How to Calculate Conductor Swing Angle for a 380 kV Transmission Line
Conductor swing is an important consideration in the design of overhead transmission lines. When wind acts on a conductor, it produces a horizontal force that causes the conductor to move away from its normal vertical position.
For a 380 kV transmission line, the conductor swing angle can be calculated by comparing the horizontal wind force acting on the conductor with the vertical force due to the conductor’s weight.
This article explains the calculation step by step, including the input data required, the wind-force calculation, the swing-angle formula, and a complete worked example.
1. What Is Conductor Swing?
Under normal conditions, an overhead conductor hangs approximately in its vertical position. When wind acts on the conductor, the wind applies a horizontal force.
As a result, the conductor moves sideways and forms an angle with its original vertical position. This angle is called the conductor swing angle.
The swing angle depends mainly on two competing effects:
- Horizontal wind force pushing the conductor sideways.
- Vertical conductor weight acting downward.
2. Input Data Required
For the simplified conductor-swing calculation described here, the following three inputs are required:
| Input Parameter | Symbol | Unit | Example Value |
|---|---|---|---|
| Wind pressure | P | N/m² | 927 N/m² |
| Conductor diameter | d | mm | 27.72 mm |
| Conductor weight | W | N/m | 14.32 N/m |
3. Why These Three Inputs Are Required
3.1 Wind Pressure
Wind pressure represents the intensity of the wind acting on the conductor. It is normally expressed in:
N/m²
In this example:
P = 927 N/m²
3.2 Conductor Diameter
The conductor diameter is required because the wind acts on the projected area of the conductor.
The example conductor diameter is:
d = 27.72 mm
Because the wind pressure is given in N/m², the diameter must be converted from millimetres to metres:
3.3 Conductor Weight
The conductor weight provides the vertical force acting downward.
In this example:
W = 14.32 N/m
4. Calculate the Wind Force on the Conductor
The horizontal wind force is obtained from:
where:
- Fw = horizontal wind force
- P = wind pressure
- A = projected area of the conductor
5. Determine the Projected Area
For the simplified calculation, we consider a 1 metre length of conductor.
The projected area is:
For:
- d = 0.02772 m
- L = 1 m
Therefore:
A = 0.02772 m²
6. Calculate Horizontal Wind Force
Now substitute the projected area and wind pressure into the wind-force equation:
Therefore:
Fw = 25.69284 N
Since the calculation is based on one metre of conductor, the wind load can be expressed as:
7. Calculate the Swing Angle
The conductor swing angle is obtained by comparing the horizontal wind force with the vertical conductor weight.
The basic relationship is:
Therefore:
Substituting the calculated wind force and conductor weight:
This gives:
tan(φ) = 1.79447
To obtain the angle, take the inverse tangent:
φ = 60.86°
Therefore, the conductor swing angle is approximately:
8. The Complete Swing-Angle Formula
The complete calculation can be condensed into one equation.
Since:
Fw = P × d
when considering one metre of conductor, the swing angle can be written as:
where the conductor diameter d must be in metres.
Using the example values:
φ = tan−1(25.69284 / 14.32)
φ = tan−1(1.79447)
φ = 60.86°
φ ≈ 61°
9. Summary of the Calculation
| Step | Calculation | Result |
|---|---|---|
| 1. Wind pressure | P | 927 N/m² |
| 2. Conductor diameter | 27.72 / 1000 | 0.02772 m |
| 3. Conductor weight | W | 14.32 N/m |
| 4. Projected area for 1 m | 0.02772 × 1 | 0.02772 m² |
| 5. Wind force | 927 × 0.02772 | 25.69 N/m |
| 6. Force ratio | 25.69284 / 14.32 | 1.79447 |
| 7. Swing angle | tan−1(1.79447) | 60.86° |
| Final adopted angle | 60.86° rounded | 61° |
10. General Formula
For the simplified method used in this example, the conductor swing angle can be calculated using:
Where:
| Symbol | Meaning | Unit |
|---|---|---|
| φ | Conductor swing angle | degrees |
| P | Wind pressure | N/m² |
| d | Conductor diameter | m |
| W | Conductor weight per unit length | N/m |
11. Important Unit Check
One of the most important points in this calculation is maintaining consistent units.
If wind pressure is expressed in N/m², the conductor diameter must be expressed in metres, not millimetres.
Therefore:
Using 27.72 directly instead of 0.02772 would produce an incorrect result by a factor of 1,000.
12. Final Result for the Example
Given:
- Wind pressure = 927 N/m²
- Conductor diameter = 27.72 mm
- Conductor weight = 14.32 N/m
The horizontal wind force is:
Fw = 25.69 N/m
The conductor swing angle is:
φ = 60.86°
Therefore, the conductor swing angle may be taken as:
Conclusion
The calculation of conductor swing angle is straightforward when the required input data are known. The basic process is:
- Obtain the design wind pressure.
- Obtain the conductor diameter.
- Convert the conductor diameter from millimetres to metres.
- Calculate the horizontal wind force per metre.
- Obtain the conductor weight per metre.
- Divide the horizontal wind force by the conductor weight.
- Take the inverse tangent of the resulting ratio.
In formula form:
For the example considered:
φ = tan−1 [ (927 × 0.02772) / 14.32 ] = 60.86° ≈ 61°
Thus, for the specified loading condition, the calculated conductor swing angle is approximately 61°.