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It is a pity that one cannot read the designer’s mental process in formulating the concept of the Walschaerts’ arrangement, particularly where inside and outside gears under different space constrictions have to match in performance. Much can be gleaned from the motion drawings, yet only the final results appear clear; rather it is akin to viewing a painting without being privy to the preliminary sketches and perceptions.

Initial appraisal of the motion drawing:

How useful to have both the inside and outside gears readily viewable together!  The relative disposition immediately reveals different connecting rod lengths, a much shorter inside radius rod, and the usual heavily inclined eccentric rod inside to keep the size of the eccentric down.  These differences will count when we see how well the designers have managed to match the inside events with those outside, where the longer rods have the timing advantages. As an example, both use the same combination lever. On the face of it one would expect the lap and lead functions to be identical, as we desire, but experience suggests that the same combination lever ratio is no guarantee of this.

On the outside gear the weighshaft position is fixed by dimensions but not the trunnion – one has to assume that it lies on a straight line running to the front pin of the radius rod, but only when the crank is on back dead centre.  The long union link appears to be horizontal (to the gear line) and erection of the gear using CAD shows that this is so.  Also, the tailpin of the expansion link appears to lie on a line vertical to the frame and not square to the expansion link in mid gear.  This is deceptive, especially as the trunnion position is not dimensioned.  In fact it is fore set by 0.012″

The inside gear presents different problems in CAD erection. The weighshaft is positioned by one dimension square to the gear and another square to the frame! The drawn centreline through front radius rod pin and weighshaft is again misleading, as the crank is in an ‘indeterminate’ position (though crank 120o from outer gear) and the expansion link tailpin has no dimensions. In fact the weighshaft is not quite in line with the trunnion and the tailpin has to be finalised on the simulator because scaling from a drawing that is obviously scanned precludes accuracy at this stage.

Investigating by CAD the outer combination lever lower pin travels 26″ and the valve pin movement is symmetrical about a vertical centreline. The inner gear lever travels 26.026″ but the valve pin travels a fraction under that of the outer pin (3.488″ to 3.492″) and is quite asymmetric (rearward bias). This is achieved by shortening the union link and the cylinder bore to valve bore is less. The magnitude is therefore closely similar but the input is skewed to suit the oddities generated by the eccentric drive. Whilst this practice is fairly widespread it is extremely difficult to define logically in design – the simulator can show the veracity but there does not appear to be any set procedure at the design stage to ensure the desired result. The variables involved are too manifold to predict a result without considerable experience and understanding of Walschaerts’ gear well beyond the mathematical basis.

The expansion link swings are unequal and deliberately so (inner gear).  The absence of dimensioning for the drive pin requires some astute deliberation in order to give the simulation fair trial. My guesstimate to match with the outer gear proved to be accurate, as varying the amount of fore set temporarily will show up in the equality of events graphs.  Although my guesstimate was logically based this was not a mathematical estimate and sheer luck may have played a part, however much the simulation verifies my judgment. Backset (fore set in this case) is a recognised modifier both for equalisation and timing manipulation.

Essentially what we have is the combination of two distorted component inputs designed to complement each other.  It is difficult enough to design a good symmetrical layout of Walschaerts’ gear with the minimum of input distortion, without having to distort elements deliberately to match inherent distortion in one or other of the components. It is important to realise that the distortions are timing distortions and vary throughout a 360o cycle.  This pernicious problem has to be overcome by the application of considerable experience before fine-tuning either on a large model or by simulation – simply altering various parts in a simulator on a trial basis frequently leads into a morass.  In the case of the A1, simulation verifies the efficacy of the resultant gears but gives few clues as to design parameters in the first place. To the great credit of the LNER design people the results verify their expertise.


Simulation applies dynamic calculation and interpolation and therefore converts nominal design figures into actual amounts. Note that no allowance for bearing clearances is used unless specifically addressing the results of wear. Some nominal dimensions are listed on the drawing. Lap is a physical quantity added to the valve bobbins and must be accounted for in the gear design.  A1 lap is 1.625″, and as the valves are line-in-line exhaust each bobbin measures port width + lap from outer ring edge to outer ring edge. Lead is not a machined item but a timing advance produced from the gear.  The 1/8th″ lead listed is apparently optimistic as the simulation reveals around 0.088″.  The nominal full valve travel stated as 6.688″ on the drawing is a variable depending on die depth. Expect the reverse gear to show a different full travel for the same angle of lifting arm.  In fact the simulator requires an angle of 37o to achieve a nominal 75% cut off at a travel of 6.66″.  This is 2o more than the draughtsman appears to have laid down.

As the cut offs for inside and outside gears need to match closely, the cut off curves require matching, then the actual cut off pattern throughout the working range warrants attention.  The event curves match reasonably on the A1 but the inside full cut off for the same angular displacement of the lifting arm tends to be 1 to 2% greater. The inside ‘reach rod’ arm of 1’ 2½″ operates an auxiliary arm of 1’ 2″ to act as a magnifying element. One would expect the opposite to be required.

Unfortunately, the much shorter radius rod of the inner gear, with its tighter curve of expansion link, causes the scale from full to mid gear to differ from that of the outside gear.  It also causes more difficulty in keeping the close match of cut off curves. If the depth in gears are arranged to coordinate in full gear there is a discrepancy of around 5% by the time we reach 30% cut off. The net result is that more work is done by the inside cylinder – the age old problem afflicting all the Gresley conjugated gears!  I thought that this was Thompson’s and Peppercorn’s main objection to the Gresley gear, but that they saw no problems with divided drive.

Fine-tuning each quadrant of each gear:

Peppercorn and his crew may not have been surprised that not all the middle big end troubles were attributable to the levers he so despised.  The tighter curvature of the inner radius rod is a major contributor.  The evidence supporting this view lies in the subtle differences in the extending reach rod to apply different angles to forward and reverse for each gear, yet Peppercorn appears to have strayed opposite to that required.  Perhaps we shall never know why.

When the full forward lifting arm angle of 37o is applied to the outside gear the nominal starting cut off of 75% (as specified) is obtained.  The LNER auxiliary reach rod then applies 39.27o to the inner lifting arm, which in concert with the different inner gear elements exacerbates the problem of equalising inner to outer gears. The relative % differences assessed by comparing cut off curves is good, but the relative setting of inner to outer working ranges results in extra work from the inside cylinder – the Gresley ghost.

When this reach rod bias is reversed, by applying 36.7o to the inside lifting arm, the match of both curves and cut off ranges (particularly for shorter running cut offs) becomes more exciting. The table shows the original outside fore gear and my matching inner gear.


Comparing the difference % columns verifies the proximity of cut off curves between inner and outer gears for forward running.  Comparing the cuts offs at each step in the range shows the remarkable degree of complicity across all three cylinders. By simulation the best angle of inside lifting arm has been attained to align the work done by each half cylinder.

The applied logic starts with the outer gear full forward 75% cut off, which requires a lifting arm angle of 37o.  This is basically in line with the Doncaster drawing, with 35o in full back gear.  As the table shows, excellent complicity across the range is obtained by a slight decrease in the die depth on the inside gear.  The Doncaster arrangement increases the inner depth to place the inside cylinder at risk of over-working in similar fashion to the A3s and A4s.  The problem was attributed to the 2:1 linkage but this investigation by simulation clearly reveals that the A1s did not (but could so easily have been made to) resolve the affliction, though caused by other means.

For comparison a table is shown for the angles interpolated from the Doncaster drawing. Using both tables, in fore gear at around 27% cut off the inside gear is endeavouring to match 27.36/30.48% against the outer gear’s 26.08/27.86%. Compare this to my 24.89/28.10% above. A simple reverse of the leverage on the auxiliary reach rod would have arrived at a ratio that satisfies the requirements of the inside cylinder.


The concentration has been on fore gear running since that is the prime function of the A1s. A somewhat different approach would be required to solve the similar problems when requiring equal facility in reverse gear.  Although incidental to this particular study, it is worth mentioning that Beyer-Peacock were masters of producing excellent events for engines requiring both forward and reverse running engines simultaneously matched.

Summary: the main findings of the analysis:

1)   The outer gear has good event equality and a release of 70% at 20% cut off.

2)   The small leads are in line with very much more modern thinking (Porta).

3)   As expected, the reverse gear is less good but this is of no consequence.

4)   The gear is perfectly conventional.

5)   Full forward gear lifting arm angle is 37o, with back gear at 35o.

6)   The inside gear, more compacted, has good events similarly.

7)   The auxiliary reach rod magnifies the inner depth in gear, but good in/out alignment is achieved by a slight reduction.


Additional notes:

Some of the mystery attending the LNER’s provision for a greater angular displacement of the inside lifting arm may be explained by the following details.

It may seem reasonable to assume for a given port and valve arrangement that a specific valve travel will result in specific valve events but this is not true.  It is the specific timing displacements of the valve that will determine the events. Because the A1 has of necessity a different inside gear layout the detailed valve velocities will also differ.

We have seen that the cut offs and valve travel on the drawing are nominal figures. The full forward gear cut offs of 75.22% and 72.29% for the front and rear ports respectively are produced from the outside gear simulation at a valve travel of 6.665″.  The inside gear, by comparison, achieves similar cut offs at a travel of 6.5″ because the detailed accelerations and decelerations of the valve are not the same. Furthermore, my simulation’s attempt to equalise the work done by both inside and outside cylinders shows these same cut off achievements at a valve travel of 6.477″ – significantly less than the 6.665″ of the outside gear.  Neither matching depths in gear nor matching valve travels can produce matching events. Was Peppercorn assuming that the inner gear needed more depth in gear to produce the 6.665″ of the outer valves?

Another contributory factor concerns the tighter curve of the inside expansion link, which cannot supply the same dieblock excursions as the outside link for a given depth in gear, either in amplitude or timing. Nonetheless, one would expect that a large valve gear model would supply all this detailed information and the design team’s decision to go in the opposite direction appears incredible. Why should they deliberately choose to allow the inside cylinder to work more heavily in view of the known Gresley foibles?

Mention has been made of the lead of the outside gear being rather less than the nominal on the drawing and the inner arrangement produces even less. In view of the recommendations of the more modern steam engineers (Porta) the A1 would appear to anticipate the practice, if not the theory, as suggested on the drawing. The quantity places LNER thinking in line with the GWR, opposing both the LMS and in turn BR.  In view of modern thinking this, together with many other aspects, sets BR down the wrong road. Certainly their much larger leads did nothing for the rather harsh wire-drawing at 20% cut off revealed for Britannia at Rugby.

The valve setting on the simulations are necessarily, of course, my own. I have chosen slightly disparate leads for both inside and outside gears as this produces better cut off conformity. Exactly equal leads are perfectly possible at the expense of tight equality of running cut offs, which carry greater responsibility. Also due to my interpretation, the undimensioned expansion link pin is verified by the simulation, as alterations around my figure worsen results.

Event diagrams show the LNER expertise, first in preparing the outside gear endowed with the typically decent equality obtained by Walschaerts’ gear of the day.   This consists of full gear cut offs of 2½% to 3% difference with a long range of close equality and matching release curves.


Forward gear events for the A1 outside valve motion

Forward gear events for the A1 inside valve motion

The graph for the inside gear bears adequate resemblance to the outer gear, which is no mean exercise given the quite different space in which to place the gear, the different connecting rod length and the totally different drive through a rather short radius rod. Such excellence only requires coordination of the reversing arrangements to match the working range. At 21% cut off the release is still a creditable 70% for either gear, but it requires a relative doctoring of the auxiliary reach rod arrangement to align the inside and outside depths in gear for ‘perfection’.  Whilst the actual performance of the A1s gave no reason for anxiety it is strange that this alignment attempt should fail. It also begs the question of whether this was detected by the Tornado new-build team.  That it is possible to equate matters has been presented in the tables given earlier.

Other cases where similar design alignment exercises occur are:

a)   Tank engines requiring to run as well in forward or back gear.

b)   Garratts using both fore and back simultaneously.

c)   4 cylinder engines using only two sets of gear.

d)   Mallet compounds having inside admission HP and outside admission LP valves.

It will be seen that in most cases the requirement is to align fore gear running with that of reverse, all within the same gear.  Those problems are greater in compacted Walschaerts’ layouts.