I just remembered that there was some discussion of stern lines a while back and I promised to add to it after my boat was in the water. I’ve had some nice sails, she’s ready for a cruise up to several hundred miles whenever I feel like it and the damn dog woke me up at 5:00 so here goes.
Water is incompressible and somewhat thick so, when a boat moves forward, it pushes up a hump in the water around the bow. The water level is higher in this hump so water pressure on the hull under the hump is higher than normal and is pushing back on the hull. This is a major component in wave making resistance.
The hump, as it falls back down due to gravity, turns into a wave. When operating near hull speed, the next crest of this wave is at the quarters. The water level around the stern is higher so water pressure on the run is elevated. In crude terms, the boat’s own wave system is pushing forwards on the stern. A more elegant way to say it is that the hull is recovering some of the energy it expended making the waves at the stern. It’s only getting back a small portion of the effort expended in getting the wave moving but it is enough to be a significant factor in overall resistance.
Now consider the flow of water over the hull. It follows the hull fairly closely along the bow lines and around the midsection. Aft of the midsection, the water has to close in around the hull again and, if the flow lines are too steep, it can’t do this. The flow will then separate and kind of design a new “hull” for itself, leaving a space of turbulent water between the main flow and the hull that is largely moving along with the hull.
Why should this separation be a problem? In the air, separation is often promoted as in the dimple on golf balls to reduce resistance. If the water isn’t flowing over the hull, there is less frictional resistance. The answer is in the wave train and the energy recovery from it.
The wave train can not “push” on the stern and energy can not be recovered from it through a zone of separation. The stagnant and turbulent water under the separated flow insulates the hull from the higher water pressure of the wave train. Waterline length is such a significant factor in boat speed because of how it is related to the dynamics of wave making resistance. The boat’s length essentially ends at the point where a significant degree of separation begins. A 30 foot waterline vessel with a full stern and steep flow lines might then actually be only a 25 foot waterline craft. This is why double enders are often slow.
This is not an absolute thing. There is always some degree of separation and some wave energy is recovered through a separation zone. The amount of energy recovery drops off very quickly as the zone thickens. It’s like hull speed, not a line but a region on the graph where the curve turns quickly upwards.
Significant separation begins to occur over a fairly narrow range of flow angles regardless of size. That’s why there are tow testing tanks. The exact angle is influenced by factors such as surface roughness and the shape of the lines forward but will generally be in the 12 – 15 degree range. The flow angle is relative to the axis of the vessel’s motion. The diagonals on a lines plan, if they are drawn to cross the stern station lines as closely to perpendicular as possible, will most closely approximate the water flow. If you draw a line at 15 degrees to the centerline on which the diagonals are drawn and move it up and down, the points at which it becomes tangent (just touches at one point) each diagonal is a good indication of where separation will begin in that region of the hull. The middle of the points found is essentially where the vessel’s waterline length should be measured to for predicting hull speed.
Here is an example of a hull drawn to maintain this 15 degree angle in the diagonal lines:
There has been a lot of discussion about weather helm recently. The aspect of this that is almost never discussed is the effect of these dynamics on the rudder. The wave train is not the same on each side of the boat nor are the flow lines and the degree of separation. The pressure differentials on the rudder, which are felt by the helmsman, are heavily influenced by these factors. Those rare boats which have magically neutral helm owe this fact more to the shape of their sterns and hard to predict pressure patterns rather than having exactly the right amount of “lead” in their sail plan.