Tension shown is calculated at mid-span — the design condition and worst case for a symmetric level span. Actual tension varies with carriage position. Pre-operation planning tool only.
Plan
Compare scenarios
How it works
Load builder
kg
kg
kg
Total load1.81 kN
Span inputs
Safety factor
—10:1 life-safety standard
Results — mid-span design condition
Usable Y
—m
Required tension / line
—kN
Min tracklines
—
System safety factor
—:1
T = DL / 4Y | —
Assumes: symmetric level span · load at mid-span · static loading only
Dynamic loads, off-center loading, and sloped spans require additional analysis. A 10:1 safety factor applies to life-safety rope systems.
Compare two anchor positions
Scenario A
50
7
2
—
Scenario B
70
10
2
—
—
Both scenarios use the load and WLL values from the Plan tab.
Where does T = DL / 4Y come from?
The geometry. When a load hangs at mid-span on a tensioned line, it creates two straight legs meeting at a V. Each leg pulls upward and inward toward its anchor.
The vertical component of each leg must support half the load: T × sin(θ) = L/2, where θ is the angle of the leg from horizontal.
For small angles, sin(θ) ≈ tan(θ) = Y / (D/2) = 2Y/D. Substituting: T × (2Y/D) = L/2 T = DL / 4Y
Why this matters operationally: Y is in the denominator. As Y approaches zero — as clearance disappears — tension approaches infinity. This is not a linear relationship. Halving Y doubles the required tension. Reducing Y by 75% quadruples it. Small changes in available height have large consequences for anchor forces.
The 30° threshold: When the mid-span angle exceeds 30°, the small-angle approximation used in this formula begins to lose accuracy. The formula remains useful for planning but results should be treated as conservative estimates, and direct measurement via load cell becomes more important.
What this formula does not account for: dynamic loading from a moving or struggling patient, shock loads from arrest events, off-center carriage position, sloped spans, or rope stretch under load. Each of these can increase actual system forces beyond the calculated value.
The 10:1 safety factor
Technical rescue systems operating over life-safety loads are designed to a 10:1 safety factor — meaning the breaking strength of every component should be at least 10 times the maximum anticipated load. This is more conservative than industrial rigging (typically 5:1) because rescue loads are dynamic, conditions are uncontrolled, and equipment condition in the field is variable.
In practice this means: if your calculated tension is 5 kN per trackline, your trackline needs a minimum breaking strength of 50 kN. The safety factor meter in the Plan tab shows where your current configuration sits against this standard.
Reading the angle
The mid-span angle shown in the graphic is the angle each trackline leg makes with the horizontal at the anchor point. A shallower angle means more sag, less tension, more clearance. A steeper angle means less sag, more tension, less clearance.
Practical thresholds:
Under 10° — very shallow, low tension, generous clearance, typically well within system capacity.
10°–20° — normal working range for most rescue highlines.
20°–30° — elevated tension, approaching the limit of the formula's accuracy. Confirm with load cell.
Over 30° — high tension, formula accuracy decreasing, direct measurement essential.