KEVOS® MAKEOS · Mechanics
Cable Span Design (Catenary Sag, Tension, Clearance and Stretch)
What tension does this cable carry across its span at the sag I want, is it strong enough, does the low point keep its clearance, and how much does it stretch?
Design of a cable or rope hanging between two supports at the same level: catenary parameter, horizontal and maximum tension, cable length and end angle by the exact catenary (as the catenary cable tool), the vertical reaction at each support, the cable safety factor against its breaking load, the clearance at the low point, and the elastic stretch at that tension.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Span between supports | m | Horizontal distance between the supports (at the same height). |
| Sag at mid-span | m | Sag at the middle of the span. |
| Cable weight per metre (plus any uniform load) | N/m | Weight of the cable per metre, plus ice, wind or a uniformly spread load. |
| Support height above ground | m | Height of the attachment points above the ground. |
| Least clearance at the low point | m | Least height you need under the cable. |
| Minimum breaking load | kN | Minimum breaking load of the cable or rope. |
| Safety factor required | Safety factor you require on the breaking load. | |
| Axial stiffness E × A | kN | Elastic modulus times metallic area of the cable (from the maker). |
Method and formulas
- Solve a [cosh(S ÷ 2a) − 1] = d for the catenary parameter a; horizontal tension H = w a; maximum (end) tension T = w (a + d); length L = 2a sinh(S ÷ 2a) (as the catenary cable tool).
- Vertical reaction at each support = w L ÷ 2.
- Safety factor = MBL ÷ T_max; clearance = support height − sag; stretch ≈ H L ÷ EA.
- Example: 100 m with 5 m sag pulls 2.5583 kN at the ends (factor 7.8177), and the low point is 7 m up.
Limitations
- Supports at the same level; uneven supports shift the low point.
- Point loads on the cable need a different analysis.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a catenary support wire or overhead line
- Set the sag for a guard or safety line
- Check clearance under a cable span
Who it is for
- Design engineers
- Riggers
- Electrical engineers
What you get
- Catenary tensions, length and end angle
- Support reactions and cable safety factor
- Low-point clearance and stretch
Interpreting the result
- Halving the sag roughly doubles the tension: tight cables are expensive cables.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2999. Topic reference; no source tables or recommended settings are reproduced.
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Open the Cable Span Design (Catenary Sag, Tension, Clearance and Stretch) calculator
