*
I am receiving many e-mails from people enjoying the stair topics. So I thought I would show a typical layout for an elliptical stairway.
A while back I was called to go to the jobsite to measure for a circular stairway. What I found was a foyer that was wide but shallow. A circular would not work.
This called for an elliptical stairway if I could get the numbers to behave with comfortable rise and run restraints. The floor to floor height was 126.25 inches. This divided up into 16 treads/17 risers at 7.426 in. per rise.
The header at the top of the stairs allowed 156 inches from the top riser face. The bottom riser could not be more than 116 in. from the back wall.
The stair stringers were to be 48 inches apart. This left an inside stringer with an elliptical shape with a semi-major axis of 108 in. and a semi-minor axis of 68 in.
For a stairs to be comfortable and pass code, one has to consider the run of the stairs at the walking line. This is an imaginary line roughly 15 inches in from the handrail, and is the average path a person walks, thus its called the walking line.
For this to be figured, one could draw out an ellipse such has been posted elsewheres, and divide it up by actual measure, or one could use the several formulaes for the perimeter length of an ellipse that also have been posted. In this case, the formulae of pi times the square root of
[ 2(x squared + y squared) ], is plenty accurate for seeing if the stairs layouts out nice.
The walking line has a semi-major axis of 108 in. + 15 in. or 123 in.
The walking line has a semi-minor axis of 68 in. + 15 in. or 83 in.
The length of the ellipse that the walking line follows is then
3.14159 x square root of [2 (6889 + 15129). Finishing out the equation, this ends up with 659.255 inches for the perimeter length of this ellipse. This stairs is 1/4 of an ellipse, so this figures out to 164.813 inches. Divide this by the 16 treads and you end up with 10.30 inches of run at this walking line. I am happy with any run that is greater than 10.0 inches. So this passed on the first try.
Replies
*
I am receiving many e-mails from people enjoying the stair topics. So I thought I would show a typical layout for an elliptical stairway.
A while back I was called to go to the jobsite to measure for a circular stairway. What I found was a foyer that was wide but shallow. A circular would not work.
This called for an elliptical stairway if I could get the numbers to behave with comfortable rise and run restraints. The floor to floor height was 126.25 inches. This divided up into 16 treads/17 risers at 7.426 in. per rise.
The header at the top of the stairs allowed 156 inches from the top riser face. The bottom riser could not be more than 116 in. from the back wall.
The stair stringers were to be 48 inches apart. This left an inside stringer with an elliptical shape with a semi-major axis of 108 in. and a semi-minor axis of 68 in.
For a stairs to be comfortable and pass code, one has to consider the run of the stairs at the walking line. This is an imaginary line roughly 15 inches in from the handrail, and is the average path a person walks, thus its called the walking line.
For this to be figured, one could draw out an ellipse such has been posted elsewheres, and divide it up by actual measure, or one could use the several formulaes for the perimeter length of an ellipse that also have been posted. In this case, the formulae of pi times the square root of
[ 2(x squared + y squared) ], is plenty accurate for seeing if the stairs layouts out nice.
The walking line has a semi-major axis of 108 in. + 15 in. or 123 in.
The walking line has a semi-minor axis of 68 in. + 15 in. or 83 in.
The length of the ellipse that the walking line follows is then
3.14159 x square root of [2 (6889 + 15129). Finishing out the equation, this ends up with 659.255 inches for the perimeter length of this ellipse. This stairs is 1/4 of an ellipse, so this figures out to 164.813 inches. Divide this by the 16 treads and you end up with 10.30 inches of run at this walking line. I am happy with any run that is greater than 10.0 inches. So this passed on the first try.