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QUESTION: Hello:

Can you explain mathematically how the following scales become inches to feet?

For example, how does N scale of 1:160 become 1/16" = 1'?

In N scale, (1:160) (1/16" = 1 foot)

In HO scale, (1:87) (1/8" = 1 foot)

I saw more of these different scale examples at the following:

http://www.oakridgehobbies.com/hobby-shop/modeling-in-scale-dimensions-f-a-q-s.h

I thank you for your reply!

ANSWER: 1 foot = 304.8 mm

The 304.8 is technically an approximation, but as the next 10 decimal digits are 0, it's extremely close!

In HO scale, 3.5 mm represents 1 foot.

3.5:304.8 ≅ 1:87.1

In N gauge, 9 mm represents 4 feet 8.5 inches, or 56.5 inches = 1435.1 mm

9:1435.1 ≅ 1:160

I have no idea why they used an odd quantity like 4 feet 8.5 inches. To complicate things, N scale is not consistent. It varies from 1:148 to 1:160.

---------- FOLLOW-UP ----------

QUESTION: Hello:

I want to thank you for your reply.

I'm still confused.

By using feet and inches, how does a scale of 1:160 become 1/16" = 1'? Can you indicate using a calculation how this is converted?

I thank you for your follow-up reply.

I'm GUESSING that the numbers are rounded.

12 real-in × (1 model-in)/(160 real-in) = 3/40 model-in

However, rulers aren't marked in 40ths of an inch. An Imperial rulers is typically marked to show inches, half inches, quarter inches, eighth, and sixteenth inches.

3/40 model-in rounded to the nearest 16th is 1/16 model-inch.

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