Hull Asymmetry and Minimum Wave Drag

Discussion in 'Hydrodynamics and Aerodynamics' started by DCockey, May 28, 2011.

  1. DCockey
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    DCockey Senior Member

    Leo explained in another thread that Michell's thin-ship theory predicts minimum wave drag occurs when a hull is fore-aft symmetric. (Post #9 of http://www.boatdesign.net/forums/design-software/few-michlet-godzilla-questions-35466.html) Fore-aft symmetric hulls have the Longitudinal Center of Buoyancy located at mid-ships. Analysis of tow tank tests suggest that drag is reduced by having the LCB away from mid-ships. Larsonn & Raven in the new Ship Resistance and Flow volume of the redone PNA series have a plot of optimum LCB location vs Fn with curves from Series 60, Holtrop, Jensen and Delft. At Fn below 0.21 to 0.23 the optimum LCB is ahead of mid-ships, while at higher Fn it is aft.

    So what is the reason for the apparent discrepancy between the theory and tests. Larsson & Eliasson in Principles of Yacht Design, Third Edition show a graph from the Delft systematic test series of optimum LCB vs Fn number from 0.29 to 0.46 with the optimum aft of mid-ships, and they suggest "the thick boundary layer and possible separation makes the effective hull longer". But that doesn't explain the optimum being forward for lower Fn. Paulling has a fairly extensive discussion of optimum LCB and CP location for different speed ranges with the main theme being the optimums vary because of the differing importance of viscous and wave resistance as Fn changes.He does make an interesting comment about LCB at "high displacment speeds (0.3<Fn<0.5)":A final reason for having a relatively full stern at these Froude numbers is to reduce the trim, which can be excessive approaching the last hump."

    I'm curious about changes in trim with speed and the role it plays in wave resistance.

    What does trim do as speed changes, particularly for low Froude numbers?

    Is there a correlation between the variations with speed of trim angle and optimum LCB for wave resistance?

    My understanding is that Mitchell's Thin Ship theory doesn't account for trim changes unless the hull shape input is changed. It also doesn't account for the deformation of the free surface, aka waves, and changes in the portion of the hull immersed. My understanding is most tow tank tests allow the model to trim and obviously account for waves and the portions of the hull immersed. This might be part of the explanation of the discrepancy between Mitchell's Thin Ship theory and analysis of test results as to the optimum location of LCB.
     
    Last edited: May 30, 2011
  2. NoEyeDeer
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    NoEyeDeer Senior Member

    Just guessing here, but I suspect a lot of it will come down to displacement/length ratio. IOW, if the slope of the transverse waves is shallow enough then you might expect things to be more in line with thin ship theory, while for hulls that generate steeper waves the trim effects will be more important.

    Also, pitch damping can be important for real hulls and that tends to be better with some fore and aft asymmmetry, so the performance could be improved even if the theoretical drag is slightly worse.
     
  3. Ad Hoc
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    Ad Hoc Naval Architect

    DCockey

    You’re reading too much into a one line statement. I’m sure as Leo will point out, there are endless caveats in the one liner. Since there is no “universal” one liner. Every hull has a different "optimum” and for different reasons.

    The main reason for Leo’s stamen is that it applies to long slender hull form. In other words a very high length displacement ration. This is very easily explained by the following graph.

    L-D ratio-1.jpg

    With increase slenderness, the residuary resistance decreases. Also the Fns that Leo uses are generally of the ‘low’ order.


    As speed changes, so does the wave profile along the side of the hull. Since that is Froude’s law to begin with, and how we arrive at residuary resistance. Then looking very briefly at the graph, you can see that a long slender hull shall have a lower residuary resistance, ergo, the waves it produces are less. This has a big influence on the amount of Trim and Squat experience by the hull form.

    Since the wave profile along the side of the hull affects interacts with the the pressure distribution from fore to aft generated by the hull with fwd speed through the water.

    Basically at slow speed the wave profile aft is reduced owing to the boundary layer and the hull is generally not the same as up fwd (ie symmetrical, unless a canoe), it is usually more “full”. The hull up fwd is fine and less reserve buoyancy. Thus, the wave profile (after super-positioning the pressure and wave profiles) creates more “negative” buoyancy so to speak, as there is no reserve buoyancy to support the wave profile, therefore the hull drops to find its equilibrium and trims by the bow.

    With increasing speed the reverse occurs. The wave profile aft cannot be supported by the hull form as the wave generated is now much longer and greater amplitude; so it squats to maintain equilibrium, just as it did up fwd at lower Fns. In other words, the LCB is moving aft with increasing speed. The squat also accounts for the trim, owing to the aft end dropping down to maintain the equilibrium, of buoyancy.
     
  4. DCockey
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    DCockey Senior Member

    Don't think I'm reading too much into Leo's statement. Rather it prompted some thinking on my part.

    Leo will probably join in, but I expect that the wave drag being minimized with a fore-aft symmetric hull applies to any "potential flow/ideal fluid" analysis, not just thin ship, of wave generation and resistance analysis using a simple linerizing assumption about the free-surface and immersed hull. Leo also mentions that potential flow wave drag is the same whether the vessel is forward or backwards. My hazy recollection is that does depend on any thin ship assumptions, and that it may even be valid without any assumptions beyond potential flow.

    Irregardless of Thin Ship theory and Leo's comment, there is still a question about why the "optimum" LCB is forward for low Fn and moves aft as Fn increases. Is there a fundamental, not just coincidence, connection between the trim changes Ad-Hoc explains and the optimum location of LCB? Or is it just due to viscous effects?
     
  5. DCockey
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    DCockey Senior Member

    Any idea what the magnitude of the change in wave profile is due to the boundary layer? How does it compare to the change in wave profile with changing Froude Number?
     
  6. DCockey
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    DCockey Senior Member

    A vessel which isn't pitching will be trimmed so that the instantaneous LCB is aligned vertically with the CG. Assuming the CG doesn't move LCB won't move aft as Fn increases. That's using the term "instantaneous LCB" to describe the center of the the vertical forces acting on the outside of the hull.

    If LCB is used to mean the longitudinal center of the volume below the static water plane then LCB will move aft as speed increases the the vessel trims by the stern.
     
  7. Ad Hoc
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    Ad Hoc Naval Architect

    Yes, may be i explained a bit too briefly. Maybe this simplified explanation i gave someone some time ago, may help:

    View attachment Trim-squat.pdf


    Boundary layer thickness is directly proportional to the velocity of the stream…so, depends what Fn (or speed) the hull is moving. But how much, not so easy to answer. You would need to calculate the thickness of various hull forms fwd and aft, and see the effects with increasing speed and then superposition them over the classic velox wave system.

    There is no silver bullet to explain all. Every hull, for its given length-displacement ratio and its Fn has different effects. Thus, one needs to understand the mechanisms that influence rather than finding a one line that fits all, as there isn't one. The science is pretty well understood..the application however, hmmm..not so.
     
  8. DCockey
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    DCockey Senior Member

    Not looking for a line that fits all, nor a silver bullet. Working on better understanding, both for me and others. Asking questions is one way I go about it. My fundamental question here is why does the "optimum" LCB move appear to move aft with increasing Froude number. I'm somewhat skeptical of the "visucous effects" explainations.

    The attachment appears to explain trim and squat as Froude number changes, but doesn't address optimum hull shape.
     
  9. Ad Hoc
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    Now you've hit the nail on the head. This causes so much confusion and endless circular debates :eek:

    Please define "optimum"....
     
  10. DCockey
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    DCockey Senior Member

    That's how I would approach it. In a previous post the statement was made that "Basically at slow speed the wave profile aft is reduced owing to the boundary layer ". I was wondering what the magnitude of this effect was and how significant it is compared to other factors, primarially change in Froude Number. At slow speeds is the boundary layer effect the primary factor affecting wave profile as the quoted statement might be interpreted to imply, or is Froude number as or more significant? Any knowledge of data one way or the other?
     
  11. DCockey
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    DCockey Senior Member

    Or another approach would be to run an analysis which estimates wave resistance and modify the effective hull shape with the boundary layer displacment thickness.

    One thing I've found over the years is that the various definitions of boundary layer "thickness" can be confused. Frequently one such as 99% velocity is used and it appears that the boundary layer is quite thick. But given the asymptotic nature of the velocity profile that can be misleading. For this type of analysis the much smaller displacement thickness would be appropriate.
     
  12. Ad Hoc
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    The magnitude in reality is not worth getting over concerned with, unless you're doing mathematical calculation taking all the effects into consideration to produce a theoretical result.

    Since as Fn increases, the dominant effect, is the wave profile generated by the hull through the water.

    To put into perspective, i only ever calculated the boundary layers and thicknesses and effects when a student. Never since!
     
  13. DCockey
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    DCockey Senior Member

    In this use it's the hull shape with the lowest drag while a set of other hull shape defining parameters are held constant.

    There's a reason I usually put optimum in quotes for such discussions.
     
  14. Ad Hoc
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    Well, there is the kicker, so to speak. Since the "optimum" is transitory. It has an ephemeral life-span, simply because of all the aforementioned. This assumes a hull will be of a fixed shape and fixed Fn, always, whilst maintaining all other factors. In "real" boats, this is very rarely the case.

    Hence, any deviation from this "fixed" condition the "optimum" is no longer valid....hence my "glib" statement about, no silver bullet :p
     

  15. DCockey
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    DCockey Senior Member

    Yes, but it depends in part on how precisely optimum is to be defined, and also on what the operating enevelope will be and other goals and requirements.

    One mistake a lot of engineers make when trying to optimize their design is to not consider how flat or steep the hill or valley around the optimimum is. How big an effect will a change in the parameter have on the results. Not infrequently someone will get hung up getting an "exact" answer when all that's needed is to be close enough or even in the same neighborhood.

    My questions in this thread though are rooted in seeking a better understanding of the physics, not design guidance. That's why I posted the question in "Hydronamics and Aerodynamics" rather than "Boat Design".
     
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