Conductor Force Formulas: Short-Circuit Forces
Force between parallel conductors from current and spacing: force per metre for a short circuit, total force on a span, with a worked example and a table.
The formulas
| To find | Formula |
|---|---|
| Force per metre | F / L = μ0 × I1 × I2 / (2π × d) = 2 × 10⁻⁷ × I1 × I2 / d |
| Total force on a span | F = (F / L) × L |
| Direction | Attracts for currents in the same direction, repels for opposite directions |
μ0 = 4π × 10⁻⁷ H/m, I in amperes, d the centre-to-centre spacing in metres and L the length of the span. In a short circuit use the peak current, not the RMS value. For three-phase busbars the standard (IEC 60865) gives factors for the phase arrangement and for the dynamic response of the supports, so this formula is a first estimate for two parallel conductors.
Worked example: two bars, 20 kA, 0.1 m apart
- F / L = 2 × 10⁻⁷ × 20,000 × 20,000 / 0.1 = 800 N/m
- On a 2 m span the force is 800 × 2 = 1,600 N, about 163.2 kgf
Force per metre for two conductors
| Current (each) | At 0.1 m | At 0.2 m |
|---|---|---|
| 10 kA | 200 N/m | 100 N/m |
| 20 kA | 800 N/m | 400 N/m |
| 40 kA | 3,200 N/m | 1,600 N/m |
Frequently asked questions
Why does the force matter in a short circuit?
The force grows with the square of the current. A short-circuit current many times larger than the load current gives forces thousands of times larger, which can bend busbars and break supports.
Which current do I use?
The peak current of the first half cycle, which is the RMS fault current multiplied by a factor of about 2.5 for a high X/R ratio, as in the short-circuit article.
How do I reduce the force?
Increase the spacing, use stronger supports with a shorter span, or limit the fault current.
Does the force alternate?
Yes. The force pulsates at twice the supply frequency, and the support has to withstand both the peak and the vibration.
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