Boiler stays.

All flat, or nearly flat, surfaces need to be stayed.

The ideal material for stays in copper boilers is phosphor bronze or copper. Monel is no longer recommended.

Steel stays are used in steel boilers.

The methods of fixing stays are:
Screwed into the plate and brazed/welded,
Screw plus locknut and then brazed/welded,
Plain shank and brazed or welded.
The stay may or may not be fastened by the same method at each end.

A common method is to screw, nut and braze to the inner firebox, and just screw and braze to the outer.

With steel boilers, there is an increasing tendency to use plain stays with countersunk holes in the plates and weld in place.

The stay has to withstand the force applied to it plus effect a water and steam tight joint.
Traditional "good practice" states that the stay should withstand the forces applied to it by mechanical means,
and the braze / weld just act as the seal.

In practice and with modern materials, a properly brazed or welded joint should have nearly the strength of the parent metal, and some designs only have brazed or welded stays.

Whatever the designer has done is probably correct, so it is best to keep to the design.

I have checked several old formulas which were used in the past for calculating stay sizes on full-size boilers, and many of them give misleading or uncertain results with model boilers.

The following do give acceptable results. .

Stay bolt size = A x Z / (H x V)
Where:
A = cross sectional area
H = horizontal spacing (inches)
V = vertical spacing (inches)
Z = 12,000 for steel, 4,500 for monel, 4,000 for copper


Stay bolt pitch = F² x Z x L
W
Where:
F = firebox sheet thickness (inches)
L = 2 for brazed / welded only, 2.6 for screwed, nuts & braze / weld
W = stay bolt pitch (smallest distance if not square)
Z = 12,000 steel, 4,000 copper

One formula is "Where the stay material is the same as that of the boiler shell, the spacing of the stays can be 6 x plate thickness.", and this appears to give satisfactory results with the average small model boiler
using conventional materials and construction techniques, at the pressures usual for that type of service.

To save having to do all the calculations on boiler stays etc., or as a  check on what you have already calculated, there is an excellent spreadsheet by Paul Syefrit of the Chesapeake &  Allegheny Live Steamers, that does many of the calculations for you.

See the LINKS TO OTHER SITES Page.

For larger boilers, the following may be useful.
T = v 16000 / P
Where: P = pressure in lbs. per sq. in. T = thickness of plate (inches)

The water space around the firebox of a model boiler should be at least 3/8" and preferably 7/16" or 1/2".

Boiler size.
For smaller boilers at low pressures (around 30 -40 psi), the heating surface in square inches should equal the cylinder volume (in cu.ins.) times 200.

Evaporation.
Simple "pot" boilers of a size usually used in model boats can be expected to evaporate 1 cu. inch of water per 100 sq. inches of heating surface.
More complex boilers may evaporate 2 to 3 times as much.
It is difficult to give a "rule of thumb" figure for locomotive boilers as there are so many variables.

Fortunately, it is possible to calculate some precise figures for the performance of locomotive boilers, thanks to the work by Professor W. B. Hall, who has prepared a suite of software which is extremely useful to anyone who is
designing or modifying a boiler, or who just wants to know how efficient any given installation is.
See the MODELENG SITE on the LINKS page.

Evaporation. 1 pound of coal will evaporate 14 lbs. of water if properly burned.
In practice, allow for 1 lb. of coal to generate 10 lbs. of steam.

Heating surface. The relative effectiveness of heating surfaces is:

Horizontal surface above the flame = 1
Vertical surface " " " = 0.5
Horizontal surface beneath " " = 0.1
Tubes and flues 1.25 x their diameter

BOILER TUBES.
A formula for calculating the size of boiler tubes is:    D = v L / X

Where D = tube inside diameter; L = tube length. X = 50 to 70 for imperial, or 2.0 to 2.6 for metric
measurements

Tube size is always a compromise.

A thin wall will transfer heat faster but will limit the pressure that the boiler can withstand.
Also, the flow of ash particles and regular cleaning of a tube will gradually reduce the thickness.
Larger tubes do not get dirty or blocked as
easily, but smaller bore tubes are more efficient at transferring heat to the water.

Copper tubes are more efficient at transferring heat than steel ones.

The cross sectional area of all the tubes
combined must be sufficient to allow the products of combustion to flow easily.
Calculate the airflow required, and work out the area needed to give a maximum of about 4000 ft /. minute air flow.
(A far lower figure is beneficial in a model engine.)