Gridiron Pendulum

[Ashlyn Robello]

Thegridiron pendulum was a temperature-compensated clock pendulum invented by British clockmaker John Harrison around 1726.[1][2][3][4] It was used in precision clocks. In ordinary clock pendulums, the pendulum rod expands and contracts with changes in temperature. The period of the pendulum's swing depends on its length, so a pendulum clock's rate varied with changes in ambient temperature, causing inaccurate timekeeping. The gridiron pendulum consists of alternating parallel rods of two metals with different thermal expansion coefficients, such as steel and brass. The rods are connected by a frame in such a way that their different thermal expansions (or contractions) compensate for each other, so that the overall length of the pendulum, and thus its period, stays constant with temperature.

The gridiron pendulum was used during the Industrial Revolution period in pendulum clocks, particularly precision regulator clocks[1] employed as time standards in factories, laboratories, office buildings, railroad stations and post offices to schedule work and set other clocks. The gridiron became so associated with accurate timekeeping that by the turn of the 20th century many clocks had pendulums with decorative fake gridirons, which had no temperature compensating qualities.[1][4]

The gridiron pendulum is constructed so the high thermal expansion (zinc or brass) rods make the pendulum shorter when they expand, while the low expansion steel rods make the pendulum longer. By using the correct ratio of lengths, the greater expansion of the zinc or brass rods exactly compensate for the greater length of the low expansion steel rods, and the pendulum stays the same length with temperature changes.[2]

The simplest form of gridiron pendulum, introduced as an improvement to Harrison's around 1750 by John Smeaton, consists of five rods, 3 of steel and two of zinc. A central steel rod runs up from the bob to a point immediately below the suspension.

At that point a cross-piece (middle bridge) extends from the central rod and connects to two zinc rods, one on each side of the central rod, which reach down to, and are fixed to, the bottom bridge just above the bob. The bottom bridge clears the central rod and connects to two further steel rods which run back up to the top bridge attached to the suspension. As the steel rods expand in heat, the bottom bridge drops relative to the suspension, and the bob drops relative to the middle bridge. However, the middle bridge rises relative to the bottom one because the greater expansion of the zinc rods pushes the middle bridge, and therefore the bob, upward to match the combined drop caused by the expanding steel.

In simple terms, the upward expansion of the zinc counteracts the combined downward expansion of the steel (which has a greater total length). The rod lengths are calculated so that the effective length of the zinc rods multiplied by zinc's thermal expansion coefficient equals the effective length of the steel rods multiplied by iron's expansion coefficient, thereby keeping the pendulum the same length.

Harrison's original pendulum used brass rods (pure zinc not being available then); these required more rods because brass does not expand as much as zinc does. Instead of one high expansion rod on each side, two are needed on each side, requiring a total of 9 rods, five steel and four brass.[3][4] The exact degree of compensation can be adjusted by having a section of the central rod which is partly brass and partly steel. These overlap (like a sandwich) and are joined by a pin which passes through both metals. A number of holes for the pin are made in both parts and moving the pin up or down the rod changes how much of the combined rod is brass and how much is steel.

In the late 19th century the Dent company developed a tubular version of the zinc gridiron in which the four outer rods were replaced by two concentric tubes which were linked by a tubular nut which could be screwed up and down to alter the degree of compensation.

Scientists in the 1800s found that the gridiron pendulum had disadvantages that made it unsuitable for the highest-precision clocks.[4] The friction of the rods sliding in the holes in the frame caused the rods to adjust to temperature changes in a series of tiny jumps, rather than with a smooth motion. This caused the rate of the pendulum, and therefore the clock, to change suddenly with each jump. Later it was found that zinc is not very stable dimensionally; it is subject to creep. Therefore, another type of temperature-compensated pendulum, the mercury pendulum invented in 1721 by George Graham, was used in the highest-precision clocks.[4]

A change in length Δ L \displaystyle \Delta L due to a temperature change Δ θ \displaystyle \Delta \theta will cause a change in the period Δ T \displaystyle \Delta T . Since the expansion coefficient is so small, the length changes due to temperature are very small, parts per million, so Δ T

A gridiron pendulum is symmetrical, with two identical linkages of suspension rods, one on each side, suspending the bob from the pivot. Within each suspension chain, the total change in length of the pendulum L \displaystyle L is equal to the sum of the changes of the rods that make it up. It is designed so with an increase in temperature the high expansion rods on each side push the pendulum bob up, in the opposite direction to the low expansion rods which push it down, so the net change in length is the difference between these changes

Harrison invented the gridiron pendulum (illustrated here in the background to the right), grasshopper escapement, bi-metallic strip (as you would find in your kettle) and an automatic form of maintaining power, all of which were adopted by later clockmakers and remain evidence of Harrison's enduring contributions to horology. Harrison is possibly best known for the development of a working marine timekeeper, leading to a revolution in navigation by providing a means to calculate longitude at sea.

Each of the clocks displayed here were produced by other skilled and renowned makers, but their incorporation of elements invented or developed by John Harrison pay testament to his legacy and enduring contribution to horology.

This exhibit was curated with assistance from Laura Turner and Oliver Cooke, Curators of the Horological Collections at the British Museum.

You can see the objects depicted here by visiting the British Museum Clocks and Watches galleries, Rooms 38-39.

John Harrison's own marine timekeepers are on display at the Royal Observatory Greenwich, in their Time and Longitude gallery.

A pendulum's period, or rate of oscillation, is tied to the length of its center of mass, not its weight. Because most metals expand in heat, the pendulum rod and bob will get longer, slowing the clock. The gridiron pendulum takes advantage of metal's natural thermal expansion and uses opposing expanding rods to compensate for any change in dimensions.

Gridiron pendulums are traditionally made of brass and either steel or nickel. Nickel has a higher coefficient of thermal expansion, so it's able to compensate with fewer back-and-forths. We found a stash of thin nickel rods in a drawer, so it seemed as good idea as any to make them into a gridiron.

Temperature compensation is achieved by using the different metals to alternately push up and down on each other. In this design, the outer nickel rods push down on a crosspiece that supports the inner brass bars and lets the middle nickel rod pass through. Those brass bars push up on another cross piece, which supports the center rod, holding the pendulum bob (the outer brass bars just support a locator for the center rod). Together, the opposing expansions should keep the weight of the bob in the same place... Theoretically.

The gridiron pendulum was innovated by master chronometer maker John Harrison, and in the right hands, it works wonderfully. In reality, it's tricky to get perfect, especially when the quality of the brass and nickel is unknown.

Ferdinand Berthoud (1727-1807) was one of the most important horologists of the 18th century. Born in Neuchtel and trained as a watchmaker. He emigrated to France in 1745 working as a journeyman for the Paris trade. His talents led to being received as a master watchmaker by the Paris guild in 1753. He was a prolific author, writing notably on timepieces to measure Time at sea to determine longitude. He developed his own marine chronometers that met with great success. In 1773, Berthoud published his Trait des horloges marines contenant la thorie, la construction, la main-d'œuvre de ces machines et la manire de les prouver, pour parvenir par leur moyen, la rectification des cartes marines et la dtermination des longitudes en mer. This treatise was a first, detailing all the parts required for building a sea clock. It helped seal the reputation of Berthoud's work, in particular with respect to his competitors in longitude at sea research, such as John Harrison and Pierre Le Roy. His 1763 Essai sur l'horlogerie is still highly regarded. Near the end of his life, he wrote a monumental Histoire de la mesure du temps par les horloges.

A coup perdu escapement converts a half-second beating pendulum to directly control an escape wheel at the rate of a one second pendulum, so only every other beat is registered by the escape wheel. In other words, there is a 'lost beat'. For a discussion of the clock and a diagram of the escapement, see:

Derek Roberts. Continental and American Skeleton Clocks, pp 25-26, fig. 12a, b

Another example of this timepiece was sold in Bonhams New York 6 December 2018, lot 91 for $37,500.

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