Froude and planing

Perkele, Joakim, I admire your patience and effort with this thread........keep going!

 

The circulation of the bound and trailing vortices are of opposite circulation and so cancel until the latter is shed (Kelvin explained that circulation is conserved in an ideal fluid).

You appear to confuse 'lift-off' with the onset of lift. Lift-off occurs when the lift is slightly greater than the plane's weight. The onset of lift is much earlier.

You need to stop repeating mistakes and do your hydrodynamics/aerodynamics hwk.: backflow at the trailing edge of the wing means exactly that therer is no lift! Again, this is well-known.

Your sailboat probably has a rockered bottom. A good planing hull has no rocker and no hook (no camber) on the running surface. A good rowboat has a rockered bottom and makes a terrible planing hull.

The onset of lift, the Kutta condition, is exactly the absence of backflow. The circulation density vanishes at the trailing edge. This is standard wing theory.

Stating that my interpretation of theory is false is laughable!

Your sailboat likely has a rockered bottom. Good planing hulls do not have rockered bottoms. It sounds like (with wetting and dry alternating) the boat suffers from lack of power. A boat falling off a plan will lose the lift, the transom will become wet.

 

Glad to see you're still alive.

 

Here's a sequence of photos taken whilst leaning over the transom of our 1968 Glastron v153. I will explain each photo. The view is of the port side of the transom from above. The Glastron v153 is a 15' boat, the bottom is a pure V (no pad) with deadrise = 18 degrees. Power is a 1991 Johnson 70 hp (shaft hp).


1. Idle speed, boat trim angle=0. As the boat moves forward it leaves a 'hole' that is continually filled by backflow,
by the trailing edge eddy. Every flat plate at an angle of attack creates an eddy in a flow. U≈4 mph.
2. Same as 1 with speed slightly increased, U≈6 mph. However, the boat has positive trim because the bow tries to ride up the bow wave.
The motor's trim angle relative to the boat is fixed.
3. Same as 2 at a slightly greater speed, U≈7 mph.
4. The trailing eddy has been shed, the flow separates cleanly from the bottom at the transom, which
in this case is the trailing edge. U≈8 mph. Lift has begun, the transom is completely dry. The object to the left is the top of the motor's gearcase. The drain plug is in clear view, is dry.
5.U≈13 mph. Lift is starting to compete with buoyancy. The trim angle of the boat is still large, around 10 degr. At about U≈18 mph the bow breaks over to a fixed trim angle of a few degrees and remains there as the speed is increased.

QED

 

These two videos show the onset of lift as the speed is increased from 4 mph to 8 mph, the sharp transition where the Kutta condition along the trailing edge, the line the transom meets the bottom (no backflow). While there is backflow note the flow toward the transom as the boat moves forward-that's the trailing edge eddy. The speed is continually increased throughout each video, the max. is ab out 13 mph.

Once lift sets in you see some aereated flow from one of the lift strakes. The water coming from the left and behind toward the transom is from a cooling water outlet on the gearcase above the cavitation plate.

The top speed in the videos is only 13-15 mph @3000 RPM. The camera is right beside the motor so it may sound like it's reving higher than it is. Videos are by my Frau, Cornelia Küffner:



slow speed video



The photo is from 2014 at about 45 mph.

 

What experimental data, independent of flow at the transom, are you using to determine that lift has begun? Or are you concluding that lift has begun because the transom is dry?

 

Lift begins when the Kutta condition is satisfied. At onset (8 mph) buoyancy still carries effectively all of the weight. That can be calculated by using my quasi-empirically deduced lift coefficient, which I stated above.

 

Circular logic.

 

Read e.g. this with paying attention to what is Kutta condition and what it is used for.

Then you may realize that the flow with backflow at the trailing edge cancelling the circulation at the forward edge does not exist in real life. It's just an artefact of the limited model used to calculate the flow around the wing etc. Panel method is the most common one and it needs the Kutta condition to get the correct result. The one that nature does by itself due to viscosity. Here is a nice description of what Kutta condition means in panel method.

Note that Kutta condition in practice can just be that the pressure is the same at both sides of the trailing edge. Would you think there is a pressure difference in your Glastrons hull vs. transom while the transom is wet? Do you see flow sharply rounding the edge of the transom having very high velocity?

I'm not confusing onset of lift to lift off. There is no onset of lift. Lift begins at the very moment the plane starts to move. While accelerating the lift may be reduced (up to 50%) compared to constant speed at the same speed due to Wagner effect. This is just what the Prandtl figure you have in your paper is about. Accelerating flow with formation of starting vortex and thus lower lift than at constant speed. Here is something just for you to read.

How do you apply your misuse of Kutta condition to a rotating cylinder producing lift? Where is its trailing edge? No backflow?

Yes certainly there is some rocker in my sailboats hull. The transom is maybe 10 cm in the air while stationary. Then with increasing speed it is no longer in the air, but stays dry. Further increasing speed in is so deep below water level that it becomes wet. Finally speed is high enough for the transom to become dry despite being well below water level.

Well, your theory is laughable. So even replaying to this thread is laughable. It's just a shame that someone not familiar to fluid dynamics might even believe your theories about magical onset of lift and Kutta conditions. I just hope you didn't teach fuild dynamics at the university.

 

The heart of the matter here seems to be that your definition doesn't work, as the water ski example shows and as my windsurfer showed today.

 

My two cents :
Perhaps the heart of the problem is a planing has little to do with a wing. Obviously there is no circulation around a planing hull and no starting vortex (only eddies aft the transom)
and the lift mechanism is only the growing of the dynamic pressure on the bottom with boat's velocity.

 

Sorry :
is a planing (hull) has little to do...
And also the Kutta condition is not a physical law but a boundary condition necessary to simulate lifting wings with inviscid flows

 

Sorry for you.

 

Half circulation folows from one side of a vortex sheet. I think that you would benefit by learning D'Alembert's Theorem in hydrodynamics. Then, you will see that the vortex sheet is necessary. The dynamic pressure integrates to zero unless there is vorticity.

 

Your confusion is great.