Arch Forms for Oven Door - The Calculation?

[david s]

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]

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]

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]

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]

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

[brickie in oz]

I use a plastic strip or aluminium ruler or a thin piece of plywood, bend to shape with the aid of a few nails and mark.

[Powindah]

Neil2:
The paragraph you quote from goes on to say "I just need to know how long the string should be." Another paragraph contains "What is the radius of the circle I would need to draw on the plywood? "

This indicates the original poster was happy to use string and pencil to draw the arch, but wanted to know how large a radius was required for his requirements. The calculated method would give him exactly that.

[Amac]

Saves all that bother wih the nightmares of highschool trigonometry!

Very nice and elegant solution. Not only does it save bother with trigonometry but it is also more accurate:

Since nobody took the trouble to correct kemos original solution here is my go!
I'll use powindahs notations for the lines:

kemos original equations 1 and 2 are OK albeit with rounding errors becuase of the irrational numbers involved - eg sqrt of 104 etc. But I have no idea where he came up with equation 3.

anyway here goes.
Angle X = 11.31
Lets call A the angle between Y and R
and B the angle between Y and Z
and C the angle between G and R
A = B = 180-(90+11.31) = 78.69
C = 78.69 - 11.31 = 67.38
C is an angle of the right angled triangle hypoteneuse R and adjacent G,
cosine C = G/R = 10/R = .384
R = 10/cosC = 10/.384 = 26.0416667
and of course R=Z
more accurate but still not as good as powindahs solution which is exactly right
This thread btw is only for people with too much time on their hands
Amac

[wotavidone]

Brickie in Oz's solution is quick, simple and is the way boat builders have drawn curves to fit desired dimensions for hundreds, if not thousands, of years.
I have been messing around with radii and graph paper for some time getting my dome and arch shape to come up right for different brick measurements, mortar thicknesses and stuff, and I reckon a lath bent around nails inserted at various points is the simplest and best way to do it.

[Amac]

I wouldn't dispute that too much wotavidone - just I do like to see puzzle solved in an elegant manner, and powindahs was elegant compared with the trigonometric calculations.
One thing though. Boat builders are probably trying to achieve a different curve than arch builders and will be limited by the strain that the lath will sustain without breaking. I would say it would be good for a gentle curve but for anything more rounded it is surely easier to work out the radius and use a compass to draw the outline. Certainly in my case since I made a completely semicircular arch and all I needed to know was what entry width I could tolerate.
Aidan