center of flotation calculation and implications?

[Leo Lazauskas]

Originally Posted by Eric Sponberg

I would be very surprised if the center of wetted surface drag played any significant role in boat behavior. The more important factor is the wetted surface itself--in sailing yacht design we frequently like to minimize it. We also know that long narrow hulls have less drag than short wider hulls of the same wetted area. The volumetric effects play a much bigger role, and so the centers of volume and gravity have an overshadowing effect. We don't really care where the center of wetted area is because it usually is very closely in line with the direction that we are moving and drag forces due to the wetted area will not be located at the center of the wetted area. Rather, they will be governed more by the distribution of volume and the centers of volume. Center of wetted area falls out of the problem because it is so insignificant and does not play a role in where the centers of forces actually are. You can certainly study it more, but I think that is what you will find.

I totally agree with you regarding the longitudinal location of the centroid, at least for small yaw angles. However, the same argument does not necessarily apply to the *vertical* location of the centroid and its effect on the attitude of a boat at speed.

In the calculation of the trim, there is a term involving Zw*Rf, where Zw is the vertical location of the centroid of wetted area, and Rf is the skin-friction.

Now, Rf is clearly important, otherwise you would not be concerned with minimising wetted area to reduce it. That is indisputable.

My argument is that if Zw is not small, then the moment, Zw*Rf, is also not small. I am happy to concede that in many cases Zw will indeed be small, but I want to see an actual calculation to be completely convinced. Hand-waving arguments and guesswork are not always reliable. OTOH, unnecessary calculations are a stupid waste of time

There are also unusual cases (e.g. SWATH and SLICE) where Zc could be quite large, but the moment Zc*Rf is small compared to other terms in the trim and sinkage equations.

All the best,
Leo.

[Leo Lazauskas]

Originally Posted by fredschmidt

I agree with you, but.... Leo put me in doubt.

Then I have achieved my purpose

[fredschmidt]

Leo

Undoubtedly......doubt.

Fred

[ancient kayaker]

In the case where the hull is heeled so the wetted surface is asymmetric, the asymmetric drag would result from the effect of lateral flow especially across chines.

[Brent Swain]

The biggest drawback of assymetric hulls is not wetted surface , but changes in centre of buoyancy when heeled , which leads to loss of directional stability.

[TeddyDiver]

No Brent.. The center of buoyancy stays where the CG (and the vertical vectors of the heeling forces) make it to be.. It's the position of the hull and alignment of the wetted form compared to sail and keel/rudder alignment that changes. If that change has an effect to directional stability is another matter but not allways negative.. thou reckon you meant helm balance but that's not so simple either

[capt vimes]

as explained so well by eric - if a boat heels the CB, CF tends to move aft (the wider the stern the more they do so) - causing the hull to trim...

what would be an 'acceptable' trim for a ship at - lets say - 30° of heel?

considering the vessel is designed as an 'all arounder' and should have good compromise between down- and up-wind performance...
i have no doubt that 10° would be way too excessive but i also have no clue what would be 'in range'...

[Eric Sponberg]

Originally Posted by capt vimes

as explained so well by eric - if a boat heels the CB, CF tends to move aft (the wider the stern the more they do so) - causing the hull to trim...

what would be an 'acceptable' trim for a ship at - lets say - 30° of heel?

considering the vessel is designed as an 'all arounder' and should have good compromise between down- and up-wind performance...
i have no doubt that 10° would be way too excessive but i also have no clue what would be 'in range'...

Ideally, trim should be near to zero no matter what as the boat heels. In particularly, trim down by the bow, is undesirable. But that is the ideal and we do not live in an ideal world. As stated above in a prior post, some trim down by the stern is OK, which, on a sailing boat, tends to lift the hull and point the keel to windward. In modern designs that does not happen too much. In a powerboat, you want some trim down by the stern to help start the boat planing, and then once the boat is on plane, you don't want trim to be very much, maybe 2-3 degrees by the stern. Hydrodynamic drag is directly proportional to trim--if trim doubles from 2 degrees to 4 degrees, drag doubles, at least according to most hydrodynamic calculations.

In sailing yacht design, I typically check my heeled waterline at 15 degrees heel without correction for displacement and trim to see where the CF moves to momentarily--it gives me a snapshot of what will happen to trim before the hull settles into a steady state of flotation. And 15 degrees heel is a normal and comfortable heel angle.

Eric

[Eric Sponberg]

To the class,

The plan for the following few weeks will go as follows:

• Speed/Length ratio and A/B ratio (these are not related, but they are both relatively short topics so that I can get them out of the way, in preparation for a more detailed discussion on:
• Displacement-Length ratio, then:
• Sail Area-Displacement ratio and Sail Area-Wetted Surface ratio, which will then lead us to a surprise topic....
• The S number--a neat, different, and very sensible way to rate boat performance.
• The Multihull Ratios: L/B ratio and the Bruce Number.

Stay tuned!

Eric

Nice thread!

Danke Herr Kollege.

Thanks Eric for taking the time!

Regards
Richard

[Fanie]

Hi Erich,

Interestingly, I typically design my sailboats with a Cp of about 0.60. I did the same with my Moloka’i Strait motoryachts. This is just below hull speed, Speed/Length ratio = 1.34. (We can take that up in another post, if you wish). You can also see that approaching planing speeds (Speed/Length ratio => 2.50), Cp reaches 0.70. This goes along with very long and narrow hulls—that is, being still in displacement mode at S/L = 2.0, you need a high Cp. This is why catamarans and trimarans (which have long narrow hulls) have very high Cp ratios.

The cat I designed has a Prismatic coefficient of 0.6103, LWL is 9.889m and the WWL each hull is 0.892m.

You stated that catamarans and trimarans (which have long narrow hulls) have very high Cp ratios. Is 0.6 in this case low, average or high ?

This is where the caper resistance calculation is about as low as I get it, it is around 210N at 7 kn.
Displacement is at 2000kg each hull.

[Eric Sponberg]

Originally Posted by Fanie

Hi Erich,

The cat I designed has a Prismatic coefficient of 0.6103, LWL is 9.889m and the WWL each hull is 0.892m.

You stated that catamarans and trimarans (which have long narrow hulls) have very high Cp ratios. Is 0.6 in this case low, average or high ?

This is where the caper resistance calculation is about as low as I get it, it is around 210N at 7 kn.
Displacement is at 2000kg each hull.

Fanie,

I don't know what you mean by "caper resistance calculation"--that is an unfamiliar term.

As you probably know, there are three major components of resistance for a boat traveling through the water: Frictional resistance, Form resistance, and wave-making resistance. At slow speeds, below hull speed (speed-length ratio V/Lwl^0.5 <= 1.34, or Froude Number V/(g*Lwl)^0.5<= 0.4) Frictional and Form resistances make up the larger part of the total. Above this limit, Wave-making resistance overshadows frictional resistance and becomes the major component--in most conventional designs. It's possible to break through that 1.34*Lwl^0.5 speed barrier if the hull is light, long, and narrow. Such hull shapes have been shown to achieve speed/length ratios greater than 2.0 without planing--that is, still in displacement mode. Such hulls have very small waving making resistance, and part and parcel to that is that they also have a Cp of about 0.70. This is a limit--generally to achieve even higher speeds, Cp does not have to go any higher--it levels off. All you need to go faster is to add more power.

So, in your case, it depends on how fast your boat is intended to go. At Cp = 0.6103, your target speed is at or just below hull speed. If you want to go faster, your Cp should be larger, according to the chart I posted earlier.

Eric

[Fanie]

Hi Eric,

The caper resistance is a chart in Freeship that indicates I guess how easy your boat would move and displace water, so frictional and form resistance.

I doubt any one designs a hull to be slow so if you want to ask how fast the boat is intended to go, when the pirates appear it has to have unlimited speed
If the fish bites it must remain right where it is

I'm trying to visualise what the interaction of the water with the boat would be when the CP changes, say from 0.6 to 0.7
Does this prolong the following wave making when a certain speed is achieved so a higher speed can be achieved before wave making becomes more than the friction and resistance
or
does it merely improves the friction and form resistance ?

[Fanie]

Well, how about that, I actually answered myself there

[Eric Sponberg]

Form and friction resistance go up with the square of speed, but they stay pretty much the same proportion to each other. Wave-making resistance is inhibited with longer narrower hullforms. We see this all the time in vessel design--long narrow hullforms have lower overall resistance because of lower wave-making resistance. The flow interactions that play with changes in prismatic coefficient--the ends of the hullform are fuller, have more volume--are very difficult to visualize outside of a model tank, or outside of a full-scale side-by-side comparison of differing hullforms.

Eric