This is an example calculation for sag and tension in the transmission line. You may opt to review first the fundamental principles and formulas from this post.

The foregoing calculation is based on the** linear cable model** on which plastic elongations are ignored. Also, the loading of the conductors is based on the National Electrical Safety Code 2017.

**Problem:**

A transmission line conductor was strung between two towers, 300 meters apart and same elevation. During the time of installation, the conditions were t =15°C and initial horizontal tension = 25% of Rated Tensile Strength (RTS).

Calculate the sag and tension at:

- No Load Conditions (no wind / no ice)
- Heavy Loading District: Ice Thickness = 12.5 mm, Wind Pressure = 190 Pa, t = -20 deg C
- Maximum Conductor Temperature : t max = 90 deg C, no wind, no ice

## Solution:

Conductor Name | 403-A1-37 |

Conductor Common Name | 403 mm2 AAC (Arbutus) |

Span Length | 300 m |

Outside Diameter | 26.1 mm |

Conductor Unit Weight | 10.89 N/m |

Rated Tensile Strength | 81.8 kN |

Modulus of Elasticity | 58.9 GPa |

Coefficient of Thermal Expansion | 23 x 10-6 / deg C |

Total Conductor Area | 402.9 mm2 |

### 1. No load conditions (no wind/ice load)

- t
_{1}= 15°C - H
_{1}= 25% RTS = 81, 800 * 0.25 = 20,450 N - A = 0.0004029 m
- S = 300 m
- W
_{1}= 10.89 N/m - E = 58.9 x 10
^{9}Pa

Total Conductor Length:

Initial Sag:

2. Heavy loading district: Ice thickness = 12.5 mm, Wind load = 190 Pa, t = -20 °C

#### a. Calculate ice load (assume ice density is 915 kg/m^{3}

#### b. Calculate Wind Load

#### c. Total Unit Weight

Note: We will not include the “k” factor of NESC.

#### d. Final Conductor Tension, H_{2}

Initial Condition | Final Condition |

t_{1} = 15 °C | t_{2} = -20 °C |

H_{1} = 20, 450 N | H_{2} = ? |

A = 0.0004029 m^{2} | A = 0.0004029 m^{2} |

S = 300 m | S = 300 m |

W_{1} = 10.89 N/m | W_{2} = 26.34 N/m |

E = 58.9 x 10^{9} Pa | E = 58.9 x 10^{9} Pa |

α = 23 x 10^{-6}/°C | α = 23 x 10^{-6}/°C |

From the conductor state change equation:

Simplifying to a cubic equation:

By trial and error method or goalseek in excel or modern pocket calculator:

**H _{2} = 44,921.94 Newtons (55% of RTS)**

#### e. Calculate final sag and blowout angle

DOWNLOAD THE DETAILED COMPUTATION FROM EXCEL HERE.

### 3. Maximum Conductor Temperature: t_{max }= 90° (no wind/no ice)

#### a. Calculate Final Horizontal Tension

From the conductor state change equation:

By substitution of values and simplification:

Using excel or pocket calculator or manual trial and error:

**H _{2} = 13,364.66 Newtons (16% of RTS)**

#### b. Calculate final sag (note that there is no change in conductor weight)

DOWNLOAD THE DETAILED COMPUTATION FROM EXCEL HERE.