Volume 1
ESTIMATING TENSION WHEN Even with these differences, the friction coefficient
in cable pulling continues to depend on cable jacket
PULLING CABLE INTO CONDUIT type, conduit type and lubricant type. "General"
coefficients don't mean much. The most accurate
tension estimates come from friction coefficients
The Problem specific to the cable, conduit and pulling lubricant.
When you calculate cable pulling tensions, what
friction coefficient should you use? User responses Pulling Equations
vary . . . some answer "0.5" . . . others "0.4," or
"0.35". Who's right?? What coefficient of friction Tension estimation in cable pulling is calculated
provides the best tension estimates and correlation using the cable pulling equations. The equations
for field planning and optimal cable system design? apply the physics from our simple example to the
unique character of cable pulling. This includes the
non-gravitational forces in conduit bends.
The Basics Looking at a simplified form of the equations will
clarify:
To answer this question, we need to understand
more about "coefficient of friction." What exactly is Straight Conduit Tout = Tin + LWµ
a “coefficient of friction” (COF). Can we find friction
coefficients in an appropriate reference book?
Conduit Bend Tout = Tin eµθ
Let's start with a simple physics class example . . .
Where:
a wooden block (say, 5 kgs in weight) on a
Tout = Tension Out
horizontal steel plate. Say it takes 2 kgs force (19.6
Tin = Tension In
N) to pull (drag) the block across the plate. The
L = Length of Straight Run
coefficient of friction (wood on steel) is defined as
W = Weight of Cable (per length)
the ratio of this "dragging force" (2 kgs) to the
normal force (weight of 5 kg). In this case, the µ = Coefficient of Friction
friction coefficient would be .4. Note that the COF is θ = Angle of Bend
a dimensionless number. e = Natural Log Base
Experience tells us that if we replace the wooden Note the significant effect on tension that small
block with a 5 kg rubber block, it will take a greater changes in µ (friction coefficient) can cause,
force to drag the rubber block (say, 6 kgs force). especially in conduit bends where this friction
The measured coefficient of friction (rubber/steel) coefficient is in the exponent. Inaccurate friction
would be 1.2. What's important to note from these coefficients lead to poor correlation of tension
examples is that there is no single coefficient of calculations with actual tensions. Unfortunately, it is
friction. The friction coefficient varies with the in multi-bend pulls, where the tension and sidewall
rubbing surfaces. pressure are of most concern, that the use of an
inaccurate coefficient of friction produces the
greatest error.
Where can you find or how can you determine
Cable/Conduit meaningful friction coefficients?
Replace the block with cable and the plate with
conduit, and we have cable pulling . . . with a few EPRI Study Helpful
complications. Neither the cable nor the conduit is
flat. There may be more than one cable, which can The Electric Power Research Institute (EPRI) is a
result in complex rubbing surfaces. Pulls are not utility funded research group in the United States.
straight, and forces other than gravitational weight The EPRI study, "Maximum Safe Pulling Lengths for
occur at conduit bends. Finally, our Polywater Solid Dielectric Insulated Cables," provides insight,
Pulling Lubricants change and lower the friction and some surprises, on lubricated cable friction and
coefficient. its measurement.
The EPRI research showed that lubricated Where the lines converge on the above graph, and
coefficient of friction changes with varying normal the slope levels, the low bearing pressure friction
force (the force pushing the cable against the has disappeared and the cable and lubricant are in
conduit wall). The EPRI report defines two a high bearing pressure mode. By calculating the
different friction coefficients, one at "high sidewall sidewall-bearing pressures (defined as tension out
bearing pressure" (High SBP) (going around of the bend divided by bend radius) at the point of
bends) and the other at "low sidewall bearing convergence, we find that the change from Low
pressure" (Low SBP) (straight pulls). Surprisingly, SBP friction to High SBP friction is complete at 6
the High SBP friction coefficient is usually lower Kg/M bearing pressure.
than the Low SBP friction coefficient, often lower
by a factor of more than 2. Because power cable's stiffness and resulting
"spring" tend to increase conduit contact pressure,
The EPRI report goes on to recommend that the power cable pulling ends up in the "high bearing
High SBP friction coefficient be used in pressure" mode most of the time. Field-measured
calculations when normal force on the cable is tensions tend to support this conclusion.
over 220 Kg/M (150 lbs/ft), and that otherwise the
Low SBP coefficient of friction be used. On the other hand, lighter, flexible cables (fiber
optic, etc.) often demonstrate both types of friction
Polywater Research Clarifying during pulling. This is one reason why a lower
viscosity, liquid lubricant like Polywater F is best
American Polywater studies confirm the variance for the installation of this type of cable.
in friction coefficient with normal pressure. We
have determined that the friction at low normal
bearing force is a measure of hydrodynamic Pull-Planner 2000 Has Friction Data Base
friction, which is roughly proportional to lubricant
viscosity (internal gel strength of the lubricant). We’ve seen that coefficient of friction varies with
cable jacket and conduit type, and that it is
In contrast to the EPRI work, however, our necessary to use accurate coefficients to calculate
research indicates the conversion in friction to the meaningful pulling tensions.
High SBP type occurs continuously and at bearing
pressures much less than 220 Kg/M (150 lbs/ft). American Polywater's laboratory has developed
extensive friction data for different cable jacket and
Pulling Tests conduit types, at appropriate bearing pressures.
This data is in an internal data base in our Pull-
One test illustrating this "variable” friction Planner 2000 for WindowsTM Software.
coefficient involves pulling cable through multiple,
consecutive 90° duct bends (a helix). The The Pull-Planner 2000 provides a convenient way
incoming cable tension and total degrees of bend to calculate cable pulling tensions on a PC. It
can both be varied. From the pulling force enables “what if” scenarios with cable, conduit, pull
(measured with a load cell) required to move the length, COF, incoming tension, and more.
cable, we can calculate a coefficient of friction Lubricant quantities can be calculated, and
using the pulling equations we studied earlier. calculations can be saved or printed out. The full
version of the planner runs in metric or english
The graph below shows measured friction units.
coefficients plotted against the tension on the cable
as it enters the conduit helix. For this graph, the
conduit was high density polyethlene with 540° of Pull-PlannerTM 2000 Preview
bend. The cable had a polyethylene jacket.
A preview of the Pull-PlannerTM 2000 is available.
"Polywater" J "Polywater" F Use the internet to go to www.polywater.com to
preview or order the Pull-PlannerTM 2000.
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Our web site (www.polywater.com) also has
Coefficient of Friction
copies of other technical studies of interest in cable
installation. Visit and leave us your e-mail to stay
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up-todate.
Feel free to call or write us if you have questions or
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would like to discuss friction measurement or
tension calculation. If you wish to view a 12-minute
video on "Cable Installation Engineering," please
call and ask for our Customer Service Department.
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0 5 10 15 20
Incoming Tension
To explain the graph, first you must know that P.O. Box 53
Stillwater,MN 55082
Polywater J and Polywater F are two of
USA
American Polywater's high-performance cable
pulling lubricants ("J" is usually used for electrical
cable and "F" for fiber optic cable). They are Phone: 1-(651)-430-2270 Fax: 1-(651)-430-3634
similar chemically, except that "J" is a gel lubricant E-Mail: tkeditor@polywater.com
(higher viscosity) and "F" is a liquid.
