Grandfather Clocks are Pendulum Clocks

Grandfather Clocks for Home

The Harmonic Oscillator……………

Grandfather Clocks are Pendulum Clocks, and obviously use the pendulum (swinging weight) as the primary timekeeping element. Since the mid-1600s the Grandfather Clock was the world’s most accurate timekeeper. Its use and popularity were widespread for nearly 300 years.

We see ornate antique Grandfather Clocks and often view the woodwork of the artisans with awe. But… Have you ever looked inside the Grandfather Clock? The mechanics, mathematics, skills, and craftsmanship inside are awesome as well.

The pendulum that your Grandfather Clock uses as that swinging weight, is a harmonic oscillator (See the “Grandfather Clock Terms” page for Harmonic Oscillator, and Deadbeat Escapement.). When the pendulum was added to standing mechanical clocks, timekeeping accuracy improved from a loss/gain of about 15 minutes per day down to a loss/gain of only 15 seconds per day. Therefore, clocks using the older verge escapement (See “Grandfather Clock Terms”)began to be… ‘retrofitted’ with pendulums to increase accuracy.

In addition to increased accuracy, this allowed the clock’s case to accommodate longer, slower pendulums, which needed less power and caused less wear on the movement.

[The seconds pendulum (also called the Royal pendulum), whose swing takes one second in each direction, is about one meter (39.1 inches) long, was widely used. Clocks with long narrow towers that were built around these pendulums (first made by William Clement circa 1670-1680), ultimately became known as Grandfather Clocks.]

As we can well imagine, daily home life was organized around the accurate pendulum clock. During the same period of time (The Industrial Revolution), the even more accurate regulator pendulum clocks were added to businesses and became essential in scheduling work, employees, and other clocks.

[Until the development of the quartz clock (1927), accurate regulator pendulum clocks were used as the ‘standard’ through the end of World War II. This marvelous invention remained the world standard for accurate timekeeping for 270 years. The French used pendulum clocks as part of their group of ‘standard clocks’ until 1954 ]

The most accurate regulator pendulum clocks, known as ‘astronomical regulators,’ were used in observatories for astronomy, surveying, and celestial navigation (See “Grandfather Clock Terms”). This is why you will see notations and connections to mathematics, researchers, explorers, astronomical scientists, and observatories throughout my writings on Grandfather Clocks.

Perhaps you did not realize that your Grandfather Clock was so amazing and intricate.

And we arrive at the main point of exploration for this article, the Harmonic Oscillator.

In a rather imprecise ‘nut shell,’ here is the Harmonic Oscillator, as it applies to the pendulum.

The Harmonic Oscillator Model is important in physics…

Classical Mechanics includes the Harmonic Oscillator…

The Grandfather Clock is a mechanical clock.

The pendulum of the Grandfather Clock is a harmonic oscillator,

a system in and of itself.

When the pendulum (harmonic oscillator) is displaced (moved) from its position of equilibrium (Its regular, stable and still position), there is a restoring force that is proportional to the displacing force.

This is Classic Mechanics.

[‘F’ is the restoring ‘force.’ ‘k’ is a positive constant. ‘x’ is the displacement.]

Here is an example of a simple pendulum referencing harmonic oscillation.

“A simple pendulum exhibits simple harmonic motions under the conditions of ‘no damping ad small amplitude.’” Damping and amplitude will not be discussed for this very simplified explanation.

“The differential equation governing a simple pendulum is…

I won’t even go into the solution for the equation.

The solution to this equation is given by:

where θ₀ is the largest angle attained by the pendulum. The period (length of time), the time for one complete oscillation, is given by 2π divided by whatever is multiplying the time in the argument of the cosine ( here).

Ah, the simple pendulum, simplified, is not so simple.

It is enough to say that the scientists of ‘old’ put a lot of work into the pendulum clock (Grandfather Clock).

Here it is in layman’s terms…

Within the escapement, the gears push the pendulum. Gravity takes over and the pendulum begins to swings in the opposite direction, and so on… The clock movement continues its work, and the pendulum swings again. (Until the clock completely unwinds.)

There are other considerations for calculating the accuracy of the pendulum (Harmonic Oscillator).

Leveling:

The pendulum clock (Grandfather Clock) must be absolutely level to function accurately as intended. The accurate and continued operation of the escapement depends on being level and stable, and with regular intervals. The clock’s escapement must go… tick-tock… tick-tock… tick-tock… tick-tock… If it goes… tickity… tick… tick… tockity… tock… it will not be accurate. Your pendulum clock may even stop working altogether. It is a common reason for expensive service calls. Some precision regulator clocks have a built in level for this task.

Your Local Gravity:

Gravity (among others) is the force that propels the pendulum. Did you know that local gravity varies? Your Grandfather Clock will need to be adjusted, if you have moved it from the first floor showroom of an antique shop to the 28th floor of your condominium building.

I trust that this has been clearer than ‘mud.’

Keep Discovering…