Cable Pulling Tension, Sidewall Pressure, Jam Ratio & Fill

The section method follows Southwire, Power Cable Manual, 4th edition (2016), chapter 7, with General Cable's 9th-edition installation manual (2011) as a cross-check. Total moving weight per length is $W=nW_c$, where $W_c$ is the weight per length of one cable. For a straight inclined by $\beta$ in the direction of travel, $T_o=T_i+WL(\sin\beta+w\mu\cos\beta)$. Reverse pulls traverse sections backwards and reverse every straight slope.

For the requested capstan option, $T_o=T_i\exp(w\mu\theta)$ (Southwire 7-15). The horizontal self-weight option uses Southwire 7-10: $T_o=T_i\cosh(a)+\sqrt{T_i^2+(WR)^2}\sinh(a)$, with $a=w\mu\theta$. Angles are converted to radians. This option avoids a zero load for a bend entered with zero tension.

For equal moving cables, $q=d/(D-d)$, triangular $w=(1-q^2)^{-1/2}$, cradled $w=1+4q^2/3$, and four or more $w=1.4$. Two cables use the conservative triangular factor. Three loose cables use cradled geometry when $D/d\ge2.5$; a bound triangular assembly remains triangular.

Sidewall bearing force per length is $T/R$ for one cable, $(3w-2)T/(3R)$ for three cradled cables, and $wT/(2R)$ for triangular, dual or complex configurations (Southwire 7-20–22; Polywater configuration guidance). The larger bend-end tension is used. The manufacturer's limit remains an independent input.

Conductor-eye tension is allowable metal stress times conductor area and the gripped count, reduced to 80% for more than three conductors (Southwire 7-4–6). A cable rating is kept separate; multiplying it by cable count requires verified equal sharing. The assembly limit also respects the pulling head and line working load, including the selected line reserve.

Fill uses outside areas $\pi d^2/4$ for every moving and existing object, divided by bore area. NEC 2023 Chapter 9 uses the count-dependent area allowance; the short-nipple option requires a route no longer than 24 in. Dimensions are entered rather than reproducing Tables 4 or 5. The maximum count uses the integer area budget, checking the one- and two-object allowances separately.

The equal-three-cable jam screen uses General Cable §3.7.3.4: $J=1.05D/d$, possible at 2.5–2.8 and probable at 2.8–3.2. Raw $D/d$ is also retained in the calculation. Brent's method finds the friction coefficient at which the first entered mechanical limit is reached. The root residual is bounded away from the root so both bracket endpoints stay finite. Results distinguish a solved limit, no feasible coefficient and a limit at or beyond the investigated maximum of 1.5. Horizontal bends use an algebraically equivalent scaled-hypotenuse and expm1 evaluation to avoid overflow and cancellation.

Steady sliding, constant dynamic friction, round uniform bore, circular cables, and equal moving-cable diameters and masses. Existing wires stay stationary: their weight is not added to the moving assembly. Their contact drag must already be represented in the chosen effective friction coefficient. Default cable diameter 5.69 mm, weight 0.32361945 N/m (33 kg/km at standard gravity) and loaded bend radius 57.2 mm are from Belden 2412, revision 20 February 2026; the conservative 110 N four-pair rating follows category-cable practice. The route, existing-wire dimensions, feed tension and line ratings are illustrative editable planning inputs.

The capstan option is the manufacturer's commonly used bend approximation. It neglects bend weight and vertical gravitational change; low entering tension (below 10WR) triggers a warning. Use the exact horizontal option for weight-sensitive horizontal bends; vertical bends at low tension require the full oriented-bend analysis outside this tool. Straight-run gravitational effects are included. Sidewall pressure is the conventional tension-induced bearing force per length, not material contact stress or a cable crush-test rating.

A fill result is an area screen, not a packing, clearance, obstruction or pullability proof. NEC 2023 rules are implemented conservatively without the equal-conductor fractional-count rounding exception; special wiring articles and local amendments may differ. The short-nipple exception applies only between enclosures. For IEC 61386-1:2008+A1:2017 conduit systems, enter the local installation fill limit; no universal IEC fill percentage is implied. Check against the standard in force. Rules and source data were reviewed on 7 November 2026.

The corrected jam bands apply only to three loose, equal moving cables in an otherwise empty conduit. A bound assembly, mixed sizes, existing wires or four-plus cables needs separate clearance and snagging assessment; a low jam-band number does not establish freedom from jamming. With existing wires, the standard geometry factors describe only the moving assembly and cannot predict crossing or cable-on-cable contact.

A missing sidewall limit leaves that check unrated. The friction ceiling covers only the entered tension, head, line and optional sidewall limits; it cannot overcome fill, bend-radius or jam problems. “No feasible coefficient” means that even zero friction exceeds an entered load limit. “≥1.5” means that the limits are met throughout the investigated range; it does not claim a solved upper limit. A numeric zero is displayed only when zero friction itself is the solved limiting coefficient. It is not a lubricant specification. WLL must already include termination and knot derating; the additional reserve is not a substitute for a manufacturer's safety factor.

Negative demand is clipped at zero because a cable cannot push. Such cases require controlled feeding/braking and a separate transient assessment. Restart friction, acceleration, pull-line stretch, winch/anchor reactions and damage to existing insulation are outside the model. The drawing is a schematic bend detail. Profiles are sampled directly from analytic section formulas at 60 intervals per active section; this sampling does not approximate the reported endpoint loads.

For pairs, this tool applies the conservative triangular three-cable weight factor only where D/d > 1 + 2/√3 ≈ 2.155. This is a domain restriction of this calculator, not a physical two-cable packing limit. Tighter pair geometry requires a dedicated contact analysis. Unsupported geometry is rejected before bend and friction-limit calculations are attempted; result cards are withheld.