center of flotation calculation and implications?

[mcollins07]

Eric,
this question may be jumping a bit ahead, so if you want to wait to address it I understand. But, it is related to wave form resistance.

What difference does the shape of the Sectional Areas Curve (SAC) make in this regime around length to speed ratio of about 1.8 to say 3.0. It seems there are a number of equations used for a reference SAC. The sine/trochoidal SAC is based on wave theory model, I believe. It seems that the volume distribution to satisfy the wave from is less important in this regime than in a full displacement mode. Is the volume distribution considered irrelevant for a hull while planing? For a semi-planing sail boat, perhaps a good strategy is to have Cp = 0.7, a SAC with anything close to a bell shaped curve with the aft end truncated, as long as we have a flat section on the aft end of the actual hull? Should the size of the flat section be determined more by the SAC, or perhaps the weight (portion of displacement) we expect it to carry in a planing mode?

I'm trying to get an idea of how the shape of a reference SAC should change as we move from displacement mode to planing mode.

~ Michael

[Leo Lazauskas]

Originally Posted by Eric Sponberg

Form and friction resistance go up with the square of speed, but they stay pretty much the same proportion to each other.

Just to put that into perspective...
For length-based Froude numbers between about Fn=0.35 and 0.56, wave-making resistance can go up with the 6th power of speed in deep water, i.e. U^6.

In finite depth water, it can sometimes vary like U^8 or even U^10.

Leo.

[Eric Sponberg]

Originally Posted by mcollins07

Eric,
this question may be jumping a bit ahead, so if you want to wait to address it I understand. But, it is related to wave form resistance.

What difference does the shape of the Sectional Areas Curve (SAC) make in this regime around length to speed ratio of about 1.8 to say 3.0. It seems there are a number of equations used for a reference SAC. The sine/trochoidal SAC is based on wave theory model, I believe. It seems that the volume distribution to satisfy the wave from is less important in this regime than in a full displacement mode. Is the volume distribution considered irrelevant for a hull while planing? For a semi-planing sail boat, perhaps a good strategy is to have Cp = 0.7, a SAC with anything close to a bell shaped curve with the aft end truncated, as long as we have a flat section on the aft end of the actual hull? Should the size of the flat section be determined more by the SAC, or perhaps the weight (portion of displacement) we expect it to carry in a planing mode?

I'm trying to get an idea of how the shape of a reference SAC should change as we move from displacement mode to planing mode.

~ Michael

Yes, we are talking about displacement mode only here. Once the hull is planing (speed-length ratio => 2.5), the science changes and we have to deal with hydrodynamic lift and drag which are both independent, really, of the SAC, particularly in still water. In the planing regime, we would be more concerned with the shape of the bottom planform, the deadrise, the chine shape, steps if we have them, all manner of things not really related to the SAC. Certainly, the SAC is going to change, and as you suggest, it will be squared off at the back end, both at still water and when running. We know that we would have a certain hull length, breadth, deadrise, and that the hull will have to support a certain intended weight, do some speed-power calculations to ensure that we have enough power to achieve planing speeds. Work the design to achieve the bottom shape suitable for planing (or semi-planing) and see where your Center of Buoyancy (CB) and Center of Gravity (CG) fall out for floating level in still water. The SAC will fall out where it will, and the Cp will be what it will be. We don't typically analyze the SAC when the boat is on plane--it's not important.

Generally, you know that the Cp has to be between 0.5 and 0.6 for most hull forms, and up to 0.7 for high speed displacement hull forms. If Cp is outside this range, start over. Planing hulls will be within the 0.5-0.6 range in still water, and then the other factors of bottom shape take over.

I hope that answers your questions.

Eric

[Fanie]

Thank you Eric. I always try to understand what something does by reasoning it out in my mind. If you get the idea home and understand what happens, it usually becomes easier to design something specific.

Not that 'home' is always anywhere near and 'understand' is something imaginary

[mcollins07]

Eric,
thanks! Yes that helps clearify a few things. I have a fair graps on design parameters for displacement mode and the steps toward designing a planing hull, but still a little fuzzy on the semi-planing design. A sailboat that surfs well is what I'm calling semi-planing design. (I'm still learning terminology too.) Your input helps, and I think I need to attempt a few more hulls now. Thanks again.

~ Michael

[Eric Sponberg]

This week we are going to cover two totally unrelated ratios, both of which are relatively short topics: A/B ratio and Speed-Length ratio. The first is very silly and worthless, the other extremely important.

First, A/B ratio—a really a dumb and useless concept. Definition: The A/B ratio is the ratio of two areas, usually in motoryacht and trawler design. The “A” area is the profile area of the whole boat above the waterline, and the “B” area is the profile area of the hull and appendages below the waterline. See the figure attached. The ratio of A to B is supposed to be a measure of the boat’s stability and seaworthiness. Nothing could be further from the truth.

A/B ratio comes from Robert Beebe’s book “Voyaging Under Power.” In that book, Beebe’s total discussion of stability in yacht design centers around the A/B ratio. Metacentric height, the essence of stability, isn’t even mentioned and you can’t find it in the index. Yet, Beebe claims that A/B ratios higher than some unmentioned limit would scare him if the boat were going offshore. He does not define what that limit is. Beebe completely ignores everything else about stability: displacement and center of gravity, submerged volume and center of buoyancy, beam and form stability, free surface effect, righting arm curves, stability tests—everything truly related to stability.

Naval architects, in their formal training, are not taught anything about A/B ratio. You can have two boats, each with the same A/B ratio, and they would have totally different stability characteristics due to those factors just mentioned above. So, get it into your heads right now that A/B ratio is totally meaningless!

Now, Speed-length ratio—very important. You have no doubt heard this term, studied it, and have an understanding that the speed-length ratio equal to 1.34 is called “hull speed.” Indeed it is.

Definition: Speed-length ratio is the speed of the vessel in knots divided by the square root of the vessel’s waterline length in feet = V/Lwl^0.5. At speed-length ratios less than 1.34, the vessel is in displacement-mode motion—that is, the hull is simply moving the water out of the way as it moves forward. When speed-length ratio is between 1.34 and 2.5, the vessel is in the semi-displacement or semi-planing mode—that is, it is trying to rise up over its own bow wave to get onto plane. Some boats are designed to operate at these speeds. Above speed-length ratio of 2.0 to 2.5, the vessel is planing and relies on dynamic lift to raise and hold it out of the water so that it can skim along the surface of the sea.

That’s the general definition, and there are exceptions to these characteristics. Where does speed-length ratio come from?

Speed-length ratio is a law of physics and nature. The length of a free-running wave on the sea is equal to:

L = 2*Pi*V^2/g

Where:
Pi = 3.14159
V = wave speed in feet/second
g = acceleration of gravity = 32.174 feet/second^2

Therefore, wave length is a function of wave speed and gravity, and that is why sea waves are called gravity waves. If you take the constants to the left side of the equation and put the variables on the right side and convert it to get rid of the speed squared, you have:

(1/2*pi)^0.5 = 0.39894 = V/(g*L)^0.5

V/(g*L)^0.5 is Froude Number, Fn, a dimensionless ratio. It was invented by William Froude, a British naval architect back in the 1870s, who developed the system of measuring and analyzing ship resistance in towing tanks that we use to this day. His contribution was that ship resistance was made up primarily of frictional resistance, form resistance, and wave-making resistance. If you towed a model of the ship that was geometrically similar (same shape only smaller) to the one you wanted to build, you could reduce the drag to dimensionless coefficients that would apply either to the model or to the ship. The coefficient of frictional resistance varied with Reynolds number, another dimensionless ratio. The coefficient of form resistance was the same for both model and ship. And the coefficient of wave-making resistance varied with Froude number.

Through experimentation it was found that when Lwl, the length of the waterline on the ship, equaled L, the length of a free-running wave, ship resistance went up dramatically. This made sense—the length of the wave was as long as the ship, and if the ship tried to go any faster, it would have to create a wave longer than itself, and this requires a tremendous amount of added energy—i.e. more power. The ship would have to start climbing up the back of the wave that it was creating.

Well, if we convert Froude number such that speed is in knots and we put the acceleration of gravity over on the right side of the equation above, we get the following:

V/Lwl^0.5 * (6076 feet/nautical mile)/(3,600 seconds per hour) = g^0.5 * 0.39894

Or

V/Lwl^0.5 = g^0.5*0.39894*3600/6076 = 1.34

And because of this conversion, speed-length ratio is not dimensionless.

So, when speed in knots divided by Lwl^0.5 = 1.34, the length of the ship’s wave will be as long as the ship’s waterline length, and we can expect resistance to go up dramatically. The boat hits a barrier of resistance—we have “hull speed.”

And, when we are using Froude Number in model tank analysis, of course the L that we use is Lwl of the ship. We can round the decimal fraction above up a hair from 0.39894 to 0.4, and we have equivalence: That is, Fn = 0.4 is equivalent to speed-length ratio of 1.34. In boat design we use speed-length ratio, in model testing we use Froude Number because it is dimensionless. Naval architects like to use dimensionless numbers.

Now, we mentioned before that long narrow hullforms like multihull hullforms tend to not obey this speed-length ratio limit. That’s due just to the nature of long narrow bodies generally having less tendency to make waves. Therefore, they can easily go faster than hull speed. This is why speed-length ratio = 1.34 is not a hard and fast rule or law. It is just a really good guideline that is based on physics.

As you are aware, all hydrodynamic resistance is dependent on vessel speed. If a vessel isn’t moving, it does not have any resistance. We can get an idea of relative speed where resistance changes by paying attention to speed-length ratio or Froude Number, and this is why speed-length ratio is so important.

Questions?

Eric

[Eric Sponberg]

Figure for above discussion is attached.

[Landlubber]

Again, thank you Eric, my saved notes are making a lot of sense to me ....very kind of you.

[Fanie]

Hi Erich,

If I have a slender displacement hull like that of a cat with a LWL of 10m then the hull speed is going to be around 13.4kn or 24,8km/hr...
Ok I see, if the CP is 0.62

If the CP is 2 for the same hull then the speed for the same hull would be 20kn or 37km/hr

Is this correct ?

Originally Posted by Fanie

Hi Erich,

If I have a slender displacement hull like that of a cat with a LWL of 10m then the hull speed is going to be around 13.4kn or 24,8km/hr...
Ok I see, if the CP is 0.62

If the CP is 2 for the same hull then the speed for the same hull would be 20kn or 37km/hr

Is this correct ?

NO,

in our metric world we have to use 2,43 instead of 1,34 !!!

square root of 10 x 2,43 is hull speed. thats 7,68kn in this case.

[Fanie]

Richard, my boat just slowed to a crawl

Can you please explain why the Sqr rt of 10

And how did you get 2.43 ?

[mcollins07]

1 m/sec = 1.9438 Knots
g = 9.8 m/s^2 = 32.174 ft/s^2

V = ( g / (2 PI ) )^0.5 x L^0.5

Factor = (( 9.8 m/s^2 ) / ( 2 PI) )^0.5 x 1.9438 Knots / (m/sec) = 2.4275

V = 2.43 (Lwl)^0.5 [ knots]

If you check your units, there is a m^0.5 that I did not carry through the equation. It must be multiplied by the m^0.5 in the last equation with (Lwl)^0.5 in order to cancel out.

Originally Posted by Fanie

Richard, my boat just slowed to a crawl

Can you please explain why the Sqr rt of 10

And how did you get 2.43 ?

Square root of LWL Fanie. and the 2,43 is the equivalent to the 1,34 used in the US. Both are fixed numbers.

When you do it the wrong way round (using the ancient system), you have roughly 33ft LWL right?

sq. root of 33 = 5,744 by 1,34 = 7,69kn
metric
sq. root of 10 = 3,162 by 2,43 = 7,68kn

you see?

So calculate always with feet, thats speeds up!

Regards
Richard

[capt vimes]

i cannot thank eric and all other more often for all your contributions...

just for clarification:

Originally Posted by eric sponberg

Speed/Length ratio Cp
1.0-------------------------0.52
1.1-------------------------0.54
1.2-------------------------0.58
1.3-------------------------0.62
1.4-------------------------0.64
1.5-------------------------0.66
1.6-------------------------0.68
1.7-------------------------0.69
1.8-------------------------0.69
1.9-------------------------0.70
2.0-------------------------0.70

if we have a hull working in displacement mode only and we want to reach hull-speed - i.e. speed/length ratio = 1.34 (2.43 in metric) - we need a Cp of 0.63 to even reach hull speed...
if the hull has a Cp lower than that and is not of a long and narrow persuasion - we would end up with a highest achieveable speed less than this - am i right?

to fully comprehend this and understand what happens there is really giving me troubles...

Cp defines the fullness of a hull - so the more the hull 'fills out' the block of water between the perpendiculars and beam at WL the faster it could go in displacement mode...

could it be that with a higher Cp the ratio between wetted surface and displacement is getting lower (less wetted surface for a given displacement) and thus reducing frictional resistance enabling a 'fuller' hull to reach higher displacement speeds?

[sorenfdk]

Originally Posted by capt vimes

if we have a hull working in displacement mode only and we want to reach hull-speed - i.e. speed/length ratio = 1.34 (2.43 in metric) - we need a Cp of 0.63 to even reach hull speed...

No - a Cp of 0.63 is the optimum Cp at hull speed. That is, the Cp that (at least according to Skene's) gives the lowest resistance at hull speed.

Many modern round-the-buoys racing yachts have a low Cp. This gives a low resistance at low speeds, which helps them to accelerate quicker. Offshore racers don't need quick acceleration, so they have higher Cp in order to minimize resistance at higher speeds.

If you expect to sail at hull speed all the time (and we're talking monohulls now!), then you should design your hull with a Cp of 0.63. But isn't that a bit optimistic?