How to use the bonjean curve to calculate the displacement and buoyancy center of the hull?

In general, when the ship principle introduces the trim of the hull, the displacement and buoyancy center of the hull can be calculated by bonjean curve. If the ship has heeling and trim angles, how to use the bonjean curve to calculate the displacement and buoyancy center of the hull?

 

You would have to calculate the Bonjean curves for the heel angle and then proceed with them the same as when the boat is at zero heel.

 

As stated by TANSL, displacement and LCG by a set of modern Bonjean curves (i.e. there are more than one type of sets) generally only work for the no heel case. However this was/is not always the case. Depending on by who and when the the Booklet of General Plans and the Displacement and Other Curves where developed, there may be ways to determine TCG also.

Bonjean Curves, of all their various types, occupy a specific temporal niche in the history of Naval Architecture. This period starts in Belle Epoque France and ends about 1960. It is bounded by the development of the mathematical and graphical theories used by Bonjean and the development of electronic calculation. In todays' digital world, the graphical and tabular methods employed by Bonjean and some of us older Naval Architects are absolutely quaint. If you really want to know how to accomplish the displacement, LCG, and TCG calculations by Bonjean Curves, I suggest a late 1800's/early 1900's Naval Architecture text like Attwood's.

 

When you got heeling and trim angles to deal with, the Bonjean curve can still help you out. It's a bit more complex, but you can break it down into sections for different angles. Then, you sum up the areas under each curve to calculate displacement and buoyancy center.