Hi Duncan,

The first material in my collection were responses by Martin Evans and D.E. Lawrence to an article by E.C. Martin in the M.E. for March 19, 1971. The article by Evans gives some background to the Keiller tube factor; it seems this was derived by C.M. Keiller from correlation of the proportions of full size locomotive boilers. In addition, all the boilers "correlated" seemed to be express or mixed traffic standard gauge examples. (Choosing the data to suit the theory perhaps?) Keiller recommended a factor in the range 55 – 70, which many these days seem to think is a bit high – which rather ties in with Julain's comment "I have always used generous tube diameters via length for both ordinary flues and superheater flues."

Keiller quoted work by Dr. Wagner of the German State Railways. Dr. Wagner had concluded that for maximum heat transfer, the gas flow area to heat transfer area should be around 0.0025, equivalent to L = 100 D – which has been called into question at the recent ASTT conference! Tubes of that length would certainly give good efficiency of the BOILER, but not necessarily of the whole loco.

If you look at the Ewins boiler factor

Eb = Grate Area in square inches x Tube Length in inches

Number of tubes x (tube diameter in inches)²

you will see it contains the Keiller factor. Ewins did a write up in EIM in the '80s but I don't have the reference by me just now.

As you know, I happen to think that with the computing power we all have these days, we can do a lot better than these formulae.

I am currently producing some worked examples starting with a "Speedy" boiler, which shows performance will be remarkably insensitive to changes in flue size – provided you keep roughly the same flow area. Things are a little more sensitive to flow area, but there is still plenty of leeway in practice.

Hope that helps a bit Duncan.

Martin

Lot of leeway and insensitivity to change means either :-

1) the system really is insensitive

2) everything is well off optimum so messing around with one parameter doesn't do much, basically lots more ways of being half right than dead right.

3) the system is self regulating over a useful range so varying one parameter sets off compensatory changes in other parameters.

Good luck with sorting that out on an ordinary digital computer. Job for hybrid digital and analog one but they are bit our of fashion these days.

1 and 2 usually look the same but seriously aren't.

Clive.