The double three-legged gravity escapement is a turret-clock escapement, designed by Edmund Beckett Denison in 1854, that delivers impulse to the pendulum from two small gravity arms instead of directly from the train. It solves the problem of variable driving torque corrupting timekeeping in large outdoor clocks where wind, snow, and frost load the hands unpredictably. Two three-legged escape wheels, offset on a common arbor, alternately lift and release the gravity arms. The result is famously consistent — Big Ben holds within about 1 second per day despite gale-force loads on its 4.3 m hands.
Double Three-legged Gravity Escapement Interactive Calculator
Vary pendulum timing, wheel step, fly braking time, and lift angle to see the escapement beat timing and gravity-arm lift relationship.
Equation Used
The calculator treats each pendulum beat as one escapement release. For a double three-legged gravity escapement, the escape wheel advances by the step angle on each half-period, while the fly fan should brake that step within the specified fly time. The lift ratio shows how much of the pallet contact arc is used by the gravity-arm lift.
- One escape-wheel step occurs on each pendulum beat.
- The double three-legged wheels advance roughly one 60 deg step per beat.
- Fly braking speed is approximated as constant over the step.
- Lift ratio compares gravity-arm lift angle with pendulum pallet contact arc.
The Double Three-legged Gravity Escapement in Action
The whole point of the Denison gravity escapement is to break the link between the going train and the pendulum. In a deadbeat or pin-wheel escapement the wheel teeth push the pendulum directly, so anything that changes train torque — wind on the hands, frost on the leading-off rod, a bird sitting on the minute hand — changes the impulse and shifts the rate. Denison's answer was to let the train do nothing more than lift two small weighted arms a tiny distance, then let those arms fall under gravity onto the pendulum. The pendulum always gets the same impulse, because gravity is the same yesterday, today, and at 3 a.m. on Christmas morning.
The geometry uses two escape wheels with three legs each, mounted on the same arbor but rotated 60° relative to one another, plus three lifting pins on each wheel set behind the legs. As the pendulum swings, it unlocks one leg, the train rotates roughly 60°, and a lifting pin raises the opposite gravity arm by 1.5° to 3°. That arm then rides down with the pendulum, dropping its tiny stored energy onto the impulse pallet. The other arm gets lifted on the next half-swing. If you set the lifting angle wrong — too high and the arm crashes back hard, too low and it fails to clear the locking face — the escapement either tripping (running away) or stalling. Workshop rule of thumb is around 2° of lift for a 2-second pendulum.
A fly fan on the escape wheel arbor air-brakes the rotation between unlocking and re-locking. Without it the legs would slam, the lifting pins would batter the arms, and you'd hear it from the street. The fly should bring the wheel to rest gently, with the next leg landing on its locking face and not on the pallet. Common failure modes are worn lifting pins (causes irregular impulse and audible knock), bent gravity arms from a botched setting-up, and a sluggish fly with dried-out pivot oil — the last of which is the single most frequent cause of a Denison escapement starting to trip after 5–10 years of service.
Key Components
- Twin three-legged escape wheels: Two wheels with three legs each, on a shared arbor, rotated 60° apart. Each wheel locks alternately against one of the gravity arms. Leg tip radius is typically 0.2–0.4 mm; any rounding from wear past 0.5 mm causes the lock to slip and the clock to gain wildly.
- Gravity arms (impulse arms): Two pivoted weighted levers, one on each side of the pendulum, that fall under their own weight to deliver impulse. Arm mass is typically 60–120 g for a turret clock, with the centre of gravity set so the impulse torque equals 5–10% of the pendulum's swing energy.
- Lifting pins: Three pins on the back of each escape wheel that raise the gravity arm by a set angle on each beat. Pin diameter is held to within ±0.05 mm; oversized pins lift too far and the arm bounces on return.
- Locking blocks (banking): Hardened steel stops that arrest the gravity arm at the bottom of its fall and rest the escape-wheel leg. Drop onto the locking block must be 0.3–0.6 mm — any more and the clock loses on heavy-load days.
- Fly fan: An air vane on the escape-wheel arbor that damps the wheel's rotation between unlock and re-lock. Vane area is sized so the wheel completes its 60° step in roughly 0.4 s on a 2-second pendulum.
- Pendulum and impulse pallet: The pendulum carries a pallet at its top end that the gravity arms rest against. On a 2-second turret pendulum the pallet contacts each arm for about 4° of pendulum arc, receiving the same energy on every beat regardless of train torque.
Industries That Rely on the Double Three-legged Gravity Escapement
The Denison double three-legged gravity escapement lives almost exclusively in the world of large public timekeepers — places where the hands are big, the weather is bad, and an accuracy specification has to be honoured under conditions a domestic regulator never sees. You will not find this escapement in a wristwatch or a mantel clock, because the lifting energies and arm masses don't scale down sensibly. Where it appears, it is almost always paired with a 1.5-second or 2-second pendulum, a fly fan, and a heavy seconds-beating going train.
- Public turret clocks: The Great Clock of Westminster (Big Ben), 1859, designed by Edmund Beckett Denison and built by E. J. Dent — the original and still the textbook example.
- Cathedral and civic clocks: Salisbury Cathedral's 1878 Dent turret clock and the King's Cross station clock both use double three-legged gravity escapements driving 2-second pendulums.
- University and parliamentary clocks: The Royal Liver Building clock in Liverpool (1911) by Gillett & Johnston runs a double three-legged gravity escapement on hands 7.6 m in diameter — larger than Big Ben's.
- Heritage clock restoration: Smith of Derby and Cumbria Clock Company routinely recommission Denison-pattern escapements during turret-clock overhauls across UK churches and town halls.
- Astronomical and precision regulators: A handful of late-19th-century observatory regulators by Dent and Frodsham used a scaled-down gravity escapement variant for self-winding precision standards before quartz.
- Demonstration and educational horology: The British Horological Institute's teaching workshop at Upton Hall maintains a working sectioned double three-legged gravity escapement used in BHI courses.
The Formula Behind the Double Three-legged Gravity Escapement
The number that matters most for a gravity escapement is the impulse energy delivered to the pendulum on each beat, because that is what determines whether the clock will keep running and whether it will keep good time. Too little impulse and the pendulum's amplitude decays until the arms fail to lift cleanly — the clock stops on a cold morning. Too much impulse and amplitude grows until the pendulum's circular error swamps the gain you bought from the gravity arms in the first place. The sweet spot for a typical 2-second turret pendulum sits around 2 millijoules per beat. At the low end of normal operation, around 1 mJ, you are running on the edge of stall in winter. At the high end, 4 mJ, you are heating the suspension spring and seeing 4°+ of amplitude with measurable circular error. The formula below gives the impulse energy as a function of arm geometry.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| Eimp | Impulse energy delivered to the pendulum per beat | J | ft·lbf |
| m | Mass of one gravity arm | kg | lb |
| g | Local gravitational acceleration | m/s² | ft/s² |
| r | Distance from arm pivot to centre of mass | m | ft |
| θ | Lift angle of the gravity arm | rad | rad |
Worked Example: Double Three-legged Gravity Escapement in a Victorian railway station turret clock
A heritage transport trust in York is recommissioning an 1889 Potts of Leeds turret clock on a former North Eastern Railway station, fitted with a double three-legged gravity escapement and a 2-second pendulum. Each gravity arm has a measured mass of 90 g, with the centre of mass 110 mm from the pivot. The trust wants the impulse energy at the nominal 2° lift angle, and bracketing values at 1° and 3° to set the lifting-pin geometry before final timing.
Given
- m = 0.090 kg
- g = 9.812 m/s² (York, latitude 53.96°N)
- r = 0.110 m
- θnom = 2 ° (0.0349 rad)
Solution
Step 1 — convert the nominal 2° lift angle to radians and compute (1 − cos θ) for the nominal case:
1 − cos(2°) = 1 − 0.99939 = 6.09 × 10−4
Step 2 — multiply through to get nominal impulse energy per beat:
Enom ≈ 5.9 × 10−5 J ≈ 0.059 mJ
Step 3 — at the low end of acceptable lift, 1°, the (1 − cos θ) term collapses by a factor of 4 because cosine error scales with θ2:
Elow ≈ 0.015 mJ
That is on the edge of what the pendulum needs to overcome air drag and suspension-spring losses on a winter night. A clock set this low will run, but it will stop the first time a starling lands on the minute hand. Step 4 — at the high end, 3°:
Ehigh ≈ 0.133 mJ
Now the arm crashes onto the pallet hard enough to be audible from inside the clock room, the pendulum amplitude grows to over 4°, and circular error starts adding 0.3 s/day of variable rate depending on barometric pressure. The 2° nominal sits exactly where Denison wanted it — enough to drive the pendulum through bad weather, not enough to spoil isochronism.
Result
Nominal impulse energy is approximately 0. 059 mJ per beat at the 2° design lift angle. In practical terms that means each gravity arm drops the equivalent of lifting a 1 g weight by 6 mm onto the pendulum twice every 2 seconds — small, but absolutely repeatable. Across the operating range the energy varies by roughly 9× between 1° and 3° lift, which is why getting the lifting-pin diameter and locking-block height right is the entire game on this escapement. If your measured rate drifts after recommissioning, the three most likely culprits are: (1) lifting pins worn flat on the leading edge, which raises the effective lift angle by 0.5°+ and makes the clock gain in summer when the pivots run free, (2) drop onto the locking block exceeding 0.6 mm, which audibly knocks and chews up the banking, or (3) a gravity arm bent during setting-up so its centre of mass sits at 105 mm instead of 110 mm — small enough to miss with a steel rule, big enough to drop impulse energy by 5%.
Choosing the Double Three-legged Gravity Escapement: Pros and Cons
The Denison gravity escapement was built for a specific job — keeping public time to within seconds per day under heavy and variable train load. Compared against the deadbeat (Graham) escapement that ruled regulator practice before it, and the pin-wheel escapement common on French turret clocks, the gravity escapement trades simplicity and ease of setup for immunity to torque variation. Pick the wrong escapement for the job and you fight it for the next 100 years.
| Property | Double three-legged gravity escapement | Graham deadbeat escapement | Pin-wheel escapement |
|---|---|---|---|
| Typical accuracy under variable load | ±1 s/day at Big Ben scale | ±5–15 s/day on a turret clock with wind-loaded hands | ±10–30 s/day |
| Sensitivity to driving torque | Effectively zero — gravity does the impulse | High — impulse force scales with train torque | Moderate |
| Setup and adjustment complexity | High — lift angle, drop, fly damping all interact | Low — pallet depth and drop, that's it | Low to moderate |
| Suitability for small clocks (<1 m pendulum) | Poor — arm mass and lift do not scale down | Excellent — used in regulators and longcase | Good — used in French mantel clocks |
| Maintenance interval before rate drift | 8–12 years (fly pivot oil) | 5–8 years (pallet faces) | 5–10 years (pin wear) |
| Component count and machining cost | High — 2 escape wheels, 6 pins, 2 arms, fly | Low — 1 wheel, 2 pallets | Low to moderate |
| Audible signature | Two-tone tick from alternating arms | Single sharp tick | Soft tick |
Frequently Asked Questions About Double Three-legged Gravity Escapement
Tripping under wind load almost always means the fly fan is too small or its pivots are dragging. When the wind gusts the leading-off rod, the going train suddenly has more torque available; the fly is supposed to absorb that surplus during the 60° step, but if it can't, the escape wheel races, the next leg overshoots its locking face, and the wheel runs on for one or more extra steps — the clock gains a few seconds and you'll hear a double-tick.
Diagnostic check: pull the fly arbor, oil the pivots with a light clock oil, and confirm the fly takes about 0.4 s to bring the wheel to rest on a 2-second pendulum. If it stops in 0.2 s or less, you need a bigger vane.
Use the three-legged version on 1.5-second or 2-second pendulums where the train can comfortably make a 60° step per beat — that is most UK turret-clock practice. Use the four-legged on shorter pendulums (1-second or below) where 90° per beat keeps the wheel teeth at a sensible size. The four-legged also takes a slightly smaller fly because each step is shorter in time, but it doubles the wear rate on lifting pins.
If you are restoring an existing tower, match what is there. Mixing patterns mid-restoration breaks the original maker's tooth-count arithmetic in the going train.
Nine times out of ten this is amplitude-driven circular error from too much lift. Measure the gravity arm lift angle directly with a protractor against the locking block. If it has crept up to 2.5° or 3°, your lifting pins are oversized — either replacement pins were turned to the wrong diameter, or the originals are worn rough on the leading edge and dragging the arm higher than they should.
Reduce lift by reshaping or replacing the pins. A 0.5° reduction in lift typically pulls 2–3 s/day off the rate on a 2-second pendulum.
Possible but rarely worth it. The gravity escapement needs a going train delivering steady torque sufficient to lift the arms but no more — too much torque and the lift becomes violent. Most deadbeat trains are geared for direct impulse and have wheel counts that don't divide cleanly to give 60° per beat at the new escape arbor.
You'll usually end up re-cutting at least the contrate and escape-wheel pinion, adding a fly, and reworking the leading-off work to clear the new arms. By the time you have done all that, you have built a new clock around the old frame.
That's the whole design intent. The train's only job is to lift the gravity arm to its set angle θ — once the arm is lifted, the train disengages and the falling arm alone delivers impulse to the pendulum. The energy is m·g·r·(1−cos θ), which depends only on geometry and gravity, not on how hard the train is pulling.
This is why a Denison clock can have a kilogramme of frost on its hands and still keep time to a second a day. The train works harder, but the pendulum never knows.
Aim for 0.3–0.6 mm of drop on a turret-scale escapement. Below 0.3 mm and the leg can fail to lock cleanly when the arm bounces — you get the occasional skipped beat that shows up as a 2-second loss with no obvious cause. Above 0.6 mm and the leg slams the block hard enough to dent it over a few years; you'll see the rate drift gradually as the banking deforms and effective lift angle changes.
Check drop with feeler gauges between leg tip and locking face at the moment of lock. If the figure has changed since last service, look for a bent arm or a worn pivot before adjusting the block itself.
References & Further Reading
- Wikipedia contributors. Gravity escapement. Wikipedia
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