Run is defined as the horizontal distance (the X axis), not distance traveled.  So 100% grade == 45 degrees.

Furthermore, here is a grade to degrees calculator, which confirms it -https://www.calcunation.com/ca...rcent-conversion.php.

For our modeling purposes though it's close enough - a 100" run at 4% grade = 100.08" of track.

don

Jim,

I agree, bottom line, there is not much difference for shallow angles.

One last try though.  If you look at Rich's diagram which is similar to yours.  The two measurements are the length of the level and the height at the right end of the level.  The purpose of the level is to measure the horizontal distance.  There is no measurement along the slope in the diagram.

At the Cass Scenic Railroad, Shay 5 shoves hard on its train through a place colloquially named 'Sugar Grove', just below Whittaker Station.
From this area to the Whittaker Station sign the grade is 11%.
NO Cables, NO Cogs, just brute power from a Shay locomotive.

For me, part of what makes the Cass Scenic Railroad special, is the motive power really works and works hard, just like they were designed.
No 'trailer queens' or stuffed and mounted static museum pieces here...just coal smoke, soot and cinders

Most of the references I can find use the mathematical definition of slope.  A number of the definitions are ambiguous.  After further search I found an article that seems to indicate American railroad practice uses the length along the slope and British uses the mathematical slope.  I was not able to find an "official" definition in the U.S. context.

I added a comparison to my spreadsheet and found the two approaches yield the same result within 1% up to a 14% grade.  (Example: A mathematical grade of 14% corresponds to an along-the-slope grade of 13.86%.)  However, the grade calculated in Rich's diagram is the mathematical slope.

I do not see anything in the Mt. Washington description that would lock down which approach is used.

I guess everything in life is a can of worms.

A key fact that I din't see mentioned in the discussion about Lionel's 8 % (or whatever) grade.  That grade trestle was not intended for adhesion traction.  By that time, any Lionel loco used on the grade would have had Magnetraction.  In the real world, the only locomotives capable of pulling cars on an 8 % grade were geared locomotives - Shay, Heisler and Climax, all used mainly on logging railroads.  The WM did have a few in coal mine territory.

In the railroad industry, the word 'degree' was used for curves, never grades.

Grade is a method of representing slope.  I guess railroads calculate it differently than the rest of the civil engineering world?

Jim I'll agree with you if you can provide a reference showing that railroads use distance traveled vs horizontal distance for grade calculation.

GRJ I was wrong when I looked again last evening Imy grade is just over 16 feet not 8 feet my mistake glad you caught that. Thank You.

GUYS - All I can say is "Where's the Moderator when we need him?" Enough already. You're using up all my memory storage in my iPad! 😉

Seriously though, can we just get back to running and enjoying our trains rather than arguing about 'incline' during these COVID-19 uncertain times?

W

PH1975 posted:

GUYS - All I can say is "Where's the Moderator when we need him?" Enough already. You're using up all my memory storage in my iPad! 😉

Seriously though, can we just get back to running and enjoying our trains rather than arguing about 'incline' during these COVID-19 uncertain times?

No worries, we need something to do since we're locked inside our houses!

PH1975 posted:

GUYS - All I can say is "Where's the Moderator when we need him?" Enough already. You're using up all my memory storage in my iPad! 😉

Seriously though, can we just get back to running and enjoying our trains rather than arguing about 'incline' during these COVID-19 uncertain times?

Why do you need the moderator to make this decision for you (us)?

You have the power to disengage right here by un-checking, "Following This Topic".

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In regard to

"Jim I'll agree with you if you can provide a reference showing that railroads use distance traveled vs horizontal distance for grade calculation. "

I'd be a bit surprised if railroads didn't use horizontal distance.  There are some track charts on line that I believe show horizontal distance, elevation and grade on the same page.  I'll do some calculations and post them later.

http://www.zekedev.com/sites/boston_line/

I'm inclined to keep reading this discussion.  I'd give this topic a high grade for being interesting.  I wouldn't come at this with a "shut this thread down" angle.  If we do that, we are on a slippery slope of moderator intervention.   I think it's a sine that we should continue this discussion since we've already traveled such a long distance.

I just don't want to see this thread go downhill too fast.  I'm 8 percent sure that we can continue to have a decent discussion without anyone going off on a tangent. Sorry if this gets a rise out of any of y'all.  I gotta run.

It's a respectful discussion, not an argument.

It occurred to me last night I had recently bought a book on railroad engineering.  It is Railroad Curves and Earthwork, C. Frank Allen, S. B., member of American Society of Civil Engineers, professor of Railroad Engineering in the Massachusetts Institute of Technology.  It is a textbook first published in 1889.  I have the seventh edition from 1931.

There is an interesting section on grades.  Unfortunately it doesn't directly answer the question at hand.  But it describes the process of determining a route to achieve a specified maximum grade by a survey team.  I expect the answer is in the surveying speak and it follows established surveying practice for civil engineering.

Chapters go into great detail on curves, easement curves, turnouts, cut and fill planning.  It is 290 pages about half of it is tables.

It defines 13 members of the survey team.  One is the Axeman responsible for clearing brush on the line being surveyed.

My college roommate was in civil engineering, I remember when he had his surveying course.  As an EE, I was into other things.  But I remember when he came back from a class one day and told me how you had to include graft and corruption in the cost estimate for a project.

I may try to scan some pages but it is hard bound and may be tricky.

I found a similar book on railway engineering from 1928.  I'll post separately a scan of the title page and of a text page.  The forum is giving me errors when I try to upload the images as attachments.

This book isn't written by an MIT professor, but as an alumnus myself, I know that MIT isn't the best place to learn practical civil engineering.  It describes the same survey team as Cam's book along with tools needed by the party and the duties of each member.

I looked into the question of horizontal vs. actual length for grade calculation, thinking it might be easier to calculate the track length.  We're looking here at right triangles with a base of 100 and height being the % grade.  Here are the nubers for the hypotenuse of the triangle for various grades.

 Height 0 0.5 1 1.5 2 2.5 3 Length 100 100.001 100.005 100.011 100.02 100.031 100.045

Note that for a 2% grade, the difference is only a quarter inch.  That's one foot in a mile, which is insignificant for railway location.

You might think it difficult to put enough tension on a 100 foot tape to hold it exactly horizontal.  There is about half a page in the book about using "broken chains" in such situations - see the attached image.

The reason the word "chain" is used is that in the time before invention of the tape measure, surveying was done with 100 foot chains.

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I have always had a lot of respect for surveyors all over the world.  If you think about the exacting detailed work they do in rough terrain it is amazing.  I wonder what rail lines we all know were surveyed by students that used these textbooks in 1889, 1928, 1931...

It has always amazed me to see how a simple question, which can be answered with an equally simple answer, gets over-complicated with a bunch of irrelevant nonsense.

This thread is a poster child for this. Do you really need to know your percentage of grade to 3 decimal points? Good grief. Get a 2-foot level, measure and you’re done. It’s not rocket science.

Rich, it's what happens when you're told to stay at home and get stir crazy!

as more completely irrelevant information,  a chain length is not 100 feet as stated above

A chain (ch) is a unit of length. It measures 66 feet, or 22 yards, or 100 links,[1] or 4 rods (20.1168 m). There are 10 chains in a furlong, and 80 chains in one statute mile.

Now we can also calculate Monte Python's speed of " furlongs per fortnight squared "

Forget the math and test what you run.  That tells you what you can or can't get away with; for sure

Grades are a lot of "throttle work" to run in conventional once the intrigue of the grade challenges fades.  I kinda quickly ended up with 4 blocks on a Z, one throttle per wall to run one line "no handed" around a 12x15. (two 15' walls hold the 7" rise and downhill (1.5% grade difference off ceiling between these east/west walls), short wall tracks hold mostly level track, but a ¼" rise on each end too; the 1st transitions)

Rises in curves don't play well with unsprung axles ; Tri-podding happens. So in a curve go flat or very lightly graded < ⅛" or super elevate (even more transition math; oh  boy

Think about "old rollercoaster rails"(before tube type), note you got positioned for a curve before it happened. All to keep the car(s) flat and stable, always 4 wheels on track. Bending rail up/dwn/left/right evenly is easy. Use super elevation if you must rise more than 1/8" in a curve. (Eyeballing it in would be better than nothing )

Rich Melvin posted:

It has always amazed me to see how a simple question, which can be answered with an equally simple answer, gets over-complicated with a bunch of irrelevant nonsense.

This thread is a poster child for this. Do you really need to know your percentage of grade to 3 decimal points? Good grief. Get a 2-foot level, measure and you’re done. It’s not rocket science.

I think Rich has missed the point of what I said.  My purpose in showing the table was to illustrate that it doesn't matter.  Nothing to do with whether you need to know it.  Some of are interested in the details.  In real world track work, a missed detail can kill people.

My incline goes from 0" to 7" in 118".......some times it needs a little help...But it works.That's all the room I had...I constructed the incline with Precision Board, carved and painted the masonry with acrylic and stone finish spray.

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Does anyone use grades for scenic purposes only?  It seems the usual context is to go to another level and cross over or under other track.  What about modelling a hilly or mountainous area that forces the (model) railroad to use a grade?

Many years ago (1960s), Linn Westcott had a article in MR about making the scenery first and then adding the track with cuts and fills like the prototype.  Pretty hardcore I admit.

gene maag posted:

My incline goes from 0" to 7" in 118".......some times it needs a little help...But it works.That's all the room I had...I constructed the incline with Precision Board, carved and painted the masonry with acrylic and stone finish spray.

Do you use Magnetraction on the grades ?  Looks as if you redecorated a couple of 259's, I doubt Magnetraction.  Can they make the grade ?

I offer this as a practical example of what happens when you violate the incline rules.

I had an incline on an old layout and man it was rough like 7-8% grade maybe more if I understand the term. Like Gene said that was all the space I had.

Funny thing was Lionel Alcos postwar and Lionel GG1 ran that incline fine. Alcos had to be the 2 motor type. Others not so much. It was o27 with Lionel trestle sets. Was like a roller coaster but fun. I had forgotten how much fun.

Pretty thrilling on the declines also.

The engines going up or down is on thing, especially on straight track.  Add curves into the formula and it gets trickier.

You also need to consider how many cars you are going to pull & their weight. If you do it right no problem, done wrong and the consist derails like a jack knife, believe me I know.

The best I ever did was the Tehachapi  over/ under 3% over100" radius 40' long , 14" tall at the bridge, 1 engine pulling over 30 boxcars, nice slow and steady.

Heaviest cars up by engine lighter cars at rear.  Be careful of a to heavy caboose behind lightweight cars.

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mlaughlinnyc posted:
gene maag posted:

My incline goes from 0" to 7" in 118".......some times it needs a little help...But it works.That's all the room I had...I constructed the incline with Precision Board, carved and painted the masonry with acrylic and stone finish spray.

Do you use Magnetraction on the grades ?  Looks as if you redecorated a couple of 259's, I doubt Magnetraction.  Can they make the grade ?

Some of my trains have Magnatraction like my GG1 but most of my trains make it up the incline depending on the amount of cars they are pulling. The 259's sometimes need a head start and some sand!

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Assuming that same color car behind the tender is extra sand, is there a pipe from it to the engine ?

I must say this is a very entertaining thread, although I almost quit it after John Ochab's post ( I won't quote it here).  After that I had to get a drink.

So here's another can of worms for you guys to play with- vertical easements. I haven't heard them mentioned, but they are kind of necessary on the steep toy train grades we are talking about. They would make all the difference in smooth operation. In other words the grades aren't constant.

mlaughlinnyc posted:

Assuming that same color car behind the tender is extra sand, is there a pipe from it to the engine ?

No... that is a Hood's milk car. But it's an interesting idea, I'll work on that for my next restoration!!

Jeff_the_Coaster_Guy posted:

I'm inclined to keep reading this discussion.  I'd give this topic a high grade for being interesting.  I wouldn't come at this with a "shut this thread down" angle.  If we do that, we are on a slippery slope of moderator intervention.   I think it's a sine that we should continue this discussion since we've already traveled such a long distance.

I just don't want to see this thread go downhill too fast.  I'm 8 percent sure that we can continue to have a decent discussion without anyone going off on a tangent. Sorry if this gets a rise out of any of y'all.  I gotta run.

I got a rise out of that!! LOL!

For what it’s worth, I know from experience, you DON’T want a 7% grade!

Say what you will, this thread has been entertaining. And I even learned a few things. Thank you all.