Track Ratios

Ever wondered how big to make your model railway?  A couple weeks ago, I had recently signed on to an online forum for large scale called mylargescale.com.  This site is where the question popped into my mind.  At first, it seemed as though a simple ratio of trains: track length would be enough, however it wasn't.  The reason why is because multiple trains, traveling in opposite directions, need places to get around each other and some elbow room on the mainline.  After reading what other people thought about the subject, I realized that instead of a ratio, an equation may work.  The key to any equation relating to real life is that ALL of the variables must be taken into consideration.
The variables with this particular problem are the following :

• number of trains (roughly half traveling one way and half traveling the other way)
• scale speed of travel
• length of trains (average)
• derailments and other obstacles (requires time to fix)
• distance between trains

And here is what I was trying to find out:

• length of main line
• % of the main must be double (to allow for passing trains to get by)

So after much thought, it came to me and here is the equation:

number of trains X length of average train (inches) = total average length of all the trains (inches)

length of average train (inches) X 3 at least = total distance between each train (inches)

total length of all trains (inches) X total distance between each train (inches) = total mainline (inches)

50% of mainline should be double main line.  This is because half of the trains are going one way, half the other way.

Should a derailment occur, this is how much time there would be to fix the problem :

average scale speed of trains/scale of the models ie.. 87 (1/87th =HO) =  true average mph of trains   

average true mph of trains/ 3600 = average feet per second of a train

feet per second X 5280 feet in a mile

distance between trains (inches)/ 12 (inches per foot) = feet between trains

feet between each train/ average fps (feet per second) = number of seconds between each train.

Confused yet?  It makes more sense if you take your numbers for each variable and put it into the equation.  Let me use an example :

• each train is going to be 60" long
• there are 6 trains on the track at any given moment
•  scale mph for each train will be 30 scale mph

Now I can plug those figures into the equation:

6 X 60" = 360"

60" X 4= 240" between each train

360" X 240" = 86,400" of total mainline

43,200" of the main line has to be double main line.  This means that 3,600 feet of main line for all of these trains and 1,800 of the main line needs to be double main line.

To find out how many seconds there are between trains:

60 scale mph/ 87 = 0.69 true mph

0.69/ 3600 seconds per hour = 0.00019 or 1.9 ten-thousandths of a mile are traveled per second

0.00019 X 5,280 feet in a mile = 1.0032 feet per second

240"/ 12"= 20 feet between each train

20 feet between each train/ 1.0032 feet per second = 19.94 seconds between each train.

Of course, that is a HUGE train layout!  Most of us could barely fit 50 feet of main line into the space we have to work with.  However, if you want to know how big your dreams really are, then use this equation. 

 The example train layout can defiantly be smaller by doing the following:

• Reducing the length of trains two 36"
• Reducing the number of trains to two or three
•  Having a double main line to automatically reduce the total main line to half of itself.  This means that each main line is 50% shorter than if the main was a single track.

So try it out, you will be surprised how big or small your dreams may be.

By the way, I can't download diagrams here so you will have to use your imagination on this one : )