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Author Topic: Scaling Woes 1  (Read 574 times)

GG

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Scaling Woes 1
« on: October 06, 2019, 12:29:27 PM »

We must have all heard of, or even experienced, the problems of altering a plan size to suit the model we want to build.  It could be that something a "bit bigger" is desired so the plan size is doubled only to find that it has created an impractical monster.  Or, the alternative of making a "handier smaller" model has produced something that sinks worryingly low in the water when you try to sail it.


All these problems could be avoided with a decent understanding of what is happening and a little mathematics.  The latter is sadly why a few people avoid thinking about it.


Lets consider what happens when you scale things up in size.  Starting with a "Unit Cube" in Fig 1.  A Unit cube simply means that the length of each edge is one unit in length, the actual units don't matter but could be inches, centimeters, or for ancient die had Imperialists- rods, poles, chains, furlongs.....


Each of the six cube faces has a an area of one square unit and a the cubes volume is one cubic unit.  Now, what happens if we double the length of the edges?  This is what "doubling" the size means to most people.


Looking at Fig 1 and it is clear that each face of the cube now has an area of 4 square units.  The enlarged cube still has six sides so the total surface area is now 4 x 6 = 24 sq units.


As for the volume, the "double size" cube now contains 8 units cubes!


"Trebling" the size of the unit unit cube (each side being 3 units long) has even more dramatic results.  Again from Fig 1, the area of each side is increased by nine-fold and the volume by a massive 27 times!


If we carried on this sequence it would become clear that the surface areas increase by the "square" of the factor by which we change the original shape and volumes by the "cube" of this factor.  That is:


2 x 2 = 4  and 3 x 3 = 9 for Areas


2 x 2 x 2 = 8 and 3 x 3 x 3 = 27 for Volumes


This is why simply doubling the length of a plan will give you a model with 8 times the displacement of the original, which might be a shade more than expected!
Glynn Guest
[size=78%] [/size]





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GG

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Re: Scaling Woes 2
« Reply #1 on: October 06, 2019, 12:45:48 PM »

What about going the other way, reducing a plan size?


Fig 2 shows this effect and we start with a Unit cube but this time multiply the length of the sides by a half, again what most people would say was "halving" the size.


It ought to be clear that a "half size" cube now has face areas only one quarter of the original. Since you would need eight of these "half size" cubes to build the original unit cube, the volume of the half size is now one eighth of the original


Halving again to  what people usually call "quarter size"  gives us one sixteenth the surface area and one sixth fourth the volume of the original cube.


This is also due to squaring or cubing of the scaling factor used.  But, this time because the factor is less than one, things diminish in size.


1/2 x 1/2 = 1/4  and 1/4 x 1/4 = 1/16 for Areas


1/2 x 1/2 x 1/2 = 1/8  and 1/4 x 1/4 x 1/4 = 1/64 for Volumes


Which is why your "half scale" model can only have 1/8 the displacement of the original if it is to float on the original waterline.
Glynn Guest
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GG

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Re: Scaling Woes 3
« Reply #2 on: October 06, 2019, 01:24:43 PM »

I suspect that most people will only change the size of a by no more than half (either reduced by a half or half as much again) I've attached a table showing the changes in area and volume you can expect.  The Scaling Factor is given in decimal form (easily converted to a decimal change - just multiply by 100) as this is simpler to use with a calculator or if you get a copy shop to change the plans.


If you wanted to double the weight of model, then the table suggests that a scaling factor between 1.2 and 1.3 ought to double the hull volume ( or 1.25992 to be a shade more accurate).


Increasing the scaling up by 50% (i.e. scaling factor of 1.5 ) would produce a model some 3 1/3 times heavier than the original, maybe more than you need?


Scaling a plan down by a mere 10% (0.9) and you have lost over a 1/4 of the originals displacement.  A further 10% reduction to 0.8 and you are down to almost half....!  This might be more than you can afford and a session weighting the planed internal items plus an estimation of the models structural weight could be called for?


So with a little forethought and a few simple calculations, your personalized plans can be made to work without having shovel lots of ballast on board or (perhaps even worse?) desperately trying to shave weight out of an already small model.


As for the area changes with altering model sized, this is perhaps more of value the effect of wind, yes yachts but scale models with significant side areas too!  The effect of wind on a model depends of the ratio of area to weight.




Consider making a "half scale" model of a yacht design, that is a scaling factor of 0.5.  Its weight will be 1/8 of the original whilst its sail area will be 1/4.  So the the area/weight ratio is doubled from the original value, and such a small model could be pain to sail.  OK, there is more to this but, in general, scaling a sailing model plan up will give you less problems than scaling down.


Glynn Guest
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Mark T

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Re: Scaling Woes 1
« Reply #3 on: October 06, 2019, 02:47:22 PM »

Thanks for that information Glynn its very interesting and food for thought.  Its not something I've tried yet but I have no doubt I will need to scale a build in the future.
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ballastanksian

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Re: Scaling Woes 1
« Reply #4 on: October 06, 2019, 11:29:06 PM »

This is super material for a new 'Facts and figures' page on the forum where only facts and formulas etc are posted. Any spurious wiffle is deleted to reduce the page's band width and make scrolling down easier due to the smaller amount of traffic.
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mudway

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Re: Scaling Woes 1
« Reply #5 on: October 07, 2019, 12:40:14 AM »

Just look at the effect of downsizing a Type 22 frigate Batch 1 from 1/72 down to 1/96 scale. Doesn't sound much difference but look at the figures.



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malcolmfrary

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Re: Scaling Woes 1
« Reply #6 on: October 07, 2019, 09:48:06 AM »

A scaling recipe, button press by button press for use with a calculator like the app that lives on many phones, to help guess the weight to see if it is going to work or be feasible.
Enter the known weight, times scale, times scale, times scale, equal.  Divide by new scale, divide by new scale, divide by new scale, equal.
Shows that a 1:72 Revell corvette weighing about 6 pounds becomes a 2.5 pound boat if you go for a 1:96 version.  Or 12 oz if you try the 1:144 kit.  If going the other way for a 1:48 version, you end up with a 20+ pound lump.
Once you know the all-up weight of the complete thing, it is possible, with a plastic kit, to weigh the kit parts and gauge what it is going to be able to carry.  Or, if going the other way, whether or not you are going to be able to carry it and launch/retrieve ir without joining it in the lake.
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mudway

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Re: Scaling Woes 1
« Reply #7 on: October 07, 2019, 10:05:28 AM »

I just have that formula stored in an excel spreadsheet for 1/72, 1/24, 1/32 and 1/35th scales. Enter 1:1 scale numbers and the pc does the rest.
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malcolmfrary

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Re: Scaling Woes 1
« Reply #8 on: October 07, 2019, 10:28:39 AM »

I just have that formula stored in an excel spreadsheet for 1/72, 1/24, 1/32 and 1/35th scales. Enter 1:1 scale numbers and the pc does the rest.[/size]
The trouble is that while some of us know how to use and create spreadsheets, an increasing number of people know less and less about numbers and what they mean.  Throw in a mix of imperial and metric measurements, and you get total confusion very rapidly.  Anyone for roods, perches and cubits?
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Colin Bishop

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Re: Scaling Woes 1
« Reply #9 on: October 07, 2019, 11:31:07 AM »

Yes, people often don't have a feel for numbers and have no idea whether the decimal point is in the right place when they read off a calculated result, sometimes with unfortunate consequences.

Colin
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warspite

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Re: Scaling Woes 1
« Reply #10 on: October 07, 2019, 02:29:07 PM »

The trouble is that while some of us know how to use and create spreadsheets, an increasing number of people know less and less about numbers and what they mean.  Throw in a mix of imperial and metric measurements, and you get total confusion very rapidly.  Anyone for roods, perches and cubits?


When trying to explain to my eldest about multiplication i.e. the 2 x 2 example and then the cubic version 2 x 2 x 2, we raided the kitchen cupboard and used the OXO cubes as these are cubic  %) , still didn't get it though, thats why he still works in McDonalds as a floor manager
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roycv

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Re: Scaling Woes 1
« Reply #11 on: October 07, 2019, 04:50:26 PM »

Hi Warspite, I hear Mac's has a very good employee progression system.
I think calculators and smart phones remove you from basic numbers and quantities.

I posted a little gem in May this year that fell on stoney ground.  X% of Y is the same as Y% of X.
Or 10% of 90 is the same as 90% of 10.  Apparently quite well qualified maths people had not appreciated it.
Is it just us that will get it?  You can use it for changing scales as well.
Regards Roy
 
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roycv

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Re: Scaling Woes 1
« Reply #12 on: October 07, 2019, 05:07:22 PM »

Having been down the line of trying to increase buoyancy especially scale yachts it just needs thought.  Making the keel a bit thicker is good and I found on a metre long yacht adding a 3mm depth of extra planking mainly below the waterline added the extra displacement I needed.
So the distortion in width was about 2 % hardly noticeable, it did also lead to a slightly longer hull at the pointy end but that hardly noticed either.
The keel width can easily be doubled or more, however I thought the Blue Leopard kit went too far with a very fat keel.
Depth of keel can be either extended or a false keel fitted for sailing.  Bearing in mind that a wider keel has to be taken as extra bouyancy.

 Sometimes the sails do not work especially for overlapping jibs but cutting back and re-balancing has only very few knowing what has been done.
Regards Roy
 
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skierdive

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Re: Scaling Woes 1
« Reply #13 on: October 07, 2019, 08:04:51 PM »

Scaling up may also introduce structural integrity problems. Requiring the need for thicker material to be used, or the introduction of extra bulkheads/bracing pieces, in turn, adding extra weight to the model.


Ian.
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