Math Is Fun Forum

YZF

Member

Registered: 2012-04-24

Posts: 6

Voussoir Formula

Evening All,
Does anyone know how to calculate the size of each voussoir for a stone arch
Lets say the following :-

Radius = 24 inch
Voussoir Height = 6 inch
Number of Voussoirs = 9 (this would be 4 either side and 1 in middle as keystone)

This is also based on a Roman Semi Circle arch

I need to know the 4 angles of each vioussoir and the length of the intrados and extrados

I know that this must be a simple formula for you guys but its doing my head lol

Is there any chance of instead of saying x/y+c=gg could you please use the numbers above and show how you get the results

Thanks in advance
Jason

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Voussoir Formula

I'm sorry,but,what is a voussoir?

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

YZF

Member

Registered: 2012-04-24

Posts: 6

Re: Voussoir Formula

Sorry, a voussoir is the piece of stone or brick etc. that are wedged shape that make up the arch.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Voussoir Formula

Hi YZF;

Welcome to the forum!

Based on the figurine at the top I would say this is Medieval. In the construction of their aqueducts the Romans used arches. Is there a difference between Medieval and a Roman arch?

Here is a roman arch:

Yet another:

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

YZF

Member

Registered: 2012-04-24

Posts: 6

Re: Voussoir Formula

Hi,
The picture with the red arrows is exactly what I am trying to achieve.

I need to work out the sizes of each block (angles, lengths etc.) based on 3 criteria, Radius of arch, # of blocks and height of each block.

Thanks

Jason

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Voussoir Formula

Hi YZF

Assuming you want the arc to be a semicircle,you can use these formulas:

,where n is the number of voussoirs.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.