# Coefficient of Friction in Cable Pulling – Part 2

We define friction coefficient, introduce pulling equations and measuring coefficient of friction and the lubricant effect.

Coefficient of friction (COF) is a measure of frictional resistance to movement. An earlier post introduced the science behind COF and discussed the factors that can influence this value.

Figure 1 helps clarify and more formally define “friction coefficient”.

Where:

N (*Vector*) = Normal force perpendicular to horizontal table

G (*Vector*)* _{ }* = Gravitational force on block of mass m.

P (*Vector*) = Pulling force placed on the block to slide it horizontally

F (*Vector*) = Frictional force resisting movement

The example shows a block sitting on a horizontal table. A Gravitational force G (*Vector*) (= mg) acts on the block. The block does not fall because there is an equal and opposite force from the table that we call the Normal force (N (*Vector*)).

If we apply another force perpendicular (P (*Vector*)) to the normal force, we find that some minimum force is required before the block will slide. This pulling force must overcome the frictional resistance to movement or frictional force (F (*Vector*)) for the block to move. The coefficient of friction is defined as the ratio of the force required to move the block divided by the normal force (block weight).

So, if μ is the friction coefficient: μ = P(*Vector*)/ F(*Vector*) (Equation 1)

To illustrate, say the block is wood (5 kgs). It requires 2 kgs of force to drag the wood block across a horizontal steel table. The COF for wood on steel is the ratio of the “dragging force” (2 kgs) to the normal force (weight of 5 kgs). So, the friction coefficient is 0.4. Note that the COF is a dimensionless number, as it is the ratio of the magnitudes of the two forces.

Experience suggests that if we replace the wooden block with a 5 kg rubber block, an even greater force is required to produce movement (say, 6 kgs force). So, the measured COF of rubber on steel would be 1.2.

It is important to note from these examples that the COF can vary with the materials that are rubbing.

Related Content: Coefficient of Friction in Cable Pulling — Part 1 |

**Pulling Equations**

Replace the block with cable and the table with a conduit, and we have cable pulling. Tension estimation in cable pulling is based on the physics in equation 1. Pulling tension is determined through a series of cable pulling equations that use weight and friction as inputs.

Straight-section cable pulling equations add the incoming tension from the reel or the previous section of the pull. The straight conduit section formula looks like this:

Straight Conduit T_{out} = T_{in} + LWμ (Equation 2)

Where:

T_{out }= Tension Coming Out of the Straight Section

T_{in }= Tension Going into the Straight Section

L = Length of Straight Run

W = Weight of Cable (per length)

μ = Coefficient of Friction

So, the friction add-on is the total cable weight multiplied by the friction coefficient. To use this formula to estimate tension, we need to know friction coefficients for typical cables, conduits, and lubricants.

Related Content: Coefficient of Friction in Cable Pulling Tension from Conduit Bends |

**Measuring Cable and Conduit COF**

To measure the COF between a variety of cable jacket and conduit materials, Polywater developed the Friction Table shown in the photo above. The device places a measured downward pressure on a cable / conduit sample and then measures the force required to pull the cable perpendicular to this normal force. The friction coefficient, as before, is the ratio of these forces.

We can also lubricate the cable and conduit interface and determine the effect of a lubricant on the friction coefficient. Data gathered from thousands of tests over several decades have allowed us to optimize lubricant formulation and selection. As cable manufacturers develop jackets with new properties, such as toughness or fire resistance, we can measure and provide feedback on the friction properties of these new materials.

Related Content: Hawaiian Electrical Company (HECO) and the Pearl Harbor Cable Pull |

**The Lubricant Effect**

Cable jacket materials show significant differences in friction behavior, but are usually developed for reasons other than “ease of pulling.” If an effective cable lubricant can lower friction values without impacting the other aspects of cable jacket performance, then installation issues can be minimized.

The data shows that is exactly what happens. Effective pulling lubricants lower friction coefficient significantly. Figure 2 shows the dramatic reduction in friction from lubricant use.

Related Content: FAQ – Cable Pulling, Lubrication, and Tension |

**Cable Pulling is a Little More Complicated**

The friction table tests the wide variety of materials used in cables and raceways. However, real cable pulls are more complicated. Pulls are not straight and forces other than gravitational weight occur at conduit bends.