Arch Forms for Oven Door - The Calculation?

[Kemo]

All,

I have been troubled trying to figure out how to make the perfect Door Arch Form for my oven door and landing. I have heard that there are charts and calculators to tell you how to draw out the arch based on rise and run...

Anyway, I was hoping to come up with a DIY method for getting the Door Arch Form, just right, using a string, marker, and a piece of plywood. Basically, i would tack a string in the center of the plywood sheet and run a pen along the outer swing creating an arc. I just need to know how long the string should be.

I would like to make my oven opening one firebrick high at 9" with the width of the opening to be 20". Now, I also want an arch with a max height of 11". What is the radius of the circle I would need to draw on the plywood?

After some heavy cyphering and Internet searching ...

I found some equations from basic geometry online and realized that I have grossly forgotten alot of this stuff over the years. After going over the equations a few times, I threw some numbers at it to see how it all panned out.

Everything seemed to work on paper with this method and I was hoping some of you guys could double check the logic here to make sure I'm not losing it

If it checks out, hopefully it will help someone out with their door arch forms down the road.

I'm just trying to get all this calculated before I start...

[Wlodek]

Re: Arch Forms for Oven Door - The Calculation?

It might be a stupid question, but does the arch have to be a part of a circle?

I have a slight feeling that an optimal (not sure in what way though) arch has something to do with the curve that a chain makes when you hold it by its ends and let the middle bit droop.

Just to stir things up of course, as it probably does not matter at this scale.



Greetings from sunny Cumbria,

W.

[Kemo]

Re: Arch Forms for Oven Door - The Calculation?

this is only cosmetic! i was just trying to get a smooth curve given the dimensions. And mostly for sh*ts and giggles

[dmun]

Re: Arch Forms for Oven Door - The Calculation?

My cad program shows 26 exactly (or to within .001")

[Hendo]

Re: Arch Forms for Oven Door - The Calculation?

In the calculation where you've arrived at z=y/2sin(x), you've assumed that you're working with a right-angled triangle, but I don't think it is. The angle appears to be slightly less than 90?, and would reduce with increasing opening width.

This might explain the small discrepancy between David's CAD figure and your calculated one.

Paul.

[Dutchoven]

Re: Arch Forms for Oven Door - The Calculation?

The answer is no, it does not have to. The shape you refer to is a catenary arc which is the arc created when a chain of equal density is hung and gravity is allowed to act upon it uniformly. It is very stable physically. In the case of a door arch it would be called an inverted catenary. For brick arch forms it is a bit simpler to do the arc of a circle I think.
Best
Dutch

It might be a stupid question, but does the arch have to be a part of a circle?

I have a slight feeling that an optimal (not sure in what way though) arch has something to do with the curve that a chain makes when you hold it by its ends and let the middle bit droop.

Just to stir things up of course, as it probably does not matter at this scale.



Greetings from sunny Cumbria,

W.

[Wlodek]

Re: Arch Forms for Oven Door - The Calculation?

Just out of interest I calculated and plotted the 3 arches (circular, parabolic and simple catenary) for a specific height/width ratio of the opening of 1/2 and the plot is attached.

Interestingly, for this particular ratio, the catenary is very close to the parabolic one. Presumably meaning that not only do you get the focal effect, but also the strength of the catenary for pretty much the same arch .... not that it matters with the door.

Oh, dear, do I have too much time? No!

W.

[Powindah]

Re: Arch Forms for Oven Door - The Calculation?

I know...

This is old and dusty thread but I came across it in the wee small hours while playing online poker and reading about all the great WFOs I'd like to have.

And then I'm a sucker for the odd puzzle.

The calculations shown seemed a tad complicated for arriving at the radius of curvature so I though I'd while away some time while folding dud starting hands.

This might be a simpler way to do it if anyone's still interested, or even if they're not!

In the given diagram...

Let's call the green line G and it is known to be 10 inches long.

Let's call the blue line on the left R as it is a radius of the circle.

Let's call the red line Z, but only the length from the centre of the circle to where it meets the green line G.

The radius line that Z lies on is bisecting the chord formed by the 10 inch line G and it's counterpart so these two lines G and Z meet at right angles.

So the three lines G, Z and R form a right angled triangle and the old Pythagorean ruling can be applied directly.

That is...

1) G^2 + Z^2 = R^2

Sorry about the formatting, but I can't find an easy way to get supscripting for the squared terms, have to make do with ^2 to mean squared.

Now we know that if the line Z were extended by that extra 2 inches it would be equal to the radius of the circle, namely R.

So R = Z + 2

Substituting this and the known G = 10 into the equation 1) above gives...

10^2 + Z^2 = (Z + 2)^2

Expanding...

100 + Z^2 = Z^2 + 4Z + 4

Tidying up...

4Z + 4 = 100

Z + 1 = 25

Z = 26

Saves all that bother wih the nightmares of highschool trigonometry!

[Laku]

Re: Arch Forms for Oven Door - The Calculation?

isn't that Z = 24? Remember that +1 changes to -1 when you move it to the other side.

[brickie in oz]

Re: Arch Forms for Oven Door - The Calculation?

For the size and stresses of a wood fired oven arch I wouldnt think too hard about it, the only problem you will encounter is lack of sideways buttressing if you put a load on top of the arch.

You could make the arch almost flat if you wanted to.

[david s]

Re: Arch Forms for Oven Door - The Calculation?

There is an advantage in having the sides of the arch steeper than the centre. This becomes self evident when you begin to work the oven. This set up is actually opposite to what you get with a catenary arch. It is easy to sketch the curve on paper, then fold it in half to attain a symmetrical shape.

[Powindah]

Re: Arch Forms for Oven Door - The Calculation?

Laku:
Yes, you are of course right.

Z = 24 and as R = Z + 2, R = 26

As an excuse I maintain that the late night online poker game also involved a bottle or two of red wine, must have got a bit distracted by the game, or the glass, toward the end of that calculation.

I'm amazed that a four year old thread gets so many immediate responses. I llok forward to this sort of interest when I get around to building my own... Soon...

[Neil2]

Re: Arch Forms for Oven Door - The Calculation?

Use an ellipse.

Use two nails, a piece of string and a pencil:

http://www.mathopenref.com/constellipse1.html

That's it, done. No math required.

[Powindah]

Re: Arch Forms for Oven Door - The Calculation?

Why all this fear of a little mathematics?

String & pencils may work for some, but the mathematical method goes somewhat further in answering the original potser's question.

[Neil2]

Re: Arch Forms for Oven Door - The Calculation?

From Steve's original post:

"Anyway, I was hoping to come up with a DIY method for getting the Door Arch Form, just right, using a string, marker, and a piece of plywood."

The ancient Roman and the Medieval/Renaissance stone builders did not have computers.

The probably used strings, nails and pencils.

The Advantages Of The Elliptical Arch | LIVESTRONG.COM