Heeling angle maths

Occasionally it's desirable to reduce the draft on your boat, to get over a sand bar for example, or to reduce the height of the mast to fit under a bridge. A common solution to this problem is to heel the boat over by hanging a large weight or pull with a dinghy at right angles to the boat either from the end of the boom held out to the side or from a halyard from the top of the mast.

As you can see from the diagram below, by heeling the boat over, the length of boat left underwater decreases.

How much did we need to tip our boat over to get into Vuda Marina?

Since the draft (d) and the underwater length of the boat (L) when the boat is heeling over form a right angled triangle, we can use a well proven ratio from trigonometry which says that Cosine(θ) = L/d. In our case, with a 4.2m draft and a desired underwater length of 3.6m, we needed a heeling angle of θ = Arccosine (L/d) = Arccosine (3.6/4.2) = approx 31 degrees.

There's a little bit more to it than this. As the boat heels over, the volume of water displaced by the hull remains the same and the centre of buoyancy (c) changes. This causes the keel to be partially lifted out of the water when the boat heels, further decreasing the underwater length of the boat as shown below.