Very nice!
Fantastic, Dave!
While talking with another 315 guy, the question of steam usage came up, and we didn’t have a real best guess clue as to how much steam we use when were runnings. So I thought that I’d try to figure it out.
First off there is a gazillion variables that can and do get introduced into any steam locomotive formula. And since I am not an engineer (PE, ME, ) trained person, nor have I studied up on Thermal Dynamics and that kind of stuff, I will stick to “ Close enough, Good Enough for the girls I run with” thinking. And maybe along the line learn something also.
So… Anyone with more knowledge about this stuff then me, feel free to chime in, and correct me on things or assumptions that I get wrong.
Basic Specs on D&RGW 315:
Cylinders: 16”
Stroke: 20”
Drivers: 38”
Boiler Press: 160 psi.
Assumptions: Boiler pressure stays constant ( we know this is not true ).
Throttle position stays constant ( we know this as could be true ).
Slide valve stays constant at full open setting ( we hold this as true ).
On to the Math: Volume of a cylinder = (Pi * ( r * r ) ) * L
( 3.1415 X ( 8 X 8)) X 20
(3.1415 X 64 ) X 20
201.05 X 20 = 4,021 Cubic Inches per stroke per cylinder.
1,728 cu in per cu ft. = 4,021 / 1728
Cubic Ft per stroke = 2.33 Per
Revolution of the driver = 2 cyl. X 2 strokes = 4 strokes
4 strokes X 2.33 cu ft = 9.32 cu ft
TAA DAHH ! About 9.32 Cubic Feet of steam every time the driver goes around.
WOW. Thats a lot of steam!
Visualize a box lying on the floor 1 ft wide by 1 ft tall by 9 1/3 ft long.
That much physical steam used every time the driver goes around. No wonder you have to shovel so much coal!
That is why the slide valve is not left open after the train is rolling . . . if it was left open you’d run out of steam in a HURRY. . . . . so the engineer “hooks up” by pulling back on the Johnson Bar once he has the train rolling.
ps. Dave . . what are the plans / if any . . . for 315 this year ?
Yea, the Johnson bar changed the steam cut off so not that much steam is used. Steam at boiler pressure expands in the cylinders, so even if you have the same volume coming out of the cylinders, its at a lower pressure when the cutoff is earlier in the stroke.
But your calculations are very interesting. Now taking the circumference of the drive wheel, and figuring out how many rotations per mile (assuming no slip), times 9.32 cubic feet of steam, is…it boggles my mind.
Don’t forget pressure. A small amount of steam at 160 psi can expand to fill a cavernous space.
Well. Lets see if we can get a little deeper into this.
38" driver diameter Pi X Diam = circumference
3.1415 X 38" = 119.38" circumference
12" to the Ft. 119.38" / 12" = Ft 9.95 per revolution
5280 Ft in a mile 5280’ / 9.95’ = 530.65 rev per mile
@ full throttle 9.32 Cu Ft per rev. X 530.65 = 4,945.65 CuFt mile
Steam per Ft 5280’ / 4945.65 Cu Ft = 1.06 Cu Ft per Ft
1.06 Cu Ft of steam per foot of motion. And of course thats at full Johnson Bar setting, which is rarely used except at starting a heavy train. The train engineers that I have talked to, have said that on 315 they have never had to use the bar in the max position. When asked if the bar at about half way, would that be 50% steam, they had no idea. They drive by the “feel” of the engine, not by a given “notch” setting.
I’ll do a little more research into the setting percentage for cut off, and see what comes up. Unless someone here can provide the numbers. This is just one of the gazillion variables.
Close enough numbers say about a 1:1 ratio of steam to foot of travel ( at full Johnson Bar setting).
How much steam does a cup of water produce?
Vol@pressure might be a measurement…
Calories of heat required to make said steam?
Well, let’s see…
One cup is 250 ml, give or take a dram or two. One calorie of heat is required to raise one ml, one degree C. Water boils at 100°C. Therefore, 100°C X 250 ml = 25000 calories of heat to boil a cup of water. Now, what do you want to do with the data?
Steam is a variable best measured in pressure… therefore water is the only constant in the equation as postulated previously. Looking for something that could be measured … with meaning.
Almost a good job, you failed to mention the volume of steam produced… I suppose at zero pressure for a constant.
John
I just did what you asked for, John. What you do with it is up to you. “Almost a good job,” my foot.
How much steam does a cup of water…
Enough of my side track.
Dave, et al,
To further the confusion over how much steam is used, to get back to a volume we all can relate to here is a link to a page http://www.gutenberg.org/files/22657/22657-h/chapters/steam.html with all nature of steam explained (some over my head). Go to Table 23 (about half way down the page) and it will tell how may cubic feet of steam at a given pressure. The volume of steam varies asa function of the pressure of the steam. Now to bring it back to the understandable, one gallon of water is 7.48 pounds. So, assuming 160 PSIG (I seem to remember Dave giving that as operating pressure), that will be 2.834 cubic feet of steam per pound of water, and 2.834 x 7.48 pounds per gallon yields 21.2 (rounded) cubic feet or steam at 160 PSIG.
If I am off on the pressure, the table is quite inclusive, and if the operating pressure is in between listed values, extrapolation is always an option.
WHEW! (http://www.largescalecentral.com/externals/tinymce/plugins/emoticons/img/smiley-embarassed.gif)
Mr. Narrow et.al.
As of now, There is no scheduled operations for D&RGW 315 this year.
BUT: ( there is always a but) there is tentatively a week long maintenance and work secession scheduled for mid June.
I have heard rumor that the D&S has made inquires about running for “Railfest 2015”. I am not in on the board meetings for this kind of discussions nor do they consult with me over this kind of thing. But now that I’m un-employed, I should have much more time for playing with trains.
Railfest 2015
http://www.durangotrain.com/node/892#.VRgNsmNFCM8
I wish that I could get there. The photos in “True West” magazine of the past railfests have been great. In order to “play wild west” for 8 months each year I do have to do a very easy job for 4 months of the year. But that four months is from early July to the end of Oct. and is located in Stockton Ca. . . . so getting to “narrow gauge country” in August is not possible. DAMN ! 
Well… Sad News… The wife’s painting of 315 at Chama did not get excepted into the show (http://www.largescalecentral.com/externals/tinymce/plugins/emoticons/img/smiley-frown.gif). They give no reasons why or why not. But we have learned that the judge was/is a “Modernist” style painter. What ever that style is. Apparently she doesn’t like Marilyn’s style or Trains or both. Oh, Darn, I guess that I get to keep it for a little while longer. BTW, It is available for purchase Both the orig., or a canvas Giclee print at any size.
Edit: She is also a Art professor/department chair at UNM in Albuquerque. Enough said!!
Not to worry Dave. She is in good company.
Monet was refused a “hanging” as well for a few years!
(I have often wondered whether some of these judges/critics can paint anyway!!)
My wife an artist is of the same opinion.(http://www.largescalecentral.com/externals/tinymce/plugins/emoticons/img/smiley-tongue-out.gif)
Well… the wife has asked be to work up a couple more pics of trains to paint, Haven’t found the right one to paint, But I did find one that I like a lot, and worked it up. Another night shot from a set up I did in 2013.
Of course its of D&RGW 315, Late night in Osier CO. On the C&T.
Enjoy.