Strokes Within the Span and the 0.6 Backflashover Factor

The first simplification in a backflashover study is to assume lightning terminates on the tower top or the shield wire at the tower. This is convenient because the tower-stroke case normally gives the highest tower voltage and the most severe insulation stress. But in reality a stroke can terminate anywhere along the shield-wire span, so a complete study must ask:

A span stroke can produce a voltage across the span air gap (shield wire to phase conductor), a voltage across the tower insulator string, travelling waves toward both adjacent towers, reflections from footings, and a possible flashover in the span or at the tower. The engineering result is that span strokes can cause flashovers, but tower flashovers remain dominant — and this is captured by a single span-location correction factor:

The factor 0.6 accounts approximately for all possible stroke-termination points along the shield wire. This note explains where it comes from.

Stroke to the tower. The current enters the tower directly and divides between the tower body, the footing resistance and the shield wires to adjacent towers. The tower voltage rises quickly and stresses the tower-to-phase insulation — the classical backflashover case:

so higher coupling \(C\) lifts the phase conductor and reduces the stress. Stroke within the span. The current is injected between two towers, and the shield-wire voltage at the stroke point initially tries to rise to:

The factor \(\tfrac{1}{2}\) appears because the injected current splits into two travelling waves propagating in opposite directions — one toward each tower. The span stroke is therefore a travelling-wave problem. The key span-location variables used throughout this note are collected here:

The most useful way to define where the stroke lands is by travel time rather than distance:

The location strongly affects when reflected waves return from the towers and how much they reduce the stroke-point voltage.

The voltage is highest at the stroke point, where the current is injected. Before reflections arrive it tries to reach \(Z_g I/2\), but reflections from the adjacent towers can pull the crest down — if they arrive before the current reaches its crest. The key timing condition is:

i.e. the round-trip reflection from the far tower returns at or before the current crest. So a slower front leaves more time for the helpful reflections:

Along the span the voltage is largest at the stroke point and falls toward the towers:

But voltage magnitude alone does not decide flashover — what matters is the stress-to-strength ratio. And the two insulation paths are very different:

So even when the span voltage is higher, the much stronger span insulation may still withstand it. The two paths compared side by side:

Take a stroke at \(T_{sT}/T_s = 0.20\) with \(t_f = 2\,\mu\text{s}\) and \(R_i = 20\,\Omega\). The voltage ratio (midspan to tower) and the insulation-strength ratio are:

Considering all stroke-termination points, the chance of a span flashover depends strongly on the current front time:

Slower fronts allow reflections from the adjacent towers to reduce the span voltage before the current crest. A faster front gives less time for reflections to cut the span voltage, so \(t_f\downarrow \Rightarrow V_{\text{span}}\uparrow \Rightarrow\) more span flashover; a slower front does the opposite. A second effect helps too: at high overvoltage, predischarge currents flow from the shield wire toward the phase conductor, inducing a phase-conductor voltage that reduces the gap stress:

Predischarge therefore inhibits span flashover. It is hard to quantify by hand, but it reinforces the conclusion that span flashovers are not the dominant contribution.

Even without a span flashover, a span stroke still sends travelling waves to the towers, producing tower voltage and insulation stress. The decisive comparison is the tower voltage from a span stroke versus a direct tower stroke:

The reason: a direct tower stroke injects the full severe current at the tower immediately, while a span stroke reaches the tower only after a travel delay — by which time part of the wave has propagated the other way, reflections have begun, and the crest is reduced. The two become comparable only when the relevant reflection has not yet acted before the crest:

but generally \(V_{\text{tower, span stroke}} < V_{\text{tower, tower stroke}}\).

The tower voltage is represented by a coefficient \(K_{TT}\). The \(K_{TT}\) ratio compares the tower-voltage coefficient produced by a stroke within the span with the coefficient produced by a direct tower stroke, \(K_{TT,\text{span}}/K_{TT,\text{tower}}\). For a span stroke this coefficient is lower, and the ratio sits in a fairly narrow band:

So the tower voltage from a span stroke is about 70% of the direct-tower-stroke value. Because the tower voltage is lower, a higher current is needed to flash the tower:

A significantly larger stroke is required, so the span-stroke contribution to the BFR is lower.

To fold in all possible stroke locations, a span factor \(K_s\) compares the BFR over all locations with the BFR assuming every stroke hits a tower. It is not truly constant — it falls with the tower critical current:

The span factor is applied in two steps — the general form, the recommended value, and the practical result:

In the CIGRE-style method the critical current \(I_c\) is computed for the tower-stroke case, then the 0.6 factor accounts for span-termination effects — replacing an explicit, per-location calculation with tower-stroke severity × span correction:

CIGRE-style hand methods commonly fold stroke-location effects into a single span-location correction factor. IEEE-type and computer-based methods also recognise stroke-location effects, but the implementation depends on the adopted modelling procedure — they differ from CIGRE mainly in the wavefront treatment, footing-resistance reduction, corona, power-frequency angle and current distribution. In detailed travelling-wave or EMT studies the stroke location can be represented explicitly. On the span issue the physical conclusion is shared: a direct tower stroke is usually more severe, and span flashovers are secondary.

The span analysis assumes each insulation path can be represented by a non-standard CFO, \(\text{CFO}_{\text{NS}}\), taken (for a first approximation) proportional to the gap spacing — which is what lets us compare \(V_{\text{span}}/V_{\text{tower}}\) with \(\text{CFO}_{\text{span}}/\text{CFO}_{\text{tower}}\). A fuller CIGRE calculation makes \(\text{CFO}_{\text{NS}}\) depend on wave shape, gap length, leader progression, front and tail times and the tower/footing components. The main sensitivities:

• Front time \(t_f\): fast fronts raise the span voltage (16% span flashover at \(2\,\mu\text{s}\) vs 2% at \(4\,\mu\text{s}\)) — fast-front lightning is the more severe case.
• Span length: \(T_s = L_s/v\); longer spans delay the helpful reflections, so \(L_s\uparrow \Rightarrow T_s\uparrow \Rightarrow\) higher stress — consistent with span length increasing BFR.
• Footing resistance: \(R_i\uparrow \Rightarrow V_{\text{tower}}\uparrow \Rightarrow \text{BFR}\uparrow\); the tower-footing reflection also feeds back into the span, so good grounding helps both tower and span strokes.
• Shield-wire height: higher portions collect more strokes, so the spatial distribution is not perfectly uniform; including this lowers \(K_s\) slightly, but \(K_s = 0.6\) is kept for hand calculation.

Even when \(V_{\text{span}} > V_{\text{tower}}\), it is usually still true that \(\dfrac{V_{\text{span}}}{\text{CFO}_{\text{span}}} < \dfrac{V_{\text{tower}}}{\text{CFO}_{\text{tower}}}\), because \(\text{CFO}_{\text{span}} \gg \text{CFO}_{\text{tower}}\). So tower flashover remains the more likely outcome.

Memory map. Stroke hits the shield wire within the span → highest voltage near the stroke point → but the span air gap is much stronger → span flashover is possible but usually minor → travelling waves reach the tower → tower voltage is lower than a direct tower stroke → apply the span factor \(K_s \approx 0.6\) → \(\text{BFR} = 0.6\,N_L\,P(I \ge I_c)\).