Delft Hull Series

(assuming we define 0 pressure at the surface of the undisturbed water line)

atmospheric_pressure-(water_density*g*depth-of-hollow)

does not equal zero unless there is no hollow.


Put another way: If the hollow has zero pressure then why does the hollow close? But it does close, not instantly, because the water that does the closing has mass and therefore inertia.

The water surface in the hollow can be considered to have a pressure deficit equal to rho*g*depth_below_undisturbed_surface.

Havlock suction?

 

That deficit is required because there is no (hydrostatic) pressure on the dry
transom. It can be considered as an additional resistance component.
It can be further refined to account for the loss of pressure on a partly-wet
transom.

 

but that deficit on the water surface in the hollow can create a wave just as much as a pressure excess could. Maybe?

 

If the hulls were only scaled, the 3 curves would collapse into one. Since the hulls are identical below the designed waterline, the curves are identical at low speeds. At higher speeds one would expect, that the curves show at least a similar behavior which they do. But it seems that nobody (including me) can explain, why case 1. with the crude assumption for the wavemaking length gives better results than case 2. with the more realistic wavemaking length.

 

That's what confuses me.

Suppose for a moment that wave-making was proportional to the hull slope
(and the longitudinal slope of the hollow), as it is in thin-ship theory.

Then the greatest wave-making should occur at the end of the hollow, i.e.
where it closes up and where the slope is largest.

In that case we should see something like stern waves emanating from the
end of the hollow. I have never seen any waves emanating from the end of
the hollow behind the transom in any wave patterns. Instead, waves tend
to emanate from the sides of the transom.

So, maybe not

OTOH, there are cases like this:
http://www.marin.nl/web/Facilities-Tools/CFD/CFD-for-Ships/Wave-pattern-Prediction.htm
which seem to show waves emanating from the end of the hollow!
However, why are there waves starting at the edges of the transom
if there is a smooth detachment there?

 

But you haven't shown that it is a more realistic wavemaking length.
If the hollow was replaced with a solid surface that could sustain a pressure
(or if it was created by a downwards air pressure) the assumption would be
correct

 

I have discarded case 3 (the one with the transom hollow) right after your remark.
I am just considering cases 1 and 2. For case 2 I used the wetted length as measured by de Ridder et al. for Sysser 27. Above FN=0.35 the transom is submerged and the wetted length is the distance from bow to transom. For the three models this is 2.0, 2.1 and 2.2 meters. If I use these realistic (because measured) lengths in the denominator of FN, I get the shifted curves. I can only conclude that the wetted length as measured is not the wavemaking length.
It is surprising that the constant (designed LWL) length of 2 meters gives better results for all three models (case 1).

 

To me, it's obvious that wetted length is not the wavemaking length... The aft overhang only helps so much, and at higher speeds, as your figure 3 shows. But wetted length does contribute to skin friction. Quoting Olin Stephens "Estimating the effective length of a yacht is the most difficult task of the designer, or someone writing a VPP".

 

What is meant by "wavemaking length"? Perhaps a simple question, perhaps not.

 

can the hollow behind a transom create waves

Can the hollow behind a transom create waves?

Perhaps it makes more sense to look at this from the other way around. What conditions would be required in the wake for waves to appear to be originating from the hollow, or anywhere else aft of the transom?

There has to be an energy source. Wake relaxation is a drop in kinetic energy, so there is some energy to work with.

I have a suspicion that if all the water that started out on the surface in front of the boat ends up back on the surface aft of the boat then there is no real opportunity for the creation of new waves. But if the original surface gets folded and pinched behind the boat, then perhaps the wake relaxation process can generate new waves.

Put another way, how do we distinguish between a solid hull pushing on the surface and disjoint chunks of the surface collapsing together?

 

Thanks David for challenging me. It helps to keep my thoughts clear.
In a way you are asking for the definition of the Froude number.

For geometric similar models (just scaled) you have described the situation in post #75. A dimensional analysis will yield the Froude number as one of the dimensionless parameters. The length that is used to make the variables dimensionless, can be arbitrarily chosen. It does not matter, which length is used in the denominator of the Froude number, the resistance curves will always collapse, since all dimensions are scaled by the same factor.

The picture changes, if different hulls are compared, if a correlation with measurements is intended or if the task is the prediction of the wave-drag.
One could argue that Froude number is only defined for scaled, geometric similar hulls and can not be used for differing hulls. Nevertheless in practical work Froude number is a helpful parameter, if the right quantity for the length in the denominator is used. Wat is "right"? Intuitively it can be called the "wavemaking length". I would say it should be proportional to the distance between the bow- and the stern-wave. In the end it is the quantity that gives the best correlation for the intended task.
Uli

 

This is the "rooster tail", the result of the inward travelling waves colliding. The pressure deficit "pulls" a wave toward the centerline from each side of the hollow. The area of the collision dominated by dynamics beyond the linear superposition assumption.

 

I agree that there are some strong non-linear and viscous phenomena
happening there, but the rooster tail can be roughly simulated using linear
theory. However, you also need to include near-field effects in the calculations,
to simulate the "pull" of the flow inwards, as you said.

Would anyone like to hazard a guess at the hollow length from, say, the
simulation in this beautiful example that many of us here have seen before?
https://www.youtube.com/watch?v=A-0fVE_pPNg

 

I'ma hazardous enough a guy to make my guess....

In the 7 knot example the hollow is actually filled partially by water pouring in from the side and at the point where it actually enters the hollow, the slope of the hollow is so steep that some of the water tumbles down that slope toward the transom. in a similar condition, dam engineers discuss this as a "hydraulic jump". BTW, In this state my thought to use 2d+t in transom hollow applications is worthless because the major assumption of 2d falls apart since the water in the hydraulic jump is actually traveling faster than the friggin boat!

So the hollow is longer than it looks but is filled with a hydraulic jump.

 

That's what makes it such a difficult problem! And well beyond the
capabilities of linear theory.