Important factors to consider when setting out model railway track are the sharpness of track curves forced by space limitations and the type of rolling stock employed. For satisfactory operation the criteria set out in Table 1 are recommended when selecting the minimum radius for a given layout. It is possible to build long vehicles to go round sharp curves, the Hornby O gauge Princess Elizabeth was designed for 3ft radius curves, but it is necessary to arrange increased side play to allow for this.

Table 1. Rolling stock and curvature.

Note: The above figures are based on stock being pulled. Where stock has to be propelled through curves into sidings or station areas the type of coupling employed is important. With loose couplings where the thrust is carried by buffers of scale diameter, (tighter curves need bigger buffers – up to 12mm diameter depending on wheelbase) it is recommended that the minimum be increased by at least 30% to limit the possibility of buffer locking. Where the thrust is taken by some form of rigid centre coupling, e.g. Buckeye, single link or similar, and the buffer faces are not in contact the above recommendations should prove satisfactory.

Harold Jones has written a piece on his practical experience of a minimum radius layout using bogie coaches and long wheelbase locos. This may be useful for others considering the same approach.

Where stock has to be propelled through reverse curves a short length of straight track should be introduced between the two curved portions.

Prototype curves of less than 10 chains are fully checkrailed. The equivalent model radius is 4.6m (15ft). For appearance purposes it is suggested that curves less than 1.0m (40ins) be fully check railed.

In prototype practice, except in goods yards and similar locations where speeds are low, a direct change from straight track to a circular curve is avoided. On running lines a sudden change of direction at the beginning and end of a curve causes lurching (and passenger discomfort) which increases wear and causes some disturbance to the track. To minimise these effects transition curves or easements are introduced between the straight portion and the true circular curve. On large radius model curves a transition has only visual significance but where space considerations require tight curves, transitions will improve running and prevent derailments due to buffer locking.

To permit higher speeds when passing round curves, full size lines raise the outer rail to counter-act the overturning effect of centrifugal force acting on the rolling stock. The amount of 'banking' or super-elevation depends on the radius of the curve and the speed at which it is traversed; the higher the speed, the higher the super-elevation. The maximum prototype super-elevation used is 150mm (6in) and on tight curves this limits the maximum operating speed. In modelling terms there is no need for super-elevation, the light weight and slow operating speeds of models do not generate the same forces as the full sized vehicles. (The fact that a Hornby No 1 clockwork tank engine, fully wound and running at a scale 200 mph will fly off a 610mm (2ft) radius tinplate curve is recognised but does not invalidate the statement). Super-elevation can be used to improve the appearance of model trackwork but should not normally exceed 3.5mm (1/8in) to match prototype practice.

If it is decided to use super-elevation, it must be increased gradually from zero to the maximum height chosen. This change in level is called the run-off and is usually confined to the transition curve, although if the transition curve is short it may be necessary to extend the run-off into the circular curve; extending run-off into the straight portion of the track is bad practice as it causes uneven running. Take particular care when laying the run-off track, the change in level may exaggerate any errors, so avoid rail joints here.

The length of a transition curve is a complex calculation using a number of factors including the radius of the circular curve that it connects to, the maximum train speed through the curve and the super-elevation. Taking the recommended minimum curvatures listed in Table 1 and assigning nominal figures for speed and super-elevation, lengths of model transition curves can be derived. Because tram tracks are laid in roadways and operating speeds are low Group 1lines have not been included in the calculations.

Table 2. Recommended maximum super elevation and minimum length for transition curves.

Figure 1. Transition curve.

In Figure 1 a transition with a length L is shown then AB and DE would coincide but, if one is added joining straight track to a circular curve with a then DE must be offset from AB by a distance X radius of R and a centre at C. The line AB is the which varies with the length of the transition and tangent to the circular curve while DE is the line of the radius of the circular curve. Recommended the straight track. If there were no transition curve offset distances are shown in Table 3.

Table 3. Recommended offset distances

One of the easiest methods of setting out a transition curve which requires the minimum of calculation is to make use of a guide stick, i.e. a flexible piece of material that will take up a natural curve under light pressure. If the transition is short enough a piece of straight undamaged rail can be used. Alter- natively, a length of whippy straight grained wood, free of knots and cracks, or a piece of plastic curtain rail from the local DIY store would be equally satisfactory.

Referring to Figure 2, once the radius of the circular curve and the length of the transition have been decided setting out the curve is as follows:

1. Draw the straight track line extended to point A and mark off a line AC at right angles.
2. Locate C, the centre of the circular curve, where AB is the offset distance read from Table 3 and BC is the radius of the circular curve.
3. Draw the circular curve round to the point B.
4. Mark the point E in the middle of AB and measure off ED and EF, each equal to half the transition length.
5. Clamp the guide stick along the line of the straight track so that it is held rigid up to the point D.
6. Steadily bend the other end of the guide stick until it touches the line of the circular curve at F. Secure the end along the line of the circular curve and check that the centre falls on the point E.
7. Mark off the line of the transition.

If the same transition length and circular curve radius are used a number of times on a layout the above method can be used to draw the transition on a piece of heavy card which can be cut to form a transition template. A selection of two or three standard transition templates can often be sufficient for a layout.

Figure 2. Setting out a transitional curve.

The Guild recommended track centres are 80mm for standard track and 90mm for sidings. The increase for sidings follows prototype practice where additional space is allowed to provide safe access for staff. These dimensions are satisfactory for straight track and for long modern rolling stock on curves greater than 2 metre radius but, if space considerations require the use of sharper radii then the possibility of vehicles striking one another when passing on curves must be taken into account.

Assuming that the maximum model vehicle width is 65mm (2.82m or 9ft 3in prototype width), the clearance on parallel straight tracks is 15mm. If a safety margin of 3mm is retained then the maximum throw-over that can be allowed is 12mm. A throw-over greater than this requires the track clearances to be increased. This can be determined by graphical or calculation methods.

Figure 3. Measuring throw-over graphically.

A graphical method of working out the extra clearance required is shown in Figure 3. For drawing convenience the measurements shown in this figure can be scaled down from full size. The procedure is as follows:

1. Draw a curve representing the centreline of the smallest radius curve on the layout where two or more tracks are adjacent to one another.
2. Draw a straight line cutting the curve at points A and B such that the distance AB is equal to the rigid wheelbase or bogie centres of the longest vehicle planned for the layout. (See also Part 3, Section 5 which deals with sideplay in locomotive chassis)
3. Extend the line at either end to C and D so that CD is equal to the overall length of the vehicle including buffers, etc.
4. Measure the centre and end throw-over distances as indicated in Figure 3.
5. For a simple throw-over (Figure 4), if the end throw is greater than 12mm increase the track centre distance by the difference, e.g. end throw is 15mm, increase the track centres to 83mm.
6. For compound throw-over (Figure 5), if the combined throws are greater than 12mm in- crease the track centre distance by the difference, e.g. end throw 8mm, centre throw 10mm, 8 + 10 -12 = 6mm, increase track centres to 86mm.

Figure 4. Simple throw-over when a branch or a crossover approaches a parallel track.

Figure 5. Compound throw-over when long vehicles pass on curved tracks. In the sketch VL = Vehicle length and WB = the rigid wheelbase or the bogie centre distance.

For those who prefer to calculate the clearances rather than draw them, it is relatively simple to find the minimum track centres necessary for vehicles to pass by using the following formulae. (It is convenient to make the calculation with all dimensions in cm and convert the centre distance to mm at the end). Table 4 gives the calculated minimum track centres for typical coaches assuming 3mm clearance.

Table 4. Typical curved track clearances. These are the minimum track centres for typical coaches to pass on curves.

Distance between the track centres = VDi + VDo + VW + Cl

• VDi = Vehicle centre displacement to the inside of the curve
• VDo = Vehicle end displacement to the outside of the curve
• VW = Vehicle overall width
• Cl = Clearance between passing trains, (taken as 3mm minimum)

Note: For vehicles with tapered ends the calculation must be made for both the full width and the reduced end width using the corresponding lengths from the centre (see table 4). C1 should be not less than 3mm.

VDi = Rc - R'

• Rc = Curve radius
• R' = √(Rc² - Bc²)
• Bc = Half the bogie centre distance or rigid wheelbase
• VDo = √(R'² + LV²)•Rc
• LV = The greater of the lengths from the bogie or rigid wheelbase centre to the end of the vehicle. (Half the overall length of a symmetrical vehicle)

Note: For those who prefer trial and error, make up card templates of the longest vehicles, set them with their bogie centres on the curve(s) and move the track until they just clear by about 3mm. The technique is also useful to check that the graphical or calculated solution has provided satisfactory clearance.

The recommended track centre spacing is 80mm for running lines and 90mm for sidings. These values are usually sufficient, but for long stock on sharper curves the 80mm value sometimes requires to be increased (denoted by bold entries in Table 5).

Table 5. Minimum spacing between track centres for various curves and vehicle widths.

The limiting dimensions for structures are shown in Fig. 6. On curves, horizontal dimensions in this structure gauge must be increased to take into account the effect of the throwover (see Figs. 4 and 5). This is done by including a factor E in the structure gauge. E can be calculated for all types of vehicle using the formula given above, and the results of this are shown in Table 6 for common varieties of rolling stock and model curves. This table was created using the formula method of calculation, but the graphical method can also be used.

Additional width is required on curves for two reasons. The first is that the vehicle ‘cuts the corner’ of the curve by drawing a straight line between its axles, or, for bogie stock, between its bogie centres. This causes an overhang on the inside of the curve (VDi, Vehicle centre Displacement, inside curve). There is a corresponding overhang on the outside of the curve caused by the fact that the vehicle extends beyond its outer axles or bogie centres, termed VDo (Vehicle end Displacement, outside curve).

The value of E that should be used is the maximum of VDi and VDo. For long vehicles on sharp curves, VDi is significantly larger than Vdo. Values of Ei = VDi and Eo = VDo may be calculated separately. Figure 6 shows Ei and Eo individually, with the inside of the curve on the left. However, in most cases it is advisable to take Ei = Eo = E, and use the values in Table 6.

Figure 6. Structure gauge, showing larger horizontal dimensions to give clearance on curves.

Table 6. Table of values of E for various vehicle lengths and curve radii.

Shaded region shows curves below the recommended minimum radius for the groups listed in Table 1.

Prototype rail sections vary widely from the early top hat and Tee sections through bullhead rail to flat bottom rail. Most British main lines used bullhead until about 1950 and it can still be seen in sidings and certain special locations like the London Underground. Flat bottom rail was preferred overseas and also found use in light railway practice in Britain. Modern British main line practice is to use a heavy section flat bottom rail resting on pads and mounted on concrete sleepers.

The code numbers shown below are based on the system used by model manufacturers to identify the sizes of model rail. The figures represent the height of the model rail in thousandths of an inch, e.g. code 124 model bullhead rail is 0.124 in. high and could represent 80 lb/yd rail. The heavy section (Code 200) has no prototype in O scale but could represent a 100 lb/yd rail in 10mm scale narrow gauge (1n3) or 60 lb/yd rail in 16mm scale narrow gauge (SM32).

The code can only be used as a guide as it does not indicate the width of the head, web or foot of the model rail. A full table of prototype rail dimensions is found here.

Table 7. Prototype rail heights and their equivalent model code numbers for bullhead rail (BS9 1935).

Table 8. Prototype rail heights and their equivalent model code numbers for flat bottomed rail (BS11 1985).

This article was prepared for the Gauge O Guild Manual by Ken Sheale and Richard Chown. It was adapted for the GOGWiki by Nick Baines.