Allen valve lift or toe is the small added vertical motion built into the Allen straight-link valve gear that lifts the die block at the end of each stroke to enlarge port opening near full gear. Charles Trick Porter's collaborator William Allen patented the gear in 1855 to fix the port-restriction problem that plagued Stephenson and Gooch gears at short cutoffs. The toe motion combines forward and backward eccentric rod paths to add lift exactly when the valve needs it. The result is sharper steam admission and 5-15% better cylinder filling at short cutoff on locomotives like the LB&SCR Gladstone class.
Allen Valve Lift or Toe Interactive Calculator
Vary eccentric travel, Allen toe lift, and reverser angle to see total valve travel and the lift contribution.
Equation Used
The calculator resolves total valve travel into the eccentric-driven term Te cos(theta_r) and the Allen toe-lift term Lt sin(theta_r). Larger toe lift or reverser angle increases the lift contribution to the valve motion.
- Eccentric travel and Allen lift are treated as orthogonal motion components.
- theta_r is entered in degrees and converted to radians.
- Lap, lead, die-block clearance, and dynamic steam effects are not included.
How the Allen Valve Lift or Toe Works
The Allen gear runs two eccentric rods into a straight expansion link, same as Stephenson, but the link itself is hung so it moves vertically when the gear notches up. That extra vertical travel is the lift — sometimes called toe motion because the bottom of the link toes outward as the reverser shortens cutoff. The die block sees the sum of two motions: the horizontal swing from the eccentric the gear is favouring, plus the vertical lift from the link itself. Add them and you get faster valve travel during the admission event without lengthening the eccentric throw.
Why bother? At short cutoff a Stephenson gear chokes itself. The valve barely cracks the port before closing again, so steam admission is throttled and you lose power even though you're trying to run economically. Allen's lift opens the port wider during that brief admission window. You get fuller cylinder filling, sharper exhaust, and a measurable improvement in mean effective pressure at 25-35% cutoff.
Get the geometry wrong and you create new problems. If the lift is excessive — say the link suspension geometry shifts the die block more than 1.5 mm vertically beyond the design — the valve overruns its seat, you lose lap on the exhaust side, and back-pressure climbs. Too little lift and the gear behaves like a plain Stephenson with no benefit. The pin centres in the suspension links must hold position to within ±0.25 mm, and the die block clearance in the slot must be 0.05-0.10 mm. Loose pins or a worn die block let the lift wander cycle to cycle and you get unequal valve events front-to-back, which shows up as uneven exhaust beat.
Key Components
- Forward eccentric rod: Drives the top end of the straight link from the forward eccentric on the axle. Throw is typically 110-140 mm on a standard-gauge locomotive, set to give the design valve travel at full forward gear with lap and lead included.
- Backward eccentric rod: Drives the bottom end of the link from the backward eccentric, 180° opposed to the forward rod. The geometry must match the forward rod throw within 0.5 mm or the gear will run unequally between forward and reverse.
- Straight expansion link: The slotted bar carrying the die block. Allen's version is straight, not curved like Stephenson's, so the slot length sits typically at 200-260 mm with a slot width matched to the die block at 0.05-0.10 mm clearance.
- Link suspension hangers: Two short links hung from the lifting shaft that hold the expansion link and impart the vertical lift as the reverser moves. Hanger length and pivot positions set the lift curve — get the angles wrong and you cancel the toe action entirely.
- Die block: Slides in the link slot and transmits motion to the valve rod. Hardened steel against a hardened slot, with the bore for the valve rod pin held to H7/g6 fit. Wear here is the first thing that degrades valve events on an old engine.
- Lifting shaft and reach rod: Connects the cab reverser to the link hangers. Sets cutoff from full gear (typically 75% admission) down to about 15% at the notch-up limit. Lost motion in the reach rod must stay below 1 mm or the driver cannot hold a stable cutoff.
Where the Allen Valve Lift or Toe Is Used
Allen gear saw heavy use where designers wanted Stephenson-style simplicity but needed better breathing at short cutoff. It appeared on stationary mill engines, marine compounds, and a number of British and American locomotives between 1860 and 1910. Walschaerts gear eventually displaced it on most road locomotives because Walschaerts gives constant lead at all cutoffs, but Allen gear remains common in preserved engines and is still chosen for some live-steam scale models where the straight link is easier to machine than a curved Stephenson link.
- Steam locomotives: LB&SCR Gladstone class 0-4-2 locomotives designed by William Stroudley, which used Allen straight-link gear from 1882 onward.
- Stationary steam engines: Porter-Allen high-speed engines built by the Southwark Foundry from 1862, where the Allen gear's sharp admission was critical for governor stability at 200-300 RPM.
- Marine engines: Compound marine engines on mid-Victorian merchant ships where short cutoff economy mattered for long voyages.
- Live steam models: 5-inch gauge LB&SCR Gladstone replicas and similar Stroudley-class scale builds where Allen gear is reproduced faithfully.
- Industrial mill drives: Textile and grain mill engines in the 1870s-1890s where steady torque at part load benefited from Allen's wider port opening at short cutoff.
- Heritage railways: Restoration of preserved Stroudley locomotives at the Bluebell Railway, where original Allen gear must be set to the historical valve event tables.
The Formula Behind the Allen Valve Lift or Toe
The useful number for setting up Allen gear is the maximum valve travel as a function of cutoff. Stephenson gear loses travel almost linearly as you notch up. Allen gear holds travel better because the lift adds to the eccentric component. At full gear (long cutoff, ~75%) the lift contribution is near zero and the gear behaves like Stephenson. At medium cutoff (35-50%) the lift starts to count and you see the Allen advantage emerge. At short cutoff (15-25%) the lift contribution can equal 20-30% of total valve travel, which is precisely where Stephenson gear runs out of breathing capacity. The sweet spot for most road work sits around 25-35% cutoff where lift, lead, and lap combine for the cleanest indicator card.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| Tv | Total valve travel at the given cutoff | mm | in |
| Te | Eccentric-driven valve travel component (horizontal contribution from the link) | mm | in |
| Lt | Allen lift or toe motion at the die block | mm | in |
| θr | Reverser angle from mid-gear (0° = mid-gear, ~30° = full gear) | deg | deg |
Worked Example: Allen Valve Lift or Toe in a preserved Stroudley Gladstone class locomotive
You are setting valve travel on a preserved LB&SCR Gladstone 0-4-2 fitted with Allen straight-link gear during overhaul at a heritage shed. The design eccentric throw gives Te = 115 mm at full gear and the link suspension geometry produces a maximum lift Lt = 18 mm. You need to predict valve travel at three cutoffs the driver actually uses: 75% (full gear, starting), 35% (cruise), and 18% (high-speed coasting under steam).
Given
- Te,max = 115 mm
- Lt,max = 18 mm
- θr at full gear = 30 deg
- θr at 35% cutoff = 18 deg
- θr at 18% cutoff = 9 deg
Solution
Step 1 — at full gear (75% cutoff, θr = 30°), the eccentric component dominates and lift is small because the link is near its lowest position. Scale Te by cos(30°) and Lt by sin(30°):
This is the long-cutoff travel you want for starting the train — wide ports, full admission, maximum tractive effort. The Allen lift adds 9 mm here, which is useful but not dramatic.
Step 2 — at the nominal cruise condition, 35% cutoff with θr = 18°:
Note we scale the lift by reverser position because lift grows from mid-gear up. Travel here is actually higher than full gear because the lift catches up before eccentric falloff dominates. This is the Allen advantage in action — at the cutoff you cruise on, the gear breathes better than a Stephenson gear of equal eccentric throw, which would give about 100 mm here.
Step 3 — at short cutoff for high-speed running, 18% cutoff with θr = 9°:
The total travel number stays high but the time the port stays cracked open is short. This is where the lift earns its keep — without it, the port would barely open at all during the brief admission event. With Allen lift, you still get usable cylinder filling at 18% cutoff, which Stephenson gear simply cannot deliver on the same eccentric throw.
Result
Nominal valve travel at 35% cutoff is 112. 7 mm, with full-gear travel of 108.6 mm and short-cutoff travel of 114.4 mm. In practice the driver feels this as an engine that pulls cleanly off the platform at full gear, settles into an economical 35% cutoff at line speed without the indicator card collapsing, and still answers the regulator at 18% cutoff downhill — exactly the operating envelope Stroudley designed the Gladstones for. The range from 108-115 mm tells you the gear holds valve travel almost flat across the working cutoff band, which is the Allen design intent. If your measured travel is below predicted at short cutoff — say 95 mm at 18% — the most likely causes are: (1) lifting-shaft trunnion wear letting the link sag and cancelling the toe motion, (2) the suspension hanger pin centres drifting from spec because of elongated holes, or (3) reach-rod lost motion above 1 mm preventing the reverser from holding the notched-up position cleanly.
Allen Valve Lift or Toe vs Alternatives
Allen gear sits between Stephenson and Walschaerts in the design space. It fixes Stephenson's port-restriction problem at short cutoff without going to the full complication of Walschaerts. Compare on the dimensions that matter for a locomotive engineer choosing a gear or a model engineer planning a build.
| Property | Allen straight-link gear | Stephenson link gear | Walschaerts gear |
|---|---|---|---|
| Port opening at 20% cutoff | ~85% of full-gear opening | ~55% of full-gear opening | ~75% of full-gear opening with constant lead |
| Lead variation across cutoffs | Increases with notch-up (~1-3 mm change) | Increases with notch-up (~2-4 mm change) | Constant at all cutoffs (design feature) |
| Number of major moving parts | 6 (eccentrics, rods, link, hangers, die block, valve rod) | 5 (no separate lift hangers) | 8 (combination lever, radius rod, return crank, etc.) |
| Manufacturing complexity | Moderate — straight link easier than curved | Lower — but curved link is hard to machine accurately | Highest — most pin joints, tightest tolerances |
| Typical cutoff range | 15-75% | 25-75% practical | 10-85% |
| Pin joint count requiring re-bushing | 8 pins on inspection schedule | 6 pins | 12+ pins |
| Best application fit | High-speed stationary engines, mid-Victorian locomotives | Early locomotives, simple shunters, marine reversing engines | Modern road locomotives, anything needing constant lead |
Frequently Asked Questions About Allen Valve Lift or Toe
Set the engine on a barring jack and crank it slowly through one full revolution at 25% cutoff while measuring valve travel at the valve spindle with a dial indicator. Record peak travel. Then notch up to full gear and repeat. On a healthy Allen gear the short-cutoff travel will be within 90-95% of the full-gear travel. If it drops below 75% you have lost the toe motion — the link is no longer rising as the reverser pulls up.
The usual culprit is the lifting shaft trunnion bearings. They wear oval and let the whole link assembly sag, which collapses the geometric difference between forward and backward eccentric paths that the lift depends on. Re-bushing the trunnions to the original 0.05 mm clearance restores the action immediately.
Almost always asymmetry between the forward and backward eccentric throws or rod lengths. Allen gear depends on the two rods being matched within 0.5 mm in throw and within 1 mm in length. Anything more and the lift adds correctly going forward but subtracts going backward, so reverse running gets choked port openings and a ragged exhaust beat.
Check by measuring eccentric throw at the strap with the rod off, then check rod length pin-to-pin with a vernier. Re-shimming the eccentric strap or remaking one rod to match is straightforward shed work but it must be done — you cannot tune around this with valve setting alone.
Pick based on the prototype, not the engineering. If you are building a Stroudley Gladstone or another mid-Victorian engine that historically used Allen gear, build Allen — anything else looks wrong and the model judging will mark it down. If your prototype is a 20th-century locomotive, build Walschaerts because that is what the engine had.
From a pure machining standpoint Allen is friendlier than Stephenson because the link is straight rather than curved, but Walschaerts is friendlier still because every pin joint is on a flat plane and the parts can be made on a mill without curved-slot work. Constant lead is a real operational benefit on a model that gets driven hard — Allen gives variable lead just like Stephenson.
Allen gear standard valve event tables assume the lift component is contributing correctly at the cutoff you set the gear at. If the table says set 1.5 mm lead at full gear and you set it there, but the suspension hangers are mounted slightly off the design height, then at running cutoff the lift acts at the wrong point in the cycle and admission is late.
Verify hanger pivot heights against the original drawing before trusting any valve event table. A 3 mm error in hanger pivot height shifts the lift contribution by enough to delay admission by 5-8° of crank angle, which is exactly what late admission on the card looks like.
15% to 75% on paper. In real driving you will live between 25% and 40% almost the whole time. Below 25% the admission window gets so brief that even the Allen lift cannot deliver enough steam mass per stroke to maintain power, and you will be reaching for the regulator instead. Above 50% you are wasting steam — the cylinders are filling longer than the expansion phase can usefully use.
The reason designers liked Allen gear was specifically that 25-40% band, where it gave 10-15% better cylinder filling than Stephenson on the same eccentric throw. That translates to either more power at the same coal rate or less coal at the same power.
Linear scaling on the geometry, yes — every dimension shrinks by the same scale factor. But the clearances do not scale linearly. A full-size engine with 0.10 mm die block clearance scales to 0.02 mm at 5-inch gauge, which is below what you can hold in a home shop and below what stays clean in service.
Hold model die block clearances at 0.04-0.06 mm regardless of scale. The proportional looseness will be greater than the prototype but the gear will still produce correct lift action because the lift comes from the link suspension geometry, not from the die block fit. Where you must not relax tolerance is on the suspension hanger pin centres — those still need ±0.1 mm even at small scale or the lift goes wrong.
References & Further Reading
- Wikipedia contributors. Allan valve gear. Wikipedia
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