A Fusee is a conical, spirally grooved pulley that sits between the mainspring barrel and the going train of a clock or watch, equalising the falling torque of the mainspring as it unwinds. A correctly cut fusee holds delivered torque within roughly ±2% across an 8-day run, against a raw mainspring that loses 40-60% of its torque from full to flat. We use a fusee where rate stability matters — pocket watches, marine chronometers, and precision longcase movements. John Harrison's H4 sea watch of 1759 ran on a fusee, and that is the geometry that won the Longitude Prize.
Fusee Torque Equalization Interactive Calculator
Vary spring torque and small-end fusee radius to size the required large-end radius and see the torque compensation diagram update.
Equation Used
The fusee keeps drive approximately constant by increasing its effective radius as mainspring torque falls. For endpoint sizing, the torque-radius product is held constant, so the run-down radius equals the full-wind small radius multiplied by the full-to-low torque ratio.
- Fusee radius is inversely proportional to mainspring torque.
- Endpoint torques represent full wind and run-down states.
- Friction, chain stretch, groove pitch error, and barrel-radius effects are ignored for relative sizing.
Operating Principle of the Fusee (form)
The mainspring inside a barrel does not deliver constant torque. Wound tight, it can push 60-80 mN·m through a typical pocket-watch barrel; nearly run down, that figure falls to 25-35 mN·m. That fall — the spring's torque curve — is the enemy of any escapement whose rate depends on drive force, and a verge or cylinder escapement very much does. The fusee fixes this by acting as a variable-radius lever. A chain (or in early work, a gut line) runs from the barrel to the fusee. When the spring is fully wound the chain pulls on the smallest radius of the fusee cone, giving the train a small lever arm against a large force. As the spring unwinds, the chain walks down the spiral groove toward the largest radius, increasing the lever arm exactly as the driving force drops.
The whole trick is in the fusee curve — the profile of the cone. It is not a simple straight taper. The radius at any point along the axis must be inversely proportional to the spring torque at that state of wind, and that relationship is empirical for the specific mainspring fitted. Cut the curve for the wrong spring and the watch will gain on full wind and lose on low wind, or the other way round. Tolerances are tight — the groove pitch must match the chain link pitch within about 0.05 mm or the chain will jump the groove on transition. The cone runout at the great-wheel end must be under 0.02 mm or you will see beat-error variation through the day.
Three things commonly fail. The chain stretches or fatigues at a hook end and snaps — when it goes, the mainspring releases through the barrel and the train spins free, which is why every fusee carries stopwork to prevent overwinding and a maintaining power spring to keep the train running while you wind. The groove wears at the small-diameter end where chain tension is highest. And the fusee curve is sometimes wrong because someone fitted a replacement mainspring of different strength without recutting or shimming the cone.
Key Components
- Fusee cone: The grooved conical drum that delivers variable mechanical advantage. Typical pocket-watch fusee is 12-18 mm at the great-wheel end and 5-8 mm at the small end, cut from hardened steel with the spiral groove pitch matched to the chain — usually 0.30-0.45 mm pitch. Cone profile is empirical to the fitted mainspring.
- Fusee chain: A miniature roller chain that transmits force from barrel to cone. A marine-chronometer chain runs roughly 150-200 links at 0.6 mm pitch with a working tension of 20-40 N. Chain breakage is the single most common fusee failure — replacement is the only fix, and link pitch must match the cone groove exactly.
- Mainspring barrel: Houses the mainspring and acts as the chain's input pulley. Barrel diameter is fixed (constant lever arm on this side) so the entire torque equalisation happens at the fusee. Going barrels in cheaper movements skip the fusee and rely on stopwork plus a long, flat-curve spring instead.
- Stopwork (Geneva stop): A two-piece cam-and-finger arrangement that limits the mainspring to its central, most linear winding range and prevents over-winding the fusee chain. Without stopwork the chain hook can be torn off the cone at the small-diameter end.
- Maintaining power spring: A small subsidiary spring (Harrison's invention) inside the fusee that drives the train forward during winding, when the main chain force is reversed. Without it, the watch loses 5-15 seconds every wind. Standard on any fusee chronometer.
- Great wheel: The first wheel of the going train, mounted on or coupled to the fusee. Typically 70-100 teeth in a pocket watch, cut module 0.1-0.15. The great wheel transmits the now-equalised torque into the rest of the train.
Who Uses the Fusee (form)
The fusee earns its place wherever the escapement rate depends on drive torque and the user demands constant rate over a long run. That used to mean almost every precision portable timekeeper. With the spring-detent escapement and later the lever escapement, isochronism improved enough that a flat-curve mainspring in a going barrel became acceptable for most wristwatches — but for marine chronometers, fusee verge pocket watches, and museum-grade longcase clocks, the fusee remains the correct answer. Restorers and replica builders still cut fusee curves today.
- Marine navigation (historical): John Harrison's H4 (1759) and the Kendall K1 copy carried by Cook on the Resolution voyage — fusee with maintaining power, set the standard for chronometer rate stability.
- Precision pocket watches: Breguet, Arnold, and Earnshaw fusee verge and lever pocket watches of 1780-1850 — typical rate variation under 4 seconds per day across a 30-hour run.
- Longcase and bracket clocks: English bracket clocks by Thomas Tompion and George Graham used twin fusees — one for going train, one for striking — to keep both running at consistent torque across the 8-day cycle.
- Marine chronometer manufacture: Mercer, Thomas, and Ulysse Nardin box chronometers built into the 1960s — fusee with helical mainspring, 56-hour run, rate stability under 0.5 seconds per day.
- Modern haute horlogerie: A. Lange & Söhne Pour le Mérite tourbillon and Romain Gauthier Logical One — fusee-and-chain reintroduced to wristwatches as a constant-force device.
- Restoration and replica work: Specialist clockmakers cutting replacement fusees for 18th-century English verge watches when the original has been lost or recut for a wrong spring.
The Formula Behind the Fusee (form)
The defining condition for a fusee is that the torque delivered to the great wheel stays constant as the mainspring unwinds. That gives a direct relationship between the fusee radius at any chain position and the mainspring torque at that state of wind. At the high-wind end of the typical operating range the cone radius is small and the lever arm is short — this is where chain tension is highest and groove wear concentrates. At the low-wind end the radius is large, lever arm is long, and chain tension is lowest but most sensitive to friction in the great-wheel pivot. The sweet spot sits in the middle two-thirds of the run, which is exactly the range stopwork is designed to keep the mechanism inside.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| Tout | Torque delivered to the great wheel (target: constant) | N·m | lbf·in |
| Tspring(θ) | Mainspring torque at wind angle θ | N·m | lbf·in |
| rfusee(θ) | Effective fusee radius at the chain contact point for wind angle θ | m | in |
| rbarrel | Mainspring barrel radius (constant) | m | in |
| Fchain | Tension in the fusee chain | N | lbf |
| θ | Wind angle of the mainspring (0 = fully wound, θmax = run down) | rad | rev |
Worked Example: Fusee (form) in a restored English fusee bracket clock
A heritage trust in Bristol commissions you to verify the fusee curve on an 1820s John Thwaites bracket clock with an 8-day run. The mainspring measures 70 mN·m fully wound and 30 mN·m near the run-down point. Barrel radius is 15 mm. You need to compute the required fusee radius at full wind, mid-wind (50 mN·m), and run-down so the great-wheel torque sits at a constant target of 22 mN·m.
Given
- Tspring,full = 70 mN·m
- Tspring,mid = 50 mN·m
- Tspring,low = 30 mN·m
- rbarrel = 15 mm
- Tout target = 22 mN·m
Solution
Step 1 — at full wind (high-end of the operating range), compute the chain tension from the spring side:
Step 2 — solve for the required fusee radius at full wind so the output torque hits 22 mN·m:
This is the small-diameter end of the cone. Chain tension is at its peak here, which is why this end of the fusee always shows the most groove wear in old movements.
Step 3 — at nominal mid-wind (50 mN·m), repeat:
Step 4 — at the low-wind end (run-down, 30 mN·m), the chain has walked down to the largest cone radius:
So the fusee profile sweeps from 4.71 mm to 11.00 mm — a 2.34:1 radius ratio, which matches the 2.33:1 spring-torque ratio (70/30) as it must. At full wind the cone is acting as a heavy reduction, sparing the train from the spring's peak torque. At run-down the cone has handed the train almost three times the lever arm to compensate for the weakened spring. The middle of this range — roughly 6-8 mm radius — is where the clock spends most of its 8-day run, and where stopwork should keep it.
Result
The fusee must taper from 4. 71 mm at the chain-on (full-wind) end to 11.00 mm at the chain-off (run-down) end to hold output torque flat at 22 mN·m. In practice this means the great wheel sees the same drive force on day 1 of the wind cycle as it does on day 7, so the escapement amplitude — and therefore the rate — barely shifts. The full-to-low radius swing of 4.71→6.60→11.00 mm shows where the geometry is most sensitive: the curve is steep at the small end where a 0.1 mm error costs you 4-5% torque, and gentle at the large end where the same error costs under 1%. If you measure the assembled clock and find rate drifting more than 4 seconds per day across the run, the usual culprits are: (1) a replacement mainspring with a different torque curve than the original cone was cut for — check stamped values against bench measurements; (2) a stretched fusee chain riding high on the groove flank instead of seating, which shifts effective radius by 0.1-0.3 mm; or (3) excessive friction in the great-wheel pivot that loads the low-torque end of the run worse than the high-torque end.
Choosing the Fusee (form): Pros and Cons
The fusee is the right answer for one specific problem — equalising mainspring torque in a portable timekeeper — but it is not free. You pay in cost, height, complexity, and a chain that can break. The two real alternatives are the going barrel (with stopwork and a flat-curve spring) and the modern constant-force escapement (remontoire). Compare them on the dimensions that actually decide the design.
| Property | Fusee | Going barrel + stopwork | Remontoire (constant-force escapement) |
|---|---|---|---|
| Torque variation across run | ±2% over 8 days | ±15-25% over 8 days (mitigated by stopwork to ±10%) | <±0.5% (re-armed every few seconds) |
| Movement height penalty | +8-15 mm (cone plus chain run) | Baseline | +3-6 mm (remontoire spring stage) |
| Manufacturing cost (relative) | High — fusee curve is empirical, chain is precision part | Low — standard barrel and stopwork | Very high — extra escapement-grade stage |
| Common failure mode | Chain breakage, groove wear at small end | Mainspring fatigue, stopwork cam wear | Re-arming spring fatigue, added pivot wear |
| Typical maintenance interval | Chain inspection every 5-10 years; cone re-cut rarely needed | Service every 4-7 years | Service every 3-5 years |
| Best application fit | Marine chronometers, precision pocket watches, 8-day longcase | Modern wristwatches, mass-production clocks | Haute horlogerie tourbillons, observatory regulators |
| Resilience to wrong mainspring | Poor — cone is cut for a specific spring curve | Good — any spring within torque band works | Moderate — re-arm timing must match |
Frequently Asked Questions About Fusee (form)
The replacement spring almost certainly has a different torque curve than the one the fusee cone was originally cut for. The fusee profile is not generic — it is matched empirically to the spring's torque-versus-wind characteristic. A modern alloy spring is often more linear (or less linear) than a Victorian carbon-steel original.
Two practical fixes: source a spring with a torque curve closer to the original (measure both on a torque gauge before fitting), or accept the rate variation and let the watch be regulated for mid-wind, which is where it spends most of its time. Re-cutting a fusee cone is possible but it is a specialist job and destroys originality on a collector piece.
Decide on the escapement first. If you are using a verge, cylinder, or any escapement whose rate depends measurably on drive torque, you need a fusee or a remontoire — a going barrel will give you several seconds per day of drift across the wind cycle. If you are using a detent or a high-quality lever escapement and the clock runs in one position, a going barrel with proper stopwork limits you to the central, most linear portion of the spring and that is usually good enough.
Run length matters too. Anything over 30 hours and the spring's non-linearity starts to dominate — fusee territory. For 8-day longcase or 56-hour marine work, fusee is still the gold standard.
This is almost always a pitch mismatch between chain and groove. The groove pitch must match the chain link pitch within about 0.05 mm. If you have replaced the chain with a modern reproduction, measure the link pitch with a loupe and compare to the cone groove — even a 0.1 mm difference accumulates over 150 links and forces the chain to bridge instead of seat.
Less commonly, the cone has worn so the groove flanks are shallow at the small-diameter end, and the chain rides the rim. A diagnostic check: run the watch up to full wind by hand under a loupe and watch the chain on the last few turns. If it lifts visibly off the cone face on the small end, the groove is worn or the pitch is wrong.
You can, but the watch will lose 5-15 seconds every time you wind it, and on a marine chronometer that is unacceptable. During winding, the chain force on the fusee reverses momentarily — the train would stop or even run backwards without the maintaining power spring driving it forward.
If you are seeing time loss only at winding, check the maintaining power click and detent. The spring itself rarely fails; the click that holds it engaged during winding wears or fouls with old oil and stops latching. Clean and re-tension the click before assuming the maintaining power spring is dead.
Chain tension is highest at the small-diameter end of the cone, which is the full-wind position. That is where peak spring torque divided by the smallest lever arm produces the largest chain force — roughly 2-3× the run-down tension. Repeated full-wind cycles fatigue the end links and the hook fitting first.
If your chain is breaking at the barrel end instead, suspect a sharp edge on the barrel hook or a missing radius on the chain entry — that is mechanical damage, not fatigue, and it will keep breaking new chains until you dress the edge.
On a verge or cylinder escapement, a properly cut fusee will hold rate to within roughly 2-4 seconds per day across the full run. The same movement on a going barrel with Geneva stopwork — limited to the central five turns of a six-turn spring — will drift 15-30 seconds per day across the cycle, because even the linear portion of a mainspring still falls 10-15% in torque.
On a modern lever escapement the gap closes dramatically. A high-quality lever is largely isochronous to drive torque, so a going-barrel wristwatch can hold COSC chronometer spec (-4/+6 s/day) without any fusee. That is why fusees disappeared from production wristwatches after about 1900 — the escapement got good enough that the fusee's benefit no longer justified its cost and height.
References & Further Reading
- Wikipedia contributors. Fusee (horology). Wikipedia
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