# Calculate the force required to pull a bungee cord taut, creating a straight line

• I
Gold Member
10 feet would be perfect.

And this might get close. Spectra braid line rated for 78 pounds with specific gravity of .98. And 2000 meters weighs about .37 lbs.
0.37 lbs. for what? The whole 2000 meters?

fascinated
Could you provide a better link to that video?
Timestamped at the description:

0.37 lbs. for what? The whole 2000 meters?
Yes, if my math is correct.

Gold Member
Yes, if my math is correct.
Interesting but misleading. The world is not flat. I hope your project is not related to that idea.

https://flatearth.ws/laser

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fascinated
Interesting but misleading. The world is not flat. I hope your project is not related to that idea.
LOL, at flat. There must be some reasonable explanation. I am more curious about using a laser with the beam being visible as suggested. Catenary handled.

Gold Member
LOL, at flat. There must be some reasonable explanation. I am more curious about using a laser with the beam being visible as suggested. Catenary handled.
If we are talking about only one mile it is easier. The beam diverges a lot over 16 miles and is not focused at a point across the lake. Your line above would still sag 2.5 feet over one mile. Try using that calculator I referenced.

fascinated
If we are talking about only one mile it is easier. The beam diverges a lot over 16 miles and is not focused at a point across the lake. Your line above would still sag 2.5 feet over one mile. Try using that calculator I referenced.
I actually came across that same calculator, but didn't understand how to enter the right numbers.

And you are saying that line I found above would sag 2.5 feet or that the laser will curve that much?

Homework Helper
What would it be over that distance? He claims 16.4 miles.

Is this a trick?
16.4 [nautical] miles = 16.4 minutes of arc. Likely we are dealing with refraction. A laser beam in air need not be straight.

But let us do the math. Over a 16.4 mile span, how much higher does the curvature of the Earth make the midpoint than the ends? For convenience, let's call it 1/4 of a degree.

Think of the lake as an arc of a circle centered directly above the Earth's center. From there it extends left and right by 8.2 miles, curving slightly downward both ways.

The lake's midpoint should have a height above the center of the Earth of 6000 miles times cosine of zero degrees. The endpoints should each have a height of 6000 miles times the cosine of 1/8 degree.

The cosine of 1/8 of a degree is 0.9999976. Which is 0.0000024 less than 1. Multiply 6000 miles by this and you get 75 feet. So yes if there were no refraction and no diffraction and both sender and receiver were near ground level, that laser should have been hard to see behind a 75 foot tall arc of water.

The amount of refraction depends on many factors. Notably humidity and temperature gradient. A cool lake under hot air would tend to produce downward-curving refraction. By contrast, hot pavement and cooler air produces upward-curving refraction [aka mirages].

But we are supposed to be talking about cords, tension and sagging. Not flat Earth conspiracy theories.

Gold Member
I actually came across that same calculator, but didn't understand how to enter the right numbers.

And you are saying that line I found above would sag 2.5 feet or that the laser will curve that much?
If I understood how to enter the data properly, the line sags about 2.5 ft. if it is one mile long and has the tension you wanted. You have to put in how much tension the line can handle, the length and the weight per unit length in consistent units..

Shane Kennedy
If it is held at anything other than vertical, it will get closer and closer to a straight line, but never achieve it.

Gold Member
You could use an almost invisible thin cord in a catenary to uphold a more visible cord in a straight line like a suspension bridge.

Gold Member
Any idea for how much sag with piano wire and if these lengths are accessible?
2000 pounds, more or less.

Please don't try this. When this wire breaks it turns into an unpredictable flying Ginsu knife that could maim or kill someone.

BoB

phinds and bob012345
Gold Member
or that the laser will curve that much?
Laser beams don't curve (except when they do because of refractive atmospheric conditions along the path : think "mirage"... oh, and technically gravity affects light as well as everything else : good luck measuring that).

Gold Member
@fascinated This whole project worries me. You can't go hanging lines over roads and other peoples' property without satisfying loads of regulations, getting way leave and (unless you are mad) getting insurance.

The picture of a rubber band is a complete red herring but you could measure a finite sag in it, using interferometry.

Imo this is a finite safety risk and some of the above posts make this clear, regarding the energy stored. (Did you ever consider how you might install this thing?)

Gold Member
@fascinated This whole project worries me. You can't go hanging lines over roads and other peoples' property without satisfying loads of regulations, getting way leave and (unless you are mad) getting insurance.

The picture of a rubber band is a complete red herring but you could measure a finite sag in it, using interferometry.

Imo this is a finite safety risk and some of the above posts make this clear, regarding the energy stored. (Did you ever consider how you might install this thing?)
I suspect it is some sort of outdoor art exhibition/festival probably in a large field.

Gold Member
some sort of outdoor art exhibition
Haha - right. So it would require "some sort of" qualified Engineer to design a safe version, particularly if the general public would be exposed to it. I think it may be legal to expose oneself to high risks but . . . .

The Energy stored in stretched lines can be dangerously high and the bungier the line, the more Energy is stored. It scares me.

berkeman and jbriggs444
Gold Member
Haha - right. So it would require "some sort of" qualified Engineer to design a safe version, particularly if the general public would be exposed to it. I think it may be legal to expose oneself to high risks but . . . .

The Energy stored in stretched lines can be dangerously high and the bungier the line, the more Energy is stored. It scares me.
I wonder if it might be possible to make the line out of colored paper, the kind of strips for party decorations?

Gold Member
I wonder if it might be possible to make the line out of colored paper, the kind of strips for party decorations?
A short length could self-support but any wind would tear it. Then here's the problem of rain . . . . . .

The best thing (for a much shorter installation) would actually be steel wire. Minimal stretch so less sag and less stored Energy.

Gold Member
The Energy stored in stretched lines can be dangerously high and the bungier the line, the more Energy is stored. It scares me.
The more I think about it, the more I concur. There's almost no way to do this that doesn't involve a dangerous amount of stored energy. That should not be understated.

berkeman
fascinated
Thanks again for all the replies.

If it is held at anything other than vertical, it will get closer and closer to a straight line, but never achieve it.
Yep, got that.

You could use an almost invisible thin cord in a catenary to uphold a more visible cord in a straight line like a suspension bridge.
View attachment 290058
This! It was brought up before as I couldn't see how this gets done. With the spectra braid line, we have the sag down to 2.5 feet. This would allow us to hang the first line at 12.5 feet and have a perfect line at 10 feet.

My question again is, what can be used for the bottom line? If it is just another "more visible" line, how could it ever form a horizontal line without nearly infinite vertical supports? Or am I totally missing this one too?

Thanks again

Please don't try this. When this wire breaks it turns into an unpredictable flying Ginsu knife that could maim or kill someone.

BoB
Lol... at least when the bungee snaps, it goes almost perfectly straight to where it broke.

The picture of a rubber band is a complete red herring but you could measure a finite sag in it, using interferometry.
I got you on everything else, but this one is still tough. I *almost* think that's true.

I suspect it is some sort of outdoor art exhibition/festival probably in a large field.
Private land owner... but who knows.

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fascinated
Haha - right. So it would require "some sort of" qualified Engineer to design a safe version, particularly if the general public would be exposed to it. I think it may be legal to expose oneself to high risks but . . . .

The Energy stored in stretched lines can be dangerously high and the bungier the line, the more Energy is stored. It scares me.
It's impossible. We have to do it a different way.

The more I think about it, the more I concur. There's almost no way to do this that doesn't involve a dangerous amount of stored energy. That should not be understated.
I think the supported, more visible line would work, if that is possible. I still don't see how we guarantee a horizontal line.

Thanks again, folks.

Gold Member
I think the supported, more visible line would work, if that is possible. I still don't see how we guarantee a horizontal line.
It won't. All it will do is make more (granted, shorter less saggy) caternaries.

Homework Helper
5000 feet of helium-filled tube constructed of aluminized Mylar and deployed on a dead calm day?

russ_watters
Homework Helper
Gold Member
High voltage electricity pylons are generally about 1,000 ft apart. You want something 5 times further apart. Forget it.

Mentor

Mentor
I wanted to keep going, but the wife got scared. We were next to a highway.

Please don't try this. When this wire breaks it turns into an unpredictable flying Ginsu knife that could maim or kill someone.

Private land owner... but who knows.

Okay, this has gone on long enough. There have been several reports of safety concerns in this thread, and not knowing the actual application prevents us from proposing safer alternatives. Thread will remain closed.

@fascinated -- if you need a long straight line, the laser is the way to go. Please keep laser safety considerations in mind, though, to ensure that nobody is exposed to laser light at any level that can cause eye damage.

hmmm27 and bob012345