Stair Geometry at top of Sphere
Stair Geometry at top of Sphere
(OP)
We're trying to model a stair that goes to the top of a high pressure storage sphere (LPG tank). I'm having trouble working out the geometry and wanted to know if any of you have a guide for this sort of thing.
The stair is a normal, straight stair up to the mid-point of the sphere, then it curves with the surface of the sphere up to a small platform at the top. The sphere is about 60' in diameter.
Thanks!
The stair is a normal, straight stair up to the mid-point of the sphere, then it curves with the surface of the sphere up to a small platform at the top. The sphere is about 60' in diameter.
Thanks!
-5^2 = -25 ![]()
http://www.eng-tips.com/supportus.cfm






RE: Stair Geometry at top of Sphere
RE: Stair Geometry at top of Sphere
Ideally, you'd hold uniform rise for all treads, and uniform run either at the inner end or at the center. Once you get past the 45 degree line, I'd put a platform and run it up radially from there.
If you can locate some similar tanks, Google satellite photos might be adequate to show the general arrangement used.
RE: Stair Geometry at top of Sphere
In plan view, the stair would come straight from a quarter point, tangent to the equator of the sphere, to the ground. From that tangent point, it curves up and around the arc of the sphere until reaching the side of a small platform mounted on the "north pole" of the sphere.
A picture would be best - see enclosed...
-5^2 = -25
http://www.eng-tips.com/supportus.cfm
RE: Stair Geometry at top of Sphere
Every point along the inside stringer meets the tank wall at precisely 30' from point A at various angles horizontally and vertically. The top of the nth riser is precisely n*R above point A. The sloping distance from the top of one riser to the top of the next riser is S = (R2+T2)1/2. We have a series of identical isosceles triangles, with dimensions 30', 30' and S where the elevation of each node is known. From that, it should be possible to model the inside stringer.
BA
RE: Stair Geometry at top of Sphere
Rn is the radius of the circle cutting the sphere at the elevation of the tread. d-theta is the angular dimension with chord length 10" and radius Rn, so d-theta = 2(arcsin(5/Rn)).
X, Y and Z are the Cartesian coordinates of the bottom of the next riser at the level shown. X = Rn*cos(theta), Y = Rn*sin(theta) and Z = Elevation of tread, taking 0 as center of sphere.
Each value of X, Y and Z satisfies the equation of a sphere, i.e. X2 + Y2 + Z2 = 3602 which serves as a partial check of the procedure.
BA
RE: Stair Geometry at top of Sphere
-5^2 = -25
http://www.eng-tips.com/supportus.cfm
RE: Stair Geometry at top of Sphere
You are welcome. D-theta does have meaning. D-theta is the rotation with variable radius Rn which has a chord length of 10" (my assumed tread width). The sum of d-thetas at the nth step is the total rotation from the beginning to the nth step.
BA
RE: Stair Geometry at top of Sphere
-5^2 = -25
http://www.eng-tips.com/supportus.cfm
RE: Stair Geometry at top of Sphere
BA
RE: Stair Geometry at top of Sphere
RE: Stair Geometry at top of Sphere
BA
RE: Stair Geometry at top of Sphere
BA
RE: Stair Geometry at top of Sphere
You can see in the picture posted earlier that at the top few treads are supported by the vertical struts on the inboard side, just as they are on the outboard side lower down (just above and to the right of the "55").
You are correct in saying that the there is no inner stringer from the equatorial landing up, however, it's also apparent that the inner edge of the treads must pull away from the shell at some point. You can even tell that the axis of the tread quickly deviates from a radial line pointing to the vertical central axis of the sphere as you go above the equator.
That said, your sheet has given me an idea and I'll work on it further.
Thanks for your replies...
-5^2 = -25
http://www.eng-tips.com/supportus.cfm