Having just created a free body diagram and rough calculations to consider the two scenarios, I've confirmed that over the hull or under the hull does not directly influence the righting arm. The driving force to righting the boat is gravity, which is acting purely in a vertical fashion. Therefore, the ONLY driving influences on righting ability are:
1) weight of the person or persons righting the boat, and
2) distance of the center of mass from the lower hull's center of buoyancy.
Whether the righting line goes over the top of the hull or underneath/inside of it, the only way to get more righting moment is to get your weight further out from the hull (get your body closer to parallel with the water surface). If your righting line is of fixed length, inside the hull would offer an advantage in that it will allow you to get your body closer to the water. That's not to say that it's going to be easier to grip the line one way or the other.
Also note that, as long as your sails are unsheeted and not holding any water, the greatest moment needed to right the boat will be when the mast is also parallel with the water surface - once you've got enough of a moment to get past that point and maintain it, the boat will right easily.
I agree that it is somewhat counter-intuitive that the righting line inside or outside the hull would have no effect, but the thing you have to remember is that you're not pulling in a "straight line" laterally from the outside of the hull, you're pulling at an angle. If you run the righting line inside or outside the hull, that angle changes, as does the tension on the righting line (you are not hanging from the line, therefore only a percentage of your weight is held by the line, the rest is held up by the lower hull - and it all changes when the angle changes). If your body remains in the same position in both scenarios, the righting moment stays the same. Once the boat passes the point of greatest heeling moment (mast parallel to water), the amount of righting moment needed begins decreasing. Only when you are hanging freely from the righting line and no longer standing on the lower hull does it become definitively advantageous to have the righting line on the outside of the hull, but by that time your body is in the water and the boat's own momentum and position of the center of gravity between the hulls will finish the righting maneuver.
Technical explanation (for those interested):
You can look at either the moment as a result of the person's body weight, or as a result of the tension on the righting line. For simplicity's sake, I'm only comparing the effect of the location of the righting line, and assuming that the length is such that the person's body will be in the same position either way. In either case, a longer righting line would get the person closer to the water and improve righting moment.
In the first method, you can see that the two critical factors, the person's weight (Wp) and the rigthting arm (dp) are the critical factors in creating a righting moment. That moment must overcome the heeling moment of the boat, caused by the weight of the boat (WB) and the heeling arm (dB). This person needs either more weight, or more leverage.
In the second method, the righting arm (di) perpendicular to the tension on the righting line (Ti) is slightly longer than if the line were on the outside of the hull (do), but because the person's weight is not hanging directly from the righting line, the tension in the line is reduced by the angle between the direction of the force and the righting line. Tension (Ti) is less than (To) because (To) is more in line with the force (Wp), but given the shorter righting arm (do) for the outside and the longer righting arm (di) for the inside, the end result is that the righting moment remains the same. In other words, RM = di x Ti = do x To = dp x Wp, and in order to right the boat, we need RM > HM = dB x WB.
Login
Register
FAQ
