How Cable Tension and Sag Work Together
Look closely at almost any cable strung between two towers — a gondola's haul rope, a chairlift's track cable, even a power line — and you'll notice it never runs perfectly straight. It dips, ever so slightly, toward the middle of the span. That dip is called sag, and understanding why it happens, and how much of it to expect, is one of the first things ropeway engineers learn.
Why a cable can never be perfectly straight
A cable has weight. Pull it as tight as you like between two fixed points and gravity still acts on every meter of it, pulling the middle down relative to the ends. The only way to eliminate sag entirely would be infinite tension, which no real tower, anchor, or rope could survive. So every suspended cable settles into a curve, and the question becomes how to predict and control that curve rather than how to eliminate it.
The catenary, and the shortcut engineers actually use
The exact shape a hanging cable takes under only its own weight is called a catenary — a curve described by a hyperbolic cosine function. It's mathematically elegant but awkward to compute by hand. Fortunately, when the sag is small compared with the span — which is the normal case for a taut ropeway cable — a parabola is an extremely close approximation and much simpler to work with. That's the model behind a standard rule of thumb:
sag ≈ (w × L²) / (8 × T)
where w is the cable's weight per unit length, L is the span between supports, and T is the horizontal tension. Notice what each variable does: a heavier cable or a longer span increases sag, while more tension reduces it. All three effects match your intuition if you've ever tried to tighten a clothesline.
Why towers feel more than the "flat" tension
The tension you dial in at midspan isn't the whole story for the towers. Because the cable also has to support the weight hanging below every point along its length, the pull at the supports has both a horizontal component (the same T from the formula above) and a vertical component equal to half the cable's total weight. The resultant force at the tower is the vector sum of the two:
support tension = √(T² + (wL/2)²)
On a long, heavy span this can meaningfully exceed the horizontal tension, which is exactly why tower design has to account for more than just the number quoted for "line tension."
The trade-off engineers are always balancing
Pull a cable tighter and sag drops, which is good for ground clearance over roads, ridgelines, or other lines — but every additional unit of tension has to be reacted by the towers and anchors, which means heavier structures and stronger foundations. Let the cable sag more and the towers see less load, but the clearance underneath shrinks, and on a long span a deep sag can also make the parabolic approximation itself start to break down, since it's only accurate while sag stays small relative to span. Real ropeway design walks this line carefully, checking sag under every combination of temperature, ice loading, and wind the line might see over its lifetime, not just on a calm day.
Seeing it with real numbers
Take a 200-meter span with a cable weighing 1.2 kilograms per meter, held at 5,000 newtons of horizontal tension. Plugging into the formula above gives a sag of a bit under 12 meters — a substantial dip over that distance, and a good illustration of why tension has to be chosen deliberately rather than "as tight as it'll go." Double the tension and the sag falls to roughly a quarter of that value, since sag scales inversely with tension in this model.
You can run your own numbers on the Cable Span Sag Calculator, which applies this exact formula and also reports the support tension and the extra cable length the sag adds across the span — useful alongside the Rope Length for a Span Calculator if you're curious how much cable a given sag actually costs.
What this model doesn't capture
Worth saying plainly: this is a simplified, educational model, not a certified engineering calculation. Real ropeway cable design also accounts for temperature-driven expansion and contraction, ice and wind loading, cable stretch under load over time, and the safety factors required by ropeway codes such as EN 12929. None of that is optional in a real system, and none of it is estimated by a simple formula — it's the domain of a qualified ropeway engineer working through certified design software and standards. What the parabolic model gives you is the intuition: why sag exists, which direction each variable pushes it, and roughly how big an effect to expect before you ever open a proper design spec.