How to calculate the total central angle of railroad curves

[railroadhoodlum]

Homework Statement

Bailey Mine Branch
Consolidation Coal Company’s Bailey Mine can produce and load 10,000 tons of coal
per shift. The mine works three shifts per day five days per week for 50 weeks out of the
year. They have a 19 mile-long track known as the Bailey Mine Branch that connects to
a former Conrail line located in southwestern Pennsylvania. The only traffic on the
branch is empty and loaded unit coal trains that consist of three locomotives weighing
200 tons each, and 100 hopper cars that are loaded at the mine to their full 100-ton
capacity per car.
The branch is laid with 132# rail, and has 5% on level tangents, 25% on tangents with a
1% grade, 20% on 6° level lubricated curves, 35% on 6° lubricated curves on a 1% grade,
and 15% on 10° lubricated curves on a 1.5% curve.

What is the total central angle through which the Bailey Mine Branch turns?

Relevant Equations

Length of curve is = Number of 100 foot chords or Length of curve =100 * Delta/Dc

0.3​	19​	5.7​	tangent track miles
0.55​	19​	10.45​	6 degree curves
0.15​	19​	2.85​	10 degree curves
Length of Curve	=	I ?
			Dc

 

[256bits]

Not that I know anything about lubricated curves, but what have you tried to solve for an answer?

 

[railroadhoodlum]

In asking for help from my professor I was told this: As far as the specifics, you know the formula for determining the length of a curve, L=100*I/D. Knowing the D and the L, you can determine the I angles. Then you need to add the I angles for the various degrees of curve to come up with a total. I answered the parts of the question that were germane to the lubrication, the total central angle as far as I know is not affected by with the rails are lubricated or not.

 

[Dr.D]

I must be missing something, but I fail to see the connection between the angle and lubrication. Where are these related, other than creating separate categories?

 

[railroadhoodlum]

You're correct, I omitted the portion of the question that was related to lubrication. Rails that are lubricated will have a greater life span in terms of tonnage it can handle before failing.

 

[Dr.D]

You're correct, I omitted the portion of the question that was related to lubrication. Rails that are lubricated will have a greater life span in terms of tonnage it can handle before failing.

Yes, I knew that, but how does that relate to the original question, "What is the total central angle through which the Bailey Mine Branch turns? "

 

[railroadhoodlum]

It does not relate to it.

 

[Dr.D]

So this is just a red herring?

 

[railroadhoodlum]

This is the entire problem:
Bailey Mine Branch
Consolidation Coal Company’s Bailey Mine can produce and load 10,000 tons of coal
per shift. The mine works three shifts per day five days per week for 50 weeks out of the
year. They have a 19 mile-long track known as the Bailey Mine Branch that connects to
a former Conrail line located in southwestern Pennsylvania. The only traffic on the
branch is empty and loaded unit coal trains that consist of three locomotives weighing
200 tons each, and 100 hopper cars that are loaded at the mine to their full 100-ton
capacity per car.
The branch is laid with 132# rail, and has 5% on level tangents, 25% on tangents with a
1% grade, 20% on 6° level lubricated curves, 35% on 6° lubricated curves on a 1% grade,
and 15% on 10° lubricated curves on a 1.5% curve.
What is the average expected rail life in years on the Bailey Mine Branch if the rail must
be replaced when it is worn 0.25 inches?
What is the total central angle through which the Bailey Mine Branch turns?
If all the grades are in the same direction, what is the total change in elevation over the
length of the branch? What is the average grade in percent?