Cable Pulling Calculator

Method

Pulling tension and sidewall bearing pressure along a conduit route, in both directions, by the equations of IEEE 1185 and the Southwire Power Cable Installation Guide (2005). Each result in the calculator opens to show its steps. Notation follows Southwire: T tension (lb), W cable weight (lb/ft), w weight correction factor, μ coefficient of friction, L length (ft), r bend radius (ft), φ bend angle (radians), θ slope from horizontal.

Route

Segments

Straights (length and slope), horizontal bends (left or right), vertical bends (up or down) and offsets (two opposite bends with the straight between them computed from the offset distance: L = (offset − 2r(1 − cos θ)) ÷ sin θ). A straight follows the slope the previous bend leaves unless a slope is entered. A horizontal bend is taken as level.

Directions

A is the start of the first segment and B the end of the last. The pull is calculated from A to B and from B to A; the direction with the lower ratio to the limits is recommended.

3D view

The route is drawn to scale in feet (the elevation can be exaggerated). The tube is colored by the tension in the direction shown, green through yellow to red: by default from the lowest to the highest tension of the pull, to show where it builds up (red never above the allowable), or from zero to the allowable. Purple is over the allowable. The colors also darken toward red, so the order reads without color vision. Dashed lines drop from each segment end to the grid.

Tension

Straight, level

T₂ = T₁ + μ′ W L (Southwire E-7), with μ′ = w μ in every equation.

Straight, sloped

T₂ = T₁ + W L (μ′ cos θ ± sin θ), + pulling up, − pulling down (E-8, E-9). Vertical runs are θ = 90°. A negative result means the cable slides under its own weight; the tension is held at zero and the feed end must be controlled.

Horizontal bend

Exact, with the cable weight: T₂ = T₁ cosh(μ′φ) + √(T₁² + (W r)²) sinh(μ′φ) (E-10). Simplified: T₂ = T₁ e^(μ′φ) (E-15), which leaves out the weight and is never higher than the exact value.

Vertical bend

The four textbook cases (concave up or down, pulling up or down, E-11 to E-14) are solved for any start and end angle θ₁, θ₂. With the cable on the inside wall: T₂ = T₁ e^(μ′φ) + (W r/(1 + μ′²)) [e^(μ′φ)(2μ′ sin θ₁ ± (1 − μ′²) cos θ₁) − (2μ′ sin θ₂ ± (1 − μ′²) cos θ₂)], + concave up, − concave down.

Low tension in a vertical bend

The textbook equations assume the tension holds the cable against the inside of the bend. In a concave-up bend where T < W r cos θ, the cable lies on the bottom (outside) wall instead, and the textbook equation gives too little, at zero entering tension even less than the weight lifted. The calculator follows the wall the cable bears on, changing walls where T = W r cos θ (as described by Griffioen, Jicable 2023), and shows the textbook value beside it.

Feed tension

Reel with horizontal feed: T₀ = 25 W (Southwire E-34), or a value entered, or none. At an open duct end it enters the conduit; at a vault it is the tension at the reel, at grade.

Numerical check

Every segment is also integrated numerically in 3D, dT/ds = μ′ |T κ n − W z⊥| + W (z · t), which needs no case selection. The two methods agree to better than 0.002 % on the checks below and on 300 random routes in both directions.

Vault ends

Each end is an open duct end (a riser, a stub or an open trench, where the cable enters and leaves at the duct mouth) or a vault. For a vault, the cable path in the vault is added to the pull in the direction it applies: at the end the cable is fed in, from the reel to the duct mouth; at the end it is pulled out, from the duct mouth to the cable head. Depth h is from grade to the duct centerline. The duct route, its length and its bends are the same either way.

Fed in

From the reel at grade: a 90° turn down at the opening, a vertical drop of h − 2r, and a 90° turn into the duct, of radius r. With the reel on the duct side, the cable leaves the top of the reel and runs into the duct in one continuous arc with no reverse bend (Southwire Fig. F-1); the depth limits the radius to h/2. With the reel across the vault, in line beyond it, the turn into the duct is a reverse bend; where the vault is too shallow for 90° turns, the two turns are made smaller, cos θ = 1 − h/(2r). Over sheaves both turns are at the sheave radius. With a feeder tube, the turn at the opening is over a sheave and the turn into the duct is in the tube, a conduit bend with μ′. In line, the reel feeds straight into the duct and nothing is added.

Pulled out

Southwire Fig. F-1: the pulling rope exits the duct directly to a pulling sheave. The cable turns 90° up around the sheave at the duct mouth and rises h − r to the opening, where the cable head is at the end of the pull. With the second arrangement it also turns 90° over a sheave at the opening and leaves at grade, the two turns made smaller where the vault is too shallow. In line, the puller is in line with the duct and the cable leaves it straight.

Sheaves

A sheave that turns with the cable is taken as having no friction, so the bend has no multiplying effect (Southwire); the tension changes only by the weight lowered or lifted, T₂ = T₁ + W Δz. This is the ideal of a well-maintained sheave: where the sheaves are in doubt, choose sheaves not turning freely, which are calculated as conduit bends with μ′. Hanging in the vault, a vertical run is T₂ = T₁ ± W L (E-32, E-33).

Below zero

If the weight of the cable dropping into the vault is more than the feed tension, the cable would run off the reel under its own weight. The tension is held at zero, the reel brake holds the cable back, and the duct is entered with no tension.

Sidewall pressure on a sheave

The equation of the configuration in the conduit, with r the sheave radius (Southwire E-20 to E-22; Fig. F-4) and the higher of the tensions entering and leaving it. Taking the cables to keep their conduit configuration on the sheave is an approximation: the groove sets their arrangement there. Where a vault arrangement is over the limit, the smallest radius within it is found by recalculating the vault path for each radius (its drop or rise, smaller turns in a shallow vault, the depth limit of the arc), with the tension entering the vault unchanged, and rounded up to 0.01 ft; where none up to 50 ft is enough, that is said. Each sheave radius is also checked against the cable minimum bending radius. Standard sheaves are up to 24 in in diameter, so a large radius needs a sheave assembly, or a puller in line with the duct (IEEE PES, medium-voltage cable constructability).

Drawing and chart

The 3D view shows each vault at true scale from its floor to grade, with radius sheaves (a roller about every 15°) and a feeder tube as a sleeve, for the direction shown; the vertical exaggeration applies to the duct route only. Vault A and Vault B show each close up. In the tension chart, the cable in vault A is left of the A duct mouth and in vault B right of the B duct mouth, each widened to at least 8 % of the chart so its pieces can be read; the elevation of the cable in each vault is dashed in the color of its pull.

Cables in the conduit

Weight correction factor

One cable: w = 1. Two cables and three triangular (triplexed): w = 1 ÷ √(1 − (d/(D − d))²). Three cradled: w = 1 + 4/3 (d/(D − d))². Four cables: w = 1 + 2 (d/(D − d))². More cables or mixed sizes: 1.4. Three loose cables are taken as triangular below D/d = 2.5 and cradled above it, unless chosen.

Clearance

With d′ = 1.05 d for ovality in bends. One cable C = D − d′; triangular C = D/2 − 1.366 d′ + (D − d′)/2 √(1 − (d′/(D − d′))²); cradled C = (D − d′)(1 − (d′/(D − d′))²). At least 0.5 in; 1 in is preferred for long pulls with bends.

Jam ratio

J = 1.05 D/d for three or more loose cables of one size. Between 2.8 and 3.2 the cables can jam in bends.

Sidewall pressure

At each bend with the higher of the entering and leaving tension: one cable P = T/r; two cables and triangular P = w T/(2r); cradled P = (3w − 2) T/(3r); four cables, from the statics of the diamond, P = (w − 1) T/r but not less than T/(2r); more cables, the cradled equation.

Conduit fill

Shown for reference against NEC Chapter 9 Table 1 (53, 31, 40 %).

Drawings

The conduit cross-section and the enlarged cable section are to scale. The cables sit in the configuration used for the weight correction factor (four or more settle under gravity), drawn at the diameter used in the calculation. Layers are drawn from the construction: data sheet dimensions where listed, otherwise the ICEA thickness rules. The arrangement of fibers, buffer tubes and telephone pairs is representative of the construction, not of one manufacturer's layout.

Limits

Conductor tension

T = S × A per conductor (Southwire Table 4: copper 0.008 lb/cmil; aluminum hard 0.008, 3/4 hard and AA-8000 0.006, 1/2 hard 0.003, soft 0.002), summed for three or fewer conductors and 80 % of the sum for more (E-5, E-6). Shields, concentric neutrals and grounds are not counted unless chosen.

Pulling device

Pulling eye: its rating, not over 10,000 lb. Basket grip: 1,000 lb by default (traditional practice; some manufacturers allow more). A line tied to the conductors or the strength members has no separate limit.

Communications cable

The manufacturer's rated pulling tension per cable (TIA-568.2-D: 110 N, 25 lbf for 4-pair cable), summed with the same 80 % rule for more than three cables.

Sidewall pressure

Southwire Installation Guide (2005) Table 7 by default: 500 lb/ft for 600 V and 1 kV nonshielded and 5 to 15 kV power cable, 300 lb/ft for 25 to 35 kV and interlocked armor. Southwire medium-voltage and 600 V data sheets allow 1,000 lb/ft, and the General Cable guide 1,200 to 2,000 lb/ft by construction; either can be chosen, or a value entered.

Bend radius

Medium voltage by NEC 300.34: 12 × OD for shielded single conductors; the greater of 12 × the shielded conductor and 7 × the overall diameter for multiconductor and triplexed cable. 600 V: 4, 5 or 6 × OD (OD to 1 in, 1 to 2 in, over 2 in). Communications: the data sheet radius under load.

Friction and lubricant

Coefficient of friction

Southwire Table 6 with adequate lubrication, by the cable exterior (PVC, PE, XLPE, nylon, CPE, CSPE) and the duct (metallic, PVC, fiber, asbestos cement). HDPE and other smooth plastic ducts use the PVC column. A factory pre-lubricated jacket uses the same value; with no lubricant the value is doubled (a dry LLDPE jacket measured 0.27 against 0.14 lubricated in Southwire's test). A value can be entered.

Quantity

Q = 0.0015 × L × D gallons, L in ft and D the conduit inside diameter in in, up to 50 % more for difficult pulls (Polywater).

Cable data

Power cable

Diameters and weights from Southwire data sheets where listed: THHN (SPEC 10000), XHHW-2 (10006, 10015), RHH/RHW-2/USE-2 (10010, 10020), URD triplex and quadruplex (83013, 83018), TC-ER (45252) and medium voltage (81102, 81112, 81242, 81264). Other sizes and the generic ICEA, LADWP and TO29 medium-voltage constructions are computed from the layer dimensions and material densities; for the Southwire cables this reproduces the data sheet weights within about 3 %.

Communications cable

Belden, Siemon, Corning, CommScope, Superior Essex and General Cable data sheets: diameter, weight, rated tension and bend radius under load.

Checks

Each case is solved live by this calculator and compared with the published equation or value.

Limitations

• Conduit and duct, with sheaves and feeder tubes at vault ends. Cable tray, rollers, push-pull and blown installation are not covered.
• A vault is taken as a pull point at one end only. A pull through a vault to a further duct is two pulls; enter each section separately.
• In a vault the cable runs in the vertical plane of the duct, with the reel and puller in line with it. The weight of the pulling rope and the friction of the reel are not included.
• The coefficient of friction is taken as constant; it varies with the lubricant, the sidewall pressure, the temperature and the duct condition.
• Weight correction factors and sidewall pressure for four or more cables, and for mixed sizes, are approximations.
• Bends that are both horizontal and vertical (rolling offsets) are not modeled; enter them as separate bends.
• Confirm cable data, allowable tensions and sidewall pressure limits with the cable manufacturer for final design.