Stairs

[James VanFossen]

When building curved stairs a horizontal radius is used. But iif you want to cover the bottom of stairs you need the radius on the slope. I think there is a formula for this but don't know it. Can someone tell me what that is??? Thanks.

 

[mmm4444bot]

When building curved stairs a horizontal radius is used. But [if] you want to cover the bottom of stairs you need the radius on the slope. I think there is a formula for this but don't know it.

To me, the phrases in red are ambiguous.

Please define your terminology, and explain more precisely what you want. My guess is that you want to determine the area of some surface, but I cannot determine a shape, from what you typed.

Can you supply a labeled diagram or a reference?

If not, you'll need to invest more time in typing out clear descriptions. (In my house, the phrase "bottom of stairs" describes a general region of either the living-room or basement floor -- heh, heh. I'm not a carpenter.)

 

[James VanFossen]

I am talking about covering the bottom side of the steps from the basement floor to the main floor. The stairs are usually built in a shop equiped to do this. Posts are placed on the floor at a horizontal radius to reach from the designated spot on the first floor to a designated spot on the basement floor. The sides of the stairs,called stringers, are placed on a slope to reach from the desired spot on the first floor to the desired spot on the basement floor and fastened to these posts to form the desired curve. For instance if the required radius on a horizontal line is, say 5', then the radius on the slope is totally different. This is the radius that is needed to form the curve on the slope to make cover and trim on the bottom of the steps. I don't know if this explains it good enough or not. If not I will have my son try his explanation. Please let me know if this helps. Thanks. James.

 

[Denis]

How close is this:
http://www.decks.com/Calculators/Stairs.aspx

Your "wording" is unclear to me...

 

[James VanFossen]

That is what I'm referring to. Now imagine you are looking down from above them and they are curved. This curve is on a horizontal radius as you look down at it, but on the slope that radius changes. That is the radius I need The equation for.

 

[Denis]

WHAT do you mean by "radius"?
A radius is half a circle's diameter; how does that "fit in" here?

 

[chrisr]

He may mean a helical staircase, possibly along an invisible "cylindrical curved surface".

 

[Denis]

He may mean a helical staircase, possibly along an invisible "cylindrical curved surface".

Yikes! Just to climb up on the deck :shock:

 

[chrisr]

[attachment=0:13jqspr3]stairs2.jpg[/attachment:13jqspr3][attachment=1:13jqspr3]stairs.jpg[/attachment:13jqspr3]Or just a small arc of one, even, to prevent dizziness!

 

[James VanFossen]

Yes, that is the idea. How does the radius as built in the second picture relate to the radius on the slope in either of the other pictures?? What I need is a simple formula or equation for that, if there is such a thing. Thanks for the thoughts and humor!

 

[chrisr]

The next clarification step, James, is to be sure about the geometric shape for which the stairs contour follows.
Is it a cylinder, a cone or alternative spiral?
When you know the shape, you can find appropriate formulae.
From what you have written, as you mention a floor radius,
it "appears" you are dealing with a cylindrical structure,
but that may not necessarily be correct.

 

[James VanFossen]

It follows as a cylinder.

 

[mmm4444bot]

… the radius that is needed to form the curve on the slope to make cover and trim on the bottom of the steps …

What does the cover look like? The phrase "bottom of steps" is still not clear, to me. When you build this cover, what will it look like?

You also repeated the ambiguous phrase "horizontal radius". If we're talking about a cylinder, there is only one radius. The width of a step is not a radius; that width is a segment of the radius.

Can you upload a labeled sketch ?

 

[chrisr]

\(\displaystyle The\ situation\ still\ needs\ further\ clarification,\ James.\)

\(\displaystyle When\ you\ mentioned\ \textbf{radius\ on\ the\ slope},\)
\(\displaystyle are\ you\ thinking\ of\ calculating\ the\ arc\ of\ a\ circle,\)
\(\displaystyle where\ the\ stair\ handrail\ and\ stringers\ are\ part\ of\ partially\ underground\ circles?\)

\(\displaystyle Normally,\ helical\ stairs\ follow\ a\ sinusoidal\ contour\ around\ a\ cylinder.\)

\(\displaystyle Are\ you\ trying\ to\ calculate\ the\ length\ of\ the\ stairs\ if\ the\ steps\ were\ laid\ out\ in\ a\ ladder\ formation?\)

 

[James VanFossen]

I refer you to the photo you sent previously. At the top of that photo you can see the underneath side of steps. That is what I want to cover so that no one can see the underneath, or bottom side, of the steps. Each step is fastened at each end to what is called a stringer. These stringers are bent to a desired cylindrical radius and sloped to reach a desired spot on the opposite end, depending on which end you start from. The radius on the slope, as you may be able to see or comprehend, is significantly different from the cylindrical radius. This radius on the slope is what is needed to cut the material to be placed on the underneath side of steps. I don't know how to explain any differently. Hope this explains it. If not let me know. Thanks.

 

[chrisr]

\(\displaystyle You\ need\ the\ dimensions\ of\ this\ undercarriage\ then, James?\)

 

[chrisr]

[attachment=0:3u89394y]spiral stairs1.jpg[/attachment:3u89394y][attachment=1:3u89394y]spiral stairs2.jpg[/attachment:3u89394y]

\(\displaystyle These\ sketch\ illustrate\ calculations\ for\ the\ length\ of\ the\ edge\ of\ the\ stairs\)
\(\displaystyle against\ the\ cylinder.\ Similar\ calculations\ give\ the\ length\ of\ the\)
\(\displaystyle outer\ edge\ of\ the\ stairs\ if\ you\ consider\ it\ winding\ around\ a\ wider\ cylinder.\)

\(\displaystyle Is\ this\ getting\ there, James?\)
\(\displaystyle The\ drawings\ illustrate\ the\ length\ for\ a\ full\ period\ of\ the\ spiral\)
\(\displaystyle and\ for\ a\ fraction\ of\ a\ period.\)

\(\displaystyle The\ lower\ sketch\ shows\ the\ cylinder\ unravelled\ to\ calculate\ the\ unwound\ spiral\ length.\)

 

[chrisr]

\(\displaystyle However,\ if\ you\ want\ to\ cut\ wood\ panels\ and\ join\ them\ together,\)
\(\displaystyle these\ panels\ will\ be\ in\ the\ form\ of\ stretched\ circle\ arcs,\)
\(\displaystyle more\ like\ the\ arcs\ of\ an\ ellipse.\)

\(\displaystyle I\ will\ draw\ another\ illustration\ later.\)

 

[chrisr]

[attachment=1:1gmvkbmy]"radius on the slope".jpg[/attachment:1gmvkbmy]
\(\displaystyle This\ illustration\ shows\ the\ shape\ of\ the\ edge\ of\ the\ underside\ of\ the\ stairs\)
\(\displaystyle against\ the\ inside\ cylinder,\ the\ inner\ edge\ of\ the\ stairs.\)
\(\displaystyle It\ is\ elliptical.\ An\ ellipse\ doesn't\ have\ a\ fixed\ radius.\)
\(\displaystyle It\ is\ a\ stretched\ circle\, however.\)

\(\displaystyle You\ must\ first\ decide\ on\ the\ cylinder\ height\ and\ the\ number\ of\ periods\)
\(\displaystyle of\ the\ spiral\ (could\ be\ a\ fraction)\ from\ base\ to\ top\)
\(\displaystyle before\ finalising\ the\ undercarriage\ shape\ to\ be\ machined.\)

\(\displaystyle More\ needs\ to\ be\ added\ for\ the\ outside\ edge\ of\ the\ undercarriage,\)
\(\displaystyle in\ order\ to\ have\ the\ entire\ dimensions\ of\ the\ undercarriage.\)
[attachment=0:1gmvkbmy]undercarriage of spiral stairs2.jpg[/attachment:1gmvkbmy]

\(\displaystyle The\ area\ between\ ellipses\ shows\ the\ flat\ surface\ of\ the\ underside\ of\ the\ stairs\)
\(\displaystyle laid\ flat\ on\ the\ floor.\)