The discussion revolves around calculating the depth of a fishing lure behind a moving boat, considering factors such as boat velocity, lure weight, and distance from the boat. Participants explore various approaches to derive a formula for this calculation, addressing the forces acting on the lure and the geometry of the setup.
Participants express differing views on the relevance of buoyant forces and the correct approach to calculating the lure's depth. No consensus is reached on the best method or the assumptions that should be made.
Participants mention various factors such as the shape and density of the lure, the tension in the line, and the drag forces, indicating that the problem may depend on additional information not provided in the initial query.
BruceW said:Since the lure travels behind the boat at constant velocity, the forces acting on it must cancel in each direction. This gives the angle of the line. Using this and the total length of the line gives the depth of the lure.
depth = L \times \frac{weight \ difference}{tension}
Where L is the total length of the line, tension is the tension in the line, and weight difference is the weight of the lure minus the weight of an amount water that has the same volume as the lure.
But I think an easier way would be to measure the angle of the line going down into the water.
When the angle is defined such that it is zero when it lies on the water surface, then:
L\sin(\theta) = depth \ of \ lure