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# Zip Line Across a Lake

08/25/2011 1:24 PM

Hello,

I hope this isn't too frivolous a question, but my granddaughters have asked me to put a cable across our lake so they can, with the use of a pulley fly back a forth across the lake. Now, while they are light in weight, my son isn't and he'll be the testing the strength of the system. So to the question.

Assuming a reasonable slack in the cable, (not taunt) how much tension would the wire have to hold if a 250lb man were half way across a 300' length of cable and what about a 500' length? If I increase or decrease the slack, how much affect does that have on the tension?

Thanks, Charlie

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#1

### Re: Zip line across a lake.

08/25/2011 1:30 PM

You'll need plenty of tension else they will get stuck in the middle.
Del

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#2

### Re: Zip line across a lake.

08/25/2011 1:35 PM

Thank you Del, I plan to have two cables, one to go and one to come, the the start will be 10' off the ground and the end will be at the ground. I can change those heights until I get it so they will drop into the lake just at the shore.

Thanks for the fast response!

Charlie

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#3

### Re: Zip line across a lake.

08/25/2011 1:38 PM

It's the weight of the cable itself that needs to be factored into the equation.

The Load Remains constant, but it's the length that may vary.

It's not like a moment arm, where the distance from the load to the connection point is critical. The 250lb load will always be a 250lb load, but the load will be transfered depending on the slope of the cable and which connection point it's nearest to.

Some of the factors which you will need to know to select the proper cable are:

• The tension force on the static cable not under load to obtain the tautness you desire. This is additive to the actual Load.
• The weight of the cable.
• The maximum Load (250lbs) force acting directly on a single connection point, (not out in the middle, shared by both ends) We want to design for the worst case scenario.
• The Method, and location of the connection point... IE is it looped around a tree, anchored into a cliff face, side of the barn etc. (Make sure the Full load including safety factor can be safely handled by whatever you are attaching it to.)
• Safety Factor... I personally would use at least a 3:1, preferably more.

My first thoughts...

If it's going across the lake, with a slope in the cable, the trolley will be out over the middle of the lake after it's used (or the downward sloped end). How do you plan on bringing the trolley back to the start for the next use?

Sounds like a fun Project.. Build it safe.

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#4

### Re: Zip Line Across a Lake

08/25/2011 1:40 PM

This may (or not) help.

You may also find help here

You may also want to consider some pitch to the zip line, else you may have trouble getting the granddaughter/pulley back from the middle.

Sounds like a fun project for you and the granddaughters

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#6

### Re: Zip Line Across a Lake

08/25/2011 2:01 PM

Thank you RVZ and KJK, I'm sorry I didn't put in part about the different heights at start and stop. I can vary these greatly as we have steep hills on both sides, with large trees on both banks. I'm hoping after drop off into the lake the trolley will continue to the bank or at least stop within reach of a pole or something like that.

It's been 45 years since my physics exposure, but I thought I remembered a problem about a bird landing on a telephone line and the middle was the worst case scenario? Right now I'm looking at 5/16" cable rated at 11,000 pounds, which would seem plenty as I don't think the tree would even allow that much weight. But then since my son has seen me make mistakes on what I "seemed to be about right", I thought I better make sure.

Charlie

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#8

### Re: Zip Line Across a Lake

08/25/2011 2:09 PM

I'm going to assume 11,000lbs or so would be just fine.

If the load is dead center in the middle of the wire, the load is being shared evenly along the length of the wire to the connection point. If the load is off to one side, the side the load is nearest to will see more force from the load than the other... but in any case, the wire you have selected should do the job just fine...

Be aware of environmental issues causing the line to corrode over time which will greatly reduce it's load carrying capacity.

Stainless braided wire rope would be your best bet... but \$\$\$\$

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#30

### Re: Zip Line Across a Lake

08/26/2011 10:19 AM

you can put light ropes onto the platform or carriage so that the platform or carriage can be pulled forward or back. Continuous loop.

Don't forget the safety aspect - they are your grandchildren!

Sleepy

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#5

### Re: Zip Line Across a Lake

08/25/2011 1:47 PM

Ever the worrier, are there any boats on your lake?

500' of 3/16" cable will weigh 31 pounds and have a minimum breaking strength of 3,700 pounds. That's probably overkill.

Maybe one of our mechanical genuii will crunch some numbers. Where's nickname?

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#9

### Re: Zip Line Across a Lake

08/25/2011 2:10 PM

Thanks Lyn, My old age has made me a worrier as well and for many good reasons. I can still hear my son of nine asking, "dad, are you sure this is going to be strong enough", that was just prior to him landing flat on his back in a cloud of dust.

Charlie

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#7

### Re: Zip Line Across a Lake

08/25/2011 2:07 PM

The more slack you allow (bigger h) , the lesser is the tension.

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#10

### Re: Zip Line Across a Lake

08/25/2011 2:24 PM

Thanks Bravo,

That looks like the equation required, but like Jethro would say, I'm going to have to cyfer on that for a while, did I mention 40 years since my limited education?

Really thanks,

Charlie

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#11

### Re: Zip Line Across a Lake

08/25/2011 3:09 PM

Don' t worry. Here it is:

If you allow 5 ft sag, Theda = arctan(150/5)=1.53 , cos (theda)= 0.0333

mg= 250/2.2*9.8= 1113.6 Newton

the tension T = 1113.6/ (2x 0.0333) = 16713 N = 3752 lb .

So, choose a cable that will give you a few time safety margin .

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#12

### Re: Zip Line Across a Lake

08/25/2011 3:50 PM

Thank you Bravo! Showing me how to solve the problem is even better than just giving me the answer!

I'm thinking it would be better to tie off to a tree that was not guy wired, then as the weight approached the middle, the tree would bend to the max load and slowly return to it's straight original start position. I can't see any other way than trial and error to do that, so the sag which is critical will be unknown. But then I have some practical experience from pulling on trees with a truck winch that shows they will bend a lot, so the sag should be self compensating.

Well, if the big boy lands in the lake, it'll be better than on his back in the dirt. lol

Thanks, Charlie

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#13

### Re: Zip Line Across a Lake

08/25/2011 5:06 PM

Not sure if this will help. It sort of extends the sag point.

It reduces the angle once you get to the other side, I think.

Good luck, Ky.

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#27

### Re: Zip Line Across a Lake

08/26/2011 3:29 AM

If your browser supports the CR4 menu bar, the icon Ω brings up a character set that includes Greek. θ = theta (not theda).

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#16

### Re: Zip Line Across a Lake

08/25/2011 7:07 PM

Homer and Jethro (Jethro is on the left, above)

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#19

### Re: Zip Line Across a Lake

08/25/2011 11:26 PM

Essentially if you have a 10 degree off straight angle then at the center you will have about 6000 lbs of tension from a 250 lb load. And that is a "dead" load. If there is any fooling around and you get 3G's then you are pushing 18000 pounds tension. If it gets really slack with say 20 degrees from straight you should probably design for 1000lbs tension.

Be careful of the fastening points, it can easily half the cable strength as you bend and crimp.

If that is a navigable water (and I have seen a stream 6 inches deep meet that criteria) there may be laws against putting a cable across.

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#14

### Re: Zip Line Across a Lake

08/25/2011 5:10 PM

Thermal expansion/contraction of the cable may give unacceptable variation in sag. This could be compensated by spring loading or a pulley/weight connetcion at either end.

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#15

### Re: Zip Line Across a Lake

08/25/2011 7:04 PM

In my past life as a designer of highlines for replenishment at sea between ships, the highline is always kept at a high tension, never slack (I don't remember the actual figures, but it was on an 1-1/4" wire rope). Off course there was another cable that hauled the load from ship to ship, but the highline is always taut. Actually much more taut than you could achieve with your lake setup. Regardless of the tautness of the line, there will always be a vertical component until the destination is 2-blocked. To overcome this, the sending end has to be higher than the receiving end. and the tautness of the line will determine what that height difference will be. The receiving end needs to be at least 10 feet from the edge of the water for a "clean" descent without landing short in the water.

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#17

### Re: Zip Line Across a Lake

08/25/2011 9:43 PM

Some of us found a rope and tied it to the remnants of the walls of a bombed building. I had difficulty in explaining the bruises and grazes on my face and hands from banging into the wall at the low end, without admitting we were playing in the bombed buildings I recommend tying to a tree branch instead of the trunk.

It should be rigid or guyed. Consider one of the wires, there will be a high end, a low end and an equilibrium point somewhere towards the low end. The equilibrium point is one where a load will not try to move in either direction. The passenger will start at the high end, accelerating quickly at first but the rate will drop until the equilibrium point where it will reverse and start to slow the passenger down.

If we ignore the self weight of the wire and if the high point is say 10" above the low point, and the equilibrium point is another five feet down, the equilibrium point will be one quarter of the way from the low point to the high point.

I'll try to remember to post a diagram tomorrow.

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#18

### Re: Zip Line Across a Lake

08/25/2011 10:50 PM

Since you're carrying humans, you'd better get it right. You might want to talk to a yacht rigger that works with stainless steel concerning the various clamps and rollers needed. Stainless steel can be strange about hydrogen embrittlement if your clamps or swages hold water. Rollers can bind and generate fast wear. And you make me a little nervous expecting kids to let go before they get to shore. They won't come down where they let go, especially at high speeds. How are you bringing the rolling rig back? Got insurance? It's called an "attractive nuisance" and you'll need to keep an eye on it, at night, when you're away, etc.

http://en.wikipedia.org/wiki/Attractive_nuisance_doctrine

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#31

### Re: Zip Line Across a Lake

08/26/2011 10:20 AM

Thank you for your concerns. But I believe I can make it all but impossible for a young trespassing child to find these cables a source of entertainment . I also found this part interesting "If a child of injured child's age is able to understand and appreciate the hazard, the doctrine of attractive nuisance will not likely apply". I will keep the cables high enough off the ground to avoid accidental contact by simply raising both ends proportionately and also remove the platform ladder after use. Thanks again.

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#20

### Re: Zip Line Across a Lake

08/25/2011 11:34 PM

Although the cable will sag a bit on either side of the load, it will be nearly straight each way, with the load and attachment points forming a triangle. Thus the load pulley's trajectory will be (part of) a tilted ellipse, with foci at the cable end points. This will give a relatively steep "kick start" of acceleration. The rider's speed will increase until the lowest point of the elliptical arc, which will be near the low end of the cable. Then the rider will decelerate from there toward the low end of the cable. If the design is balanced out right, the speed will be zero as the rider approaches the end point, and he/she can step onto a platform (or maybe even the ground). If the rider misses the step-off, or is not caught, he/she will then start going backward to the low point of the arc, which may be only a few feet away, and which can be tuned by adjusting the cable tension. I say proceed cautiously, but go for it! (Try it with a bag of rocks or something before putting people on it.)

I also fantasize that safety nazis will go to their own special circle in hell, where Sir Lawrence Olivier will drill their teeth, asking over and over, "Is it safe?"

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#21

### Re: Zip Line Across a Lake

08/25/2011 11:42 PM

Maybe such bureaucrats and pettifoggers will just go into the same already existing circle as the lawyers.

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#23

### Re: Zip Line Across a Lake

08/26/2011 12:45 AM

Is Dante playing bashful today?

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#22

### Re: Zip Line Across a Lake

08/26/2011 12:43 AM

You can probably find good answers by doing a search for "cable deflection and loads". You will find the tighter the line is the less it will hold. Pic is from North Fork of the Clearwater River in Idaho, USA.

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#25

### Re: Zip Line Across a Lake

08/26/2011 2:12 AM

Interesting. I've driven through there several times without seeing this setup, which looks like some sort of gauging station. I would consider this one of the great scenic drives; lots of kayakers, and a couple of hot springs along the way.

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#24

### Re: Zip Line Across a Lake

08/26/2011 1:00 AM

GA; excellent reference.

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#26

### Re: Zip Line Across a Lake

08/26/2011 2:50 AM

It's a USGS water reporting site but the cable crossing is maintained by the Forest Service. They have another one up the river about 30 miles +/- downstream of Kelly Creek Ranger Station. It's beautiful country.

LOCATION.--Lat 46Â° 50'26", long 115Â° 37'16" (NAD83), in SE1/4 SE1/4 NE1/4 sec.6,
T.40 N., R.7 E., Clearwater County, Sheep Mountain quad., Hydrologic Unit
17060307, Clearwater National Forest, on left bank immediately upstream from
forest road bridge, 0.1 mi upstream from Beaver Creek, 1.7 mi downstream from
Canyon Ranger Station, and at mile 58.0.

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#28

### Re: Zip Line Across a Lake

08/26/2011 5:30 AM

Hi, I have just got back from an expedition taking my grandchildren to an activity centre called Rope Runners near Ongar in Essex, UK.

The Rope Runs had high and low wire/rope runs which the children could access (there was an induction first before they were let loose on the whole course). There were 3 or 4 zip wires for descent and unforthunately I did not look at exactly how they were constructed. All of the Zip wires went from high to low. The Low point was a pile of wood shavings which somewhat dented their fall and the participants were told to be running in the air just before impact.There was little slack in the wires so the particpants got a fair measure of speed! For my grandchildren it was their second time so they found it good but not as hair raising as their first occasion might have been when my son, their uncle took them around! Regulars could be seen descending by zip wire, horizontal, upside down, whatever! My kids were 13 & 15 but have done this a couple of years younger.

For your lake you could have a high/low in each direction, starting off with a rope climb to a platform.

You can make the zip return with an extra wire,a counterweight and a gadget that they install in the zip as they climb on it and uninstall to release it for return under the steam of the counterweight.

A visit would be educational! and you would learn more than I did as I was not thinking about making one of these gadgets!

All participants were hooked on to safety wires by themselves- and had to transfer to the next section by clicking on to the next session before unclicking the last safety. The safeties were then moved back by the next particpant pulling on a light rope. Lots of pulleys!

There were lots and lots of safety features built in all the way around the courses. Occasionaly a child would get stuck and have to be talked down!! Safety features included mandatory harnesses, helmets and non mandatory gloves (rope burns).

If you want the address and contact of Rope Runners I can supply it. I am sure that you will have similar facilities in the USA!

Sleepy

Great Fun for all!

Sleepy

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#29

### Re: Zip Line Across a Lake

08/26/2011 6:47 AM

Bravo 88 has given you the answer you need. Please may I come and have a go when it's finished: sounds great fun.

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#32

### Re: Zip Line Across a Lake

08/26/2011 10:23 AM

ME TOO - ME TOO!!!!!!!!!!!!!!!

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#33

### Re: Zip Line Across a Lake

08/26/2011 10:37 AM

Thanks to all for your help! Randy, that was a great reference you linked.

lyn, It was Jethro Bodine that fancied himself a master at cyphering. Youtube has a pretty funny skit of him training to be Double Naught Spy 10, that "puts me one up on Double Naught Seven."

sleepy- Yes a high to low platform at both ends, with some kind of quick release trolley that would be used both directions.

Thanks again to all! This site is unbelievably loaded with good people ! I'll keep all your ideas in mind.

Charlie

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#34

### Re: Zip Line Across a Lake

08/26/2011 10:47 AM

OOPS!

Wrong Jethro. Now I remember.

I grew up in rural Arkansas in the '50s, so the other Jethro first came to mind.

We had a rope swing at our swimmin' hole, no cable.

Have fun. Call us when it's ready. I'll bring the beer.

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#37

### Re: Zip Line Across a Lake

08/27/2011 5:06 AM

I have one more concern in my mind. The sag in wire rope may change with ambient temperature and so the tention. To have constant tention you can think of a suspension pully where weights tied with wire rope can be hanged (on 10' high side).

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#35

### Re: Zip Line Across a Lake

08/26/2011 11:31 AM

Nothing to add to the discussion on the cable but may be worth discussing the trolley a little.

There's an assumption in some posts that the trolley would be a permanent fixture. Needn't be - the simplest solution is probably the standard zip-line trolley that you hook on to with a carabiner.

In the picture above the line coming from the top of the trolley is simply to keep the trolley tied to your harness so you don't lose it and is the longest line of the three tied to the abseil harness. The line from the carabiner that's attached to the trolley is the primary hanging line. The 2nd (reserve) carabiner, over the wire, is a second attachment to the harness in case the first breaks. The cable to that second caribiner is longer than the cable to the carabiner hooked through the trolley.

However, for more speed, you can hook the reserve carabiner over the trolley as shown:

My son, ready to go zip-wiring (in Scotland, in Summer, hence the clothing...) showing the trolley clipped to the belt out of the way and the two hanging wires (primary and reserve) over his shoulder.

So no worries about bringing the trolley back along the line. Carry it back!

Evan

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#36

### Re: Zip Line Across a Lake

08/26/2011 2:31 PM

Thanks Evan, Your post was a great help. I went to Ebay, typed in Zip line trolley and low and behold there was every thing I needed! I'd been searching for "wire rope", "steel cable" and everything else except "Zip Line Trolley".

I love this place!

Charlie

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#38

### Re: Zip Line Across a Lake

08/28/2011 3:03 AM

the manufacturer of the wire rope would be a good starting point. they will be able to tell you the sag concerning lengh, tension and load. the anchor point at the end of the zip line will need to be lower than the cable sag of course. speed will be determined by the drop from anchor points. i think you will have to use trial and error to adjust the speed. there's too many unknown factors to consider.

i'ld suggest using a come-a-long at one end of the cable for adjustment. a compression spring, like one used in a chain binder, should lessen cable shock.

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#39

### Re: Zip Line Across a Lake

08/31/2011 8:51 PM

I wondered about acceleration and speed. Using 300' horizontal and 10' vertical offsets, the diagonal, much to my surprise it almost exactly 300'-2"long. Allowing for a low point maximum of 5' below the lower end, which occurs 75' from the low end. the wire is only 300'-8" long, again, to my surprise.

At the start at the high end, with the 6" vertical and the sloped section at about 2o from the horizontal, the initial acceleration is a full "g". This diminishes to about g/30 at the halfway point diminishing to zero at the quarter point and going to negative g/30 at the low end.

I suppose I really should diagram this.

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#40

### Re: Zip Line Across a Lake

09/01/2011 6:23 AM

passingtongreen

But it will not be a diagonal.

The zip wire will approach a Catenery, actual shape changes as the passenger rides! I would have thought and the deflection caused by the weight(passenger) will lengthen the line, provided the designer allows for that! Lots of fun experimenting.

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#41

### Re: Zip Line Across a Lake

09/01/2011 1:56 PM

If I understand, the weight would no longer be accelerating at mid point, but what would the velocity be with a 90 pound weight? Also, if I understand, 8" - 2" = 6", 6" will produce a 5 foot sag?

The reason I ask how much sag will be added by increasing the cable length by a few inches is back to me hooking the high end to a tree that will progressively bend to heavier loads. There by reducing the peak cable loads when my 240 pound son takes a ride. From my experience, using a 8,000 pound winch, you can bend a fairly large tree a good amount when hooked up high.

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#42

### Re: Zip Line Across a Lake

09/01/2011 5:45 PM

You can't use what I did for any practical purpose, it neglected the weight, and one or two other significant things about the wire. I can't find any way to usefully generalize the problem. Randyl's link confirms that you have to start with a proposed layout and rope and check that case, if it doesn't work, modify and start again.

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#43

### Re: Zip Line Across a Lake

09/02/2011 11:49 PM

Make sure all involved have a healthy respect for the dangers of lightning!

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