BIZOMAT 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). |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Span between supports
- What it is
- The horizontal distance between the two cable supports, which the tool assumes are at the same height.
- Units and format
- Enter a number in m: metres. The form accepts 0.000001 m to 10000 m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Sag at mid-span
- What it is
- The vertical drop from the level of the supports to the lowest point of the cable at mid-span.
- Units and format
- Enter a number in m: metres. The form accepts 0.000001 m to 1000 m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Less sag means a much higher cable tension.
What this means: Cable weight per metre (plus any uniform load)
- What it is
- The weight of the cable per metre of its length, plus any ice, wind or other load spread evenly along it.
- Units and format
- Enter a number in N/m: N/m. The form accepts 0.000001 N/m to 100000 N/m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 N/m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- All tensions rise in direct proportion.
- Get it right
- Convert kg/m to N/m by multiplying by g (9.81 m/s²).
What this means: Support height above ground
- What it is
- The height of the cable attachment points above the ground or surface below the span.
- Units and format
- Enter a number in m: metres. The form accepts 0 m to 1000 m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 12 m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Least clearance at the low point
- What it is
- The least clearance you need between the lowest point of the cable and the ground, for traffic, people or equipment.
- Units and format
- Enter a number in m: metres. The form accepts 0 m to 1000 m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6 m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Minimum breaking load
- What it is
- The minimum breaking load of the cable, rope or strand, from the maker’s certificate.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0.000001 kN to 100000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- In kN, not tonnes or kilograms.
What this means: Safety factor required
- What it is
- The factor by which the breaking load must exceed the largest tension, which occurs at the supports.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 20. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Axial stiffness E × A
- What it is
- The axial stiffness of the cable: its elastic modulus times its metallic cross-section area, from the maker’s data.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0.000001 kN to 100000000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5000 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The elastic stretch falls in inverse proportion.
- Get it right
- Use the rope modulus from the maker; stranded rope is less stiff than a solid bar of the same steel.
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