# Escape Wheel Calculation (Pendulum Clock)

#### Atlantic

##### New User
Hi,

I have constructed a 3D printed 4 wheel pendulum clock with a 30 tooth escape wheel and a pendulum length of 39", which works fine (PIC BELOW). If I wanted to create a clock with a shorter pendulum, what calculation(s) do I need to work out the correct escape wheel size/teeth #?

Any advice would be most welcome.

Regards,

Atlantic

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#### Richard Cedar

NAWCC Member
Atlantic,

Welcome to the Clock Construction Forum. It would be great to see some photos of your current creation.

As to escapement design, take a look at the following thread Shape of escapement teeth? for references on escapement design.

I use the Gearotic software package to design and layout clock wheel trains. Gearotic includes a few basic escapement design options and has various options for writing out the geometry in formats that your should be able to print from.

Please do not hesitate to post follow-up questions.

Richard Cedar.
Cedar Clocks
www.CedarClocks.com

#### Atlantic

##### New User
Hello Richard,

Many thanks for your support and quick response.

This is my first attempt at clock making.

I attach a pic of the clock. Its only a prototype for now. It runs ok from the minute wheel and keeps in beat.

The issue I have is that I want to significantly shorten the pendulum, but have no idea how to make adjustments to the escape wheel whilst useing the existing gear train.

I must have spent hours trawling through the internet to no avail. Any advice would be most appreciated.

Many thanks

Alan

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#### wisty

##### Registered User
If you want to use the rest of the train, then you need an escape wheel that rotates once per minute as the current one does. Your current pendulum has a period (left, right, left) of 2 seconds also known as seconds beating. Each period corresponds to one tooth escaping on the wheel so a 2 seconds pendulum and 30 teeth = 60 seconds (assuming a conventional anchor escapement). Which is what you have.
The period (T)of a pendulum is 2ᴨ * Sqrt(L/g) where L is length in metres and g is gravity (9.8).
Rearranging gives the length of the pendulum (in metres) as ((T/2ᴨ)^2)*9.8
You want a period (T) in seconds which is an exact number of teeth (60/No of teeth). so 40 teeth is 1.5 seconds, 45 is 1.3333, 60 teeth is 1 second etc. Choose a period and calculate the length of the pendulum. A spreadsheet helps.
 Inches​ Metres​ Period secs​ Teeth​ 39.09​ 0.99​ 2.00​ 30​ 21.99​ 0.56​ 1.50​ 40​ 17.37​ 0.44​ 1.33​ 45​ 9.77​ 0.25​ 1.00​ 60​ 7.18​ 0.18​ 0.86​ 70​ 5.50​ 0.14​ 0.75​ 80​
Hope this helps.

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#### Richard Cedar

NAWCC Member
Alan - It is amazing what you can 3D print. As Wisty notes, reducing the length of the pendulum results in the need for a greater number of escapement teeth if you want to maintain the same train. This reduces the space between the teeth, and the design and construction of the pallet can become a problem.

For more information about clock design, I recommend Clayton Boyer's book (in .pdf format) called "A Practical Guide to Wooden Wheeled Clock Design" ( Wooden Gear Clock Plans from Hawaii by Clayton Boyer). Clayton is a very prolific clock designer who sells plans of his designs either on paper or in a digital format. His book describes the step-by-step process of clock design, including selecting the pendulum length, wheel teeth count, geometric construction of a simple escapement, etc. Although the book focuses on clocks made from wood, most of the information is relevant to clocks made of any material.

Richard Cedar.
Cedar Clocks
www.CedarClocks.com

#### Atlantic

##### New User
Alan - It is amazing what you can 3D print. As Wisty notes, reducing the length of the pendulum results in the need for a greater number of escapement teeth if you want to maintain the same train. This reduces the space between the teeth, and the design and construction of the pallet can become a problem.

For more information about clock design, I recommend Clayton Boyer's book (in .pdf format) called "A Practical Guide to Wooden Wheeled Clock Design" ( Wooden Gear Clock Plans from Hawaii by Clayton Boyer). Clayton is a very prolific clock designer who sells plans of his designs either on paper or in a digital format. His book describes the step-by-step process of clock design, including selecting the pendulum length, wheel teeth count, geometric construction of a simple escapement, etc. Although the book focuses on clocks made from wood, most of the information is relevant to clocks made of any material.

Richard Cedar.
Cedar Clocks
www.CedarClocks.com

Thanks for your help. I'll checkout the PDF and come back with any questions I may have if that's ok? I've discovered myself that the more teeth you have the bigger issues that occur. I've also discovered that using a module 1 for the wheel teeth is not very efficient, now using 1.5.

Regards,

Alan

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#### Atlantic

##### New User
If you want to use the rest of the train, then you need an escape wheel that rotates once per minute as the current one does. Your current pendulum has a period (left, right, left) of 2 seconds also known as seconds beating. Each period corresponds to one tooth escaping on the wheel so a 2 seconds pendulum and 30 teeth = 60 seconds (assuming a conventional anchor escapement). Which is what you have.
The period (T)of a pendulum is 2ᴨ * Sqrt(L/g) where L is length in metres and g is gravity (9.8).
Rearranging gives the length of the pendulum (in metres) as ((T/2ᴨ)^2)*9.8
You want a period (T) in seconds which is an exact number of teeth (60/No of teeth). so 40 teeth is 1.5 seconds, 45 is 1.3333, 60 teeth is 1 second etc. Choose a period and calculate the length of the pendulum. A spreadsheet helps.
 Inches​ Metres​ Period secs​ Teeth​ 39.09​ 0.99​ 2.00​ 30​ 21.99​ 0.56​ 1.50​ 40​ 17.37​ 0.44​ 1.33​ 45​ 9.77​ 0.25​ 1.00​ 60​ 7.18​ 0.18​ 0.86​ 70​ 5.50​ 0.14​ 0.75​ 80​
Hope this helps.

Many thanks, very informative.. In no way could I have worked this out without your help. I'll do some more prototypes next week, however I have found it is extremely difficult to 3D print escape wheels with more than 45 teeth, using my current setup. I'll probably have to use 40, or 45 teeth.

I'm not quite sure what you mean by Period. Every "tick and tock" of my clock is exactly 1 second, you mentioned "left, right, left" which to me means "tick, tock, tick"? Please help me understand this.

Regards,

Alan

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#### gmorse

NAWCC Member
Hi Alan,
I'm not quite sure what you mean by Period. Every "tick and tock" of my clock is exactly 1 second, you mentioned "left, right, left" which to me means "tick, tock, tick"? Please help me understand this.

If you start with the pendulum at rest, move it fully out to the right, back to the middle, fully out to the left and return to the middle, that's one period. Since an escape tooth is locked (the 'tick') on each swing, alternately by the entry and exit pallets, you hear two 'ticks', each one second apart, in each period. You can also regard the period as the interval between consecutive drops onto the entry pallet.

Regards,

Graham

#### Bentrider

##### Registered User
I've written a spreadsheet to calculate pendulum length which you're welcome to try. There are various formats available.

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