Brad_Blazer said:
If I may jump in,
As the water speed goes up, the contact patch required to support the weight of the plane will get smaller and smaller until a layer of air is finally forced between the hull and the water. At this point the drag will be less than or equal to that of a wheel on a conveyor.
I don't know? THIRD BASE!
Brad, In my previous post I allowed as how the float would eventually get up on the step and hydroplane with a resultant loss of hydrodynamic drag that would necessitate an increased water speed to compensate. At this point the plane has effectively zero air speed and thus no lift. Simply passing water under the float with no air speed will not "pack" air under the float in sufficient quantity to eliminate hydrodynamic drag.
The problem as stated is NOT equivalent to having a boat (or float plane) run across the surface of the water where the float or boat would have a relative wind (air speed) as well as a speed through (or across) the water. In the case of the boat or plane going across the surface the relative wind (airspeed would indeed tend to pack air under the float. A properly designed hydroplane hull form is shaped to generate and encourage "foam" under the hull to reduce skin friction.
Now, back to the case at hand where the plane is not moving through the air so no air is being packed under the float(s). Not having specified the type of flotation we must allow for a flying boat where the fuselage is boat-like or there may be a pair of pontoons where the wheels of the landing gear would be in a land plane. The design of the flotation not having been specified, there may in fact be no hydroplane step, just a couple of canoe shaped floats, not conducive to having air directed below them to make friction reducing foam.
As regards "contact patch" area. This assumes that the hull form will induce hydroplaning. If it doesn't and the float(s) remain in the displacement mode drag will increase dramatically when the speed of the water past the flotation devices exceeds approximately 1.3 times the square root of the length of the floats at their water line. The phenomenon of bow-stern wave trap will lower the floats deeper and deeper into the water as the water speed increases until ultimately they are submerged. As a matter of practicality they would be sheared off (if the plane had sufficient thrust) but if we can have a "magic" submerged prop and motor to run it why not magically strong floats and their connection to the plane too.
Anyway, even with hydroplaning since the air speed is essentially zero or a very low value there is no packing of high pressure air under the flotation devices as would be the case in say a racing hydroplane which has both water and air speed.
Thanks for your interest and input but sorry, no pantella.
Pat