/hr... so I tried it. If I have to I can run faster than that. Sucks... it's really sloooowww.

On the water it feels much faster though...

[Fanie]

This effect of Cp is on wave-making resistance only

Now we know a boat with a Cp of 0.7 have the least wave resistance around 1.3 x hull length.


What's next

[frank smith]

Good stuff. I am trying to get a handle the quality of the waves at different Cp.

[Leo Lazauskas]

Originally Posted by Fanie

Does any one have a curve to show what happens beyond hull speed ?

Here's a few graphs (from Harvald) of the residuary resistance coefficient versus Froude number (and speed-length ratio) for various values of Cp and L/(D^1/3). Sorry, but I don't have much that goes very far beyond hull speed.

Cr = Ct - Cfittc,
where
Cr is the residuary resistance coefficient,
Ct is the total resistance coefficient, and
Cfittc is the skin-friction coefficient using the 1957 ITTC line.

Note:
1. the graphs assume that the LCB is close to an "optimal" position.
2. Small adjustments should be made if the LCB is significantly
different. see Harvald's book.
3. The graphs are for ships; results for smaller vessels could be a bit different

Leo.

[Tad]

Today is my first look through this thread....please excuse the tardy comments.

On the A/B ratio......

I have to defend Robert Beebe a bit (as he's not around to do it himself), he did not invent this silliness for Voyaging Under Power(1975). Naval Architect Douglas Phillips-Birt, in his Motor Yacht and Boat Design (1953) illustrates the ratio of above water area to submerged lateral area. I have no idea were Phillips-Birt got the notion from, but it was long before the three story wonder was ever dreamt of. Beebe was really a amateur yacht designer in the days before compact computers, real stability calculations were rarely done for small boats. Like most amateur designers his work was more social commentary than naval architecture, and all the richer for it.

On CP values....

I think Eric mentions using a Cp of .6 for sailing vessels...this is slightly surprising. I haven't yet come across anyone willing to own up to going that high. The highest I can find in my own work is about .557 (lowest about .515) for a full keel sailing vessel. Bob Perry mentions .54 as a "medium" and personally using .54-.55 for cruising boats. The Valiant 40 without keel is .531. Ted Brewer mentions .56-.58 for heavy weather hulls and .54-.55 as average. Perry also mentions designers using a forward CP and an aft CP, as being more useful in describing the form.

I guess if one takes to heart the comments that a too high CP hurts overall less than a too low CP limits top speed, it makes sense to go higher....as always it's a question of degree.

[TeddyDiver]

Originally Posted by Tad

The highest I can find in my own work is about .557 (lowest about .515) for a full keel sailing vessel.

One thing not clear yet.. Is full keel sailboat Cp calculated with or without the keel. Eric mentions that keels aren't usually included, but in fishing vessels they are.. so reckon with??

[capt vimes]

regarding my information for full-keeled or vessels with 'integrated' (whatever that means) keels the keelarea is taking into account for Cp calculation... only fin-keels are ignored when midshipsarea and thus Cp is calculated...

[Eric Sponberg]

Originally Posted by TeddyDiver

One thing not clear yet.. Is full keel sailboat Cp calculated with or without the keel. Eric mentions that keels aren't usually included, but in fishing vessels they are.. so reckon with??

I think my highest Cp for a sailing vessel is about 0.62, a cruising sailboat that requires some considerable capacity. If it is not sailing near hull speed, it will require more power to cruise a slower speeds compared to its more nimble counterparts. So I gave it lots of sail area to compensate.

Yes, on a sailboat with a full length keel, I would include the keel in the Cp calculation.

As an example of the variance than one can get on sailboats with a deep narrow keel, my design Saint Barbara has a Cp without the keel (canoe body only) of 0.539. With the keel the Cp is 0.382 which is way outside the normal range. The influences of the keel on a sailboat can vary greatly depending on the keel geometry. Narrower-deeper the keels tend to have lesser influence on wave-making resistance. Omitting such keels from the Cp calculation keeps our minds in the normal range of expectations and analysis. This is a judgement call, however, depending on what the designer is thinking and trying to achieve. For example, he may compare a variety of designs that he has done with narrow-deep keels, and being aware of their performance characteristics, may derive some meaning from Cp calculated with the keel as well as without.

Eric

[Eric Sponberg]

In class today we cover Displacement-Length Ratio, DLR in short-hand notation. This is a commonly used ratio for comparing designs and estimating speed. Here is the definition:

DLR = Displacement/(Lwl/100)^3

Where Displacement is in long tons and Lwl is in feet. A long ton is 2,240 pounds.

DLR is kind of like Block Coefficient, Cb, in that it is a comparison of volumes, really. Since naval architects usually like dimensionless numbers, Displacement should be in expressed cubic feet instead of long tons. Then you would have a dimensionless ratio of cubic feet divided by cubic feet.

Larsson/Eliasson’s “Principles of Yacht Design”, uses the inverse of this concept in Length/Displacement ratio, LDR. This is Length in meters divided by the cube root of volume of displacement in cubic meters, a true dimensionless ratio.

LDR = Lwl/Vol^0.333

I am not as familiar with this form as you folks in the metric world may be, and I don’t use it in my work. I use DLR. I want to give some history here, so I am going to stick with imperial units and DLR. In the end, you may use either one, depending on your methods of design.

DLR was invented by Admiral David W. Taylor, the father of modern model testing in the United States, and first published in 1910 in his book “The Speed and Power of Ships—A Manual of Marine Propulsion.” Taylor found that when towing models in a towing tank and following Froude’s Law of Comparison, the resistance of the model was proportional to displacement. Specifically, he stated: “At corresponding speeds for similar models, resistances which follow Froude’s Law are proportional to displacement, and hence pounds per ton are constant.”

Zowie! That is actually very, very important. There are very few things that are constant in this world, particularly in naval architecture, so a statement like this is quite profound. For similar hull forms, at the same Froude Number (or as we saw in the last lesson, at the same speed-length ratio) resistance per ton of displacement is the same. I stress the terms in italics because the resistance per ton is constant only at that speed. The resistance per ton will be different for different speeds. More on that in a minute.

So, if I test a model that weighs 100 lbs and has a certain resistance, Rm, at a speed length ratio of 1.0, then I can pro-rate that resistance up according to displacement and arrive at a resistance for a larger boat or ship with the same geometrically similar hullform at that same speed-length ratio. To be explicit: resistance per ton = r. Resistance of the model is Rm; Displacement of the model is Dm. Resistance of the ship is Rs; Displacement of the ship is Ds. Therefore:

For the model: Rm = r*Dm

We know Dm because we can weigh the model. (And in fact, that is probably why Taylor used weight rather than volume. The weight of the model is constant during model testing and easily measured on a scale. Submerged volume, on the other hand, varies with the movement of the model through the water as it rises, sinks and trims, and it has to be calculated which back then was more tedious to do than now with our computers.) Also, we know Rm because we measure it by towing the model in a towing tank. So we solve the equation for r:

r = Rm/Dm

We do this for different speeds, and we can plot r versus Froude Number, Fn, or Speed-Length ratio, SLR. Knowing r, and also designing a ship with a displacement Ds, we want to know the resistance at the same speeds. Therefore, for any given speed:

Rs = r*Ds

That is generally the way it works. I do stress that model testing gets a lot more sophisticated and complicated than that when you start breaking total resistance down into its various components. But generally, this displacement rule works.

We know that as speed goes up, the resistance-per-ton, r, goes up exponentially, following a cubic relationship with Fn and SLR. See Fig. 9.1 on page 175 in “Principles of Yacht Design” by Larsson/Eliasson. Also, Skene’s “Elements of Yacht Design” (5th edition by Kinney) has a similar graph in Figure 1, on page 85.

So, where does this leave us with Displacement-Length Ratio, DLR? If we are studying a group of boat designs that we like and which are similar to one we want to design (comparing dimensions and characteristics of a population of boats is called a parametric analysis), we can compare their DLRs and deduce some general things about their performance. (I stress the word “general” here. We can deduce trends, not necessarily specific values.) We know that for the same installed power, or sail area and wind speed, heavier boats will be slower, or, that is, boats with high DLRs will be slower than those with low DLRs. Conversely, boats with low DLRs will have more lively performance than boats with high DLRs.

Another way to look at it is, say you have a preliminary design with a certain DLR. It will have a certain r value, resistance per ton of displacement at any given speed. (Or you can say, it will have a certain curve of r over a speed range.) But if you stretch the hull out longer, keeping displacement the same, DLR goes down, and r goes down. The resistance per ton is less, therefore the total resistance will be less, yet the hull is still the same weight. Note that if length increases, wetted surface also increases, so one might expect that frictional resistance goes up, and speed might suffer. Well, that is a common notion, but, the effect on reducing r (that is, reducing the total resistance) is greater than the increase in frictional resistance, in general. This primarily plays on the resistance due to form (one of the triad of friction, form and wave-making resistance).

Be aware that increasing length while holding displacement the same also reduces prismatic coefficient, Cp. You would want to be sure that Cp does not fall outside the desirable range. If it does, you may have to change the shape of the hull to maintain Cp in an acceptable range.

Ted Brewer, in his book “Ted Brewer Explains Sailboat Design”, in the first edition (1985), page 9, gives classifications of sailing yacht types based on DLR. These or similar classifications have been stated by other designers over the years, and this is a convenient summary, repeated here:

Boat Type…………………………………...…DLR
Light racing multihull…………………………...40-50
Ultra-light ocean racing boat…..……………...60-100
Very light ocean racing boat….……………..100-150
Light ocean racing boat…..…………….........150-200
Light cruising auxiliary boat…..……………...200-250
Average cruising auxiliary boat….…………..250-300
Moderately heavy cruising auxiliary boat…...300-350
Heavy cruising auxiliary boat………………...350-400+

In my career, it has been interesting to see the trend of boat designs getting ever lighter with reducing values of DLR. When I started yacht design in the 1970s, the typical good cruising sailboat had a DLR in excess of 300. Today, that’s changed. My sailing yacht designs going back about 15 years are all under 200, for example:

Project Amazon, 1995-6, Open Class 60, offshore racing: DLR = 69.5
Bagatelle, 1998-9, ultra-light ocean racing: DLR = 50.8, later 88.0 with heavier keel
Saint Barbara, 2002, light Great Lakes racing/cruising: DLR = 119.2
Globetrotter 45/Eagle, 2004-5, light auxiliary cruising: DLR = 192.7
Globetrotter 66 (currently in design), light ocean cruising: DLR = 140

All of these designs, save the last, are on my website if you would like additional particulars. The Globetrotter 66 is an aluminum cat-schooner I am designing for a client in Southern California, who intends to take his family cruising to the far reaches of the planet. The masts will be carbon fiber free-standing rotating wingmasts.

I should point out something else about DLR. Notice that Length is divided by 100 before it is cubed. The reason for doing that is it gives DLR a more understandable and reasonable range of values, generally between about 50 and 400. If we did not divide Length by 100, the DLR would be a tiny, tiny number with about three zeros right after the decimal point before reaching the significant digits. Dividing Length by 100 just makes DLR a little easier to understand.

In another example, let’s say we are designing a boat with a certain DLR, and we want to know what size engine to install. We can look at different designs with similar DLRs and see what size engines they have installed. We can be pretty well assured that if we pick a similar size engine, we will achieve performance similar to those other boats. DLR gives us some degree of confidence in making the design decision.

We can get into a deeper discussion about speed and displacement, but we’ll save that for another time.

A final note about long tons, one Long Ton = 2,240 pounds. Where does that come from? A short ton is 2,000 pounds. Why the difference?

Aside from wanting to use dimensionless numbers, naval architects also like to use simple numbers, and if you can get rid of decimal digits to the right of the decimal point, so much the better. Sea water weighs 64 pound per cubic foot. Fresh water, on the other hand, weighs 62.4 pounds per cubic foot. In America during the 19th century, a lot of shipping traffic grew and developed on the Great Lakes (fresh water), almost as much as there was on the sea along the coasts. And coincidentally at this time, naval architecture was going through tremendously rapid development and scientific expansion. Simplifications in ship design were in order wherever they could be found.

As you know, we often convert displacement weight to its corresponding volume of sea water or fresh water. The going standard terminology for a ton, what became known as the “short ton,” was 2,000 pounds. So, for the conversion, divide 2,000 pounds by the density of the water:

Sea water: 2,000 lbs/64 lbs/cu.ft. = 31.25 cubic feet (a messy number—it has decimal digits)

Fresh water: 2,000 lbs/62.4 lbs/cu.ft. = 32.05128205 cubic feet (an even messier number)

So the naval architects of the time decided to change the definition of a ton that would be easier to use and to convert to volumes of sea water and fresh water. They finally settled on the “long ton”. Here is what happened:

Sea water: 2,240 lbs/64lbs/cu.ft. = 35 cubic feet (a very clean and simple number)

Fresh water: 2,240 lbs/62.4 lbs/cu.ft. = 35.8974359 cubic feet (messy, but close enough)

Naval architects will also round numbers up and down if it suits them, and this looks like a good candidate. For fresh water, you can round this up slightly to 36 cubic feet per ton to get a clean number without too much error.

So now, long tons of 2,240 pounds could be easily converted to cubic foot volumes of sea water or fresh water by the using simple conversion numbers:

Displacement (long tons) x 35 cubic feet/long ton = volume in cubic feet of sea water

Displacement (long tons) x 36 cubic feet/long ton = volume in cubic feet of fresh water

And since 2,240 lbs. is larger than the short ton of 2,000 lbs., that is why we have the term “long tons.”


Well, that’s a lot of material for today.

Next week, we take up Sail Area/Displacement ratio.

Questions?

Eric