Electrical conductivity measurement of the atmosphere using the Gerdien
voltage decay method in high altitude flight
Katherine O. Blackburn and Joseph T. D. Tran
Abstract
Atmospheric electrical conductivity research of the atmosphere has not had many scientific
findings since the 1980’s when Gerdien first used the voltage decay mode to determine electrical
conductivity. This paper explores the use of Gerdien’s 1980 concept of using two cylindrical
electrodes to measure electrical conductance. The condensers were created from dimensions
specified by the equations derived by K.L. Aplin et. al. cited. A unique feature of these condensers
is the specially designed caps, which promote laminar flow through the condensers, while acting
to secure the condensers in a fixed position. Previous attempts at measuring conductivity have
been limited to around 30,000 ft but because high altitude flight is now possible through the
LaACES program, the electrical conductivity measurements can be made for altitudes up to
100,000 ft.
I. Background
Introduction to the Program
The Louisiana Aerospace Catalyst Experiences for
Students (LaACES) is an intensive, one-year program
that allows students to design, implement, construct,
and test a payload that can be used to extract scientific
data corresponding to increasing altitude, pressure,
and/or temperature. The student payloads are attached
to a 3 kilogram sounding balloon by use of two flight
strings that will carry the payloads to about 100,000
feet. Data is recovered and analyses follows.
The goal of this project was to successfully design,
build, launch and recover a payload to investigate the
levels of atmospheric electrical conductivity as a
function of altitude while surviving the challenges of
extreme high altitude flight. Though a parachute failure
caused an impact condition greater than originally
tested, the launch, which took place in Lubbock, TX on
May 26, 2010, was successful.
Applications of Atmospheric Conductivity
Atmospheric conductivity is a complex variable part of
the atmosphere with many contributing factors. It plays
a significant role in many fields including Meteorology,
Environmental Science, and Radiology. Measurement
of air conductivity near ground levels is used to
determine the pollution level of air (1). Variations in the
conductivity of the atmosphere can also be used to
detect unnatural or increased radiation in an area due to
the effects of ionic radiation in the atmosphere. The
formation of thunderstorms and the coalescence process
of precipitation are also affected by conductivity.
Increased knowledge of this intriguing property of
atmosphere will lead to greater predictive abilities in
meteorology (3).
Generally,
in
any
atmospheric
conductivity
measurement, only the smallest, fastest particles
contribute greatly to the ionization in the atmosphere as
they have the greatest concentration and average
mobility. These ion clusters have radii on the order of
0.5 nm (nanometers). Many factors can increase or
decrease the rate of production of these small ions,
affecting conductivity, including wind speed, pressure,
and humidity, which all affect the concentrations of
these ions as well as their mobility (2). While the
specifics of atmospheric conductivity are debated,
certain variables are classically recognized as major
contributors such as the factors above, cosmic ray and
solar activity, and atmospheric levels of aerosols.
Cosmic rays entering the upper atmosphere cause the
majority of electrical conductivity in the atmosphere. At
lower altitudes, the cosmic rays have spent their energy
in ionizing the atmosphere and less ionization occurs.
At higher altitudes, cosmic rays have not yet lost their
energy and greatly ionize the atmosphere. As the
energy of cosmic rays is spent in the upper atmosphere,
less conductivity is seen. Finally, radiation from the
earth is also a major influence near surface level,
though not as potent as cosmic radiation, and it releases
as many as 105 ions per 4 MeV (mega electron volt)
alpha particles (5).
Conductivity ions in the atmosphere, generally of a
mobility of about 10-4 m2v-1s-1, are formed from cosmic
rays when these rays energize a particle and strip
electrons from it. These positive and negative ions now
combine with others and eventually form numerous
positive and negative ions.
humidity levels are close to 60% or higher. In Palestine,
TX (the original launch site) and in Lubbock, TX (final
launch site) relative humidity was expected to be less.
Passing through a cloud layer that is fully saturated
with water vapors would potentially have much higher
levels, causing the Gerdien condenser to temporarily
malfunction.
II. Methods
Equation 1 gives the current (i) achieved in the Gerdien
condenser where V is voltage difference between the
outer and inner cylinder, l is the length of the
condenser, σ is the conductivity, b the inner radius, and
a the outer radius.
General Background
A Gerdien capacitor consists of two coaxial cylinders.
A constant positive voltage is applied to the outermost
cylinder, repelling positive ions toward the center and
increasing the voltage on the innermost cylinder. This
voltage curve determines positive conductivity.
Measuring negativity conductivity involves applying a
negative voltage to the outermost cylinder. This
measurement mode, which our team will utilize, is
termed voltage decay mode. It is also possible to
directly measure the current.
In order to effectively measure conductivity, the ion
stream must be parallel to the axis of the cylinders. In
addition, the Gerdien capacitor can only measure ions
with a mobility greater than the critical mobility of the
capacitor. Ions encountered in the atmosphere are
expected to be in the range of 2.5 – 3 fS/m.
Effects of Humidity
Scientists have observed that humidity affects the
conductivity—in one case, Moore and Vonnegut
observed that the conductivity of dry air as twice that of
air over boiling water. Harrison, another scientist, used
mass spectrometry data to compute the relative
concentrations of different hydrations of the
atmospheric ion H+ (2). He concluded that at 300K, the
mean mobility is expected to decrease from 2.05(10 -4)
at a relative humidity of 20% to 1.74(10-4) at 100%
(17% drop).
In the lower atmosphere from 0 to 30,000 ft, relative
humidity is a global average of 10-20%. However these
values can vary greatly per location; in Baton Rouge,
Equation 1
This equation is derived under the assumption of
uniform mobility, laminar flow and Gerdien capacitor
of infinite length. The same applies for Equation 2 in
which the critical mobility, μc, or the minimum ion
mobility that can be measured, can be calculated given
µ (wind speed). The wind speed will be calculated
using the global positioning system coordinates and
known values of altitude.
Equation 2
Measuring wind flow is thus important to determine the
accuracy of a measurement and the minimum critical
mobility (2).
Voltage Decay Mode
In voltage decay mode, voltage is sampled about 1-2 Hz
for 5-20 s. After, the inner cylinder is reset to its initial
voltage (13). At this time charge injection can occur
from the atmosphere to produce a non-fixed inner
cylinder voltage. In order to get the value of dV c/dt, the
voltage decay is fit with an exponential curve. The
natural log is then taken of this curve for a better linear
fit and the derivative of this result is the value dVc/dt.
This is used in the following equation to calculate
conductivity with the constant 0 = 8.85x10-12 F/m and
the bias voltage between the inner electrodes (the
voltage on the outer electrode minus the voltage on the
inner).
Equation 3
This method does not require the Gerdien capacitance.
Alternatively, Equation 5 below in conjunction with
Equation 6 is used to determine air conductivity where
Cg is the Gerdien capacitance, Cm is the measurement
system capacitance (usually assumed to be 0), Vb is the
voltage across the outer electrode of the Gerdien
capacitor and Vc is the voltage across the inner
electrode.
Equation 5
The usage of actual Gerdien capacitance instead of the
theoretical value reduces somewhat the error associated
with the infinite length assumption. Both methods
mentioned assume a uniform ion mobility spectrum,
which is unlikely at lower altitudes due to large
particles and other contaminants. As such, observed
voltage decays curves are not exponential at lower
altitudes; however at higher altitudes, an ideal decay
curve has been observed. It is possible to derive an ion
mobility spectrum from the observed voltage decay
given the assumption that ion mobilities are similar in
concentration and that the wind speed is known.
System Interface
Equation 4
All electrical components will be contained inside the
payload box. The BalloonSat board containing the
Basic Stamp Microprocessor, the Real Time Clock, the
Figure 1 - Figure showing major functional groups and interfaces
EEPROM Memory Storage, and the Analog to Digital
Converter is the main component and the control
subsystem. Figure 1 shows the system design of the
components. The Analog to Digital Converter is
interfaced to the Gerdien condenser circuit through two
analog data lines (one for each condenser) on the
BalloonSat. The control and sensor systems are
supported by two separate power supplies, the first is a
set of 1.5 V batteries in a 15 V configuration, which
supplies 15 V of power to the BalloonSat and 12 V
through a voltage regulator to the Gerdien circuit. The
second power supply consists of 2 sets of 3 V batteries
in a 30 V configuration. These provide the positive and
negative 30 V bias required for the outer electrode of
the Gerdien condensers.
Gerdien Condenser
The circuit used to control the Gerdien condenser,
shown in Figure 2, consists of three parts: the input
circuitry, the signal conditioning, and the switch, which
will reset the voltage across the capacitor.
The purpose of the input circuitry is to act as a low
leakage op-amp buffer. It consists of a low leakage opamp, the LMC6042, along with two jFETs which allow
the switch to reset the capacitor’s voltage. The op-amp,
with an offset voltage of 2 mV, will cause a leakage
current of less than 5 fA for 40 % and greater than 20
fA for 50 % percent of a random assortment of jFETs.
A current gate leakage of less than 8 fA will result in
less than 10 % error contribution (7).
Signal conditioning is achieved via a voltage divider,
which reduces the voltage output of the input circuitry
from 0-12 V. The voltage is then fed through a high
pass filter, another op-amp buffer, and then to the ADC.
The switch (4053BE MOSFET) has two modes:
measure and reset.
In reset mode, it applies
approximately 10 V to the inner cylinder for measuring
negative conductivity and 3 V for measuring positive
conductivity. This is possible via the use of 2 jFETs,
which act as diodes and also as protection against high
voltage. In measure mode, the voltage on the inner
electrode is allowed to decay as ions collect in the
Figure 2 – Flight Schematic
Gerdien condenser.
The outermost cylinder for measuring positive and
negative conductivity will always be charged to ±30 V.
As the voltage on the inner cylinders decays, the
cylinder for measuring negative conductivity will
change from 10 V to nearly 0 V while the cylinder
measuring positive conductivity will change from 3V to
nearly 12 V (it will jump from around 10 V to 12 V
when the common mode range of the LMC6042 opamp is exceeded, however the op-amp will recover).
The outermost cylinder’s voltage will never be
transferred through the LMC 6042 op amp, thus this
voltage does not otherwise exceed its common mode
range
In order to minimize interference, the connection
between pin 5 of the op-amp input buffer and the inner
electrode was made as short as possible. Therefore, the
op-amp is located as close to the inner electrode as
possible. This particular portion of the circuit is highly
sensitive to stray voltages and currents, so the resistors
connected between the inner electrode and pin 3 and 5
of the op amp are air wired (connected directly to each
other and not to the circuit board) to each. Pins 4 and 15
of the 4053BE MOSFET are also air wired to the jFETs
and these are wired to the resistor mentioned
previously. The variable resistor in the circuit for each
condenser controls how much of the 12 V supply
voltage shows up on the inner electrode and will be set
(a)
to supply +11V to one electrode and +3V to the other.
Two 0.1 µF capacitors are soldered from the input
voltage to ground as a filter near pin 8 of the LMC6042
op-amp and pin 16 of the 4053BE MOSFET switch to
minimize signal noise.
The Gerdien condenser does not need to be calibrated,
the equations presented above in the Technical
Background are used, along with the measured
capacitance of each cylinder, to calculate the ions
encountered based on the wind-speed of the air flowing
through it and the voltage decay seen on the inner
electrode (2).
Figure 3 shows the schematic for the Gerdien condenser
interface. In this interface the output voltage to the opamp will be a minimum of 0 V and a maximum of 3 V
because of the resistor networks made up by resistors 2,
3, 6, and 7. Thus, the output matches the base and span
of the ADC, which is 0 V – 3V and needs no further
signal conditioning.
Mechanical Specification
During the flight, there are many extreme variable
conditions that can potentially destroy the payload or
render any data collected unusable if the mechanical
design and specifications are not correctly identified.
Temperatures can reach well down to-70°C while
pressures can reach almost vacuum conditions. In
addition to the physical environment, the payload
(b)
Figure 3- (a) External structure (b )Gerdien condenser with caps.
should be as light as possible, be structurally sound, and
be within the mechanical specifications such as having
two holes spaced 17 cm apart. The payload should also
be able to withstand an impact of about 20 feet per
second. Taking all of these considerations into account,
a semi-hexagonal box with weight-reducing grooves
was designed to fit all the external and physical
requirements as shown in the Figure 5a.
An important structure that is considered to be an
external component is the Gerdien condenser shown in
Figure 5b. The condenser’s unique features are its two
snap-on cap designed and made using the Dimension
Elite 3D Printer. There are two of these condenser
assemblies that are placed in the open compartment of
the payload box. The condensers were glued to the
divider and were protected using pieces of mesh fabric
to cover the top and bottom openings of the box; this
acts as a prevention method incase the condensers come
loose.
The internal structure, which is in the enclosed
compartment seen in Figure 5a, consists of the
BalloonSat board, the Gerdien circuit board, the battery
packs and supporting circuitry.
System Testing
A series of three tests were required in order to ensure
the payload was flight ready. The first test was an
impact test, which mimics the harsh flight landing
condition. This test was also done first because it was
most likely to have problems and will allow time to
make design changes. The second test was the thermal
test; the flight was mimicked using a combination of a
refrigerated compartment, a freezer, and dry ice. The
third test performed was the pressure test with the use
of a pressure chamber. The flight profile was mimicked
using a graph of the expected pressure drop from a
previous flight.
III. Results
The payload box was connected to a high-altitude
balloon, which carries the payload to 100,000 feet in
the atmosphere at an ascent rate of roughly 1000 ft/min.
This target ascent rate was used to calculate the
dimensions of the two Gerdien condensers according to
the critical mobility of the ions measured. From Launch
altitude until around 40,000 ft, the payload ascended at
a rate of approximately 1333.33 ft/min and then from
40,000 until 100,000 ft, the ascent rate was
approximately 800 ft/min. These rates are close to the
target rate of 1000 ft/min and thus impacted data
Positive
conductivity
3403
4807
7606
10532
13395
16285
19393
23006
26884
31034
35103
39357
42470
44284
46062
48436
50729
53147
55265
57558
59792
62384
64584
66757
69297
71496
73787
76116
78619
80785
83129
85270
87677
89563
91992
94202
96437
98538
68803
43954
27734
14909
5848
Conductivity (S/m)
Conductivity vs. Altitude
-5E-15
Altitude (ft)
Figure 4 – Graph of Conductivity vs. Altitude
collection only marginally.
At 100,000 ft, the payload string connecting the
payloads to the balloon was cut, allowing the payload to
fall back to earth, with a parachute attached. This
occurred during flight at about 9:30 and the payload fell
with a descent rate of about 5,249 ft/min due to
incorrect parachute operation.
Several important observations must be made to
interpret Figure 5 below. First, as noted previously, the
ascent rate of the payload was roughly 1333.33 ft/min
until 40,000 ft. After this point, the data returns
extremely low values, orders of magnitude lower than
the expected value in fS/m. From this, it is assumed that
a wind speed lower than that intended (1000 ft/min as
designed) is insufficient for good data. When the
balloon burst at around 98000 ft, conductivity is again
measured, indicating the sensor is too sensitive for a
slow wind speed. However, it can also be noted that as
the descent rate increased (reaching 11000 ft/min at
times) data was again skewed. Further investigation
into the effects of wind speed on the Gerdien condenser
is absolutely vital for continuation of this project and
will be pursued.
In this graph, only positive conductivity measurements
have been graphed. This is because the condenser
measuring negative conductivity did not function
properly during flight. The reset value of the negative
Gerdien condenser was intended to be 10V and the
condenser should have decayed to 0V, however the
average reset during flight was only 2.89V though it did
decay to 1.35V on average. Therefore, this data is
considered invalidated. The average reset voltage on the
other condenser was intended to be 3V and it should
have increased to 12V as positive ions were attracted to
the inner electrode. This condenser’s reset value was an
average of 3.67V, a perfectly acceptable number. The
decay value however is imperfect on this condenser,
giving an average value of 4.55V. It was observed to
properly decay at some points, from 3V to 12V,
however for the period in flight from 40,000 feet until
descent the condensers both worked incorrectly.
IV. Discussion
Extremely low conductivity values were expected to
some extent, because of the nature of the device. As the
altitude increases, the atmosphere thins and no decays
were observed on the devices. This also corresponded
with the slower descent rate of 800 ft/min and further
studies should be done to investigate this problem.
Interestingly, the condensers did not behave this way
during system tests, during which no wind passed
through the condensers, again bringing up questions
about the true effect of wind speed. In system testing,
during the cold test both condensers ran properly,
decaying and resetting consistently. In the pressure test,
only one condenser worked correctly (decaying and
resetting as intended), however the one that did not
function has worked intermittently throughout the entire
development process.
Due to the sensitivity of this circuitry, a first attempt at
this project was exceedingly difficult. As mentioned
previously, precaution had to be taken to keep the
condensers clean (stray fingerprints can affect the
circuit electrically) and keep connections between the
condensers and the circuit board as short as possible.
The connection to the condensers even had to be
switched at one point, effectively changing which
condenser measured positive and negative conductivity.
After this swap, the condensers worked properly even
though one had not before.
For this and other reasons, this project should be
attempted again and better data can certainly be
achieved with several minor improvements. Ultimately
however, this sensor may not be ideal for measuring
conductivity in a high-altitude situation. Few previous
studies have conducted balloon flights and even fewer
have reached the heights this flight did.
The limitation on the Gerdien condensers comes from
the effect of wind speed on the accuracy of the
measurements, which is not completely understood.
Eventually an entire new sensor may need to be
designed that has no dependency on wind speed, which
can quite possibly be done, in order to measure
regardless of a slow flight or low atmosphere at high
altitudes.
However, several minor changes can certainly be made
to this payload in order to get better data and more clear
conclusions on the accuracy of this measuring device.
One change, which should have been incorporated into
this payload, is two voltage regulators on the 30V
supplies to the condensers. All batteries experience a
decrease in voltage as temperature decreases, changing
the bias voltage between the condensers. Since this
payload had no method of measuring the voltage on the
condensers, they were assumed to be 30V and -30V
because little de-rating should have occurred due to
very small current draw on the batteries. Another minor
issue is the batteries; due to weight concerns AAA
batteries should provide adequate mAh for this flight.
Again, the dependence of wind speed must be
determined in order to achieve good results. They
should be tested for results in different configurations
relative to wind flow, i.e. parallel to wind flow or
perpendicular, etc. as well as tested in different areas
for different conductivities. Wind flow should also be
incorporated into system testing if necessary.
Finally, the issue of the reset voltage must be
addressed. Both condensers consistently reset in all
system tests, however during flight they did not. One of
the condensers also intermittently and should be
addressed. Procedures for working with the condensers
are advisable in order to prevent stray electric charges
or residue from affecting them and the sensitive
circuitry near them.
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