Gridiron pendulum

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.

[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 the suspension pivot.

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.

These overlap (like a sandwich) and are joined by a pin which passes through both metals.

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.

In the 1730s clockmaker John Ellicott designed a version that only required 3 rods, two brass and one steel (see drawing), in which the brass rods as they expanded with increasing temperature pressed against levers which lifted the bob.

[6]: p.272-273 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.

[8]: p.289 [4] By 1900, the highest-precision astronomical regulator clocks used pendulum rods of low thermal expansion materials such as invar[3][2] and fused quartz.

, so uncompensated pendulum rods get longer with a temperature increase, causing the clock to slow down, and get shorter with a temperature decrease, causing the clock to speed up.

The amount depends on the linear coefficient of thermal expansion (CTE)

CTE is usually given in parts per million (ppm) per degree Celsius.

Steel has a CTE of 11.5 x 10−6 per °C so a pendulum with a steel rod will have a thermal error rate of 5.7 parts per million or 0.5 seconds per day per degree Celsius (0.9 seconds per day per degree Fahrenheit).

Before 1900 most buildings were unheated, so clocks in temperate climates like Europe and North America would experience a summer/winter temperature variation of around 14 °C (25 °F) resulting in an error rate of 6.8 seconds per day.

The wood had to be varnished to protect it from the atmosphere as humidity could also cause changes in length.

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

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 From (1) the change in length

is the sum of the lengths of the high expansion rods in the suspension chain from the bob to the pivot.

This changes the moment of inertia so the center of oscillation is somewhat higher, above the bob in the gridiron.

Another minor factor is that if the pendulum bob is supported at bottom by a nut on the pendulum rod, as is typical, the rise in center of gravity due to thermal expansion of the bob has to be taken into account.

the geometrical condition for construction of the gridiron is Therefore the 5 rod gridiron can only be made with metals whose expansion coefficients have a ratio greater than or equal to two[4][9]: p.251 Zinc has a CTE of

[4] So from equation (3) the condition for compensation is Since to fit in the frame each of the two high expansion rods must be as short as or shorter than each of the high expansion rods, the geometrical condition for construction is Therefore the 9 rod gridiron can be made with metals with a ratio of thermal expansion coefficients exceeding 1.5.