Lcb lcf

I wonder if someone would like to attempt to explain the difference between LCB and LCF? Or point me to a site. I think I’m getting close to understanding but I need a little more info.

LCB is the longitudinal center of buoyancy. It is the point at which the upward force of the displaced water acts. It always lines up with the center of gravity of the hull.

LCF is the longitudinal center of flotation. It is the geometric center of the waterplane, that shape you get when you look at the load waterline from above. It is the point about which the hull rotates when caused to pitch, either by rough water or a change of the location of the weights in the hull. In other words, if you put a rock on the stern of your model, the stern will go down and the bow will go up, and the “axis” of that rotation is the LCF.

Experience has shown that for a directionally stable boat you want the LCF aft of the LCB, and you also want it to stay in about the same place as the boat heels (and the waterplane changes shape). This means wide transoms are a bad thing for directional stability.



Thanks Earl
Can you elaborate a bit. I would have thought that the boat would rotate around the CG. Is this where the “operateing in two different densities” thing rears its head?

Thanks for asking this and the reply.

I can visualise the LCF in my head with no problems thanks to your description, but I’m having an issue with the LCB

Does it’s plain run from stern to bow? I’m afraid I’m use to cars so I’m not sure if I’m getting those roll centres and CG’s theory mixed up a bit.


If this may help ! Out from one of my models

According to my readings and understanding ,

The Blue dots are the LCB at 0° and 30°
The Red dots are the LCF at 0° and 30°

The CF is better if move ahead when the boat is tilted !

The CB shall not move longitudinally more than 0.5-1.0% to obtain a balanced hull


Brilliant explanation from Earl & Claudio’s diagram really helps to simplify things further - however one aspect confuses me a little. From Earl’s post, LCB… always lines up with the centre of gravity of the hull, which makes sense (to me). I then look at Claudio’s diagram and I can understand the lateral shift of the LCB when the hull is heeled but not the longitudinal shift.

From Earls post again, if the LCB lines up with CoG, how can it shift longitudinally (when heeled) as I would have thought that the CoG was a fixed point in space relative to its surroundings?

I’m probably being a bit stupid, but I’d be grateful if anyone could provide an explanation.

Many thanks,


Kicking myself - thought I’d engaged brain before fore finger for typing!!

Anyway, correct me if I’m wrong but -

Obviously, the CoG has to be below the LCB otherwise our yachts would keep falling over! As a typical hull form heels, because of its shape (and hence its distribution of volume) the stern tends to lift which then accounts for the longitudinal shift aft of the LCB - but it still remains vertically inline with the CoG. Once again from Earl’s post, if a hull form had a broad transom the stern lift would be greater and Claudio’s diagram would show an even greater shift.

Have I got it now ?



Thanks for the help. Couple more questions. What would I do to the shape of a hull to move the CF forward? What would be different to move the CB forward?
Thanks again

For better understanding I suggest this reading :


Hi Claudio
I’ve read that article and something confuses me. On page 4 he says
“The weight that you
have brought on is equal in weight to a volume of seawater that is the area of the boat’s
waterplane times 1 cm thick. The center of that volume of water is located at the CF.
Now, imagine, if you will, that when you set that added weight down on the deck, you
placed it directly and vertically over the CF. The trim and heel of the boat would not
change, but the boat would sink straight down that 1 cm.”

I hate to question Mr. Sponberg but if you put the weight at the CF wouldn’t the stern go down? Everything else I have read says that a weight at the CB, not CF, will cause the boat to settle evenly.


Twister’s first post is exactly what’s got me stumped lol. I’ll go through Claudio’s recommended reading. Thanks for the lessons.

Don ,
I was asking myself the same question, probably was a simplification.

Tomorrow I will just take a slice of the volume of my last model and I will make the corresponding COA to see where the CB will be.

Certainly Spongberg was talking about a real boat, therefore 1 cm variation at the flottation level will not pay a big change at the LWL that will not change very much.
My self I often write on my plans the corresponding volume variation equivalent to 1mm variation . Instead , 5mm would imply also a LWL change at the water plan level.
I let you know

Wheww! I was thinking I was way off line. I’m glad you’re thinking like me. I think he was trying to point out that CF is center of AREA(that’s why the thin layer) and CB is center of VOLUME and got sidetracked. I do remember him saying at one point that he was writing late at night.

Claudio -

Many thanks for the Sponberg link, I’d not come across it before - it’s certainly made for educational bedtime reading.

Don -

Re boat shape required to get CF to move forward - I would have thought that a hull form that is relatively narrow with fairly long overhangs at the stern would probably give the required result. Could be way off the mark and it’s getting late here but if you can visualise the hull form described, as it heels it doesn’t have the additional volume aft to promote the arse up / nose down attitude so common in current vendee globe designs etc when making to windward.



I’m into IOM’s so I can’t think overhangs but I’m thinking squarish sections aft and wide V sections forward. As it heels the square sections turn into a V(less waterplane area) and the V sections flatten out(more WP area). CF moves forward. Now to do this without moving the CB too much. That will be the next question.

As promised I went to search how much will move the CF at a water plane sitting 5mm below the nominal one. I also retraced the COA.
Both CF and CB are moving forward at different percentage , 1.4% for the CF and 0.7% for the CB
No tilt considered.

Now a doubt call my mind, is all written in the Spongberg paper refers to a particular type of hull, or the CF has different behavoiur when applied to: Cod’s , Symmetric or Wedge types ? The paper refers also to Nat Herreshoff where the Reliance and Columbia were of wedge type hulls and the later Resolute was almost symmetric.


I played with HULLFORM for a couple of hours last night trying to design a hull that moved the CF forward when heeled. It ain’t easy. The best I could do was to get it to go back a mm or so for 10 and 20 degrees and forward a couple of mm at 30 degrees. I have to think harder and I’m getting old and it hurts.

The above figures are the ones pertaining to my last design the 43-900 published in an other tread.
You shall observe carefully the forms of the front shadows not only the under water but more specifically above water.
The shape take into account the tilt at 30°. The balance is obtained by controlling the IN & Out Wedges , where the CB shall not move more than 0.5-1.0 %.

It take time to come up with an acceptable serie of waterline curves !

Probably it is easier for me playing with a 2D soft like my old CorelDraw 5.


In And Out Wedges???

Never mind. I found Earl’s “Peculiar Properties” paper and figured it out from there.

The centre of gravity does not necessarily have to be below the centre of buoyancy. Take the situation with a kayak: the centre of gravity is above the water! As long as the CoB moves further out than the CoG when heeling, the vessel will be stable. The only rule for positive stability is to keep the CoG below the metacentre.