# Pendulum length

#### novicetimekeeper

##### Registered User
I visited a turret clock yesterday which although built in 1785 had been substantially altered in 1863. They changed it from single hand to two hand and fitted a deadbeat escapement with a 21 foot pendulum.

This seems a long pendulum to me, the Great Clock at Westminster weighs something like 5 tonnes and has a 13 foot pendulum. Is 21 foot an unusual pendulum length?

To accommodate it an enclosure extends all the way down into the bell ringing chamber in the floor below and cuts across an arch. The clock itself is of modest proportions, you could fit it in the boot af a small car.

1785 seems quite late for a single handed clock but it is a very small village, perhaps funds were limited. (I collect longcase and single handers in particular, I haven't got one as late as this though I have seen a painted dial single hander which would be contemporary or later)

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#### Jeremy Woodoff

##### Registered User
NAWCC Member
Perhaps the clock as originally configured had a short run time. Is it possible the pendulum length was made so long in order to increase the running time on a winding, without having to add another wheel to the train?

#### novicetimekeeper

##### Registered User
I was thinking that it reduces the revolutions, I did not make the connection with extending the run time. I didn't explore the weight setup, the strike has been disabled and they can't afford to reinstate it, the electric winding gear fitted in 1974 has also failed and they are awaiting a repair.

I make a 21 foot pendulum about a 5 second period, compared with the usual metre long two second period I'm used to with longcase.

#### Donn Haven Lathrop

##### Registered User
I make a 21 foot pendulum about a 5 second period, compared with the usual metre long two second period I'm used to with longcase.

Not so, unfortunately. But it would certainly make things easier for the poor clockmaker were that sort of relationship true. The period varies as T=2*Î  L/g, where T = period, g = gravity. A 22 foot pendulum works out to just over a three second period. Just as a by the way, the longest pendulum in the United Kingdom is in St. Giles Church, in Edinburgh. It's nearly 60 feet long, and beats 4 1/2 seconds. A meter long pendulum, the so-called Royal pendulum, has a period of one second.

#### novicetimekeeper

##### Registered User
Not so, unfortunately. But it would certainly make things easier for the poor clockmaker were that sort of relationship true. The period varies as T=2*Î  L/g, where T = period, g = gravity. A 22 foot pendulum works out to just over a three second period. Just as a by the way, the longest pendulum in the United Kingdom is in St. Giles Church, in Edinburgh. It's nearly 60 feet long, and beats 4 1/2 seconds. A meter long pendulum, the so-called Royal pendulum, has a period of one second.
Odd I make the period 5.075 with a 6.4 metre pendulum, perhaps my calculator is faulty. (The period for a pendulum is a complete cycle, so what we call a 1 second pendulum has a 2 second period)

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#### Les harland

##### Registered User
If it any help my local Church clock has a twelve foot pendulum with a two second tick

#### novicetimekeeper

##### Registered User
If it any help my local Church clock has a twelve foot pendulum with a two second tick
According to Chris McKay most turret clocks find themselves between the longcase and the Great Clock somewhere, so yours fits with that. (12 foot is a bit under a 4 sec period or 2 sec tick by calculation)

#### FDelGreco

##### Registered User
NAWCC Star Fellow
NAWCC Diamond Member
If it any help my local Church clock has a twelve foot pendulum with a two second tick
They've come longer yet.

At a Southern Ohio regional, my friends and I were examining a European time and strike tower clock that was located against the mart room wall. It was missing its pendulum. Calculating the beats per hour (BPH) by doing a tooth count was fairly straightforward, but then converting BPH to pendulum length sent us scrambling trying to remember the formula. Fortunately, you can find anything on Google with a smart phone, but then there was that square root to deal with, so I couldn't do the calculation in my head on the mart room floor. In addition, I kept seeing "beats per second" in the formula instead of "seconds per beat." Finally, I got my math squared away.

When I got home I simplified the calculation for future use. The length of a pendulum is calculated using the following traditional equation - the one I had to deal with on the mart room floor:

T = Ï€âˆš(L/g)
(That's pi in front of the square root. Does not show up well in the default font)

Where
T = seconds/beat (SPB);
L = pendulum length; and
g= gravitational acceleration in feet/sec squared

Note that T is the reciprocal of beats per second (BPS).

Since everything is a constant except L and T, and usually beats per hour (BPH) has been calculated, then the length of the pendulum, L, in inches, is:

L=507,000,000/(BPH x BPH)

â€ƒ
If your calculator can't handle large numbers, first convert BPH into BPS by dividing BPH by 3600. Then:

L=39.1/(BPS x BPS)

Put this in your cell phone or on a scrap of paper in your wallet.

The subject tower clock had a calculated pendulum length of 18 feet. No thank you!

Frank

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#### novicetimekeeper

##### Registered User
They've come longer yet.

At a Southern Ohio regional, my friends and I were examining a European time and strike tower clock that was located against the mart room wall. It was missing its pendulum. Calculating the beats per hour (BPH) by doing a tooth count was fairly straightforward, but then converting BPH to pendulum length sent us scrambling trying to remember the formula. Fortunately, you can find anything on Google with a smart phone, but then there was that square root to deal with, so I couldn't do the calculation in my head on the mart room floor. In addition, I kept seeing "beats per second" in the formula instead of "seconds per beat." Finally, I got my math squared away.

When I got home I simplified the calculation for future use. The length of a pendulum is calculated using the following traditional equation - the one I had to deal with on the mart room floor:

T = Ï€âˆš(L/g)
(That's pi in front of the square root. Does not show up well in the default font)

Where
T = seconds/beat (SPB);
L = pendulum length; and
g= gravitational acceleration in feet/sec squared

Note that T is the reciprocal of beats per second (BPS).

Since everything is a constant except L and T, and usually beats per hour (BPH) has been calculated, then the length of the pendulum, L, in inches, is:

L=507,000,000/(BPH x BPH)

â€ƒ
If your calculator can't handle large numbers, first convert BPH into BPS by dividing BPH by 3600. Then:

L=39.1/(BPS x BPS)

Put this in your cell phone or on a scrap of paper in your wallet.

The subject tower clock had a calculated pendulum length of 18 feet. No thank you!

Frank
That's fun with maths, I did think about calculating pendulum length from escape wheel teeth. Obviously it is just a guide as the formula for pendulum length is for a simple pendulum which is fine in physics but not so easy to make.

The thing about turret clocks, well the majority if not all, is like most of my longcase clocks they don't have seconds hands. That gives you lots of leeway in the design.

However what my original question was about was whether 21 foot was unusually long, not whether it were the longest or even nearly the longest. You can see from the picture that the pendulum gets in the way a bit, I imagine that is a limiting design factor for a lot of locations.

We have no records for what was there when it was a single handed clock, must have been shorter as the plate says about a longer pendulum being fitted during the work in 1863.

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#### dAz57

##### Registered User
Odd I make the period 5.075 with a 6.4 metre pendulum, perhaps my calculator is faulty. (The period for a pendulum is a complete cycle, so what we call a 1 second pendulum has a 2 second period)
All the calculations for beats per hour(bph) and ampiltude are done on a single swing or one tick of the escapement, this applies to pendulums and balance wheels, a seconds pendulum is one second per swing, a watch with a 18000bph train beats 5 times a second, annoyingly the swiss are using Hz in their specs sheets so now that seconds pendulum is 0.5Hz and the watch is 2.5Hz

#### Donn Haven Lathrop

##### Registered User
"You can see from the picture that the pendulum gets in the way a bit, I imagine that is a limiting design factor for a lot of locations."

Most installations don't really seem to care. There is a clock in the UK whose pendulum swings over the heads of the congregation assembled. No one seems to mind.

"We have no records for what was there when it was a single handed clock, must have been shorter as the plate says about a longer pendulum being fitted during the work in 1863."

The Ipswich clock has a 56 inch pendulum--second and a quarter.

#### Tinker Dwight

##### Registered User
I often use 39.1 as it seem easier to remember
than the metric number.
What I often get wrong is when to square and
when to square root.
I know it when I think for a while, just not off the
Tinker Dwight

#### novicetimekeeper

##### Registered User
All the calculations for beats per hour(bph) and ampiltude are done on a single swing or one tick of the escapement, this applies to pendulums and balance wheels, a seconds pendulum is one second per swing, a watch with a 18000bph train beats 5 times a second, annoyingly the swiss are using Hz in their specs sheets so now that seconds pendulum is 0.5Hz and the watch is 2.5Hz
I work in a physics dept now I've retired and that's the way it would be described there, the formula calculates the period for a simple pendulum and periods or cycles per second is Hertz.

#### novicetimekeeper

##### Registered User
I often use 39.1 as it seem easier to remember
than the metric number.
What I often get wrong is when to square and
when to square root.
I know it when I think for a while, just not off the
Tinker Dwight

Odd isn't it? It should be 39.37 given the origin of a metre, was g not 9.81 where they worked that out or did it just get changed when they moved on once they realised g wasn't the same everywhere?

#### Tinker Dwight

##### Registered User
39.1 comes out close at 1.9992 seconds?
One meter was said to be a distance to the pole. The pendulum
rate being close to a meter was just luck.
Looking it up, the once thought about using the one second pendulum
but settled on 1/10000000 of the distance between the equator and
north pole.
They couldn't measure either earth distance or pendulum accurately
enough anyway.
see article: https://en.wikipedia.org/wiki/Metre
Tinker Dwight

#### novicetimekeeper

##### Registered User
Yes, I'm familiar with the wikipedia page, but the metre derived from the pendulum period predates the French revolution and their adoption, so the coincidence really goes the other way.

Initially it was thought that the pendulum period would always be the same but it was proved by experiment that it wasn't and that gravity was not the same everywhere on the planet.

The coincidence is indeed remarkable though, that it should be so close, but as you say they didn't really have a way of measuring either at the time.

Something that may amuse you, I recently had a teacher tell me that you could not prove Newton's conservation of momentum without light gates and data loggers to do the timing. I pointed out that Newton would have been fortunate to have anything available that could measure seconds and yet he managed it.

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