Estimate the key metrics for your zip line design, including ride slope, maximum speed, and cable tension.
IMPORTANT DISCLAIMER: This calculator provides estimations for educational and planning purposes only. It uses simplified physics models and does not account for all variables, such as cable type, temperature effects, wind, trolley friction variance, braking systems, or anchor point strength. Building and riding a zip line is inherently dangerous. Always consult with a qualified professional engineer for design, installation, and safety inspections. Never use this tool as a substitute for professional engineering analysis.
function calculateZipLine() {
var length = parseFloat(document.getElementById("zipLineLength").value);
var drop = parseFloat(document.getElementById("totalDrop").value);
var weight = parseFloat(document.getElementById("riderWeight").value);
var sagPercent = parseFloat(document.getElementById("cableSagPercentage").value);
var resultsDiv = document.getElementById("zipLineResults");
if (isNaN(length) || isNaN(drop) || isNaN(weight) || isNaN(sagPercent)) {
resultsDiv.innerHTML = "Please enter valid numbers in all fields.";
resultsDiv.style.display = "block";
return;
}
if (length <= 0 || weight <= 0 || sagPercent 10) {
resultsDiv.innerHTML = "Warning: A sag greater than 10% is unusually high and may indicate an unsafe design. Please double-check your values.";
resultsDiv.style.display = "block";
return;
}
// — Calculations —
// 1. Ride Slope / Grade
var rideSlope = (drop / length) * 100;
// 2. Cable Sag in feet
var sagInFeet = length * (sagPercent / 100);
if (sagInFeet <= 0) {
resultsDiv.innerHTML = "Cable sag must be a positive value.";
resultsDiv.style.display = "block";
return;
}
// 3. Estimated Cable Tension (Simplified formula)
// Tension ≈ (Span * Weight) / (4 * Sag in feet)
var tension = (length * weight) / (4 * sagInFeet);
// 4. Estimated Maximum Speed
// v = sqrt(2 * g * h_effective) where h_effective is drop adjusted for friction
// We model friction as an equivalent "drag grade" of 2% (0.02)
var frictionFactor = 0.02;
var effectiveGrade = (drop / length) – frictionFactor;
var maxSpeedMph = 0;
var speedMessage = "";
if (effectiveGrade <= 0) {
maxSpeedMph = 0;
speedMessage = " (The slope is too shallow to overcome friction; rider may not complete the ride.)";
} else {
var g = 32.2; // Acceleration due to gravity in ft/s^2
var effectiveDrop = effectiveGrade * length;
var maxSpeedFps = Math.sqrt(2 * g * effectiveDrop);
maxSpeedMph = maxSpeedFps * 0.681818; // Convert ft/s to mph
}
// — Display Results —
var resultsHTML = "
A zip line is a simple, gravity-powered ride consisting of a pulley suspended on a cable, mounted on an incline. While the concept is simple, the physics behind a safe and enjoyable zip line can be complex. This calculator helps you understand the three most critical factors: slope, speed, and tension.
Key Factors in Zip Line Design
1. Slope (or Grade)
The slope is the primary driver of your zip line's speed. It's calculated as the ratio of the vertical drop to the horizontal length (span), expressed as a percentage. A higher slope means more potential energy is converted into kinetic energy, resulting in a faster ride.
Slope % = (Vertical Drop / Zip Line Span) * 100
A generally accepted range for a backyard or recreational zip line is between 3% and 8%. Below 3%, the rider may not have enough momentum to reach the end. Above 8%, speeds can become dangerously high, requiring a sophisticated braking system.
2. Cable Sag
Cable sag is the vertical droop in the cable when a load (the rider) is applied. It is a crucial safety parameter because it has an inverse relationship with cable tension. A small amount of sag is necessary to create the "catenary curve" that allows the rider to move. However, trying to make a cable perfectly taut (zero sag) would create nearly infinite tension, causing it to snap.
A common rule of thumb is to have 2-3% sag for an empty cable and slightly more with a rider. Our calculator uses the sag with a rider as an input, as this represents the state of the line during operation.
3. Cable Tension
Tension is the pulling force exerted on the zip line cable and, consequently, on its anchor points (e.g., trees or poles). This is arguably the most critical safety calculation. Underestimating tension can lead to catastrophic anchor failure. The tension in a zip line is significantly higher than the rider's weight. It is determined by the span, the rider's weight, and the amount of sag. A simplified formula to understand the relationship is:
Tension ≈ (Span * Rider Weight) / (4 * Sag)
As you can see, decreasing the sag dramatically increases the tension. For example, halving the sag will double the tension on the cable and anchors.
4. Rider Speed
Maximum speed is determined by the "effective grade"—the ride's slope minus the energy losses from friction. Friction comes from the trolley's wheels and air resistance. Our calculator approximates this by subtracting a fixed "friction factor" (equivalent to a 2% grade) from the total slope. If the slope is not steep enough to overcome this friction, the rider will slow down and may stop. The final speed is calculated using energy conservation principles:
Speed (ft/s) = sqrt(2 * g * Effective Vertical Drop)
Where 'g' is the acceleration due to gravity (32.2 ft/s²) and the effective drop is the portion of the drop that isn't lost to friction.
Example Calculation
Let's consider a common setup:
Zip Line Span: 500 ft
Vertical Drop: 30 ft
Rider Weight: 180 lbs
Cable Sag: 3%
Using the calculator:
Ride Slope: (30 ft / 500 ft) * 100 = 6%. This is a good, moderate slope.
Sag in Feet: 500 ft * 0.03 = 15 ft.
Estimated Tension: (500 ft * 180 lbs) / (4 * 15 ft) = 90,000 / 60 = 1,500 lbs. Your cable and anchors must be rated to handle a working load well above this value.
Estimated Speed: The effective grade is 6% – 2% (friction) = 4%. This is positive, so the rider will accelerate. The calculator will use this to estimate a maximum speed of approximately 24.5 mph.
This example illustrates how these factors interrelate to define the performance and safety profile of a zip line.