Draft effect on Resistance

[DCockey]

Most of what DCockey states above is pertty obvious and I guess we all would agree that a knife blade held vertical should slice right through the water -- But I have some problems with his summary that "Wave making resistance decreases with increasing distance below surface" -- This gets us close to my original question of draft effect on wave making resistance. But I have a hard time accepting the idea that even a streamlined body can be dragged through the water easier than something skimming across it's surface??

A streamlined body submerged just below the surface will have higher wave making drag than the same body submerged at a deeper depth. It's the way the physics of wave making works. Skin friction will be about the same as long as the body is fully submerged. (About the same and not exactly the same because the effect of wave making on the velocity field around the body is less for the body at a deeper depth.)

Comparisons of a full submerged vessel versus a body on the surface are complicated by the differences in the wetted shape and wetted area for same displacement, etc.

 

[Joakim]

Three different scenarios for comparing "similar" shape hulls with the same length. Water depth is large compared to dimensions of the hulls. Hydrodynamic effects on draft and trim are not considered; ie draft and trim are fixed.

A: Displacement is constant - the product of beam and draft will be constant. If draft is doubled then beam will be halved.

B: Constant beam - displacement is proportional to draft. If draft is doubled then displacement will be doubled.

C: Constant draft - displacement is proportional to beam. If beam is doubled then displacement will be doubled.

I don't know how "similar" is defined here, but wouldn't there be a fourth option that keeps displament and beam constant, but varies Cp and thus maximum draft? Then the least resistance producing Cp would depend on the Froude number.

And then there is fifth one as well, which keeps displacement and draft constant, but varies Cp and maximum beam.

 

[DCockey]

I don't know how "similar" is defined here, but wouldn't there be a fourth option that keeps displament and beam constant, but varies Cp and thus maximum draft? Then the least resistance producing Cp would depend on the Froude number.

And then there is fifth one as well, which keeps displacement and draft constant, but varies Cp and maximum beam.

By "similar" I mean shapes which are derived by simple, uniform scaling in the vertical and/or transverse directions. Cp, Cb (block coefficient) and Cm (midship section coefficient) remain constant.

There are an infinite number of options possible to derive a set of shapes for comparison. The comparisons and complications can be as complicated and intertwined with various effects as desired.

 

[DCockey]

Exampled of the similar shapes I used above are in the attachment.

 

[jesdreamer]

DCockey's constant displacement illustration

Exampled of the similar shapes I used above are in the attachment.

Looking at the constant displacement illustration in DCockey's post (w/o doing any of the applicable math), Wouldn't one think that the shallow wide hull should skim across the water with less wave making resistance than the narrow deep hull??

 

[Mr Efficiency]

Looking at the constant displacement illustration in DCockey's post (w/o doing any of the applicable math), Wouldn't one think that the shallow wide hull should skim across the water with less wave making resistance than the narrow deep hull??

One could think whatever one liked, and one could be quite mistaken. I see a need to have reality fit a theory here, rather than adjust the theory according to observed results. Your original thesis seemed to be that water was being displaced a long distance in a deep draught vessel, in the vertical plane, and therefore requiring a lot of work to be performed doing it, if you transfer that logic (?) to your wide shallow boat, aren't you displacing water a long way, but now in the horizontal plane ?

 

[jesdreamer]

Where does the displaced water go??

One could think whatever one liked, and one could be quite mistaken. I see a need to have reality fit a theory here, rather than adjust the theory according to observed results. Your original thesis seemed to be that water was being displaced a long distance in a deep draught vessel, in the vertical plane, and therefore requiring a lot of work to be performed doing it, if you transfer that logic (?) to your wide shallow boat, aren't you displacing water a long way, but now in the horizontal plane ?

Most water has to get displaced toward the side and up toward the surface. Little if any water can get displaced downward. And a deeper hull needs to displace water up from keel to the side. Since displacement is stated as the same for 2 different hulls, the work to displace is equal in both cases. But I believe the deeper hull has to displace "much of" it's displacement a longer distance (and through a higher pressure region) -- and to accomplish this within an equal incremental time frame should involve more power -- thus it might appear that the deeper hull might require more power to travel at an equal speed -- My inquiry was whether this might be true or not and if so why or why not??

 

[Mr Efficiency]

And you will continue to believe, despite observed results not supporting the assumption ? You would be better to consider the resistance forces on the moving hull in terms of pressure changes on it (ignoring the frictional drag, which is more related to surface area than anything else) attributable to the shape and volume of it, and the effect of the self-generated wave system on those pressures.

 

[jesdreamer]

shallow vs deep draft wavemaking

And you will continue to believe, despite observed results not supporting the assumption ? You would be better to consider the resistance forces on the moving hull in terms of pressure changes on it (ignoring the frictional drag, which is more related to surface area than anything else) attributable to the shape and volume of it, and the effect of the self-generated wave system on those pressures.

Please look at my post #35 -- does this make sense??

 

[Mr Efficiency]

Please look at my post #35 -- does this make sense??

Only if displacing water sideways is less resistance-inducing than vertical displacement, all of which seems an artificial representation of what is happening, anyway. Boats do largely overcome wave-making resistance with wide flat bottoms and dynamic lift to skim over the surface, if they are light enough, and with sufficient power to get them there, but still have drag in the form of skin friction.

 

[jesdreamer]

"wide flat bottoms = less wave resistance" (per Mr Efficiency)

Only if displacing water sideways is less resistance-inducing than vertical displacement, all of which seems an artificial representation of what is happening, anyway. Boats do largely overcome wave-making resistance with wide flat bottoms and dynamic lift to skim over the surface, if they are light enough, and with sufficient power to get them there, but still have drag in the form of skin friction.

This is getting closer to the question originally raised. Neglecting friction of a wider shallower draft and disregarding resistance (Work) which might even be similar with a deeper draft -- I originally questioned Power required (to attain similar speeds) in which it might seem that the deeper draft hull might make the displaced water travel further and to accomplish this in same time would require more power -- So my question is that if so, what supports this contention, and if not why not??

I am not questioning whether wider/shallower draft will support or provide a greater % of hydrodynamic lift and resulting less power requirement for similar speed (still disregarding friction)

 

[Mr Efficiency]

You keep asking the same question, and none of those hydrodynamics experts that answered you (not me, I'm an 'interested amateur") gave any credence to your idea, so I doubt there is much that I can do to dissuade you ! If you want to know why the idea is wrong, it is probably because it does not agree with what is observed, which ought to be enough !

 

[jesdreamer]

Stupid Post

You keep asking the same question, and none of those hydrodynamics experts that answered you (not me, I'm an 'interested amateur") gave any credence to your idea, so I doubt there is much that I can do to dissuade you ! If you want to know why the idea is wrong, it is probably because it does not agree with what is observed, which ought to be enough !

As I re-read each of the posts in response to my original question, I see no answer -- all I see is a lot of discussion as to how stupid I am for asking such a stupid question -- I didn't consider it stupid at the time and I do not consider it stupid now --

 

[Mr Efficiency]

It is going to get a sensible answer now the type-face has been re-sized, do you think ? Let me think, the deep draught boat is forced to push thay water waaaay down, and expend energy doing it, right ? What happens when the nadir is reached, and all that water is now pushing the aft of the boat along, because of the reverse slope, right ? The Lord giveth, and the Lord taketh away, what did you gain or lose ? I doubt you'll give up till you get a unanimous vote of approval.

 

[philSweet]

It's not a stupid question, its a difficult one. And an important one that costs shipping companies huge sums of money in fuel each year. Billions of dollars have been spent on finding ways to answer it. And as it turns out, in 1898, A guy named Michell figured out how to answer it, more or less. His way works better than your way.

Michell's integral actually calculates the waves that a hull shape makes. Your idea that they are in proportion to some metric of size is simply wrong, or inadequate to the point of being wrong.

What you probably didn't realize is that you just stumbled into a billion dollar business. And each year, thousands of students begin a lifelong quest for a better answer. It's like you just walked out of the woods with a bottle of this black tarry stuff that seeps out of the ground and announce to us that it is really great stuff for waterproofing boats, and you can't understand why we keep wanting to change the direction of the conversation.

This is the sort of path that leads to an answer. See section 4.2 in particular. And no, there isn't an easier way - this is the easy way. Mathematicians have spent over a century continuing to make it tractable. The notation takes some unpacking; you can find the expanded, conventional notation in other places.

http://arxiv.org/pdf/1410.2800.pdf