The Dead-beat Clock Escapement is a pendulum escapement in which the escape wheel locks dead — without recoil — on a curved pallet face concentric with the pallet arbor while the pendulum completes its swing. It is the standard escapement for precision regulator clocks and was the rate-controlling element in nearly every observatory timekeeper from 1715 to the quartz era. By eliminating the back-driving of the train that plagues recoil escapements, it lets the pendulum swing in near-isochronism, holding rate to within a fraction of a second per day in a well-built regulator.
Dead-beat Clock Escapement Interactive Calculator
Vary escape-wheel torque, lever ratio, impulse angle, and efficiency to see impulse energy per beat and the locked escapement motion.
Equation Used
The calculator applies the article equation for dead-beat escapement impulse energy. Escape-wheel torque M_w is converted from mN*m to N*m, the pallet impulse angle theta_i is converted from degrees to radians, and efficiency eta accounts for contact losses.
- Dead-beat locking face is ideal and produces no recoil.
- Input torque is the effective escape-wheel arbor torque during impulse.
- Impulse angle is entered in degrees and converted to radians.
- Efficiency represents pallet-tooth friction and contact losses.
The Dead-beat Clock Escapement in Action
The Dead-beat Clock Escapement, also called the Dead-beat (repose) pendulum escapement in horological literature, works by locking the escape wheel completely still during the supplementary arc of the pendulum's swing. George Graham introduced it around 1715 as a fix for the anchor escapement's recoil problem — where the escape wheel runs backwards every beat, dumping energy back into the train and disturbing the pendulum. In a dead-beat, the pallet has two distinct working surfaces: a locking face cut on an arc concentric with the pallet arbor, and an impulse face angled to deliver a brief push as the tooth slides off. While the pendulum swings beyond the impulse point, the escape tooth simply rests on the locking face and goes nowhere. No recoil. The wheel is dead.
Geometry is everything here. The locking face must lie on a true concentric arc — if it's cut even half a degree off, the tooth either drags during the supplementary arc (robbing energy and pulling the pendulum out of isochronism) or slips towards impulse early (giving you erratic rate). The drop, which is the small angular gap the tooth falls before locking on the next pallet, should sit around 1.5° to 2° on a typical regulator escape wheel. Less than that and the escapement risks failing to lock cleanly; more than that and you waste impulse energy as audible tick noise. Pallet impulse angle typically runs 1.5° to 2° per pallet, giving a pendulum amplitude in the 2° to 3° range — kept deliberately small because the dead-beat's circular-error contribution to rate scales with amplitude squared.
When tolerances drift, the symptoms are specific. A worn locking face shows up as a clock that gains erratically because the tooth slides forward on the curved face during the swing — this is called "galloping" and is the classic dead-beat failure mode. A bent escape-wheel tooth produces a missed beat or a stutter on one side of swing only. Oil that has gummed on the impulse faces — the dead-beat is one of the few escapements that genuinely needs lubrication on the pallets — produces a slowly losing rate over months as friction creeps up.
Key Components
- Escape wheel: Typically 30 teeth on a seconds-beating regulator, cut from hardened steel or beryllium copper. Tooth tips must be radiused to roughly 0.05 mm; sharper than that and they cut into the pallet faces, blunter and they skid on lock.
- Pallets (anchor): Carry the locking and impulse faces, usually polished hardened steel or jewelled with sapphire on high-grade regulators. The two pallet faces sit on arcs concentric with the pallet arbor — concentricity within 0.02 mm is the working spec for a quality clock.
- Pallet arbor: Pivots in jewelled or hardened steel bearings. Endshake should be 0.02 to 0.05 mm; more and the pallets walk axially and lose drop consistency.
- Crutch: The slim arm that couples pallet motion to the pendulum rod via a fork or pin. Crutch flex is a hidden rate killer — it must be stiff enough that no measurable lag develops between pallet release and pendulum response.
- Pendulum: The actual timekeeper. The escapement only meters energy to it. A 1-second regulator pendulum runs about 994 mm effective length and benefits from temperature compensation (gridiron, mercury jar, or invar) because the dead-beat's near-isochronism makes rod expansion the dominant rate variable.
Real-World Applications of the Dead-beat Clock Escapement
The Dead-beat Clock Escapement (concentric pallet) became the default for any clock where rate stability mattered more than chime complexity or robustness to dirty conditions. From precision astronomy timekeepers to the longcase regulators that set factory time across 19th century industry, the dead-beat earned its place because nothing else mechanical came close until the Riefler and Shortt free pendulums arrived — and those still used dead-beat-derived geometry. You'll find it today in modern regulator clocks, in academic horology programmes, and in any restoration where the original maker fitted Graham's design.
- Observatory timekeeping: Greenwich Royal Observatory's transit clocks from the mid-18th century onwards used Graham's Dead-beat (repose) pendulum escapement to time star transits — the rate stability was good enough to derive longitude observations.
- Horological education: WOSTEP and BHI training programmes have students cut and fit a dead-beat as the canonical exercise in pallet geometry — the concentric locking arc is the test of whether a student can read a depthing tool.
- Precision regulator clocks: Vienna regulators by Lenzkirch and Gustav Becker, English longcase regulators by Dent and Frodsham, and modern shop regulators by Erwin Sattler all run Dead-beat pendulum escapement (concentric pallet) designs.
- Public tower clocks: Many late-19th-century tower clocks fit a gravity-armed dead-beat variant — the Denison double three-legged gravity escapement at Westminster is descended from dead-beat thinking, and many smaller turret clocks use a direct dead-beat with weighted pendulums of 1.5 to 2 metres.
- Scientific reference clocks: Riefler observatory clocks of the early 20th century used a refined dead-beat running in partial vacuum, holding rate within 10 milliseconds per day — the benchmark mechanical timekeepers before Shortt free-pendulum systems took over in observatories.
- Restoration and conservation: Conservators at the British Museum and the Patek Philippe Museum routinely re-cut dead-beat pallets on period regulators, where original geometry must be preserved within a few hundredths of a millimetre.
The Formula Behind the Dead-beat Clock Escapement
The number that matters most for a dead-beat is the impulse energy delivered to the pendulum per beat — because that energy must equal the energy lost to friction and air drag, otherwise the pendulum amplitude drifts and rate goes with it. At the low end of the typical range (small drop, narrow impulse angle, light driving weight) you get a quiet, energy-efficient escapement that runs near-isochronously but dies if the train picks up any extra friction. At the high end (large drop, wide impulse, heavy weight) you get a noisy, robust escapement that overdrives the pendulum and amplifies circular error. The sweet spot for a 1-second regulator sits around a 2° impulse angle and 2° to 3° pendulum amplitude.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| Eimpulse | Energy delivered to the pendulum per impulse | joules (J) | ft·lbf |
| Mw | Torque on the escape wheel arbor from the train | N·m | in·oz |
| rp | Effective lever ratio from escape wheel to pallet arbor | dimensionless | dimensionless |
| θi | Impulse angle at the pallet, in radians | rad | rad |
| η | Mechanical efficiency of the pallet/wheel interface | dimensionless (typ. 0.35–0.55) | dimensionless |
Worked Example: Dead-beat Clock Escapement in a precision longcase regulator restoration
A specialist clockmaker is rebuilding an 1890 Dent longcase regulator with a 1-second pendulum and a 30-tooth escape wheel. The driving weight develops 0.0018 N·m of torque at the escape arbor, the pallet impulse angle is set to 2.0°, the lever ratio from escape wheel radius to pallet arbor radius is 0.85, and pallet efficiency on freshly polished steel faces measures 0.45. The job is to verify the impulse energy per beat lands in the range needed to sustain the 4 kg pendulum at 2° amplitude.
Given
- Mw = 0.0018 N·m
- rp = 0.85 —
- θi = 2.0 degrees
- η = 0.45 —
Solution
Step 1 — convert the impulse angle from degrees to radians, because the energy formula needs angular work in radians:
Step 2 — at the nominal setting, compute the impulse energy delivered to the pendulum per beat:
That's 24 microjoules per beat, twice per second — about 48 µW of mean power into the pendulum. For a 4 kg bob swinging at 2° amplitude, that sits comfortably above the air-drag and pivot-friction loss budget, so the pendulum will sustain.
Step 3 — at the low end of the typical operating range, drop the impulse angle to 1.5° (a worn or conservatively cut pallet):
You've lost 25% of impulse energy. On a clock with clean pivots this still runs, but if the bushings have any wear the pendulum amplitude collapses below 1.5° and the rate becomes unstable — the classic "clock won't keep running" complaint.
Step 4 — at the high end, push impulse angle to 3.0° (an overdriven escapement, sometimes seen on tower clocks adapted from regulator designs):
Now you're delivering 50% more energy than nominal. Amplitude climbs to 3° or more, circular error grows with the square of amplitude, and rate becomes sensitive to barometric pressure changes because air drag scales harder. The clock ticks loudly. You can hear an overdriven dead-beat from across a room.
Result
Nominal impulse energy is 24 µJ per beat, which is the right ballpark for a 4 kg, 1-second pendulum at 2° amplitude in a quality regulator. At 1.5° impulse angle the figure drops to 18 µJ — fine on a freshly serviced clock, marginal on anything with worn pivot jewels. At 3° impulse the figure climbs to 36 µJ and the clock becomes audibly loud and barometrically sensitive. If your measured amplitude doesn't match prediction, check three things in this order: (1) crutch-to-pendulum fork clearance — more than 0.1 mm of slop and impulse transmission gets erratic, (2) pallet-face polish — a matte finish from oil breakdown drops η from 0.45 to under 0.30 and you'll see amplitude collapse over 6-12 months, and (3) pivot endshake on the pallet arbor — over 0.05 mm and the pallets walk axially, changing effective drop and stealing impulse.
Choosing the Dead-beat Clock Escapement: Pros and Cons
The dead-beat is not the only escapement option, and which one you reach for depends on whether rate stability, robustness, or amplitude tolerance matters most. Compared against the recoil anchor it replaced and the gravity escapement that came after, the Dead-beat (repose) pendulum escapement sits in the precision-but-fussy zone of the design space.
| Property | Dead-beat Clock Escapement | Recoil (anchor) Escapement | Double Three-legged Gravity Escapement |
|---|---|---|---|
| Typical rate accuracy (well-adjusted, sea-level, room temperature) | ±1 to ±5 sec/day | ±30 to ±60 sec/day | ±0.5 to ±2 sec/day |
| Pendulum amplitude range | 2°–3° (small) | 4°–6° (large) | 1°–2° (very small) |
| Sensitivity to driving-weight variation | High — amplitude tracks weight | Moderate | Very low — gravity arms decouple drive |
| Lubrication requirement | Required on pallet faces | Required, less critical | None on impulse faces |
| Manufacturing precision needed | Concentric arcs to 0.02 mm | Forgiving, 0.1 mm acceptable | High — gravity arm balance critical |
| Suitability for tower clocks with variable load | Poor | Acceptable | Excellent |
| Maintenance interval before rate drift | 3–5 years | 5–10 years | 5–10 years |
| Cost / build complexity | Moderate | Low | High |
Frequently Asked Questions About Dead-beat Clock Escapement
Yes — "Dead-beat (repose) pendulum escapement" and "Dead-beat pendulum escapement (concentric pallet)" are both formal names for the same Graham escapement. "Repose" refers to the dead rest of the escape tooth on the locking face during the supplementary arc, and "concentric pallet" describes the geometry of that locking face — an arc cut concentric with the pallet arbor so the tooth neither advances nor recoils while the pendulum completes its swing.
The dead-beat is only near-isochronous, not perfectly isochronous. Increasing drive raises pendulum amplitude, and circular error makes a larger-amplitude pendulum run very slightly slower per swing — but the impulse arrives earlier in the swing as drive rises, which more than compensates and produces a net gain. On a typical regulator you'll see roughly 0.5 sec/day gain per 10% increase in driving weight.
The fix is not to add weight to compensate for a slow clock. Find the friction source instead — usually a dirty pallet face or a worn crutch fork.
Look at how clean and stable the load on the escape wheel will be. If the clock drives motion-work, hands exposed to wind, or a hammer train for striking, the load varies wildly and a dead-beat will show amplitude swings of 0.5° or more between striking and non-striking periods — rate will wander by several seconds a day. A gravity escapement decouples the pendulum from drive variation almost completely, which is why Denison's double three-legged design ended up at Westminster.
If the clock is a pure timekeeper with constant drive, the dead-beat is cheaper to build, easier to adjust, and gives you 90% of the gravity escapement's accuracy.
The locking face is not truly concentric with the pallet arbor. If the arc has been cut even 0.5° off true concentricity, the entry pallet's face slopes such that the escape tooth pushes the pallet backwards a tiny amount as the pendulum swings further into the supplementary arc. You'll see this as a faint reverse twitch of the escape wheel under loupe.
Diagnose by mounting the pallet on a depthing tool and rotating it through its working arc against a feeler — the locking face should maintain constant contact with no radial change. If the gap opens or closes, re-cut. This is the single most common error in apprentice-cut dead-beats.
Predicted-vs-measured amplitude shortfall on a dead-beat almost always traces to losses you didn't budget. In rough order of likelihood: suspension spring fatigue (an old spring flexes off-axis and dumps energy laterally — replace if older than 20 years), barometric pressure higher than design (air drag scales linearly with density), and pallet-face oil that has oxidised into a high-friction varnish.
Quick diagnostic: clean and re-oil only the pallet faces with a horological oil like Moebius 9415, then watch amplitude over 48 hours. If it climbs back toward 2°, the problem was friction. If it doesn't move, the suspension spring or train is your suspect.
No — and this is one of the dead-beat's genuine limitations. The impulse face slides against the escape tooth tip under load, which is a sliding-friction interface, not a rolling one. Run it dry and the steel-on-steel galls within months, the impulse face polishes unevenly, and η drops from 0.45 toward 0.25.
The co-axial works without oil because Daniels redesigned the geometry so impulse is delivered through near-radial contact rather than sliding contact. You can't retrofit that thinking onto a Graham dead-beat — the geometry is fundamentally different.
Beat rate is fixed by the pendulum length, so the wheel must rotate at half the speed with 30 teeth versus 15. Slower wheel rotation means lower tooth-tip velocity at the moment of drop, so the audible click of tooth landing on the locking face has less kinetic energy behind it — the clock sounds softer and more refined. That's why English regulators settled on 30-tooth escape wheels by the mid-19th century. The trade-off is that finer teeth need tighter tolerances on tooth-tip radius, typically 0.05 mm or less, or they wear the locking face quickly.
References & Further Reading
- Wikipedia contributors. Deadbeat escapement. Wikipedia
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