Scaling vs. Re-Spacing

Discussion in 'Boat Design' started by flathead65, Sep 2, 2015.

  1. flathead65
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    flathead65 Junior Member

    I have a question regarding scaling down designs. I have read that re-spacing
    the stations can be done up to 15% with reasonable results, but what about scaling a design so everything remains proportionate? I recently took a liking to the Bay of Fundy Scow Sloop in ASSC (pg. 71) and decided to scale it to a trailerable size with an 8 ft. beam. This resulted in a length of 25ft-5". I recalculated the table of offsets at .64, a 36% reduction in size, the original design being 39ft-8 1/2" x 12ft-6". I compared it to the other similar boats and they all generally fall into a 3:1 length to beam ratio. The minimum height at sheer was 24", but the boat is all decked over so that would be ok. I thought it would make a pretty cool little sailing houseboat with a longer cabin.
     
  2. Ad Hoc
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    Ad Hoc Naval Architect

    If you scale in all 3 planes the same %'age, this is called a geosim. You must scale all 3 planes by the same amount and that is fine. Then everything remains fair and the same, just smaller, or larger.
     
  3. TANSL
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    TANSL Senior Member

    Hull shapes in general can be derived with a simple scaling of the model. However, in the inner structure, probably suits to re-spacing cross members (and probably also the longitudinal) to reduce their number and their scantlings. The most convenient, in my opinion, would be to redesign and recalculate the internal structure to take the most appropriate to new proportions.
     
  4. gonzo
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    gonzo Senior Member

    The scaling of the volume to size is not proportionate. Using easy numbers, if you half all the linear dimensions, the volume will be 1/8 not 1/2. Stability doesn't scale directly either, so the behavior will change a lot too. This translates into other large changes that are not directly proportional, like rigging.
     
  5. TANSL
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    TANSL Senior Member

    It depends on what you mean by size.
    Stability: I agree with what you say but what is interesting is whether increases or decreases. What do you think?.
    Rigging: This example, in my opinion, is invalid because the rig will depend on the surface of sails, among other things, but has little to do (or at least there is a very complicated relationship) with linear dimensions (as you say ) of the boat.
    All this of course is debatable, and can open a technically interesting discussion.
     
  6. gonzo
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    gonzo Senior Member

    Using my example of 1/2 size, the sail area would be 1/4, but the stability 1/8.
     
  7. Mr Efficiency
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    Mr Efficiency Senior Member

    Learned opinion seems to be that stability scales to the fourth power.......
    (l x w x h x Righting Arm)
     
  8. HJS
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    HJS Member

     

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  9. fredrosse
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    fredrosse USACE Steam

    Scaled Design

    Changing all linear dimensions by a scaling factor of 0.64 will result in the following changes in other parameters:

    "Hull Speed", for a displacement hull, varies as the square root of waterlne length, so hull speed will become (0.64)^.5 = 80% of the original hull displacement speed. In this case, if the original large hull did 8 knots, then the scaled hull would br doing 6.4 knots. Driving the scaled hull much faster would be very difficult.

    All areas will scale as the scaling factor squared, so the surface areas will all be (0.64)^2 = 41% of the original hull. If the scaled sail plan is maintained, then you will only have 41% of the original sail area.

    Displacement (all volumes) scale as the scaling factor cubed, so at the scaled design waterline the scaled design gives (0.64)^3 = 26% of the original boat displacement.

    Displacement hull propulsive power at any given "Hull speed" is close to linear with displacement, so the scaled boat would only require about 26% of the original boats power to achieve its calculated "hull speed" of 6.4 knots. In this case the propulsive power is sail forces, heeling the hull over with wind force on the sails.

    So herein lies a potential difficulty, because the scaled boat operates on the same water bodies as the larger hull, with the same wind speeds as the larger hull. The force available on the scaled sails is more than 41% of the original hull, since the scaled hull moves more slowly (relative wind to boat speeds are relevant here). Also the sail plan might be somewhat higher, due to clearance issues with full sized humans on the boat. In this condition, the overturning moment (with scaled sail plan) grows more than the righting moment based on hull bouyancy, and stability gets worse. With raised sail plan, worse yet.

    These are some of the the numbers the previous posters have been addressing, so while the scaling project may be workable, a competent review is in order to address these issues.
     
  10. TANSL
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    TANSL Senior Member

    Well, it seems that the naval architecture is a science a lot easier than I thought. Congratulations to all NA. O the contrary, I'm sorry, because you have complicated things more than necessary.
    But let me ask those who know about this subject : can be considered waterplane area 1/4 the original value?. Is immersed volume 1/8 of the original value?. Frankly, I think not, because the weight, and therefore the volume of buoyancy, will not necessarily be 1/8 of the original boat.
    Besides all this, I think that stability, simplifying things, has a component that depends on the shapes of the boat and another component that depends on the position of c. of g. Therefore, to say that stability is 1/8 of the ship model, I think a simplification that has no theoretical base. There is, in my view, a statement that would not make any boat designer.
     
  11. flathead65
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    flathead65 Junior Member

    Thank you all for your responses. There are most certainly some highly skilled individuals at work here although I am surprised you could not all come to a consensus. The only point I could bring to this discussion is how do the RC scale models of ships perform as they do? They are very close representations of the original. I would guess that a simple hull form like a scow would have a much better result than a 64% version of a more complex shape.
    That said, considering the nature of a boat that has good initial stability and almost no reserve would make me err on the side of caution regarding a reduced sail plan to the extent of sacrificing speed for safety. The intent is far from a high performance rig but, more of a nostalgia thing.
    I wanted to add, considering the length to beam maintained at 3:1 in my scaled version, I was surprised to read about Pound Net Scows (assc pg.68) where Chapelle writes "The boats were from 25 feet upward to 50 feet in length and from 6 to 8 feet beam- some of the larger , as much as 10 feet- and were usually cat-rigged with a boom gaff sail". The illustration on pg. 69 shows a Cape Cod version sloop rigged. These are about as simple as it gets with almost no flare although they don't appear to carry as much sail as some of the others. It just seems like an awful long skinny flat bottomed boat to be sailing on the great lakes. They couldn't have been complete capsizing death traps though, or they wouldn't have used them. I guess I'm trying to demonstrate a great variance in length while maintaining a relatively narrow beam way beyond 3:1. I'm not trying to get off topic , but trying to understand whether or not this would work. I have researched it and could show you a few examples of boats that are 24' x 8' modeled after these traditional scows and they sail quite well from what I understand. There is no disputing that hull speed is determined by the square root of the waterline length but, 40 ft x 13 ft is 3:1 and 24 ft x 8 ft is 3:1. So how does the shorter boat only have 1/8 of the stability of the larger? I'm having trouble wrapping my head around that. By all accounts you couldn't raise the jib for fear of getting knocked down. Again, sorry for my ignorance.

    ,
     
  12. gonzo
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    gonzo Senior Member

    The shape is not the issue, but the proportions.
     
  13. Ad Hoc
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    Ad Hoc Naval Architect

    Only the none naval architects cannot agree because they do not understand the implications of what they are saying.

    As noted in my post above. It is a simple geosim. By that, it is not just the hull shape that is geosimed. Once the hull is scaled down to the size that the RC wishes, they have to make sure that at the displacement of the scaled down hull, matches the displacement of the scaled down model with all its bits n pieces inside.

    If it is too heavy, then the modeller must take out bits or find things that are lighter. If the bits weigh less, that is easy, one just adds ballast.

    But it is not just the weights. The LCG must also be in the correct scaled down location as must the VCG.

    If all these are satisfied, then the RC model should perform the same as the parent hull/design, but at the scale selected.
     
  14. gonzo
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    gonzo Senior Member

    Another major consideration is the percentage of crew weight (moving ballast) with respect to displacement. As boats get smaller, a crew on the rail will have much more influence on the righting moment.
     

  15. flathead65
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    flathead65 Junior Member

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