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 Post subject: Working with Scales
PostPosted: Sun Jan 13, 2008 12:04 am 
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A small guide to working with scales, unit conversions, and numbers. I might add more later. Feel free to add your own parts to it. I hope we can add this to the FAQ section.

Topics in this post:
1.Finding the dimensions of a subject in a given scale, when the real object dimensions are known
2.Going the other way (finding the length of the real thing, given the length of a scale model)
3.Converting between scales
4.Scaling up/down plans

First: What do scales represent?
The easier way to understand it is this:
There are X amount of the model required to make up the real thing.
A 1/700 Nimitz will require 700 Nimitz models in 1/700 scale laid down bow-to-stern in order to cover the length of the real Nimitz.
Note this only works along single dimensions, which is what most modellers are concerned with (ie, you'll need more than 700 Nimitz models to cover the surface area of the real Nimitz, and even more to occupy the volume of the real thing). Areas and volume are of little consequence to most of us, however.

1. Finding the dimensions of a subject in a given scale, when the real object dimensions are known:

Example:
I want to know how long the USS New Jersey, BB-62, is in 1/350th scale.

Solution:
Find the length of the NJ - it's 887 feet, approximately.
Now divide it by 350.
887 feet / 350 = 2.534 feet

So the NJ, when scaled down to 350th scale, is approximately 2.534 feet long.


2. Going the other way (finding the length of the real thing, given the length of a scale model):
Example:
I want to know how long the USS Immanukeya is in real life, given a 1/700th scale model of 35 centimeters in length.

Solution:
Simply multiply 35 cm by 700.
35cm X 700 = 24500 cm.

Now, centimeters, in real life, is rather hard to envision, especially when it's such a large number.

Solution:
Change it to a more familiar unit! Let's say we want it in feet, not centimeters, because it's easier to compare with the known length of other ships.

24500 cm X (1 meter / 100 cm) X (3.28 feet / 1 meter) = 803.6

The parts highlighted in red are known as "conversion factors". What they are, basically, is how much of one unit there are in the desired unit. The first part, for example, with (1 meter / 100 cm). That means there are 100 cm in 1 meter. Now, 100 cm is on the bottom because we started out with centimeters, and we want to get the final unit in feet. So we put it on the bottom so that it "cancels out" with the initial unit, which was on "the top". Remember, any number can be written as over one (eg. 2 feet is the same as 2 feet / 1).

But how do we know that 803.6 is in feet, and not some random unit?

Notice that 24500 cm is divided by 100 cm. Thus, cm "cancels" out. Next, the meter is also cancelled out, because it's on the top and bottom of the equation. This leaves you with feet, which doesn't get to be cancelled out by anything, because you've reached the end of the equation and you've yet to encounter a "feet" that's on the bottom of the expression. This means your final number is in feet units.

If you wish to read more about unit conversions, grab a copy of any high school Physics or Chemistry textbook. Unit conversions is one of the basics first taught to the students of the last two years of high school.


3. Converting between scales:

Example:
The plans you are working from are 1/96th scale.
The model you wish to build is in 1/200th scale.
The part you are building has a length of 5 inches on the 1/96th plan.
How long should you make the piece so that it is of the right length on your 1/200th model?


Solution:
The explanation for why is a bit more complicated for this operation, so I'll just post how to do it.

5 inch X (96/200) = 2.4 inch

In other words, multiply your measurement by the scale you have, and divide by the scale you want to convert into. This works no matter whether you're decreasing or increasing the scale.

Say your plans are in 1/400 scale.
You want to build your model in 1/100.
The measurement you made on the 400th scale plans is 3 cm.

3 cm X (400/100) = 12cm in 1/100 scale.

4. Scaling up/down plans
The number you get when you do just the scale division (in this case, 96/200 and 400/100) is called the Scale Factor. Convert this into a percentage value and it is what you put into your copier when you want to scale down/up a set of plans.

Using the second example, 400/100 = 4.
4 as a percentage is 400% (just multiply by 100), so put that in your copier to enlarge the plans from 1/400 to 1/100 scale.

Using the first example, 96/200 = 0.48.
0.48 as a percentage is 48%. Put 48% in your copier and it'll reduce the 1/96 scale plans into 1/200.

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Last edited by Timmy C on Sun Jan 13, 2008 2:09 am, edited 3 times in total.

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