How Sag is Calculated
**Sag** is the vertical distance between the highest point of the suspended cable (usually the support) and the lowest point of the cable (the mid-span). Calculating sag is critical for ensuring adequate ground clearance and meeting safety codes, especially for electrical transmission lines.
The Parabolic (Approximate) Formula
For relatively small sag (where the sag is less than 1/10th of the span length), the cable shape is approximated as a parabola. This formula is widely used due to its simplicity and accuracy in most standard installations:
Sag Formula (d)
$$d = \frac{w \cdot L^2}{8 \cdot T}$$- $d$: Maximum Sag (units of length)
- $w$: Weight per unit length (force/length)
- $L$: Span Length (units of length)
- $T$: Horizontal Tension (force units)
Cable Length & Stretch
The total length of the cable needed for the span is slightly greater than the horizontal span length ($L$). The calculator uses this common approximation for the cable length ($L_c$): $$L_c \approx L + \frac{8 \cdot d^2}{3 \cdot L}$$
Factors Affecting Sag
Environmental Loadings
- **Temperature:** High temperatures cause the conductor to expand, increasing sag.
- **Ice:** Ice buildup increases the weight ($w$), drastically increasing sag.
- **Wind:** Strong winds primarily cause the cable to swing laterally, but the added horizontal force can influence overall tension.
Design Considerations
- **Tension Limits:** Conductors must not be stressed beyond their elastic limit. Low tension means high sag, which can violate clearance requirements.
- **Clearance:** The minimum distance from the cable's lowest point to the ground, roads, or structures is mandated by local codes.
- **Conductor Type:** Materials like copper or aluminum alloy have different weights ($w$) and coefficients of thermal expansion.
Catenary vs. Parabola
The curve formed by a freely hanging cable is technically a **Catenary**. The parabolic formula used here is an **approximation** of the catenary, which is accurate for sags up to about 10% of the span length. For extremely long spans or large sags, the full catenary formula (involving hyperbolic functions) must be used for precise calculations.