Charging by Walking
Walking on an insulative floor covering produces a predictable
There are very few cases in which it is possible to quantitatively
describe an electrostatic charging process (i.e., the rate at which
the voltage of an insulated conductive system or insulator field increases).
Two important examples where this is possible, however, are the flow
of a liquid such as gasoline into an insulated container or, of more
interest in the elec-tronics world, walking on an insulative floor coveringthe
most common way people are charged.
As explained in a previous column titled "Is Static Electricity Static?"
(CE January/February 2000), the charging of a person by walking can
be described by assuming that the contact and friction between the person's
shoe soles and the floor separates a charge, Dq,
for each step.1 If the step rate is n steps per unit
of time, this corresponds to a charging current of
The current will charge the person in such a way that the voltage,
V, will initially increase at a mean rate of
where C is the person's capacitance. The increase in voltage,
DV, by the first step will be
The voltage will cause a decay current, id, through
the resistance, R, from the person to ground:
And the voltage will reach its maximum value, Vm,
when ic = id or
If the highest acceptable body voltage is Vaccep,
then the grounding resistance must fulfill the condition
where Dqmax is the maximum
value of the charge separated per step.
Figure 1. Charge separation between shoe and floor.
In the column cited, the maximum value of Dqmax
was estimated as
where e0 (the permittivity of
air) = 8.85·1012 F·m1,
Eb (the breakdown field strength in air between plane
electrodes) » 3·106
V·m1, and A
(the area of the shoe sole) » 150 cm2
(see Figure 1). Introducing these values into Equation 5, we find that
which corresponds to a charging current of
ic,max = n·Dqmax
= 8·107 A »
106 A, (9)
assuming a rate of 2 steps/sec. Therefore, if Vaccep
= 100 V, then R £ 100 MW.
Note that the values for an acceptable floor resistance derived from
Equations 6 and 9 are conservative. It is highly unlikely that the whole
area of the shoe sole would be charged to the breakdown level and that
no neutralizing discharge would occur when lifting the foot.
Equation 3 indicates the expected increase in voltage at the first
step to be
assuming a capacitance of 100 pF for one foot. To find more realistic
values for Dq and DV,
a series of measurements of the body voltage on a highly insulative
floor covering (vinyl tiles) were taken. The body resistance to ground
was measured to 1011 W, varying
over the floor from 0.5 to 1.5·1011
W. The body capacitance was 160 pF for both
feet and 100 pF for one foot.
Figure 2. Measurement of body voltage.
The experimental setup is shown in Figure 2. The person is connected
to an electrometer, which can be run as a charge meter (high capacitance)
or as a static voltmeter (low capacitance). With the meter in the charge-measuring
mode, the charge for a single step was determined. As the average of
10 determinations, the value was found to be
with a standard deviation on a single determination of 0.5·108
C. According to Equation 3, this corresponds to a voltage increase for
the first step of
With a rate of 2 steps/sec, Equation 5 indicates an
expected maximum voltage of
Vm = RnDq
= 6 kV. (13)
Figure 3 shows the body voltage as a function of time. It appears that
the voltage reaches a maximum of about 3.5 kV after approximately 15
seconds. The reason a person doesn't reach the predicted maximum value
of 6 kV from Equation 13 can be found in the decay curve starting at
21 seconds. At that moment, the person stands still and allows the charge
to be neutralized through the effective grounding resistance. An analysis
of the curve shows that the initial decay corresponds to a resistance
of approximately 2·1010
W and concludes with a value close to 1011
W. This must mean that the resistance (or
rather, the resistivity) of the floor (and sole) material decreases
with increasing voltage (or rather, field strength). The direct measurement
of the person's resistance was taken at a voltage of approximately 300
V, and the measured resistance will therefore be higher than the effective
resistance at the maximum voltage.
Figure 3. Body voltage of person walking on an insulative floor.
The value of Vm predicted by Equation 5 appears to
provide a safe upper limit for the body voltage when walking on a floor
characterized by a resistance R. One problem, however, remains.
According to Equation 3, the voltage developed by a single (the first)
step seems to be independent of the decay resistance. Further, the value
of 300 V, as predicted by Equation 12, could be a problem in many scenarios
involving electrostatic discharge. It should also be stressed that Equation
3 does not account for the unavoidable decay during the time it takes
to lift the foot from the floor and separate the charge Dq.
If this time is Dt, then the voltage
DV at the end of Dt
can be written as
If we assume Dt ~ 0.1 second, C
(one foot) = 100 pF, n = 2 steps/sec, and Dq
= 3·108 C, we can find
DV (Equation 14) and Vm
(Equation 5) as functions of the decay resistance R (see Figure
4). It appears that for low values of R, DV
is higher than Vm. For instance, at R = 109
W (1 GW)
the mean maximum voltage is Vm = 60 V, and the one-step
voltage is DV = 180 V. It may seem
peculiar that the body voltage after one step (rather, at the end of
the first foot lift) can be higher than the mean body voltage after
many seconds. The reason is that the voltage decays in the time between
the lifting of one foot and the lifting of the other foot. Assuming
Dt = 0.1 second and n = 2 steps/sec,
this decay time is approximately 0.4 second (i.e., four times as long
as the charging time).
Figure 4. Maximum voltage, Vm, and one-step voltage,
DV, as a function of the decay resistance, R.
The curves show that DV = Vm
= 270 V at R = 4.5·109
W. The implication of the results plotted
in Figure 4 is that at resistances lower than approximately 4.5 GW,
the voltage spikes connected with a single step are the primary concern,
and at higher resistances the equilibrium voltage integrated over many
steps is the dominating factor.
The upper limit of the voltage to which a person walking across an
insulative floor may be charged can be predicted with reasonable accuracy
by measuring the person's total resistance to ground. And again, at
relatively low resistances (< ca. 4.5 GW)
the body voltage after one step shows up as a voltage spike higher than
the mean body voltage integrated over several steps.
1. Niels Jonassen, "Is Static Electricity Static?" in Mr. Static,
Compliance Engineering 17, no. 1 (2000): 3036.
Niels Jonassen, MSc, DSc, worked for 40 years at the Technical University
of Denmark, where he conducted classes in electromagnetism, static and
atmospheric electricity, airborne radioactivity, and indoor climate.
After retiring, he divided his time among the
laboratory, his home, and Thailand, writing on static
electricity topics and pursuing cooking classes. He passed away in 2006.
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