Another physics question

[David Martin]

It's nativity time. 'The star went before them' etc.

In order to accomplish this I am thinking of running a tensioned cord along the apex of the church roof and then a simple string loop to pull a dangling star (probably with a flashing white LED bike light inside) the length of the building above the heads of the congregation/sunday school.

Obviously no string will stay straight when stretched over 25m, the question arises as to the necessary tension that I would need to stop it sagging too much.

If I remember correctly, the tension in the string would be weight load/sin angle of deflection, so if I was to allow for a maximum dip of about 50cm, that would give me for a load of 500g a tension of 12.5kg on the line?

I'll be using something like 250kg breaking strain line, so am not worried about that, just wondering how taut it would have to be.

Any physics/engineering advice gratefully received. Comments on the nativity to POBI.
 

[Jacomus]

I can't supply any physics, but if you believe your estimation of 12.5kg on a 250kg breaking strain line, couldn't you just tension it to say 50kgs and say 'jobs a good'un'? Or am I missing something basic like needing to take account of the loading on whatever fixings you are using?

[David Martin]

That was basically the idea, but if I needed to have, say, 100kgs tension in the line, that would seriously affect the strength of the fixings required. It's nice to get a theoretical OK before messing about on ladders[1]  a long way up.

..d

[1] or scaffolding.

[ScumOfTheRoad]

You should Google for 'catenary curves'
I'd guess there should be some tables or online calculators for the strain in a catenary cable.

[mrcharly-YHT]

It's going to sag, accept it, unless you run a rod the length of the church and hang it off that.

Your calculation I think is correct, but ignores stretch. Unless you are purchasing Kevlar, 25m of string will stretch quite a bit.

would it be possible to go a bit alternative and use something like a chinese lantern pulled along a string?

[David Martin]

It's going to sag, accept it, unless you run a rod the length of the church and hang it off that.

I know. I was trying to work out how much I can expect.

Your calculation I think is correct, but ignores stretch. Unless you are purchasing Kevlar, 25m of string will stretch quite a bit.

I was thinking that after putting XXkgs tension on it that it wouldn't stretch too much more. Having bounced on the end of a climbing rope before I am well aware of rope stretch.

would it be possible to go a bit alternative and use something like a chinese lantern pulled along a string?

That is the general idea. A tensioned line as a runner and the lantern/star suspended from a clip (with monofilament line)  over the line and moved forward and backward by a loop of string. So it appears to be suspended in mid air.

What I don't want is for it to be high at the ends and bouncing off peoples heads in the middle.

[mrcharly-YHT]

Your calculation I think is correct, but ignores stretch. Unless you are purchasing Kevlar, 25m of string will stretch quite a bit.

I was thinking that after putting XXkgs tension on it that it wouldn't stretch too much more. Having bounced on the end of a climbing rope before I am well aware of rope stretch.

I didn't mean to imply that you were ignoring stretch, just that the formula doesn't allow for it.

The degree of stretch will depend on the type of string, its construction and material. 25m is quite a span - I have a 50mm multiplat (low-stretch construction and material) mooring rope that spans that sort of gap - I used a yacht winch to tension it, put maybe 200-250kg of tension on it and it still sags by more than 50cm under its own weight.

[JStone]

I think the OP's doubled the resulting tension - with the load at mid-point & resolving vertically we have:

2T * cos(atan(12500/500)) = 0.5kg, giving cord tension T = 6.25kg.

If the arrangement of the hall allows, why not run the cord over a pulley at one end & down to ground level. Stick known weights on the end (eg in a bucket) & see what the sag looks like? General paranoia & the hall insurance will suggest an appropriate safety factor for moving overhead loads.

EDIT: suspended tensioner (eg bucket of weights) also avoids the issue of cord stretch

[Jurek]

I cannot do the physics, but I can attest mrcharly's suggestion about using Kevlar.

I fly a triplet of 2m Flexifoil kites. The difference between using Dacron / Polyester lines and Kevlar in terms of stretch is a bit like the difference between using string and solid rods of steel.
The Polyester lines are tested to 300lb breaking strain, the Kevlar is similar, but about 1/3rd of the diameter of the poly.