Froude and planing

You will not change your mind and neither will I, so let's leave it there.
Cheers.

 

I subtract crAU^2/2 from the rig's weight at a given speed to get the difference as the buoyant force. Or, we can always write w=B+L so that w/rblU^2=1/F+c/2 where F is the depth Froude nr., B is bouyancy, b is the wet beam and l is the wet length. When F>>1, as it is for any v-bottom or tunnel boat running at full throttle, then w≈L.

 

I don't think we are ever going to convince each other. Do you agree that spray is a necessary condition for planing, even though it isn't a necessary condition for he Kutta condition?

 

Side spray and waves are necessary. Without spray and waves (as with a fully submerged hydrofoil) the lift coefficient would be larger. Side spray and waves contribute only to the drag. I don't know what you want to convince me of. See my weight formula in one of the posts above, where weight is decomposed into buoyancy and lift.

Question for you: do you think a hydrofoil quits acting like a lifting surface once it plans?

 

I do not know if I understand you wrong or you are mixing the concepts because the weight can never "decompose" in buoyancy and lift, all three are forces, but of totally different origin.

 

The string of posts is long, thanks for all comments. Some have helped me to see better how to present my ideas. I want to summarize here for the discussion what I have understood from experience and theory:

1. The onset of lift is at a low speed when the boat tries to ride up the bow wave (increased trim angle of boat). At some low speed there the flow separates from the bottm at the transom. This is the Kutta condition, the onset of lift. Buoyancy is still carrying nearly all of the weight at that point. As the speed increases the boat plans and the bow breaks over to a normal trim angle (3 to 6 degrees). At this stage lift carries nearly all of the weight. There are planing hulls (some water taxis, PT boats, e.g.) that never reach this stage.

2. Let w=weight of rig, b=wet beam, l=wet length, d=submerged depth and U=speed. w=B+L where B=buoyancy and L=lift. Then
w/blU^2=1/F^2 + c/2

where F is the depth Froude nr. (F^2=U^2/gd) and c is the lift coefficient.
When F^2>>1, as is the case for boats that plan high and dry at top speed, then w≈L, buoyancy plays no role.

Wet area≈bl decreases with speed so that blU^2=constant. If the bottom is hooked then the speed doesn't increase with increased power, increased power only drives the bow deeper into the water. Therefore w/blU^2=constant as required.

3. This lift coefficient is pretty accurate for both water lift on a v-bottom or a tunnel boat sponson, it accounts for three dimensional flow:
c=f(Æ)acosb where Æ is the aspect ratio, a=trim angle of boat, and b=deadrise angle of v-bottom or sponson. f(Æ)_≈1+3(Æ-2)/2, Æ≥2,
agrees with Clement's data. This lift coefficient works for my 2 v-bottoms and for the sponsons and also for the airflow over the deck of our tunnel boat. In all cases the flow is three dimensional. For air lift beneath the boat between the tunnel sponsons the flow is 2 dimensional; the lift coefficient there is the 2 dimensional one.

From the ms for a forthcoming book.

 

I have tried a few times before, but let's try once more. You are confusing the transom becoming dry, flow separation and Kutta condition. Flow separation at the lower edge of the transom occurs at much lower speed than transom becoming dry. This is quite similar to the very basic fluid dynamics case of backward facing step
You can clearly see flow separation at the edge, very similar to the transom. There is still fluid flow behind the step in the separation bubble, but that doesn't mean the flow is not separated. A very similar thing also happens at the trailing edge of a foil with a bit thicker trailing edge.

Kutta condition is for one phase flow with the foil (or any object) totally submerged in that fluid (air, water etc). When the Kutta condition is not met, the flow will circle around the trainling edge (must have a rather big radius) and "meet" the flow going on the other side of the foil.

There is no water flowing on top of the boat and flow is separated at the transom edge (despite being wet), thus there is no way for Kutta condition not to be met.

Kutta condition is linked to circulation around the airflow. Since there is water only under the hull there can't be any circulation around the boat.

Othervise I agree that lift of a planing surface is quite similar to the lift of a submerged foil. There are many ways to describe the cause of the lift. A simple one is that both a planing surface and a foil pushes fluid downward (causimg downwash) while moving on top of or through the fuild.

 

First, I'm not confusing anything. I've looked over the back of the boat to see the sharp transition that Newman said that he observed in the kitchen sink, the sudden onset of the Kutta condition. Before that, the flow 'separates' at the transom in the since that an eddy/backflow forms. There, the transom is wet. Once the flow separates cleanly then the entire transom is dry. I suggest that you forget about simulations and steps and simply look over the back of the transom yourself. The flow will separate cleanly from a step after the onset of lift for the step. There needn't be flow over the entire boat for the Kutta condition to be met.

 

How would you know by looking at the boat when the "onset of lift" happens? There is plenty of measured data and they suggest that lift is proportional to V^2. How would you feel or see the very small lift at small V when the transom becomes dry. Even a heavy displacement boat or a sailing boat gets a dry transom at some speed, but may still have no or negative lift.

What do you think happens at a thick trailing edge of a foil? Say a rudder with a few cm thick trailing edge. Will there be eddies and backflow just like at the transom before it gets dry? Measurements show that the thick trailing edge (say NACA 0012 with cut 15% from the trailing edge) still have about the same lift properties, but much more drag.

 

Surprising.

 

The lift coefficient becomes nonzero when the flow separates cleanly at the transom. Then U^2 kicks in.
Same for the thick trailing edger of a foil, including a rotating twisted one, a prop blade. Lift/drag is a different
question. There, foil thickness matters, especially for prop blades.

 

Lift starts way before the transom becomes dry. The flow separation will also start before the transom is dry. There is a volume of water dragged behind the boat that will keep the transom wet after lift starts. "Looking over the transom" is very subjective and not quantifiable. Your eyes are not able to measure lift.

 

A shot in the dark.

 

What do you mean by "same for the thick trailing edge of a foil"? Are you saying there is no lift when there are backflow and eddies at the thick trailing edge? How could there not be? And the foil produces lift just fine. There is a 1950 Nasa paper about that.

Why would backflow and eddies at the trailing edge cause no problems, but would be a problem at the transom? Isn't the hull and transom just like a half of a foil with thick trailing edge?

 

We understand since Prandtl that there is no lift with eddies/backflow. There is no backflow up the transom of a boat with lift. Re your last sentence, the boat bottom with lift is like the bottom half of the mean camber surface, there is no thick trailing edge in the lift. Remember that the mean camber surface (a vortex sheet) generates all the lift, the thickness produces no lift.