Zipline Sag and Speed Calculator

How zipline sag changes the ride

A zipline is a suspended cable system in which anchor spacing, elevation drop, rider mass, and cable sag all affect the modeled ride. This calculator uses those inputs to estimate the rider's theoretical maximum speed and a simplified static cable-tension value. The estimates are useful for visualizing the geometry, but they do not replace engineering analysis of a real course.

The cable drawing makes the entered zipline geometry easier to inspect. As span, drop, and midpoint sag change, the orange parabolic curve changes with them. The red marker remains at midspan so that the relationship between the stated midpoint sag and the curve is visible; it is not necessarily the cable's lowest point when the end anchors are at different elevations.

Here, sag means the vertical distance from the midpoint of the straight chord between anchors to the cable at midspan. For an inclined zipline, the cable's lowest point can lie downhill from the midpoint. A deeper sag usually lowers the horizontal component of cable tension, while a smaller sag makes that component increase quickly. Rider mass and span also raise the estimated load.

Zipline speed calculation

The zipline speed estimate comes from conservation of energy: the rider's loss of gravitational potential energy becomes kinetic energy in a no-loss model. The calculator finds the deepest point of its parabolic cable model rather than assuming that the midpoint is always lowest. If the modeled vertex lies beyond the downhill anchor, the downhill anchor is used as the lowest point instead.

In this expression, $v$ is theoretical maximum speed in meters per second, $g$ is gravitational acceleration (9.81 m/s²), and $h$ is the modeled vertical descent from the launch anchor to the lowest reachable point on the curve. Friction, trolley losses, wind, braking, and cable stretch are excluded, so an actual rider's speed can differ substantially.

Estimating zipline cable tension

The tension estimate uses the horizontal component for a parabolic cable carrying a rider at midspan. With span $L$, rider mass $m$, gravity $g$, and midpoint sag $s$, the model calculates:

The displayed tension is the vector combination of that horizontal component and half the rider's weight:

This is a deliberately simplified, symmetric midspan-load approximation. It does not include the cable's own weight, unequal support reactions caused by an inclined line, moving-rider dynamics, or braking forces. It is best treated as an introductory comparison tool: halving sag doubles $H$ when the other inputs remain unchanged.

Zipline sag and speed example

For example, enter a 90 m span, 10 m end-to-end drop, 6 m midpoint sag, and a 75 kg rider. The modeled curve reaches its lowest point below the midpoint, producing a theoretical maximum speed of about 15.37 m/s. The simplified tension calculation gives about 1.43 kN. These figures describe the calculator's idealized model only; they are not a safe operating speed or a hardware rating.

Changing sag has two different effects worth separating. In this model, more sag reduces the simplified horizontal tension term. But with a downhill end anchor, the position and depth of the curve's lowest point can also change, so theoretical maximum speed does not necessarily fall as sag increases. Check both output values after every change rather than relying on a single trend.

Reading the zipline geometry diagram

The zipline diagram shows black anchor blocks, an orange cable curve, and a red midspan rider marker. Horizontal distance represents the entered span. The vertical coordinate represents the entered end-anchor drop together with the sagged cable shape. A larger separation between the orange curve and the straight anchor-to-anchor chord at midspan indicates greater entered sag.

The diagram is scaled to fit the available display area, so it should be read as a visual aid rather than a survey drawing. Its caption repeats the entered span and sag along with the calculated speed and tension. Use measured dimensions from the installation when exploring scenarios, and remember that the red marker is fixed at midspan while the model's lowest point may be elsewhere on a sloping line.

Limits of this zipline model

This zipline calculator intentionally omits several effects that dominate real installations. Trolley rolling resistance, aerodynamic drag, wind, cable self-weight, elasticity, rider posture, braking, and changing rider position all affect speed and force. The calculation also treats the cable as an ideal parabola rather than a fully loaded catenary or a dynamic cable system.

Support loads in service are not captured by a single static number. An inclined cable can have unequal reactions at its anchors, and a moving rider can create dynamic loads that exceed a static estimate. Attachment hardware, anchors, braking equipment, cable terminations, clearances, rescue planning, and local requirements must each be evaluated independently.

Use the results to understand sensitivity: a longer span or heavier rider increases the horizontal tension estimate, and less sag increases it sharply. Compare several measured or proposed configurations, but do not use the output to select cable, anchors, or safety equipment. A qualified engineer and the applicable standards should govern final design.

For routine inspections, record the actual span, anchor elevations, and measured midpoint sag, then compare those measurements over time. Changes in cable length, tree movement, hardware condition, or anchor alignment can alter the geometry. Re-running an educational model can help flag a change for review, but it cannot establish that the system remains safe.

For related geometry and load estimates, see the Catenary Sag Tension Calculator, the Projectile Motion Calculator, or the Cable Tension Calculator.

Zipline assumptions and limitations

• Assumes a single rider starts from rest at the launch anchor.
• Ignores trolley friction, air resistance, wind, braking, and cable elasticity.
• Models the cable as an idealized parabolic curve based on span, end-anchor drop, and midpoint sag.
• Uses a simplified static tension estimate for a rider at midspan.
• Is intended for education and preliminary comparisons, not structural design or safety certification.

Zipline safety disclaimer

Warning: This calculator provides approximate values only. Real-world zipline design must account for dynamic loads, fatigue, environmental conditions, safety factors, and applicable standards. Always consult a qualified engineer and follow relevant codes before building or operating a zipline.