Model Railway Constructor

March 1967


a new scale modelling standard

How tight the curve?

by Malcolm Cross

on behalf of the Model Railway Standards Study Group

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IT does not take long for the novice modeller to discover the delights of six-wheeled stock, especially if he chooses to model the pre-Grouping scene. There were many types of six-wheeled passenger vehicles on the old railways, remembered by those who knew them with affection for the liveries, if not for the riding qualities, which latter could be less than enjoyable on occasion. Fish trucks and brake vehicles often had a fixed six-wheel wheelbase, while the great majority of the goods engines, then and now, were six-coupled.

In translating these fascinating objects to model form, trouble inevitably arises when they are required to negotiate the ultra-small radii of model railway layouts. Our modeller will not lack warnings of the difficulties involved in running six-wheeled stock on curved track, but the advice is likely to be ambiguous and far from specific. What then are the difficulties of operation in these conditions? The answers can be found from several different aspects of running.

Firstly let us consider the running aspects of a single wheel. We are generally familiar with the vertical cross section of the tread from the BRMSB and other Standards specifications, but this is only part of the wheel character. In fact, the entire flange projecting below rail level may, in certain circumstances, contact the running rail. To examine this flange area, we will have to make a further section through the wheel horizontally, on a plane level with the top of the rail. At once an entirely different form of the flange is seen, and three typical wheels, sectioned vertically and horizontally, are shown in Fig. 1.

On straight track, all the above wheel sections will behave in a similar way, but it is obvious that on curved track they will behave very differently, as the wheel will be set at an angle to the rail. If we now consider the wheel as one of a pair on an axle, this angle of incidence to the rail will appear when the wheel pair is set incorrectly in the vehicle frame, which we will not take into account, or when the wheel pair is at the end of a fixed wheelbase.

As such a wheel pair enters a curved section of rail, the wheel incidence angle will increase to the point where the flange will contact the rail other than at the point opposite the bottom dead centre of the wheel. At this juncture, friction between rail and wheel will increase considerably, and the risk of derailment owing to misaligned rail ends, or irregularities in the track, will increase also. and will depend largely upon the section of the flange.

fig1s.gif (2487 bytes) In Fig. 2, the horizontal sections of flanges have been shown at their critical angles of incidence, It will be seen that in the case of the deep flange sections, 'rail grinding', or rubbing contact between the nose of the flange and the rail, takes place at an incidence angle of approximately 3 degrees. The actual angles taken by the wheel can be calculated, as the wheelbase is in effect the chord of a circle, the radius of which is the radius of our model curves. The relative angle of incidence is the angle between tangent and chord at the point of contact. This is shown in Fig 3. where the angle of incidence is indicated by "a".

As discovered in the case of the single wheel, there is a maximum acceptable value for incidence angle, and it therefore follows that our fixed wheelbase should not be operated on curves which offer incidence angles to the outer wheels of more than the critical values. Incidence angle is clearly one limiting factor in our choice of minimum curves. Thus far, we have only considered wheels as single units, or the end components of a fixed wheelbase. When we consider the six-wheeled vehicle, further complications arise. If the wheelbase represents the chord of a circle, it is clear that for the wheels to track correctly along the rails, the centre pair of wheels must have sideways play in the axleguards to adopt a relative displacement to the Outer wheels. (Fig 3.) This sideways displacement is the versine, and it also can be calculated from the values of wheelbase and radius of curvature.


Were it possible to allow unlimited sideplay to the centre wheel pair, the versine factor would not be critical. In 4mm scale operations, there is generally little hope of providing more than one millimetre of relative sideplay between axieguards. so that this figure must be taken as the limiting one for six-wheeled stock with a fixed wheelbase.

We have now established incidence angle and versine value as limiting factors in determining minimum radius of curve. There is one more aspect to be taken into account. This is the diameter of the wheel. Clearly, a large wheel will be more critical than a small one. owing to the longer horizontal flange section. This will also influence the wheel performance at the flangeway, where a maximum angle is met when the flange tip contacts both the running rail and the check rail at the same time. (Fig 2.) As a six-foot wheel is the largest commonly found on goods locomotives, this value has been taken for the construction of a graph in which the various factors are compared.

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The graph shows wheel angles of incidence and wheelbase values, set against versines and radius of curve. Several operations are possible with the graph, which, though approximate (there are too many variables) is useful in assessing reasonable limits of performance. For example, given a 20ft 0in wheelbase (80mm in 4mm scale) for a six-wheeled vehicle, with 1mm relative sideplay to the centre axle: find the minimum radius of curve that this vehicle will negotiate without difficulty. Follow the 1mm versine line to the interception of the 20ft wheelbase curve; trace vertically to find a figure of 2ft 8in on the bottom scale. At this radius the 20ft vehicle will have a wheel incidence angle of less than 3 degrees, and will therefore run effortlessly. However, if this vehicle had only a 14ft. wheelbase, it would negotiate a 1ft 4in radius curve, but the incidence angle would now be 4 degrees, and depending upon the flange section, rail grinding or poor running could be expected.

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Of course, the values found are in the "minimum comfortable" category. If one is determined to run an awkward vehicle on curves nominally below the minimum figure, certain measures are possible. These include gauge widening - already incorporated in the "Protofour" standards - which increases the effective versine value, except at the crossing flangeway, which remains critical; Cleminson arrangements of flexible wheelbase, giving considerably increased sideplay to the centre axle; radial axles on an effective versine values and a reduction in incidence angle; limitation of stock to that having small radius wheels; and finally - desperate throw - filing flat the lower part of the centre wheels so that the vehicle becomes in effect a four-wheeler, or, the commercial standby. the flangeless centre driver.

From our investigation, we can realise that though fixed wheelbases and small radii give problems, these are by no means insuperable. Clearly the most satisfactory answer of all is to use a reasonably large radius, something most modellers are strangely disinclined to do. In the event that a small radius is mandatory, it is well to be prepared for the difficulties that may arise. These relate mainly to the wheel incidence angle, for it will be seen that the Hornby Castle, for example, with a wheelbase of 14ft 9in. is in for wheel grinding on radii below approximately 2ft 0in. This is a result of the unsatisfactory contour of the flange, for our manufacturers are devoted to deep flanges of uncompromising wedge shape, the worst possible pattern for operations on the small radius curves invariably supplied with their products.

Although properly flanged locomotive wheels are unobtainable over the counter, it is recommended that rolling stock be fitted with Nucro/Jackson-type wheels as the best available at the time of writing; although these will not greatly change the critical 3 degree incidence angle, they will minimise its effects on performance.

For the modeller in the design stages of layout construction, the graph will give a reliable indication of the limitations of wheelbase on radius, and vice versa. If it is accepted that locomotives are restricted in centre axle sideplay on coupled wheels to approximately 0.5mm. it is clear that our "Castle" and other express passenger locomotives really require 3ft 0in radius curves for faultless operation with all wheels flanged. If such radii are not possible, then special measures are required; it is hoped that these notes have indicated the need for such measures, the size of corrections necessary. the factors involved, and the ultimate apparently fixed wheelbase, giving more limitations of satisfactory running.

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[Part 4 will appear next month]

Copyright - Model Railway Study Group, reproduced with permission.

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