CB/CG location with respect to CE/CLR

This is my first posting and will appreciate your comments. I am new to boat design. I have been researching and studying sailboat design concepts for the past 6 months. One question is bugging me and I can not find a reference document explaining it. I understand the CB has to be inline with CG and CE has to be inline with CLR (at least in static conditions). However, I can not figure out the relationship of CB/CG line to CE/CLR line. Should these be designed to align longitudinally, forward or aft of each other? Does the location of CLF impact the above relationship? Thanks,

 

Correct, for the float as designed.

A boat at rest always has CG and CB in vertical alignment. That is needed for the boat to be in equilibrium, the same as the weight of the volume of water displaced by the boat equals the weight of the boat, and is due to physics. Put a boat in the water and it will sink/rise until the displacement equals the weight, and trim and heel until CG and CB are in vertical alignment. (Note that the CB location changes as the boat rises/sinks, trims and heels.)

Incorrect. This is completely different than and unrelated to the hydrostatic equilibrium conditions described above.

CE and CLR are used in estimating whether a boat will be balanced under sail. CE is the centroid of the sail plan and independent of the hull shape. CLR is the centroid of the projected side view of the submerged portion of the hull including keel/centerboard/daggerboard/etc and sometimes the rudder. CLR is otherwise independent of the hull shape. The usual empirical guidance is to have the CE a percentage of the waterline length ahead of the CLR. The percentage depends on the source of the guidance, whether the rudder is included in the CLR calculation, the shape of the hull and other factors. While such guidance may be referred to as a "rule" and by be explained as a having a physical origin, the reality is the actual physics of balance the aerodynamic forces on the sails and the hydrodynamic forces on the hull, etc and is much more complex than a simple CE and CLR relationship. Hence the development of the simple empirical guidance based on CE and CLR which can be "close enough". A search of this forum will show multiple threads discussing the balance of a sailboat.

There is no set relationship between CB/CG and CE/CLR.

CLF is the location at which the addition or removal of a very small amount weight from the boat will cause the boat to sink or rise without trimming or heeling. Add weight ahead of CLF and the boat will trim bow down. Add weight aft of CLF and the boat will trim stern down.

 

I concur with David that there is no set relationship between CB/CG and CE/CLR, especially when sailing. See the figure below. There are however rules of thumb for "lead", the distance ahead of the CLR the CoE should be, for different hull forms and rig types based upon a static lateral plan.... that and years and years of experience. Naval Architecture is still kind of a guild system.

https://www.researchgate.net/public...1453971008484/Forces-on-a-sailing-yacht-4.png