Possibly due in part to an almost nonexistent liaison between locomotive designers and those concerned with small scale steam engines, and a similar lack of verifiable published information, the model world was destined to attach too much importance to ‘backset’ of the expansion link drive in Walschaerts’ gear. The singular published attempt to enlighten the fraternity was Henry Greenly’s book and faith was generally accorded since Greenly was esteemed as the designer of the fine miniature locomotives of the Romney, Hythe & Dymchurch Railway. The minimal equations therein require little attention to find them wanting.

In the 1960s and 70s those interested in the design of the gear were in good regular touch with each other in an effort to trace the efficacy and precision of backsetting, with but little intimate knowledge or confirmation of the results. Perhaps the single fact to emerge was that at some definitive point the practical application of straightforward formulae could result in precisely equal angles of swing of the expansion link, in effect replacing the exercise with trammels on paper. This was perceived as a great step forwards, satisfying the principle of lead equality at dead centres and rationalising the return crank drive system.

In some ways this was unfortunately taken as a solution to a perceived problem rather than as a datum easily calculated, from which to derive a tuning of the mechanism in order to satisfy equal steam distribution at the two ports. It should be obvious that the provision of equal curved expansion link swings cannot of itself deliver equality of dieblock movements, particularly for long valve travels, and that its provision does nothing to alleviate either the effects of crank/piston relationships or the small foibles encountered in the return crank’s excursions. There is a mitigating circumstance in the wanton way in which many earlier full size designers and most textbook authors treated these foibles as irremediable or simply not present. This hardly produces the best historical background to encourage better logic from those amateurs who boldly sought to crack a proverbial nut – Don Ashton, Jim Ewins, Ted Gowan and Alan Gettings. The ‘solution’ so found was subsequently discovered to be a reinvention of formulae printed in a German locomotive journal in 1924!

Further mathematical analysis, although by then more satisfying and applicable to the new hand-held calculators, becomes much more complex once the ‘necessity’ for equiangular swings is removed. This was tackled by Dr. F.M.Burrows, a Whitworth Fellow at Bangor University in the 1970s, who provided a Table from which straightforward interpolation could bypass the complexities adjoining unequal swings to provide solutions in these cases. The lead equality principle remained, unless one required to compromise this slightly without ill effect at the cylinder.

Unfortunately, whilst being a mathematical triumph, this evaluation remained centred around the precise backset calculation, without consideration of the valve events other than those of lead. The Burrows discussion to remove the ‘primary timing errors’ appeared not to include the piston positions other than at the dead centres, nor for that matter those of the valve. One or two practical items were also ignored: the valve setters’ primary act is to verify the equal lead principle and adjust the eccentric rod length to conform. The consequences of subsequently setting the valve to equalise leads when the gear design cannot support this were not discussed. There was praise for the King gear of 1927 as a thorough development from earlier classes without knowing the resultant events other than from the unreliable testimony of a drawing office Table: many are the cases of rudimentary or massaged figures now put to task by computer analysis. The King design is good, but not beyond improvement by simulation. Suffice to say that this example confirms that the ‘backset’ is modified as the inclination of the eccentric rod drive becomes greater, reaching zero and then becoming positive in the King.

Computer simulation reveals considerably more. In particular it shows that the two components comprising the valve movement cannot be altered individually without affecting each other. The variables are legion and do not readily submit to formulaic construction. The simple fact that the principle of equal leads depends so heavily on the return crank derived motion should warn any student of the gear that attempted separation of the component functions is doomed. It is still advantageous in the initial stages of design to regard geometric symmetry throughout the gear layout as good practice, creating a sensible datum from which to deviate only with knowledge of the consequences. By several variations, some very sensitive and others less so, the two inputs can be made to render the final output considerably improved. The chief of these concerns the anchor or union link and the backset. Alteration of the heights of weighshaft and expansion link fulcrum gain some control over a bias shift in equality between back gear and fore gear, but the method of suspension of the radius rod rear end requires very careful design if it is to avoid imparting the opposite of equality.

The progress or otherwise of equality throughout the range can be represented by two curves to show the differences between each port activity. Perfect equality would produce complete coincidence of these curves, but as this condition is almost impossible the two curves form a typical relationship irrespective of the gear used. Alteration in the simulator then becomes an exercise in achieving what is known to be possible independent of the particular layout under scrutiny - a self-evident measure of design efficacy and distributive performance. It highlights the problems faced before the advent of the simulator dramatically.

Another aspect also becomes clear: our locomotive engineers, who had no such technological aid, had amongst their number from the earliest times many of distinction, able to appreciate and attend to all the finer points of Walschaerts’ design. There are, naturally, examples displaying a more rudimentary understanding, a description that unfortunately encompasses all the smaller scale designers. Jim Ewins had a saying ‘they don’t know what they don’t know’. How telling! Simulation will lead to a better understanding and eventually enable the present trial and error to be replaced by a more logical approach.


The Stephenson’s mechanism is perhaps more readily assimilated, though essential details did not begin to appear to the miniature world before G.S.Willoughby’s rather vague explanations in The Model Engineer in 1937. Apparently his information came from Swindon Works, but the precise details were either misconstrued or misrepresented, even though precise details of the mechanism were elucidated by Auchincloss as early as 1867. These were not presented to modellers until Ted Gowan’s revelations to the SMEE nearly a century later, which laid down the principles and the methods of carrying out the necessary design work graphically. Although this was an enormous step forwards few designers appear to have realised its significance and mystery continued unabated.

With Ted Gowan’s ready permission this information was incorporated in Don Ashton’s self-published booklets on Stephenson’s Valve Gear and Walschaerts’ Gear, 6000 copies of which went all over the world. The graphical exposition was later augmented by precise calculations for the correct design of Stephenson’s gear to near perfection in Excel spreadsheet form (see the DOWNLOADS page).

There is plenty of evidence to suggest that this neat suspension, known almost since the invention of the Howe link, was a mystery to many designers – if no offset is incorporated in a design it is in error. If the wrong link type is used in the inappropriate driveline all the angularity errors combine and a large offset and less perfect distribution result, made abundantly clear when a modeller substitutes an outside admission valve in place of a prototype’s inside admission one or misguidedly employs a launch-type link to keep eccentric sizes moderate. Such a mistake was rarely perpetrated unknowingly in full size practice even where the offsetting exercise seems absent.

A simulator proves beyond doubt the veracity of correctly offsetting the trunnions, allowing steam distribution to each port in the order of 1% equality, an achievement rarely obtainable in Walschaerts’ gear designs, where a good layout can typically produce 2.5% in full gear lessening towards the shorter running cut offs. In such cases it is the front port which has the longer cut off, yet displays the least port opening, indicating that the valve is travelling more slowly here. There is a measure of compensation between the front and rear ports in spite of the graphic disclosure, and it is the primary reason why old slide valve ports were made as wide as possible.


There are other caveats rarely explained in textbooks. Some piston-valved engines with Walschaerts’ gear ran forwards with the block in the upper half of the link by using a leading return crank in place of the common trailing one. All other things being equal, this results in a slightly longer eccentric rod and a shortened return crank. However, since the resultant cut offs for the same lifting arm angle are often greater in the upper slot there is an opportunity to reduce the pitch circle in this design. Usually the leading return crank is associated with a drive to outside admission valves and the different juxtaposition of the combination lever’s upper pins results in far less travel required of the radius rod. Both the angular swing of the expansion link and the size of the pitch circle are much reduced for a given valve travel in this case and event equality is much easier to control.

It is not essential to keep the weighshaft centre in line with the expansion link trunnion and radius rod front pin – its height may vary to suit the events in forward gear, or proximity to the wheel tread may dictate its position. Where a hanger is employed events are critically involved and the designer needs recourse to simulation in order to balance the weighshaft height and placement, length of lifting arm, link, and that link’s position on the radius rod.

The weighshaft components are rather less critical in the case of Stephenson’s gear, but the best symmetry will be achieved when the lifting link is arranged vertically at the half strokes with the gear at 50% cut off. This symmetry does not apply to end suspended arrangements, where deliberate asymmetry is vital to events. Such asymmetry is also fundamental in the yoke and bell crank of Baker’s gear. The placement of the guide block unit for Joy’s gear is critical and is guesswork without simulation or final measurement of the completely constructed gear on the engine itself, as practised at Horwich.

The apparent paradox of using asymmetry in the valve gear to gain symmetry of valve events arises purely from managing the timing in the conversion of rotary to linear movement. All circles or part thereof constitute an angularity problem to be countered in most cases by an opposed angularity. These are the primary constituents of design excellence and fine tuning. The miniature designer has no environment in which to learn, and study is made the more difficult by the lack of information filtering down from full size practice. The very details that a designer wishes to know rarely appear even in the best textbooks. Although a simulator is not a design tool it provides a singular aid to understanding valve gear kinematics.


The model engineer is in a unique position. Our locomotive engineers did not see the need to leave a legacy in the form of valve gear design knowledge for those in the delightful hobby of steam engineering. With the possible exceptions of authors Auchincloss, Yoder & Wharen and H.S.Gowan there has been little to steer the minds of model designers. The legendary LBSC, without whom the hobby might still be in infancy, freely recognised his lack of detailed information regarding valve gears. He was in this respect an acknowledged ‘pins and cardboard’ juggler destined to produce some reasonable working gears and some inevitably much the poorer. In 1925 he wrote a whole column on erecting Stephenson’s gear – a brilliant exposition elucidating precisely nothing and leaving the constructer in confusion then as now.

Similarly, Henry Greenly wrote a book on Walschaerts’ gear full of useful mechanical solutions in various scales, but only half-truths in glimpses at the geometry. Martin Evans followed with another treatise of similar title and similar glossing over of facts. Even his more suitable drawing board application could not teach him what he wished to know, though in general a staid and methodical approach stood him in reasonable stead. Don Young was in a similar position. His early association with Doncaster works obviously failed to encompass the inner sanctum of the design office and he is noted for exceptionally large leads in his designs, without any scientific testing that would show this to be fallacious.

As a result, the model engineer unwittingly wastes a lot of effort making a mixture of reasonable, under-developed, or faulty motions. Rarely is it a case of renewing one part as the whole design is built around unwitting ignorance. Before simulation the performance could not be judged, and once built, few would relish starting the gear again from scratch.

The model engineers themselves comprise many different approaches strung together by the glorious thread of live steam; some are mainly interested in the mechanical production, others in romping around the track or simply pottering to amuse the grandchildren. How does one design a project suitable for all? As the steam engine is so flexible, able to limp along uncomplainingly, untested in real ability, it is little wonder that the strict design principles necessary in full size have never developed in smaller scales. The requirement to design for specific tasks and to return sufficient economy is wanting.

Perhaps there are other clues pointing to the impoverished valve gear knowledge. The appearance of a formula or some mathematics is a sudden switch-off for many model engineers, yet essential for engineers. Fortuitously, the digital age has introduced the means of better measurement in the building and the computer eats for breakfast all the dreaded maths. Initial design work is completed in minutes using a dedicated design program and the results can be fed into a valve gear simulator for fine tuning and detailed examination. Any given design can by this means be thoroughly checked for deficiency after just a little use of the program, eliminating guesswork and ensuring the best success after the laborious work of building. Absence of frustration at the first steam-up is worth the effort of learning the little required to use the programs confidently.

In fact, it was suspicions regarding the efficacy of Speedy’s valve gear that led both Professor Bill Hall, then of Manchester University, and Dr.Allan Wallace of Adelaide, to devise the simulated means of investigating the kinematics of valve motions. That the nomenclatures used in both these simulators and those of Californian Charlie Dockstader are disparate may be a little unfortunate, but the means of investigating gear performance have undoubtedly led to a much better understanding of the design details of a gear.

By studying what appears either numerically or graphically we gather new insights into the abilities of the original designers, full size or otherwise, and discover why certain principles were held dear. All valve gears have been accused of being a compromise, as if adding the facility to reverse and use intermediate expansion levels has ruined the simplicity of the single eccentric. Perhaps we now realise that even this simple eccentric has inherent cyclic faults, and the simulator proves beyond doubt that it is possible to gain near-perfection without added complexity beyond the inventions of the 1840s.

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