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Math Question about grades

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  • Member since
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  • From: East central Missouri
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Posted by Santa Fe all the way! on Tuesday, July 23, 2013 12:27 AM
Yes, I ruined two jig saw blades just trying to cut a small notch so the trains would have clearance going through the wall.
Come on CMW, make a '41-'46 Chevy school bus!
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Posted by lifeontheranch on Monday, July 22, 2013 1:00 PM

Santa Fe all the way!
P.S. as to stud spacing, my house was built by an 18 year old man for his new bride in 1899. The studs are not all evenly spaced. The house was built with hand sawed oak on the build site. There's no two boards the exact same size and its hard as a rock. Anchoring will be a combo of studs and anchors.

Sounds exactly like my grandparents house. Many, many years ago my dad and I set about rewiring the house. What a nightmare that became. Like you say, there was no predicting where studs or plates were behind lath walls and when you did find them it was almost impossible to drill through them. Spade bits were no match for 150 year old rough hewn oak. What we hoped to be a week long job turned into a month. In the end there were far fewer plugs than we had planned and we were happy we got those in place!

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Posted by zstripe on Monday, July 22, 2013 7:18 AM

Sounds like a pretty sturdy House,to me..

Cheers,

Frank

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Posted by Santa Fe all the way! on Monday, July 22, 2013 3:53 AM
P.S. as to stud spacing, my house was built by an 18 year old man for his new bride in 1899. The studs are not all evenly spaced. The house was built with hand sawed oak on the build site. There's no two boards the exact same size and its hard as a rock. Anchoring will be a combo of studs and anchors.
Come on CMW, make a '41-'46 Chevy school bus!
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Posted by Santa Fe all the way! on Monday, July 22, 2013 3:18 AM
Great info folks, I've learned a lot. When finished, the layout is going to circle TWO, 13.5' rooms, passing through the wall dividing the two rooms. I thought the grade would be nice as it gives the LoCos a bit of a real challenge. I see now that maybe 2.5% was a bit overkill. Because of limited vertical space, I don't want my track to rise that high. Around 1-1.5% might be a better choice especially as the curves increase the % as mentioned in the replies. Sorry for all this spitballing, but getting answers now will save me from another costly false start.
Come on CMW, make a '41-'46 Chevy school bus!
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Posted by peahrens on Sunday, July 21, 2013 4:18 PM

I don't know what equipment you plan to run, etc, but if you are doing a layout with 3 13.5' walls do you want to lessen the grade perhaps? I built a more compact 5' x 10' layout with a crossover and to attain this ended up with a 2.4% grade (even with cheating on the normal 3" clearance), a challenge for some solo locos.  I made my compromises with eyes wide open but if I had more layout space would have reduced the grade.  All I'm saying is you might be much happier with a 2% maximum and may have the room to accomplish that depending on a number of other preferences.

When building, I started from each end, ensuring first that the ending clearance at the crossover was correct.  I used a piece of string to measure the inches involved in the total grade.  Then determined the appropriate vertical transition at each end, then the remaining rise (not counting the transitions) was determined by the remaining inches of path.  That set the main path grade (inches of rise over inches of non-transition path, times 100).  Then the percentage of remaining path at each main grade riser point was used with the main grade rise to determine the rise at each main grade riser.  If I wanted to add a riser at a place where there was no joist, I added a frame crossmember and calculated the riser height needed there on a the same percentage basis.  I then set those risers in place with a clamp, then one screw to attain the calculated height, and used a long level to ensure I was not off my much.   When happy, I added the second screw.

Paul

Modeling HO with a transition era UP bent

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Posted by cuyama on Sunday, July 21, 2013 11:00 AM

Just to reinforce a couple of things already mentioned. You will need transitions from level to grade, so allow for them in the overall length.of run.

I typically allow one car length of transition for each percent of grade, using the longest car or engine as the measuring stick. For an HO grade of 2.5%, this will be close to Alan's suggestion for your transitions.

As mentioned, curves add to the effective grade, so you may wish to allow for that effect. This means that you must either decrease the grade in curves in order to maintain 2.5% overall or set a lower nominal grade so that the curves at that nominal grade do not exceed 2.5% effective grade. The effect of this extra effective grade is increased when the full train is in the curve.

The very old rule-of-thumb for HO is to use 32/R, where "R" is the radius in inches. The resulting number is added to the nominal grade to calculate the effective grade. So for 24" radius curves, the value is 1.33%.. This makes a 2.5% grade effectively about 3.8% through that curve. 

If you decide to reduce the grade through the curve, again transition between the two different nominal grades.

Because of the significant effect of curve friction on effective grade and the different length of tracks over a particular stretch of benchwork (curving versus straight), simply rising a certain set amount over every 18" of benchwork won't result in a very accurate grade.

I haven't found a need to angle the tops of my risers for grades of 5% or less, but it certainly does no harm

Best of luck.

Byron

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Posted by cacole on Sunday, July 21, 2013 10:44 AM

Don't forget to allow for transitions at the top and bottom of the rise.

Suddenly going from a level surface to an incline without a gradual transition can cause all manner of problems, especially on a grade a steep as 2.5 percent.

The transitions should be at least 10 inches to one foot long for that amount of incline at both ends.

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Posted by lifeontheranch on Sunday, July 21, 2013 9:43 AM

My method for calculating riser height on cookie cutter sub-roadbed that includes curved sections:

1. Lay a length of mason's string down the centerline, form it by hand to curves as best as possible, use tape to secure.

2. Leave 12" at both ends for vertical easement.

3. Mark with a Sharpie on the mason's string where it crosses benchwork edge that riser will be on.

4. Straighten out the string. Measure its total length (first mark to last mark). Use the rise over run formula stated in previous reply to calculate rise for the entire length of the string.

5. Tape the string onto a flat surface (workbench) with one end of the string 1/8" from the edge of the surface and the other end of the string at the calculated rise distance from the edge of the surface minus 1/8". The 1/8" deviation is to account for the vertical easement rise.

6. At any of the marked points on the string place a t-square against the workbench edge. Measure the distance to the string mark. That is the exact riser height for that mark.

7. If your risers attach to the side of the benchwork member then add the amount of overlap distance desired to the riser height measurement. Place a pencil mark across the riser at the overlap distance to use as an alignment when fastening to benchwork.

8. Cut the riser at the grade angle with the shorter riser height side of the cut being the measured height.

There you go. Perfect height risers at the correct contact angle for the full length of the run. 

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Posted by yankee flyer on Sunday, July 21, 2013 8:20 AM

Hi    Smile

Sounds like you have a plan.  Are the brackets mounted on the wall studs?  It struck me as strange, I  have never ran across wall studs that are 18" on center, always 16" on center.
The string or chalk line method will give you a nice grade line to work off of.

Good luck and enjoy.

Lee

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Posted by bogp40 on Sunday, July 21, 2013 8:07 AM

The rise per 18" will work OK on the straight sections where you are starting exactly @ a riser, however, you need to take into account the vertical easements/ transitions at top/ bottom of grade as well as any changes in the joist/ riser spacing as you run into a turn.  The 1/2" or closer to 7/16" rise in every 18" has already been figures. A block placed on a 2' level would help you in laying the grade. 4' would be approx 1 3/16", for the 2 ft level a block of 9/16 to just under 5/8".  Tape the block to the level and use it to figure the grade.  The 2 ft will be close enough in placing on the turns to figure the grade. You still can double check by measuring the 100" and ck to see if you rose the 2 1/2".

Modeling B&O- Chessie  Bob K.  www.ssmrc.org

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Posted by gregc on Sunday, July 21, 2013 7:04 AM

how are you accounting for the curves?  there will be more friction on a curve.   so more force is required to pull a train up  the same grade (e.g. 2%) around a curve than on if the track is straight.   you may want to have a smaller grade on the curve.   I couldn't tell you how much less.

not sure why you mention the 18".   Assuming this is the board spacing supporting your base, you'll need to determine the height at each board, for the desired grade, depending on the length of track between each board.   Obviously the track length will be greater if it is at an angle or curved.

greg - Philadelphia & Reading / Reading

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Posted by mobilman44 on Sunday, July 21, 2013 6:29 AM

Richhotrain is right on..........

To add to his explanation, note that 100 inches equals 8 1/2 feet.  So if you lay out a line along that distance on your rise (a cord will work great), then measure the difference of the height from the beginning to end of the cord.  If the difference is 2 1/2 inches, you have a 2.5 percent grade.

Of course you could measure a line of have that length ( 50 inches -4 1/4 feet) and halving the difference in height would give you the percentage grade.  And so on...........

In my last two layouts, I used this method along with a level to maintain a solid 2 percent grade over about 35 feet of track, and it worked just fine.

ENJOY  !

 

Mobilman44

 

Living in southeast Texas, formerly modeling the "postwar" Santa Fe and Illinois Central 

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Posted by richhotrain on Sunday, July 21, 2013 5:51 AM

The formula is:

grade = rise / run x 100

For example, a rise of 0.5" over a 20" run will give you a grade of 2.5% (.5/20=.025x100=2.5).

In your situation, a rise of .0.45" over an 18" run will give you a grade of 2.5%.

So, with every 18" riser, you will need to increase the height of the riser by 0.45", or something just under 1/2 inch.

With three walls each measuring 13.5', you could have 27 risers rising to a height of 12.15".

You could space 24 risers 20" apart and then each riser would increase in height by 0.5", probably an easier measurement to work with.

Rich

Alton Junction

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Math Question about grades
Posted by Santa Fe all the way! on Sunday, July 21, 2013 2:44 AM
OK, I need help figuring grades so I don't exceed, 2.5%. I'm buildind around the walls, ho, cookie cutter style. Say I have a U shaped benchwork around three walls. I want to start at 50" off the floor at one end and gradually climb at 2.5% .The walls are all 13.5' and brackets are on 18" centers. How do you figure riser height?
Come on CMW, make a '41-'46 Chevy school bus!

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