Postby rynhardt » Fri May 31, 2019 10:26 am
So... Now I have two prismatic hull shapes, with angled bottom and side faces.
They have the same volume, and the same density (in this case, say the density is 0.8 relative to water).
Their geometry is different. One hull (10% planing) is tall and narrow, and the other hull (90% planing) is short and wide.
At zero velocity (relative to the fluid), both hulls displace 80% of their volume in water, and they float. Both hulls displace the same amount of water, and geometry plays no part in the lift force (which at zero velocity is due to buoyancy).
At nonzero velocity, however, the geometry plays an important role. For now let's say the wetted surface area of both hulls are the same and we can ignore the viscous drag.
The motive force pushing the hull through the water has to overcome the reactive forces of the water it is displacing to keep the velocity constant.
These reactive forces are made up of planing lift forces and nonplaning lift forces, depending on their orientation to gravity.
This reactive force of the water is equal to pressure times area, i.e. F = A * P, [Newton]
and the pressure is proportional to the velocity squared, i.e. P ∝ v^2, [Savitsky et al]
thus, the reactive force is proportional to the area and the velocity squared, i.e. F ∝ A * v^2.
The faster the hull moves, the more reactive force (lift) the water is applying, but proportional to the square of the velocity.
For the 10% planing hull, the bottom face is proportionally tiny and does not contribute much to the planing lift force. This force is not zero, but it is small. It does still lift the hull out of the water the faster the hull moves. As it lifts the hull, there is less lifting surfaces (both sides and bottom) in contact with the water and less reactive force for the hull to overcome.
However, the side faces are encountering a proportionally much larger amount of reactive force from the water which mostly dominates the amount of total reactive forces seen by the hull.
So even though the bottom face is lifting up the hull, thereby decreasing the amount of surface area pushing against the water, the reactive force increases much faster than the decrease in surface area compensates for.
Given a sufficiently large enough motive force, the 10% planing hull will eventually start to plane, but it will take a large amount of motive force (low efficiency).
For the 90% planing hull, the bottom face is proportionally large and contributes significantly to the planing lift force. As the velocity increases, the amount of lifting surface in contact with the water decreases much more rapidly, and the total area driving the reactive forces diminishes much faster to compensate for the exponential increase in reactive pressure.
The 90% planing hull is able to reduce its reactive surface area much faster than the 10% planing hull, due to the bottom surface lifting the hull out of the water, and therefore requires much less motive force to overcome the reactive forces of the water (high efficiency).
In summary:
* All real, physical, rigid hulls displace water at zero relative velocity.
* All real, physical, rigid hulls will experience both planing forces and nonplaning forces at nonzero relative velocity.
* The geometry of these hulls will to a large extent determine how efficiently they make use of motive power to overcome the water's reactive force.
Typically when someone talks of a planing hull, they mean a hull that is efficient in overcoming water resistance above a certain relative velocity.
And yes, there are other forces and complications at play that I've conveniently ignored for the sake of simplification.

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