The Mudge gravity escapement is a clock escapement that impulses the pendulum using the weight of small pivoted arms rather than direct force from the train. Thomas Mudge designed the principle around 1760 as a way to isolate the pendulum from train-torque variations. Each beat, the escape wheel only re-lifts the gravity arm; the arm then falls under its own weight to deliver a constant impulse. That isolation gives turret-grade accuracy of better than 1 second per day on installations like the Westminster clock at the Palace of Westminster.
Mudge Gravity Escapement Interactive Calculator
Vary the gravity-arm fall angle and impulse-energy band to see the average arm moment needed for a constant pendulum impulse.
Equation Used
The worked example gives the usual gravity-arm fall range of 3 to 4 degrees and an impulse-energy range of 50 to 200 uJ. This calculator converts that energy band into the average gravitational moment the falling arm must provide: energy divided by angular fall in radians.
- Impulse energy is the gravitational energy released by one arm fall.
- Average arm moment is used over the small fall angle.
- Friction, pallet impact losses, and rebound are ignored.
- The escape wheel only re-lifts the arm and does not directly impulse the pendulum.
The Mudge Gravity Escapement in Action
The mechanism does one job — keep the pendulum's impulse force constant no matter what the train is doing. In a recoil or deadbeat escapement, every speck of dirt on a pallet, every drop in driving weight, every gust of wind on the hands of a turret dial pushes back through the wheel teeth and shows up as a rate change. Mudge's answer was to break that link. The escape wheel never touches the pendulum directly. Instead, two small pivoted arms — the gravity arms — sit either side of the pendulum rod. The pendulum, on each swing, lifts one arm out of the way and then receives an impulse from the other arm falling under gravity through a small angle, typically 3° to 4°. The escape wheel's only job between beats is to re-lift the arm that just fell, ready for the next half-swing.
Why design it this way? Because gravity is the most stable force you have access to in a clock tower. Driving weight changes as the rope unwinds from the barrel, friction in the wheel train varies with temperature and lubricant age, and wind load on a turret minute hand can spike the train torque by a factor of 5 or more. None of that reaches the pendulum in a Mudge escapement — the impulse is set purely by the mass of the gravity arm and the angle through which it falls. That is the locking pallet doing its job: holding the train still until the pendulum unlocks it, then letting the wheel advance one tooth and stop again.
Get the tolerances wrong and the whole thing trips or stalls. The lifting must occur after the pendulum has already passed centre — if lift starts before centre, you steal energy from the pendulum instead of giving it. The locking corners on the escape wheel teeth need a clean radial face within roughly 0.02 mm of true; a rounded corner causes the arm to lock late and slip, producing the classic symptom of a clock that runs but loses time erratically and audibly stutters. And the gravity arms must be free on their pivots — pivot friction above about 1% of the arm's gravitational moment will starve the pendulum of impulse and the clock will stop within a few hours.
Key Components
- Gravity Arms (pair): Two light pivoted arms, usually brass with steel pallet faces, that fall through a fixed angle of 3° to 4° to impulse the pendulum. Their mass and fall angle alone determine impulse energy — typically 50 µJ to 200 µJ per beat for a 1-second turret pendulum. Pivot friction must stay below 1% of the arm's gravitational moment or the clock loses amplitude and stops.
- Escape Wheel: In Mudge's original layout a single wheel with sharp radial-faced teeth; in Denison's later double three-legged variant, two three-armed star wheels share a common arbor. The wheel's only job is to re-lift the fallen gravity arm, never to impulse the pendulum directly. Tooth tip radius held under 0.05 mm to keep locking crisp.
- Locking Pallets: Hardened steel faces on each gravity arm that catch the escape wheel tooth and hold the train static between beats. Locking face must sit within 0.02 mm of true radial — a rounded or worn locking face causes erratic timekeeping and audible double-ticking.
- Lifting Pallets: Separate hardened faces, usually angled at 30° to 35°, that the escape wheel tooth slides up to re-cock the gravity arm. The lifting action happens entirely outside the pendulum's impulse window so that train torque never reaches the rod.
- Fly or Air Brake: A small vaned fan on the escape wheel arbor that absorbs the kinetic energy of the train when the wheel runs free between locking and re-lifting. Without the fly, the wheel overshoots the next locking corner and the clock trips. Sized so the run-down time matches roughly 1/4 of the pendulum half-period.
- Pendulum (1-second or 1.5-second): The timekeeping element itself, isolated from the train. Typical turret installations use a 1-second seconds-beating pendulum with a heavy bob (15 kg to 300 kg) and a temperature-compensated rod. Amplitude usually held between 1.5° and 2° each side of vertical.
Industries That Rely on the Mudge Gravity Escapement
The Mudge gravity escapement and its descendants found their home wherever a pendulum had to keep accurate time despite a wildly variable driving torque. That makes turret clocks, observatory regulators, and reference standards their natural habitat. The double three-legged variant Edmund Beckett Denison developed for the Westminster clock in 1854 became the de facto standard for British public clocks for the next century, and you still find working examples across cathedral towers, railway stations, and university observatories. The reason it dominated is simple — nothing else handled wind-loaded hands as well, and nothing else kept a public clock within 1 second per day across a freezing winter and a hot summer.
- Public Timekeeping: The Great Clock of Westminster (Big Ben), London — Denison's double three-legged gravity escapement, in continuous service since 1859, drives a 4.4 m, 305 kg pendulum to better than 1 second per day.
- Cathedral & Civic Turret Clocks: Smith of Derby and JB Joyce of Whitchurch fitted Denison gravity escapements to hundreds of UK cathedral and town hall clocks from 1860 onwards, including the clock at Manchester Town Hall and St Paul's Cathedral.
- Observatory Regulators: Late 19th-century Frodsham and Dent astronomical regulators used single-beat gravity escapements as a reference standard before the Shortt free-pendulum displaced them in the 1920s.
- University Metrology Demonstrators: Cambridge and Greenwich teaching collections retain working Denison gravity escapement bench models used to demonstrate constant-impulse principles to horology and physics students.
- Railway Station Clocks: Major London termini including King's Cross and Paddington fitted gravity escapement turret movements through the late Victorian period to drive multiple slave dials from one master.
- Heritage Restoration: Specialist workshops such as the Cumbria Clock Company and Smith of Derby continue to overhaul and rebuild Denison gravity escapements on listed turret clocks across the UK and Commonwealth.
The Formula Behind the Mudge Gravity Escapement
The figure that matters most when you size or audit a gravity escapement is the impulse energy delivered to the pendulum each beat. Too little and the pendulum dies; too much and the amplitude rises until the arms slam and circular error swamps the rate. The energy is set entirely by the gravity arm's effective mass, the height through which its centre of gravity drops, and gravitational acceleration. At the low end of the typical turret range — a small church clock with a 5 kg pendulum bob and 1° fall angle — you'll see roughly 30 µJ per beat. The nominal Westminster-class installation lands near 150 µJ. Push the fall angle past 5° on a heavy-bob design and you'll find the amplitude grows uncontrollably until the locking corners take a beating and the rate goes off.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| Eimp | Impulse energy delivered to the pendulum per beat | J (joules) | ft·lbf |
| marm | Effective mass of the gravity arm | kg | lb |
| g | Gravitational acceleration | 9.81 m/s² | 32.2 ft/s² |
| Lcg | Distance from arm pivot to arm centre of gravity | m | in |
| θfall | Angle through which the arm falls during impulse | rad or ° | ° |
Worked Example: Mudge Gravity Escapement in an 1890 Smith of Derby cathedral turret clock
A heritage clock workshop in Lichfield is auditing the gravity escapement on an 1890 Smith of Derby cathedral turret clock before recommissioning. The double three-legged escapement drives a 1.5-second pendulum with a 90 kg bob. Each gravity arm has an effective mass of 0.180 kg with its centre of gravity 95 mm from the pivot. The original drawings specify a fall angle of 3.5°. The workshop wants to verify the impulse energy per beat to confirm the pendulum will sustain a 1.8° amplitude swing.
Given
- marm = 0.180 kg
- g = 9.81 m/s²
- Lcg = 0.095 m
- θfall (nominal) = 3.5 °
Solution
Step 1 — convert the nominal fall angle to radians and compute the (1 − cos θ) drop factor:
(1 − cos 3.5°) = 1 − 0.99813 = 0.001866
Step 2 — compute the nominal impulse energy per beat:
That sits squarely in the band you'd expect for a heavy cathedral pendulum — enough to keep a 90 kg bob swinging at 1.8° against pivot and air losses, but not so much that the locking corners take a hammering each beat.
Step 3 — at the low end of the typical operating range, with the fall angle worn or shimmed down to 2.5°, the drop factor collapses:
Elow = 0.180 × 9.81 × 0.095 × 0.000952 = 160 µJ
That is roughly half the nominal impulse, and on a 90 kg bob you'd watch the amplitude decay over a few hours and the clock stop by lunchtime — a classic symptom of a re-bushed gravity arm sitting at the wrong height.
Step 4 — at the high end of the range, push the fall angle to 5° (a common mistake when a fitter over-corrects a slow-running clock by raising the lifting pin):
Ehigh = 0.180 × 9.81 × 0.095 × 0.003805 = 638 µJ
That is more than double the nominal energy. The pendulum amplitude will climb past 2.5° within an hour, circular error will start eating accuracy, and you'll hear the gravity arms slamming hard onto the bankings — the audible signature of an over-impulsed gravity escapement.
Result
The nominal impulse delivered each beat is 313 µJ, which is the right energy budget for a 90 kg bob swinging at 1. 8° on a 1.5-second period. In practice you should hear a soft, even tick with no double-strike and watch the amplitude settle within 20 minutes of starting. The low-end case at 2.5° fall (160 µJ) leaves the clock unable to sustain amplitude and it will stop within hours; the high-end case at 5° fall (638 µJ) over-impulses the pendulum, drives amplitude past 2.5°, and beats up the locking corners. If your measured impulse is 20% below the predicted 313 µJ, check first for arm-pivot wear that has dropped the centre of gravity, then for a worn lifting pin reducing effective fall angle, and finally for hardened oil on the lifting pallets robbing the arm of free fall.
Choosing the Mudge Gravity Escapement: Pros and Cons
The gravity escapement is not the only way to feed a pendulum a constant impulse. The deadbeat escapement is simpler, the Riefler and Shortt-Synchronome free pendulum systems are more accurate, and even the humble recoil escapement still has its place on simple bracket clocks. Where each one wins comes down to torque sensitivity, amplitude stability, and how much torque the train can throw at it before accuracy collapses.
| Property | Mudge / Denison Gravity Escapement | Graham Deadbeat Escapement | Shortt-Synchronome Free Pendulum |
|---|---|---|---|
| Daily rate accuracy (turret-class install) | ±0.5 to ±1 s/day | ±2 to ±5 s/day | ±0.01 s/day |
| Sensitivity to driving torque variation | Negligible — pendulum isolated | High — direct impulse from train | Negligible — slave drives master |
| Tolerance of wind-loaded hands | Excellent — designed for it | Poor — rate shifts with wind | Excellent — fully isolated |
| Mechanical complexity (part count) | Medium — 2 gravity arms, fly, locking & lifting pallets | Low — 1 pair of pallets | Very high — 2 coupled pendulums, electrical link |
| Typical pendulum amplitude | 1.5° to 2.0° | 2.0° to 4.0° | 0.5° to 1.0° |
| Build / restoration cost (relative) | Medium-high | Low | Very high |
| Typical application fit | Turret & cathedral clocks, civic timekeeping | Domestic regulators, longcase clocks | Observatory time standards (pre-quartz) |
Frequently Asked Questions About Mudge Gravity Escapement
Mudge's original design suffered from a problem called tripping — under heavy train torque or after a sudden shock, the escape wheel could overshoot its locking corner and run away, sometimes for several teeth. On a domestic clock that is a nuisance; on a 5 tonne turret movement it can shear teeth.
Denison's double three-legged layout splits the escape wheel into two three-armed stars on a common arbor, with the locking and lifting actions divided between them. That geometry makes tripping mechanically almost impossible because the locking corner of one star is engaged whenever the other is mid-lift. He developed it specifically for the Westminster commission in 1854 after the original Vulliamy proposal was rejected, and it has been the British turret-clock standard ever since.
A slow amplitude decay over roughly an hour is almost always thermal — the pivot oil is thickening as the case temperature drops, or the lifting pallet faces are picking up a film of oxidised oil that increases sliding friction during re-lift. Both effects are time-dependent rather than load-dependent, so the clock starts well and fades.
Check the lifting pallet faces under magnification first. If you see any discoloration or matte film, clean them with naphtha and re-polish to a mirror finish. Gravity escapements are unusual in that the lifting pallets should run dry on a polished face — oil on the lifting pallets is actively harmful because it adds a viscous load to the falling arm.
The decision comes down to bob mass and target amplitude. From the impulse energy formula, going from 3° to 4° fall increases delivered energy by roughly 78% — almost double. For a heavy bob above 100 kg you generally want the larger angle to overcome air drag and pivot losses; for a lighter bob in the 30 to 60 kg range, 3° is usually plenty and a larger angle drives amplitude into the circular-error zone above 2°.
A practical rule of thumb: target a steady-state amplitude of 1.75° ± 0.1° and adjust the fall angle to land there. If you have to go above 4.5° to maintain amplitude, your pivots are dragging or your bob is too light for the pendulum length you've chosen.
An asymmetric double-tick is a locking-geometry problem, not a timing problem. One gravity arm is locking cleanly on its escape wheel tooth and the other is bouncing off and re-locking — you're hearing the second impact.
The usual cause is one of three things: the locking face on the offending arm has worn rounded (look for a radius greater than 0.05 mm at the corner), the locking pin or banking screw on that side has shifted in its mounting, or the escape wheel sits eccentric on its arbor by more than about 0.1 mm so that one star presents a different effective locking radius than the other. Eccentricity is the most common diagnosis on movements that have been moved or had the escape wheel re-bushed.
Mechanically yes, practically almost never. A gravity escapement needs vertical clearance for the falling arms, a separate fly, and considerably more frame depth than a Graham deadbeat. You usually have to rebuild the front plate and add a sub-frame, which on a period longcase destroys provenance.
The bigger issue is that domestic longcase clocks don't have the torque variability problem gravity escapements solve. A well-set Graham deadbeat in a longcase will hold ±2 s/day without trouble, and the gravity escapement's headline advantage — torque immunity — gives you almost nothing on a clock with a clean fusee or a steady weight drop. Save the gravity escapement for turret work where it earns its keep.
The fly is the small vaned brake on the escape wheel arbor. Its job is to absorb the kinetic energy of the train as the wheel rotates between unlocking and the next locking event — typically a window of about 0.25 to 0.4 seconds on a 1-second pendulum. You want the fly to bring the wheel to rest just before it hits the next locking corner, not on it.
If the fly is too small or too light, the wheel slams into the locking corner with residual velocity and you get accelerated locking-face wear — the escapement will drift out of beat within a few months. If the fly is too large, the wheel doesn't reach the locking corner in time and the clock trips. Adjust by adding or removing fly vane area in 5% steps until you can hear a soft tick with no metallic ring.
References & Further Reading
- Wikipedia contributors. Gravity escapement. Wikipedia
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