Large Scale Central

Long Trestle Project

Track and Trestles
#41

Bob Hyman said:

David,

An incline of 45 degrees is not a 100% grade. Consider the following example:

With a 45 degree incline, the run is 1.414 units for every 1 unit of rise. Since grade is rise divided by run, the grade is 1 divided by 1.414, or 0.7071, or 70.7%.

Bob

Bob, my error was not in the calculation, it was in assuming a linear relationship between angle and grade. Rise over run, yes, but run is the horizontal distance traveled, not the slope length.

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Of course, with the low grades we deal with in our hobby, using slope length instead of run would only introduce a very small error in our calculations.

#42

David,

Thank you for pointing out my error. You are absolutely correct. Grade is rise over run, not rise over slope. The problem is in how I measure my grades. I run a tape along the track and use this measurement in my calculations. This number is the slope, not the run. That is why I used the inverse sine function rather than the inverse tangent. To be mathematically correct, I should have calculated the true run. In the example of 100 units of slope and 2.5 units of rise, the true run would be 99.9687 units. This results in an actual grade of 0.02500781 instead of 0.025. Staying mathematically correct, the angle of inclination would be the inverse tangent of 0.02500781 or 1.4325 degrees. Same answer, just a simpler way of getting there. As you say, the difference between slope and run is insignificant for the extremely small angles of inclination we deal with in railroading. Sorry for any confusion my error has caused.

Bob

#43

Without getting too far into the weeds, this seems to be the heart of the argument.

From the Wiki.

But in practice the usual way to calculate slope is to measure the distance along the slope and the vertical rise, and calculate the horizontal run from that. When the angle of inclination is small, using the slope length rather than the horizontal displacement (i.e., using the sine of the angle rather than the tangent) makes only an insignificant difference. Railway gradients are usually expressed in terms of the rise in relation to the distance along the track as a practical measure. In cases where the difference between sin and tan is significant, the tangent is used.

In the railroad world, where grades are rarely more than 2%, the difference between the run and the slope amount to a small amount that can be ignored in calculations. The difference between 1.1% and 1.101% means nothing to even a 4-4-0.

#44

Steve yes. I agree. But proper calculation is rise over run, not rise over slope, and using the proper calculation makes my statement of 100% grade equals a 45 degree angle correct. And that takes me back to my error in my first post on this subject, where I assumed, incorrectly, a linear relationship between % grade and angle above (or below) the plain. And that is what I was saying, Bob knows more about them triangular calculations then I do, because he came up with the right answer and I came up with a wrong one.

#45

And the price of perfection is insanity. Have you ever worked on a survey crew? If not, try it. You will begin to appreciate the phrase, “close enough for government work.” (http://largescalecentral.com/externals/tinymce/plugins/emoticons/img/smiley-laughing.gif)

#46

Steve, no I haven’t. But the company I work for does sell survey equipment, so, maybe, someday, I will talk to a surveyor. Till then I will just have to take your word for it.

#47

Steve Featherkile said:

And the price of perfection is insanity. Have you ever worked on a survey crew? If not, try it. You will begin to appreciate the phrase, “close enough for government work.” (http://largescalecentral.com/externals/tinymce/plugins/emoticons/img/smiley-laughing.gif)

Steve,

I DID work on a Department of Interior, Bureau of Reclamation survey crew, first summer after graduating from HS in 1961 (I was going to attend college that coming fall to become a Civil Engineer). Here I’m a "snotty-nosed 17 yr. old working with these “old” guys (maybe 30-35) and I’m trying to use the skills I was taught in HS! These guys are constantly calling out numbers and saying “Close enough for Government work!” :slight_smile: Your comment brought back some great memories of that time 55 years ago! Thanks.

#48

Brings to mind a few years ago at model railroad club trying to convince some members that a 2% grade and a 2 degree grade are not the same thing - “Hey, guys, has it ever occurred that there is a reason two different words, percent and degree, are used?”

A lot of them absolutely could not let go of the concept of degrees; I don’t know why.

And then there was “How do you do the math to figure percentage to cut the risers to make sure the roadbed is at the proper grade?” - Uhh, guys you don’t - 2 percent is a 2 rise in 100 run, which can also be 1 rise in 50 run, so take a board and put a 1 inch riser on it at 50 inches in from one end; when your level says it is level there’s your 2% grade. Mark your lumber against that.

I gave up, the fixed in place DCC HO layout is not my problem, I have 16 ft of the modular HO layout to deal with.

#49

Gary Armitstead said:

Steve Featherkile said:

And the price of perfection is insanity. Have you ever worked on a survey crew? If not, try it. You will begin to appreciate the phrase, “close enough for government work.” (http://largescalecentral.com/externals/tinymce/plugins/emoticons/img/smiley-laughing.gif)

Steve,

I DID work on a Department of Interior, Bureau of Reclamation survey crew, first summer after graduating from HS in 1961 (I was going to attend college that coming fall to become a Civil Engineer). Here I’m a "snotty-nosed 17 yr. old working with these “old” guys (maybe 30-35) and I’m trying to use the skills I was taught in HS! These guys are constantly calling out numbers and saying “Close enough for Government work!” :slight_smile: Your comment brought back some great memories of that time 55 years ago! Thanks.

Gary, the first time I heard that phrase was in the tower at an Air Force Base near Dallas, Tx. I was a 17 year old Cadet in the Civil Air Patrol, there to fly in the back seat of a T-33 for a week. It was about 0030, and a (something) was inbound, and asked for the barometer reading, so he could set his altimeter to the local conditions. The Airman (E-3) on duty in the tower by himself, couldn’t be bothered to get out of his chair to read the thing (aviation was comparatively primitive, back in 1964), so he said, “It was 29.93 about an hour ago.”. The pilot responded with, “Close enough to government work.” I had to pick my jaw up off the floor. I few of my ideals were dashed, that night.

#50

Yes, on another site we had a long discussion with an individual who also interchanged grade and angle. His track was at something like 3 degrees and his trains were struggling to climb the grade. He just didn’t get it that at 3 degrees he was at like a 6% grade or so. He actually seamed to get mad at those of us who had grades and could run trains on them since he could not, and in his mind his grade was about the same as mine.

And in our HO club we have one member who insists that a black wire and a red wire cannot be connected together. When hooking up his module I have to plug black into red because he wired his module backward. But he insists that I can not do that. Like the colour of the wire affects the electrons running through it or something.

#51

Meanwhile, back at the bridge, here’s an update with a couple of new photos. And I promise … no more math!

I added 6" x 10" girts between the two story bents. Each girt is 32 scale feet long and spans two panels (runs between three consecutive bents.) They are staggered so that all do not end at the same bent.

I also added fake “concrete” foundations to the bottom of each bent. These foundations are pieces of 3/4" x 1 1/2" (actual) PVC lumber that I spray painted with gray automotive primer. These PVC foundations will separate the timber bents from the real concrete footers and help keep the wood dry.

Here is a shot of segment #3, the highest part of the trestle, setting on the workbench at the actual 2 1/2% grade. You can see how the bents are perfectly vertical under the inclined deck.

There’s not much more left to do except pour the real concrete footers and set the segments in place. It’s supposed to get down to single digit temperatures tomorrow, so I’ll be waiting a while to do the concrete.

More to come as the weather permits,

Bob

#52

Really nice Bob, going to look great when it’s on your layout.

Chris

#53

Yup, Museum quality… Nice, Bob… (http://www.largescalecentral.com/externals/tinymce/plugins/emoticons/img/smiley-cool.gif)

#54

Nice work !

#55

i remember, what a pain it was to get the bents vertical under a grade.

very fine work.

#56

THAT is impressive!!

#57

I don’t know Bob a real rivet counter would have these

On these! Just saying!

Nice work!

#58

Sean,

Actually, the RGS used 9" or 10" nails about 3/8" in diameter, called “boat spikes”, to attach the diagonal braces to the bent posts. I have collected a few over the years from old trestles that were being demolished. I use 1/2" long 23 gauge pin nails which are a fairly close approximation. The only discrepancy is that they typically used three nails at each post, and I cheated and only use two in most cases.

Bob

#59

Bob Hyman said:

Sean,

Actually, the RGS used 9" or 10" nails about 3/8" in diameter, called “boat spikes”, to attach the diagonal braces to the bent posts. I have collected a few over the years from old trestles that were being demolished. I use 1/2" long 23 gauge pin nails which are a fairly close approximation. The only discrepancy is that they typically used three nails at each post, and I cheated and only use two in most cases.

Bob

Those would take a BFH to drive!

#60

Took advantage of a nice day and moved the five trestle segments out to the layout and clamped them in place. Here is the view looking downgrade:

Here it is looking upgrade:

Only a few bents are actually supported on bricks; most are just hanging. You can see where I removed a few inches of the soil to make room for the actual concrete footers. The white strips running along the top are 8 foot long PVC 1" x 2"s to hold the deck in alignment until the footers are poured. The missing bents are where the segments connect. These will be inserted later. Same for the missing girts.

Right now, I getting ready to head out to the store to get a few bags of concrete mix. Hopefully, tomorrow I’ll start pouring the footers. Can’t wait to run a train across this thing.

More to follow,

Bob