# center of flotation calculation and implications?

Discussion in 'Boat Design' started by capt vimes, Jan 7, 2010.

1. Joined: Apr 2009
Posts: 388
Likes: 14, Points: 18, Legacy Rep: 247
Location: Austria

### capt vimesSenior Member

a globetrotter to live aboard for a couple of years and 2 crew...

2. Joined: Dec 2001
Posts: 2,004
Likes: 209, Points: 73, Legacy Rep: 2917
Location: On board Corroboree

### Eric SponbergSenior Member

Ok, I had this all written out and hit the "send" button, but my internet connection had failed, and it got lost into the netherworld.

Today, class, we will take up Block coefficient,Cb. See the diagrams attached. These diagrams came from my notes for a class that I once taught some years ago at the International Yacht Restoration School in Newport, RI, and before that, the boat repair class at the Museum of Yachting, also in Newport.

In the first diagram, we see a perspective view of a traditional sailing yacht sitting in a block of water. The underwater portion of the hull is shaded. If we cut the hull at the waterplane, we have the view in the second diagram, the area of the waterplane. This shows the CF, the subject of last week's discussion, which is the Center of Flotation. The LCF is the Longitudinal distance that the CF is back from the front end of the waterplane. We can measure LCF from any reference point, which we can call Station 0. Traditionally, Station 0 was always the front end of the design waterplane. But with the advent of computers, Station 0 is often taken at the very front extremity of the stem, which is where I usually take it. That way, everything else on the boat is measured as a positive dimension aft of the forwardmost extremity of the boat (excepting bowsprits, of course).

We can see in the second diagram how to calculate the Coefficient of the Waterplane, Cwp. The waterplane is bounded by a rectangle of the length of the Waterplane, Lwl, and the Beam of the Waterplane, Bwl. The waterplane area is always less than the circumscribing box. The ratio of the actual waterplane area to the box area is the Cwp. Cwp = Actual WP area/(Lwl x Bwl). The value of Cwp is always less than 1.0.

Moving onto Block Coefficient, Cb, we can see it is kind of like Cwp with a third dimension added, Draft, D. It is the ratio of volumes instead of a ratio of areas. In the first diagram, we can see that the shaded portion of the hull, which is that portion that it underwater, is bounded by a box, or block, whose volume is Lwl x Bwl x D. The Block Coefficient is the ratio of the actual submerged volume of the hull to the volume of its bounding box, or block, hence the name. The equation is shown in the diagram: Cb = Actual Submerged Volume/(Lwl x Bwl x D). Block coefficient is usually more important in ship design than sailboat or powerboat design, because ship block coefficients tend to be much larger in ships than in recreational boats.

We can also see that the submerged volume of the hull displaces a volume of liquid that is equal to the weight of the boat. This is Archimedes principle which he discovered back about 220 BC. This is why the weight of a boat is called its "displacement." The density of the water also plays a role. Fresh water is less dense than sea water, so a hull floating is fresh water will sink deeper than when it sits in sea water, in order to make up the volume equal to the weight of the boat.

We can also see that we can measure weights in Long Tons, LT, or Short Tons, ST. One LT = 2,240 pounds, and One ST = 2,000 pounds. I used to know the reason why LT became prevalent in naval architecture, but I have long forgotten it. We can also talk of Metric Tonnes for you metric users. One cubic meter of fresh water weighs 1,000 kgf which equals one Metric Tonne, MT. One MT = 2,204 pounds for those of you interested in the conversion. Note the different spelling of "tons" for imperial units, and "tonnes" for metric units. This is a further clue to detect what another person may be talking about.

Finally, the ratios of Cwp and Cb, and all other coefficients all have the same values in any consistent measurement system. Usually, these coefficients have values less than 1.0. If they don't come out that way, then you have either done something wrong in your calculation, or, the hull is really unusual.

Next time we will take up Prismatic Coefficient, Cp.

Class dismissed.

Eric

#### Attached Files:

File size:
97.7 KB
Views:
6,450
• ###### Waterplane Coefficient.jpg
File size:
71.4 KB
Views:
5,001
2 people like this.
3. Joined: Dec 2001
Posts: 2,004
Likes: 209, Points: 73, Legacy Rep: 2917
Location: On board Corroboree

### Eric SponbergSenior Member

Fanie,

Yes, I think the general concept is that Archimedes did indeed discover the principle of flotation. Being the first to realize it, to my mind, is the same as discovering it. To discover, according to my Webster's dictionary, is "to be the first to find out, to see, or know about." Therefore, Archimedes "discovered" the principle which bears his name.

As for the use of tons, plural, I think that is the most common. We always use the plural when there is more than one unit of something. In America and England and other English speaking countries, we use the plural, tons, as well as Amps and Volts and Ohms and Watts. The lightbulb does, indeed, draw 2 Amps.

But let's not get sidetracked by that discussion. This is about the principles of naval architecture. Next question please.

Eric

1 person likes this.
4. Joined: Apr 2009
Posts: 388
Likes: 14, Points: 18, Legacy Rep: 247
Location: Austria

### capt vimesSenior Member

eric:
thank you very much for your contribution and effort to type all this information to shed some light on the mysteries of yachtdesign, its ratios and their correlation!

thank's fanie...

5. Joined: Jun 2007
Posts: 2,640
Likes: 124, Points: 0, Legacy Rep: 1802
Location: Brisbane

### LandlubberSenior Member

thanks again Eric, I am happy to collect any more lessons that you may wish to disclose, sometimes a full and picture description can make understanding sooooo much easier.... ta, John

6. Joined: Dec 2001
Posts: 2,004
Likes: 209, Points: 73, Legacy Rep: 2917
Location: On board Corroboree

### Eric SponbergSenior Member

I don't know what happened to Fanie's comment (he is a regular contributor to the forum) so my reply does not make too much sense. Here is what he had sent:

Put that before my previous reply, and then my reply means something.

Eric

1 person likes this.
7. Joined: Mar 2002
Posts: 951
Likes: 35, Points: 0, Legacy Rep: -12
Location: British Columbia

### Brent SwainMember

Good post Eric. Another advantage of a balanced hull for cruising boats is far better directional stability, without the need for twin rudders or powerful hydraulic steering, and powerful autopilots and the power to run them.

8. Joined: Jun 2007
Posts: 2,640
Likes: 124, Points: 0, Legacy Rep: 1802
Location: Brisbane

### LandlubberSenior Member

Brent,

Essential really in a cruising hull is that critical sail balance, (as you say) where the rudder is not working off centreline and "wasting" power.....no point putting the autopilot on if trhe boat is not balanced is there.

9. Joined: Oct 2006
Posts: 130
Likes: 11, Points: 0, Legacy Rep: 143
Location: Annapolis

### Scott CarterSenior Member

Thanks , Scott
scottthomascarter@gmail.com

(Sorry for the intrusion folks...fascinating read, though)

10. Joined: Oct 2007
Posts: 4,603
Likes: 170, Points: 63, Legacy Rep: 2484
Location: Colonial "Sick Africa"

### FanieFanie

Now what happened to every one ?

Eric, we're awaiting your next article. Means nothing if you let everything hang in the air.

11. Joined: Dec 2001
Posts: 2,004
Likes: 209, Points: 73, Legacy Rep: 2917
Location: On board Corroboree

### Eric SponbergSenior Member

I'll be back on Sunday or Monday to discuss Prismatic Coefficient, Cp, along with Midship Area Coefficient, Cmc. I am doing this once a week. For all those of you who are reading, if you have any other items that you would like discussed, please post here. In the coming weeks I also intend to cover Displacement/Length ratio, Sail Area/displacement ratio, speed/length ratio, and A/B ratio. Add anything to this list if you wish.

Eric

12. Joined: Oct 2007
Posts: 4,603
Likes: 170, Points: 63, Legacy Rep: 2484
Location: Colonial "Sick Africa"

### FanieFanie

Quite a reckless invitation, are you sure

Sure we'll come up with some stuff.

13. Joined: Jun 2007
Posts: 2,640
Likes: 124, Points: 0, Legacy Rep: 1802
Location: Brisbane

### LandlubberSenior Member

Thanks Eric, looking forward to the collection. Much appreciated.

14. Joined: Dec 2001
Posts: 2,004
Likes: 209, Points: 73, Legacy Rep: 2917
Location: On board Corroboree

### Eric SponbergSenior Member

Within reason, please, and restricted to basic naval architecture.

Eric

15. Joined: Nov 2003
Posts: 19,133
Likes: 477, Points: 93, Legacy Rep: 3967
Location: Eustis, FL

### PARYacht Designer/Builder

Damn, and I had a good one too . . .

Forum posts represent the experience, opinion, and view of individual users. Boat Design Net does not necessarily endorse nor share the view of each individual post.
When making potentially dangerous or financial decisions, always employ and consult appropriate professionals. Your circumstances or experience may be different.