Howard –
Intriguing exercise in acoustics, but I am not sure about your sound-speed with respect to temperature. The speed increases with density, so would it not fall in gases that are both very hot, and then slightly rarified as they are drawn through the tubes into the roomy smoke-box?
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Stephen –
Thank for those formulae! yes, I will take up your kind offer, please!
Equations based on the boiler's dimensions rather than cylinder are likely to be a lot more realistic on my wagon, with its rather low-pressure compound engine and long exhaust pipe.
The problem I might find is trying to apply these to a wide stovepipe nearly 3" diameter and parallel for all of its nearly 21" height. matching the manufacturer's advertising photographs, which are all that survive of the original vehicles. Maybe those designers did not trouble themselves too much with such niceties as proper draughting!
The 1:3 cone is easy enough but the 1:6 cone, which the diagrams all show touches the blast-nozzle rim, might put the blast-nozzle far too low. These geometries seem contradictory unless applied to the very short tube that is a locomotive's chimney, or to determining the chimney's total height and outlet diameter.
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Some quick sums now, from your formulae…
Grate area: 19 sq ins. (Approx. 5" dia grate – it might be 4.25 but I forget if 5" is the cylindrical firebox's internal or external size.
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Blast nozzle: 0.095 ins. diameter. Eh? Never! Have I mis-read your instructions?
If you mean Grate Area X 0.005 gives the nozzle area, then we obtain a diameter of 0.39 ins.
That is close to the sums based on cylinder diameter, admittedly for simple-expansion engines, but it seems normal practice to make the nozzle easily exchangeable with ones of different diameters to "tune" the individual engine.
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Choke: 1.14 ins .
Seems likely despite the formidable mass of tubes in the tube-plate looking as if demanding something bigger. I set the boiler's overall proportions by scaling ancient photos as best as I could, and from the GA in the original design's patent specification; and I fear it may be a bit under-scale. The tubes though were all by Western Steam's arithmetic, and I trust that.
By comparison, the chimney on my 7.25" g. 0-4-0 loco has a choke of about 1.12" expanding to 1.62" over perhaps 4" height – very roughly as it is not easy to measure.
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I tried to calculate the heights from those 1:3 and 1:6 rules, but could not see how. It's not just the two diameters above, times 3 and 6, because the two cones cross on the blast-nozzle edge and their apices are somewhere inside the blast pipe. I would have to draw it.
Also, the 1:6 ratio for the chimney height would probably not work directly with my engine's proportions, but might apply to a short inner chimney inside the lower end of the "stovepipe".
I have assembled the choke as made, for now; but can re-bore it to take a new one as an insert, or replace it completely, as it is a cast-iron insert itself, held by a couple of screws inside the fabricated-steel saddle.
Edited By Nigel Graham 2 on 22/03/2021 22:08:29