A preliminary design for an O finescale layout has a main line with a 4880mm (16ft) radius curve and a 1830mm (6ft) radius branch leading off to a group of sidings. Which semi-curved switch and crossing combination would suit and, if it is not a precise match, which curve would need to be adjusted?

R_TE = (4880 x 1830)/(4880 – 1830) = 2928mm

or

R_TE = (16 x 6)/(16 – 6) = 9.6ft

Checking the table for semi-curved switches (O fine standard) shows that there is no exact match but the B7 combination is very close with a radius of 2985mm (9.8ft). Substituting back into the original formula, the effect of altering the main or secondary route can be assessed.

Retaining the main line at 4880mm (16ft) radius

2985 = (4880 x R_T2)/(4880 – R_T2) ⇒ R_T2 = 1852mm

or

9.8 = (16 x R_T2)/(16 – R_T2) ⇒ R_T2 = 6.08ft

Retaining the branch line at 1830mm (6ft) radius:

2985 = (R_T1 x 1830)/(R_T1 - 1830) ⇒ R_T1 = 4730mm

or

9.8 = (R_T1 x 6)/(R_T1 - 6) ⇒ R_T1 = 15.47ft

This suggests that to use the B7 turnout data, only a minor adjustment to the secondary route is needed, whereas the main line would need to have its radius reduced by 150mm (6½in), which might not be acceptable.

It is proposed to insert a B8 turnout into a 1500mm (4ft 11in) radius curve. What will the major curve radius be?

Substituting, the first formula above becomes

R_T1 = (R_TE x R_T2)/(R_TE - R_T2) (Note 1)

The table of turnout curves shows that R_T for a B8 turnout is 4129mm (13.5ft).

R_T1 = (4129 x 1500)/(4129 – 1500) = 2356mm (Note 2)

Note 1: If R_TE is less than R_T2, then R_T1 is negative, which means that the major curve is the opposite hand to the minor curve, i.e. a wye turnout. If R_TE and R_T2 are equal then the major curve is a straight.

Note 2: As a B8 turnout is about the limit suggested for O fine standard; the minor and major radii of 1500mm and 2356mm conform roughly to the recommended ratio of 1 to 1½.

A design calls for a wye turnout with arms of about 1830mm (6ft) radius and 2440mm (8ft) radius. What is the nearest equivalent to suit the location?

R_TE = (2440 x 1830)/(2440 – 1830) = 1097mm

or

R_TE = (8 x 6)/(8 – 6) = 3.43ft

The nearest match in the O fine semi-curved switch table gives an A4.5 turnout with an R_TE of 1115mm (3.7ft). Substituting back into the formula, as in example 1, gives the following results:

Retaining the 2440mm (8ft) radius requires the other leg to increase to 2220mm (6.88ft)

or

Retaining the 1830mm (6ft) radius requires the other leg to increase to 2854mm (9.65ft).

If these increases are too great for the design, an alternative is to adjust both legs. To maintain the proportions the larger radius needs to be approximately 1.3 times the smaller, i.e. R_T1 = 1.3R_T2.

1115 = (1.3R_T2 x R_T2)/(1.3R_T2 + R_T2)

R_T2 = 2564.5/1.3 = 1973mm (6.55ft)

R_T1 = 1.3 x 1973 = 2630mm (8.7ft)

If instead of using the A4.5 turnout data it was decided to go to the next lower size, the A4, the result of adjusting both legs would be radii of 1508mm (4.95ft) and 2005mm (6.58ft). These curves may be considered too sharp for the application.