Zipline Cable Sag Calculator

Sag is the input, not a by-product

People tend to think of sag as something a cable does, and then are surprised that it is the field with the most influence on the page. It is more useful to treat it as the design decision it is: you choose how much sag the line runs at, and that choice sets the ride, the clearance at the middle and the pull on both anchors simultaneously.

The arithmetic is simple. Take the horizontal span and the two attachment elevations. The chord is the straight line between the attachments, and its midpoint elevation is just the average of the two. The cable at midspan hangs below that by the sag. So with the defaults — a 100 foot span, cable 12 feet up at the top anchor, 6 feet up at the bottom anchor, and 8 feet of ground fall between them — the top attachment is at 12 on the datum and the bottom at minus 2, the chord midpoint is at 5, and 3 feet of sag puts the cable at 2. The ground at the middle is at minus 4, so the cable clears it by 6 feet.

Note what dropped out of that. With straight ground between the ends, the ground fall cancels: the midspan clearance is simply the average of the two attachment heights minus the sag. The fall matters for the grade and the ride, not for the clearance at the middle. That stops being true the moment the ground has a hump in it, which is why there is a field for it.

The inverse law, and why it is on the page as a multiple

For a cable with load spread along it, horizontal tension is the load times the span divided by eight times the sag. For a load concentrated at the middle, it is the load times the span divided by four times the sag. Both have sag on the bottom, and that is the fact worth carrying away: tension is inversely proportional to sag, with no floor and no flattening.

Run the defaults. Three feet of sag on a 100 foot span gives a spread-load multiplier of 100 divided by 24, which is 4.17. Halve the sag to 1.5 feet and it becomes 8.33. Take it to half an inch of sag and the multiplier is in the hundreds. The temptation on a zipline runs exactly the wrong way here, because a tighter line is a faster line, and the person tightening it is trading a visible improvement in the ride against an invisible multiplication of the force on both ends.

The figures are given as multiples rather than as pounds on purpose. A number in pounds looks like a rating and invites comparison against a component. It is not a rating: it is a ratio between the load and the pull, and it says nothing whatever about whether any particular cable, clamp, anchor, bolt, post or tree can take the result. That question belongs to an engineer.

Cable length: less than people expect

The parabolic length of a sagging cable is the chord times one plus eight thirds of the sag-to-chord ratio squared. Because the ratio is squared and it is small, the extra length is tiny. With the defaults the chord is 100.98 feet and the sagging cable is 101.21 feet — just under three inches more. Slope adds far more length than sag does.

The practical consequence is that you cannot judge sag by cable length or set it by measuring out cable. A few inches of length is the difference between a comfortable sag and a bar-tight line, which is why sag is set by measurement at the middle and by tension, never by cutting to a calculated length. It also means the length figure here is only the span: everything at the terminations — wraps, thimbles, clamps, tails, whatever the hardware needs — is additional and comes from the hardware instructions.

What changes once someone is on it

Everything above is a static, unloaded line on a still day. A rider is a moving point load, and adding it increases the sag, which lowers the cable, which lowers the clearance at the middle — the number people care about most is the one the static calculation flatters. The line also oscillates while it is in use, and it does not return to the same place immediately after.

Temperature lengthens and shortens the cable over the day and across seasons. Water and ice add weight. Cable stretches and beds in over the first uses and then continues to creep. A line set once and left is not the same line six months later, which is why sag is something that gets checked rather than calculated once.

None of that is modelled here, and the honest reading of this page is that the midspan clearance shown is the best case: unloaded, static, at whatever temperature the sag was measured at.

The part with no numbers

A tensioned cable across a garden is a serious piece of engineering wearing the clothes of a weekend project. The energy stored in it is large, and it is released all at once when a cable, a termination, an anchor, a fastening or a trolley lets go. That energy goes somewhere, and the places it goes are where the anchors are and where the line was.

So there is nothing on this page about cable diameter, construction, clamps, thimbles, turnbuckles, trolleys, harnesses, brakes, stopping distance, anchor design, bolt patterns, or what any of them will take. Those figures exist and they are specific, and they come from a qualified engineer working on your installation and from the manufacturers of the components. Attaching a line to a living tree adds the condition of that tree, the health of the union, and the effect of the load on its roots, which is a question for an arborist and again for an engineer. The tree can fail, and unlike a post it does so on its own schedule.

Elsewhere on the site, the anchor scope calculator is the same cable-under-tension geometry for a boat, the gate sag calculator covers a diagonal member in tension, and the tree spacing calculator gives mature spread if you want to know what a route will be flying through in a decade.

Questions people ask