So, are you saying you don't know the basic geometry involved?
Is this homework?
I am trying to calculate the length of each sling needed (there are two slings in the picture below). Given diameter of the roll (D), Span at pick points (S) and the angle the slings make with the horizontal plane (A), I need to calculate the sling length needed. Also need to calculate the headroom (HR) as shown in the picture. Although this is for lifting purposes, this is more of a geometry question.
So, are you saying you don't know the basic geometry involved?
Is this homework?
Do you have have access to CAD?
Tell me and I forget. Teach me and I remember. Involve me and I learn.
No this is not homework. I am trying to generate a formula so that others can put in the values of D, S & A and get the sling length and the headroom (HR). This is a little bit more involved than just the basic trigonometry and cylinder geometry. What's tricky is that the angle (A) is what the sling makes with the horizontal plane, the sling wraps around the cylindrical shape at an angle and takes off at a tangent. I am just not able to get my head around this geometry of the sling to calculate it's length.
Step 1: Use trigonometry to calculate L1 and L2.
Step 2: Use trigonometry to calculate actual sling length.
Note: I would NOT use that slinging method unless there was some way of preventing the two slings from sliding toward each other (maintaining the S dimension).SLING LENGTH2.jpg
Jboggs, thank you for your work. But I see a couple of mistakes in your approach. Angle A is the true angle the sling makes with the horizontal plane, not the projected angle in the front view. Also in your Step 2 (Circular approximate shape), I don't know any of the angles on the triangle formed by the slings and the horizontal.
I don't like this rigging myself, but it still gets used in the field for its ease. A rigger relies on the friction between the sling and the surface of the load (roll) to resist the pull resulting from the angular slings.
Angle A is the angle of the plane in which the sling lies. In step 2, you have all the information you need to calculate the geometry of the shape. I would use the circular approximation method because it is so much easier, and just add a little fudge factor. Look at the right triangle formed by L2 (the hypotenuse) and D/2 (one side). Use geometry to calculate the length of the other side of the triangle, which is also the length of the straight portion of the sling. The curved portion of the sling is simply the segment of the perimeter of the circle defined by the angle between L2 and D/2.
What I am trying to tell you is that angle A (which is given) is not the angle that the plane (in which the sling lies) makes with the horizontal. It is the true angle that the sling (line) makes with the horizontal plane. Also in you step 2, L2 would be the height and not hypotenuse. I will probably have to use vectors/matrices to get this worked out. Thank you for your help jboggs.
SLING LENGTH DETAIL.jpg OK. Call my angle A something else, A'. Your angle A is a vector resulting from three factors, the spread S, the diameter D, and the headroom HR. I don't see how it can realistically be an input since all three factors affect it. My approach using S, HR, D, and A' starts with simple, measurable data and calculates the higher level results (including angle A if you like).
Also, L2 is indeed the hypotenuse of the triangle shown. I think the shape to which you were referring in which L2 is the height is not a true triangle since it includes a portion of the arc segment wrapping around the pipe. Maybe this image will clarify my approach.