Model Railroading > Is This Mathematically Close Enough to HO Scale?

Mike Johansen (sp?) former member of TO visited his former train club http://www.gsmrm.org on Friday night.

Sometime during the evening while giving him the 25¢ tour of the railroad, for some bizarre reason I brought up that at least two dozen years ago I did the math to determine HO Scale numerically. HO equals one half English O Scale, which is 7 mm to the foot. So, 3.5 mm to the foot equals 1:87.08, commonly rounded up to 1:87.1, or almost universally known as 1:87. I could not remember how I did the math.

Mike quickly came up with the formula 12 inches multiplied by 25.4 mm to the inch divided by 3.5 mm to the inch equals (if y’all go to https://www.ttmath.org/online_calculator ).

87.085714285714285714285714285714285714285714285714285714285 714285714285714285714285714285714285714285714285714285714285 714285714285714285714285714285714285714285714285714285714285 714285714285714285714285714285714285714285714285714285714285 714285714285714285714285714285714285714285714285714285714285 714285714285714285714285714285714285714285714285714285714285 714285714285714285714285714285714285714285714285714285714285 714285714285714285714285714285714285714285714285714285714285 714285714285714285714285714285714285714285714285714285714285 714285714285714285714285714285714285714285714285714285714285 7142857142857143

Mike said it was a never ending number, like pí.

A few minutes ago I found another online calculator that can display one million places, but I didn’t want to be redundant.

⅂ɐɹɹʎ

The significant digits in your end number cannot exceed the significant digits of the other numbers in the calculation. Going that many digits out when using 12, 25.4, and 3.5 is meaningless. If you used a more precise number for the amount of millimeters per inch then the final number with that many digits will be different than what you calculated. If you use 25.4mm=1.0in and 12.0in=1.0ft then the final number can only be 87.1. However, it certainly is close enough for all practical purposes, except for paint thickness counters.



Edited 1 time(s). Last edit at 04/08/18 01:13 by EricSP.

What EricSP said sounds right from my college days.

Cheers, jim

Posted from Android

It is not like pi in that there is a repeating pattern. The same six digits (857142) repeat over and over again. One of the attributes that distinguishes pi is that the digits never repeat. There is a mathematical term for this that I learned in school, but I have long since forgotten it.



Edited 1 time(s). Last edit at 04/08/18 04:45 by toledopatch.

Ok, now my brain hurts. But...I'm glad there are people that can do this. SOMEONE has to do my taxes!

With long division, once you realize you've reached a single repetition, there's no need to do it over and over again.

I made it easy and switched to O scale. 1/4" to a foot, 4 ft to an inch. A 40 foot boxcar is 10 inches long, and I bought a scale ruler!

Peter

There are three kinds of people in the world, those that understand math, and those that dont.

herronpeter Wrote:
-------------------------------------------------------
> I made it easy and switched to O scale. 1/4" to a
> foot, 4 ft to an inch. A 40 foot boxcar is 10
> inches long, and I bought a scale ruler!
>
> Peter

and just round the gauge up to five feet. It works out great if you are modeling the Russian railroads or some 19th Century railroads in the American south.

Jack

This reminds me of a riddle my high school math teacher told, adapted for model railroading.

A mathematician and an engineer (civil, mechanical, etc) are operating a model railroad road train. They get permission to run their train 10 miles to the next town. However their orders come with the caveat that they can only move halfway of the remaining distance every minute.

The mathematician instantly throws his hands in the air and says "This is ridiculous, we'll never get there!". The engineer shrugs his shoulders and replies "True, but in a few minutes we will be close enough, and will have arrived".

Dividing any number by 2 repeatedly forever will never get you zero. However, practically it doesn't take long to have "nothing" left, which to most engineers nothing equals zero.

Jeff Eggert

Do you think you can measure past the 4 digits behind the decimal point or even 2 digits past the decimal?

Sure there are machines which can but a modeler in the basement with an optivisor and a commercially available micrometer?

toledopatch Wrote:
-------------------------------------------------------
> It is not like pi in that there is a repeating
> pattern. The same six digits (857142) repeat over
> and over again. One of the attributes that
> distinguishes pi is that the digits never repeat.
> There is a mathematical term for this that I
> learned in school, but I have long since forgotten
> it.

Irrational number

WrongWayMurphy Wrote:
-------------------------------------------------------
> There are three kinds of people in the world,
> those that understand math, and those that dont.

HUH, I don't understand.........Good one WWM

herronpeter Wrote:
-------------------------------------------------------
> I made it easy and switched to O scale. 1/4" to a
> foot, 4 ft to an inch. A 40 foot boxcar is 10
> inches long, and I bought a scale ruler!
>
> Peter

Same with 1” scale. We call it the sane gauge.....30’ boxcar equals 30”....simple

Posted from iPhone

Hey Jack,

We are talking about scale, not track gauge. If I had it to do over, I might have done P48 and used less different locomotives, but I would have missed out on a lot of interesting steamers like my favorite 2-4-4-2.

https://www.youtube.com/watch?v=KuFtif8UL_w

I just find higher math gives me an ice cream headache!!

Peter

herronpeter Wrote:
-------------------------------------------------------
> Hey Jack,
>
> We are talking about scale, not track gauge. If I
> had it to do over, I might have done P48 and used
> less different locomotives, but I would have
> missed out on a lot of interesting steamers like
> my favorite 2-4-4-2.
>
> https://www.youtube.com/watch?v=KuFtif8UL_w
>
> I just find higher math gives me an ice cream
> headache!!
>
> Peter

Hi Peter,

Yes I know. I just like to kid O-scaler's about that because the gauge discrepancy is noticeably visible. But really I am hoping for someone to do in O-scale a circa 1870s railroad in the American south. That would definitely be worth a look.

Jack

edit: I did watch your youtube. Thank you. Everything in that scene is very nicely done!



Edited 1 time(s). Last edit at 04/09/18 05:11 by ts1457.

toledopatch Wrote:
-------------------------------------------------------
> It is not like pi in that there is a repeating
> pattern. The same six digits (857142) repeat over
> and over again. One of the attributes that
> distinguishes pi is that the digits never repeat.
> There is a mathematical term for this that I
> learned in school, but I have long since forgotten
> it.

I don't believe "e" has a repeating decimal pattern either ?
e is used for "Natural Logs" with calculus to the base e rather than a more common base 10 (log base 10; ln).
Mechanically, I used to know how to use it, but never understood the meaning behind it.

Numerically, it is actually straightforward. A number is rational if it can be described by the ratio of 2 integers, i.e. x/y. A number is irrational if it cannot be. PI is irrational, as is the square root of 2, e, etc.

Math terminology always got me. This science seems to have its own vocabulary using existing words for its own purposes. In normal English, that is not what "rational" means !

joemvcnj Wrote:
-------------------------------------------------------
> Math terminology always got me. This science seems
> to have its own vocabulary using existing words
> for its own purposes. In normal English, that is
> not what "rational" means !

Delve into the world of electrical engineering, and you will have to deal with imaginary numbers...