# TRACK MATH.....



## John J (Dec 29, 2007)

OK boys and Girls.

Engineer Brown has a stake, long piece of string and a scribe.


Engineer Brown wants top plot the arch of a 20 ft curve.

Engineer Brown thinks that if you have some 20 ft curve track and make a complete circle it should be twenty feet across.

Engineer Brown wonders is it measured to the inside rail or the outside rail?

Or the center line between the track. 

If Engineer Brown drives his stake in the ground. Then ties his 10 FT string to it then attaching the scribe to the other end he should be able to draw a 1/4 arc or 1/2 arc equal to the 20 FT curve? 

Is Engineer Brown correct in his thinking? 

Reducing the string to a 5 FT piece will give him a 10 ft curve.


Engineer Brown awaits your answer 

JJ


----------



## Gary Armitstead (Jan 2, 2008)

Posted By John J on 13 Mar 2013 03:27 PM 
OK boys and Girls.

Engineer Brown has a stake, long piece of string and a scribe.


Engineer Brown wants top plot the arch of a 20 ft curve.

Engineer Brown thinks that if you have some 20 ft curve track and make a complete circle it should be twenty feet across.

Engineer Brown wonders is it measured to the inside rail or the outside rail?

Or the center line between the track. 

If Engineer Brown drives his stake in the ground. Then ties his 10 FT string to it then attaching the scribe to the other end he should be able to draw a 1/4 arc or 1/2 arc equal to the 20 FT curve? 

Is Engineer Brown correct in his thinking? 

Reducing the string to a 5 FT piece will give him a 10 ft curve.


Engineer Brown awaits your answer 

JJ 
OK JJ, it's the CENTER line of the track and yes, Engineer Brown is correct in "his" thinking.


----------



## Greg Elmassian (Jan 3, 2008)

Normally measured to the center of the tie between the rail, BUT many manufacturers do not give the exact or proper measurement. 

Yes, 10 foot RADIUS (string) will "draw" ANY desired arc which would be a part of a 20 foot DIAMETER circle 

(you have used 20ft curve several times without specifying whether it is 20ft radius or 20 ft diameter) 

RADIUS is half the DIAMETER. 

Regards, Greg


----------



## iaviksfan (Dec 27, 2007)

20' radius sure would be nice and large. If i only had the room....... 
Greg R.


----------



## SteveC (Jan 2, 2008)

Well...
[*] The first thing that comes to mind, is that the track is actually manufactured to metric dimensions, so most of the Imperial dimensions (i.e. feet, inches) are nominal and using them you're always going to be slightly off in your calculations.
[*] The diameter of the circle is measured to the center-line between the rails.

*Edit:*
[*] Oh, I meant to mention that you would be better off to make a loop in the end of the string that is going to be placed around the stake, so you don't reduce the length of the string (i.e. and the radius of the circle) as the tied string wraps around the stake.








[/list]


----------



## Stan Cedarleaf (Jan 2, 2008)

Posted By SteveC on 13 Mar 2013 03:52 PM 
Well... 
[*]*Edit:*
[*] Oh, I meant to mention that you would be better off to make a loop in the end of the string that is going to be placed around the stake, so you don't reduce the length of the string (i.e. and the radius of the circle) as the tied string wraps around the stake.








[/list] 
Steve... You took words right out of my mouth... I was just getting ready to reply just like that... Glad I saw your post. I've know JJ longer that you have... I think...


----------



## bicyclexc (Mar 31, 2010)

Found a good article a while back on how the real surveyors did it. 

A circular curve is often specified by its radius. A small circle is easily laid out by using the radius. In a mathematical sense, the curvature is the reciprocal of the radius, so that a smaller curvature implies a large radius. A curve of large radius, as for a railway, cannot be laid out by using the radius directly. We will see how the problem of laying out a curve of large radius is solved. In American railway practice, the radius is not normally used for specifying a curve. Instead, a number called the degree of curvature is used. This is indeed a curvature, since a larger value means a smaller radius. The reason for this choice is to facilitate the computations necessary to lay out a curve with surveying instruments, a transit and a 100-ft engineer's tape. It is more convenient to choose round values of the degree of curvature, rather than round values for the radius, for then the transit settings can often be calculated mentally. A curve begins at the P.C., or point of curvature, and extends to the P.T., or point of tangency. http://mysite.du.edu/~jcalvert/railway/degcurv.htm 

Or in English, Wikipedia: http://en.wikipedia.org/wiki/Degree_of_curvature


----------



## Garratt (Sep 15, 2012)

Yes, Engineer Brown should tie a 'loose' loop around the stake or Engineer Brown will end up like a dog on a chain wound around a post. 
Good way to scribe a spiral though. 

Andrew


----------



## SteveC (Jan 2, 2008)

Posted By Stan Cedarleaf on 13 Mar 2013 04:20 PM 
Posted By SteveC on 13 Mar 2013 03:52 PM 
Well... 
[*] *Edit:*
[*] Oh, I meant to mention that you would be better off to make a loop in the end of the string that is going to be placed around the stake, so you don't reduce the length of the string (i.e. and the radius of the circle) as the tied string wraps around the stake.








[/list]
Steve... You took words right out of my mouth... I was just getting ready to reply just like that... Glad I saw your post. I've know JJ longer that you have... I think...







Stan

Hehehe, I sort of figure that John has a dual rail bender, so in reality he only needs to get it fairly close, then he can make it fit.


----------



## Dr Rivet (Jan 5, 2008)

Bicylexc 

Although you are TECHNICALLY correct, using the chord method on small radii of model railroad track, even those in ride on scales where 75-100 foot radius is used, typically result in large errors. 

JJ should know through LONG experience that "G" sectional curved track NEVER holds its manufactured radius over a long period [NOT EVEN LGB]. 

Any radius laid out out is going to be an approximation of where the track will be on the ground 15 days later. 

JJ, put a piece of rebar or pipe in the ground at the center point, tie the loop of string around the "post" so the knot can always be on the side with your "pointy thing" that you drag in the dirt. 

Good luck.


----------



## Treeman (Jan 6, 2008)

JJ Use flex track, you can make it fit.


----------



## Tom Parkins (Jan 2, 2008)

*This thread is one day early. Thursday 3-14 is Pi Day!!!!!! *


----------



## John J (Dec 29, 2007)

Why is Engineer brown asking these questions ?



He is about to make reusable concrete roadbed forms. 

He nay be making forms between 10FT and 20 FT curves. 

We are talking diameter. 

The N,R,&W has 6- 12 ton truck loads of dirt. 

There is going to be a slight enlargement of the layout.

It might involve a Mountain Mine. 

JJ


----------



## SD90WLMT (Feb 16, 2010)

Hey, JJ - I heard '' Mountain Mine'' was up north near you!! 

Dirk - Be warry ..............


----------



## Greg Elmassian (Jan 3, 2008)

JJ, be sure to put that loop in the end of the string like the guys say, otherwise you'll look like this:


----------



## Garratt (Sep 15, 2012)

Posted By Tom Parkins on 13 Mar 2013 06:36 PM 
*This thread is one day early. Thursday 3-14 is Pi Day!!!!!! * As many as you can eat!

Andrew


----------



## RCE (Sep 14, 2009)

Taste this PI


----------

