Stack exhaust design revisited: the 1 in 6 taper myth?

[DaveD]

I’m designing the exhaust nozzle and stack for my 1.6” B&O P7 and have spent several hours researching the design on this forum and other places. I’ve come up with more questions than answers, so I thought I would open up this subject to more discussion.

First, Trainman4602 has published some very informative videos on the subjects of blast nozzle and stack sizing and placement (thank you, Dave!). He uses 1 in 6 and 1 in 3 cones to help design nozzle placement and stack placement, taper, and length. Then Jim Leggett added an article that he published on exhaust cone size to the discussion of Dave’s last video, using what he reported to be 1 in 3 and 1 and 6 ratios. Some additional references to the use of these tapers were also added to this thread, and I used them to look even further into this subject. A 1 in 6 cone (stack-top diameter) has an included angle of about 9.5 degrees and a 1 in 3 cone (stack-bottom placement) has an included angle of about 19 degrees. I will use the descriptions above and these angles instead of the taper values, since it is easier for me to measure and compare. BTW, I don’t have a problem with the 1/7 main bore nozzle diameter, so I plan to use it, approximately .411 for my loco, rounded up to .425 or so.

While it is apparent that people who have sized their steam exhaust systems according to these design parameters ended up with some good steaming locomotives, I haven’t personally seen that this method was used for a number of locomotives that steam very well. Some examples:
1. The prototype P7, for which I have original blueprints. With a 6” exhaust nozzle the stack-top taper is 12.2 degrees and the stack-bottom taper is 25.6 degrees. You can bet that the prototype steamed well.
2. Coventry’s blueprints of a smaller scale P7 (and K4) use the same geometry. He had a very successful run of model locomotives.
3. The late Bruce Hamilton’s two P7s, one fired on coal and the other originally fired on oil, now converted to coal, which I am building the third of, use the prototype geometry scaled to 1.6, according to photos of the stack and inside smokebox and some rough drawings I have (I can’t tell what size nozzle he used or the exact geometry, but the stack top ID is the scaled down prototype, not the smaller ID with a thicker wall that Dave proposes). His P7s steam very well. I hope to get up to Baltimore in the near future to examine one in detail, but in the meantime…
4. Nelson’s So You Want To Build A Live Steam Locomotive.
5. My Live Steam magazines going back to 1970, and many other places.

Then I took a good look at Jim Leggett’s Steam Exhaust Cone jpg. His cones are described as 1 in 6 with a 12 degree included angle and a 1 in 3 with a 20 degree angle. They are none of the above! His “1 in 6” actually has an included angle of 19 degrees and his “1 in 3” is 37 degrees, so his is about twice the taper described. Unless the jpeg has changed aspect ratio somewhere between his creating it and my measuring it, this is way off. Plus the angles stated for the tapers are wrong anyway.

Well, then. On what authority are these tapers used? Just what is the origin of this "best practice"? Is it simply a myth? Why an even 6 to 1 and an even 3 to 1--why these rather arbitrary integer ratios? Why not a sweet spot of, for example, 6.3 to one and 2.7 to one? Or how about 12.2 degrees for stack top and 25.6 degrees for stack bottom like the P7 prototype? Better yet, how about a range of angles within which the system would work well with a “best angle” in the middle?

I’m leaning towards designing mine by scaling the prototype. The geometry of my P7 would change based on a smaller nozzle than the scaled prototype, with most likely the only change would be that the nozzle moves down an inch or so to accommodate the smaller diameter adjusting to the cone angle, not the other way around.

Comments, please!

[steamin10]

Best told, if I can frame it for you, all these numbers and solutions are a mechanical answer to a complex mathematical problem that has no definite answer. The math constantly changes, because the conditions change.

The problem worked out by the mechanics and engineers is how to move the most air (exhaust, steam, and smoke, which is actually diferent) from a confined space, using a two stage venturi system. The stack itself is generally tapered to make rising hot exhaust create more than just straight line velocity. And add to that a venturi blowing into the stack base, from the exhaust nozzle, up the stack evacuating the smokebox area. All the variables involved, from grate coverage, to the fire rate required,(makup air), smoke box area and the fact that exhaust pulses from zero to many feet per second, all have to be balanced out. I defy anyone to write such an equation, that will make sense in full form, let alone a model with it decreased physics. So, the answer that I give ou is the historic one of averages and fine tweeking by those people who lived in the world of steam, and had a sense of feel to get the best performanc over time, with or without the confines of engeneered numbers. Making it work well was paramount, and these ratios have the best ratios for success under changing conditions.

In modeling, dont sweat on the butter. A model is a caricature of a real item, or idea, and to create it, compomises are to be made. Materials, actions, and physics will all give you headaches. Just do what is practical, and logical to make it work. ( My philosophy here). If you are building for operation, rather than static dispay, you can focus on rivet counting to finish the 'WOW' factor, but it is window dressing, and not required except to complete the image.

OK, enough. they are right in copying what was. It may not be scientifically correct in all aspects.

Its not rocket science, I'm just a space cadet!

[Bill Shields]

Steam, as it expands through an orifice, always expands at a fixed angle.

This is mathematical fact and it doesn't 'always change', and should be kept in mind for sizing / placing the blast pipe.

Blast pipe sizing is a function of cylinder bore, but again, is a range and if you know what you are doing, you can violate the 'rules' - especially at the speeds we run (it's another matter at 90 MPH on a full-size Niagara).

At really high flows, the need to reduce turbulence INSIDE the stack by having the stack taper with the steam expansion angle is quite important. At the speeds we run, it is less important, but should still be considered.

Contact point of the unrestricted expansion cone should always be just inside the top of the stack, otherwise you run the risk (note risk) of getting some strange vortex shedding inside the stack that can create turbulence that interferes with the flow. It is even possible to have the resulting turbulence suck air IN to the stack from the outside under certain conditions, which is really not good.

Draughting a locomotive with a variable restriction at the feed end (depth of coal bed), can be a bit more complex than doing so with propane or diesel feed, but you can quickly get in a 'range' that will work.

If someone has a 'technique' that works for them and they are happy with it, then log their experiences / recommendations as a valid data point - but do not assume that 'their way' is the only way to do it.

No matter what, be prepared to fiddle a bit, since, as mentioned, anything the alters (restricts) the air coming IN to the system has an effect on getting everything OUT at the other end.

Something seemingly as silly as moving the arch 1/8" closer to the top of the crown sheet can have a significant effect on how you want to draught the engine.

Keep a log of what you do and how it worked, otherwise you will be running around in circles, chasing your tail before it is over with.

[LVRR2095]

So far as I can determine, the 1 in 6 and 1 in 3 cones were first suggested by Henry Greenly back in the late 1890's. I don't believe they were ever meant to be the ultimate in efficiency, but a general rule that were you to use them (in a model) you would get a reasonably good drafting boiler. Even the best of model builders that I know have made their exhaust nozzles interchangable, so they could try different orifice sizes to see which would work best. At one time I had a set of Pennyslvania RR blueprints for the stack on the K-4. There were several sheets of drawings and tables showing how to generate the most incredibly complex set of curves I have ever seen. Anybody that tried to duplicate that stack as an exact scale model would undoubtedly end up on the cracker farm.
Keith

[Fred_V]

another rule of thumb is the 1/3 rule. divide the smokebox in thirds from top to bottom. the stack should come down 1/3 and the blast nozzle should come up by 1/3. i use this as a starting point and raise or lower each if the boiler doesn't steam well.
fred v

[tburzio]

I found a neat book on Google Books that finally answered a very basic question for me. Why a petticoat? I don't have one on my Mogul, and it steams very nicely. The answer was SO simple! The length of the stack is fixed. The stack maximum height is set by clearance diagrams (bridge and tunnel height). As the boilers got bigger, they started to gobble up the stack. The part of the stack inside the boiler is called a "petticoat".

http://www.catskillarchive.com/rrextra/chapt23.Html

As you can see from these diagrams, the steam must expand to be exactly as wide as the base of the chimney as it enters. Get the stack too close to the exhaust nozzle, and you have to flair out the end of the chimney extension. Since it usually it looks like a popular woman's undergarment of the day, the railroaders called it a petticoat.


So, we know the angle the steam expands, and you can work backward and get the gap between the exhaust nozzle and the petticoat bottom. The shape of the petticoat is , well, a petticoat.

[tsph6500]

Then I took a good look at Jim Leggett’s Steam Exhaust Cone jpg. His cones are described as 1 in 6 with a 12 degree included angle and a 1 in 3 with a 20 degree angle. They are none of the above! His “1 in 6” actually has an included angle of 19 degrees and his “1 in 3” is 37 degrees, so his is about twice the taper described. Unless the jpeg has changed aspect ratio somewhere between his creating it and my measuring it, this is way off. Plus the angles stated for the tapers are wrong anyway.

Comments, please!

I wouldn't know an included angle from an ingrown toenail?

The cones in my diagram were very simply drawn in Adobe Illustrator. Three units up for one unit wide... six units up for one unit wide... cut it out and stick it down the stack. Say awwwwww!

[Trainman4602]

MYTH!
I don’t think so

I have used the 1 in 6 and 1 in 3 formula on all the locomotives that I have built.

Each one preformed tremendously. They produced more steam then needed. You will never starve for steam with any of my locomotives. Anyone who has run or seen them run could testify to that.

With the 1361 I can be working up grade with a full train say ten passengers, 120 pounds of steam and a steady gauge, both injectors on and safeties popping as well.


Why re invent the wheel. If you want to then go ahead and do so. GOOD LUCK.

[ALCOSTEAM]

DaveD, some good reading to be had in the C&O SuperPower book. In the 1930's the C&O and their AMC did extensive testing on a list of things to bring efficiency up on their locomotives. Like you they felt the "standard" accepted sizing of things needed updated, 50 year old engineering on a 1930's built engine wasn't getting the C&O the performance they were looking for. The C&O Superpower Book covers some of their findings but it would sure be nice to find the full reports, I would like to read them.

On our 12" guage mogal I applied their findings to the "accepted" standard sizings of the blast nozzle and stack. To say it steams well is an understatement considering we have little more firebox than many of the larger 1 1/2 engines.

tim

[Fender]

One factor related to the stack/petticoat/nozzle design which I haven't seen discussed much, is the ability of the loco to lift the smoke/cinders as high as possible, preferably above your head when running. (Yeah, I know, dream on ) However, I've seen engines that did this better than others, and not just from a tall stack. It helps to have a heavy train behind the tender and some back pressure from the cylinders. What else?

[Fred_V]

blast nozzle size makes a big difference. i found 2 rules-of-thumb for that.
1/7 x cyl bore
.004 x grate area

a smaller size will have greater velocity. at night i've seen sparks shoot 30 feet high.

[DaveD]

Thanks to all for the interesting comments.

Steam, as it expands through an orifice, always expands at a fixed angle.

This is mathematical fact and it doesn't 'always change', and should be kept in mind for sizing / placing the blast pipe.

Bill, please “expand” on this expansion angle. Just what is this “fixed” angle? You also state:

Contact point of the unrestricted expansion cone should always be just inside the top of the stack, otherwise you run the risk (note risk) of getting some strange vortex shedding inside the stack that can create turbulence that interferes with the flow.

This, apparently, is what the stack-top-diameter cone should set the geometry for. But that doesn’t explain the use of the stack-bottom-placement cone that is used to fix the bottom location of the stack, or in other words, the total length of the stack. Now, assuming that there is a taper to the inside of the stack, which we haven’t even discussed, the location of the bottom of the stack as set by the stack-bottom-placement cone would necessarily change as this taper changes. Should this also be a “standard” taper? If so, this standard taper cannot be the stack-top-diameter taper, as the entrance to the stack at the top of the petticoat would be too small and restrictive. Or would it? The plot thickens…

Why re invent the wheel. If you want to then go ahead and do so. GOOD LUCK.

Dave, I have a high regard for your work, and I would rather not re-invent the wheel. My problem is that I have some castings, and I would seriously rather not throw them out and fabricate replacements. The stack diameter is limited to a certain minimum size because of a fairly large bottom diameter set by the petticoat casting. To make the 1 in 6 and 1 and 3 tapers work, I would have to lower the blast nozzle so much that I would have to throw away the blast nozzle base and fabricate one of those. Also, the nozzle would be so low in the smokebox that I would end up with a self-cleaning smokebox, with me eating all the soot and ash when I am driving the loco. Finally, I would have such a small ID in the top of the stack that it would be noticeable.

I wouldn't know an included angle from an ingrown toenail?

Jim, I meant to point out that whatever the angle of your templates, your experience reworking your front end to the geometry of the cones made from the templates was positive. Or were those exact cones what you used? If so, this simply says that the 1 in 6 and 1 in 3 rule is very flexible.

. . . all these numbers and solutions are a mechanical answer to a complex mathematical problem that has no definite answer. The math constantly changes, because the conditions change.

Perhaps Big Dave’s comment says it best. Many of the parameters that are considered when designing this exhaust geometry change constantly (except, as Bill pointed out, the steam expansion angle?), so the optimum geometry also changes constantly. The best we can hope for is a design compromise that works very well for most conditions and acceptably well for all conditions.

The castings I have imposed a design geometry that made for two locomotives that steam very well. I trust that this geometry will also work for mine. While I designed my own boiler, the grate area is identical to the other two and I believe mine will perform about the same as those. My wife and I are planning a road trip to New England later this month. I believe the best thing will be to make a stop in Baltimore on the way up and physically examine one of these locomotives so I can duplicate the design.