The purpose of this work is to develop a form of Paschen's law that takes into account the flow of gas past electrode surfaces. This work was performed under a NASA Science Innovation Fund (SIF) project at the Kennedy Space Center in collaboration with the University of Central Florida. In 2010 the Electrostatics and Surface Physics Laboratory (ESPL) at the Kennedy Space Center performed an electrostatic safety analysis on the flight termination system (FTS) antenna for the Ares I rocket. Paschen's law, derived by Friedrich Paschen in 1889 to relate sparking voltage to gas pressure and electrode separation, does not take into account the effect of flowing gas between the electrodes. The safety of the FTS housing to triboelectric charging was shown only after extensive laboratory testing. Potential benefits are  of a form of Paschen's law that considers gas velocity. This work is applicable to current and planned rockets and aerospace vehicles and could lead to possible relaxation of electrostatic launch criteria. Launch aborts can cost up to about a million US dollars depending on the vehicle. [ElectroStatic Discharge (ESD)

Ahmed, Kareem

Calle, Luz M.

Cox, Rachel E.

Hogue, Michael D.

Mulligan, Jaysen

Wilson, Jennifer G.

NASA Technical Reports Server

Kennedy Space Center
Revision of Paschen’s Law Relating to the 
ESD of Aerospace Vehicle Surfaces
Day of Launch Working Group Meeting, KSC, April 24, 2019
Michael D. Hogue, PhD, NASA Kennedy Space Center
Rachel E. Cox, NASA, Kennedy Space Center
Jaysen Mulligan, University of Central Florida
Kareem Ahmed, PhD, University of Central Florida
Jennifer G. Wilson, NASA, Kennedy Space Center
Luz M. Calle, PhD, NASA, Kennedy Space Center
1
https://ntrs.nasa.gov/search.jsp?R=20190002818 2019-08-30T20:07:56+00:00Z
Kennedy Space Center
Agenda
• Introduction
• Theoretical Development
− Paschen’s Law
− Mach Number Formulation
− Mach Number and Compressible Dynamic Pressure
− A Hypothesized Effective Discharge Distance
• Wind Tunnel Experiments
− Description of Wind Tunnel Experiments
− Experimental Data
• Future work – 2019 CIF project
• Summary
2
Kennedy Space Center
• The purpose of this work is to develop a form of Paschen’s law that
takes into account the flow of gas past electrode surfaces.
• This work was performed under a NASA Science Innovation Fund
(SIF) project at the Kennedy Space Center in collaboration with the
University of Central Florida.
• In 2010 the Electrostatics and Surface Physics Laboratory (ESPL) at
the Kennedy Space Center performed an electrostatic safety analysis
on the flight termination system (FTS) antenna for the Ares I rocket.*
• Paschen’s law, derived by Friedrich Paschen in 1889 to relate sparking
voltage to gas pressure and electrode separation, does not take into
account the effect of flowing gas between the electrodes.
• The safety of the FTS housing to triboelectric charging was shown
only after extensive laboratory testing.
*M. Hogue, C. Calle, ESPL Report, “Electrostatic Evaluation of the ARES I FTS Antenna 
Materials”, ESPL-TR10-002, August 27, 2010. NASA, Kennedy Space Center.
Introduction
3
Kennedy Space Center
• Potential benefits of a form of Paschen’s law that considers
gas velocity.
– Applicable to current and planned rockets and aerospace vehicles.
– Possible relaxation of electrostatic launch criteria. Launch aborts
can cost up to about a million US dollars depending on the vehicle.
Introduction
4
Kennedy Space Center
• This effort is a first approximation at deriving a
generalized form of Paschen’s law to include gas velocity.
• We have theoretically derived a candidate revision of
Paschen’s law.
– Uses the Mach number as a mitigating factor on the number of
electron – ion pairs between the electrodes.
– Compressible dynamic pressure terms were incorporated.
– Hypothesized an apparent discharge path along the velocity
profile.
Theoretical Development
5
Kennedy Space Center
• Paschen’s law
• Nomenclature:
Paschen’s Law
𝑉𝑉𝑠𝑠 = 𝑉𝑉𝑖𝑖𝐿𝐿𝑃𝑃𝑎𝑎 𝑃𝑃𝑃𝑃
𝑙𝑙𝑙𝑙 𝑃𝑃𝑃𝑃 − 𝑙𝑙𝑙𝑙 𝐿𝐿𝑃𝑃𝑎𝑎𝑙𝑙𝑙𝑙 1 + 1𝛾𝛾
Vs Sparking discharge potential (Volts)
Vi Ionization potential of the ambient gas 
(Volts)
P Gas pressure (torr)
d Electrode separation (cm)
Pa Atmospheric pressure at sea level (760 torr)
L Mean free path at sea level (6.8 × 10-6 cm)
γ Secondary electron emission coefficient of 
the electrode metal
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Kennedy Space Center
• Hypothesis: The loss of electron – ion pairs due to gas velocity
can be expressed by a dimensionless aerodynamic term such as
the Mach number.
• The model equation must revert to Paschen’s law when the mean
gas velocity, vxm = 0.
• The Mach number is the ratio of the mean gas velocity to the
speed of sound, MN = vxm/c. Here c = 319 m/s at sea level.
• Using the Mach number to mitigate the concentration of electron
– ion pairs in the derivation of Paschen’s Law we have
• This equation reverts to Paschen’s law when vxm = 0.
Mach Number Formulation
7
𝑉𝑉𝑠𝑠 = 𝑉𝑉𝑖𝑖𝐿𝐿𝑃𝑃𝑎𝑎 𝑃𝑃𝑃𝑃
𝑙𝑙𝑙𝑙 𝑃𝑃𝑃𝑃 − 𝑙𝑙𝑙𝑙 𝐿𝐿𝑃𝑃𝑎𝑎𝑙𝑙𝑙𝑙 1 + 1𝛾𝛾 −𝑀𝑀𝑁𝑁
Kennedy Space Center
• For moving vehicles, pressure has two components
– Static pressure: Ps
– Compressible dynamic pressure: PDC
• Above Mach 0.3 the compressible form of the dynamic 
pressure must be used.
• Total pressure 
Mach Number and Compressible Dynamic Pressure
𝑃𝑃𝐷𝐷𝐷𝐷 = 𝑃𝑃𝑠𝑠 1 + 𝛾𝛾𝑎𝑎 − 12 𝑀𝑀𝑁𝑁2 𝛾𝛾𝑎𝑎𝛾𝛾𝑎𝑎−1 − 1
𝑃𝑃 = 𝑃𝑃s + 𝑃𝑃𝐷𝐷𝐷𝐷 = 𝑃𝑃s + 𝑃𝑃𝑠𝑠 1 + 𝛾𝛾𝑎𝑎 − 12 𝑀𝑀𝑁𝑁2 𝛾𝛾𝑎𝑎𝛾𝛾𝑎𝑎−1 − 1
8
𝑃𝑃 = 𝑃𝑃𝑠𝑠 1 + 𝛾𝛾𝑎𝑎 − 12 𝑀𝑀𝑁𝑁2 𝛾𝛾𝑎𝑎𝛾𝛾𝑎𝑎−1
γa ≡ Ratio of Specific Heats = CP/CV
Kennedy Space Center
• Substituting the total pressure in the model equation gives
for the sparking voltage
• This equation also meets the requirement that Paschen’s
law is returned when the mean gas velocity is zero.
• In this equation, the sparking voltage is a function of three
variables: static pressure, electrode separation, and Mach
number
Mach Number and Compressible Dynamic Pressure
9
𝑉𝑉𝑠𝑠 = 𝑉𝑉𝑖𝑖𝐿𝐿𝑃𝑃𝑎𝑎 1 + 𝛾𝛾𝑎𝑎 − 12 𝑀𝑀𝑁𝑁2
𝛾𝛾𝑎𝑎
𝛾𝛾𝑎𝑎−1 𝑃𝑃s𝑃𝑃
𝑙𝑙𝑙𝑙 1 + 𝛾𝛾𝑎𝑎 − 12 𝑀𝑀𝑁𝑁2 𝛾𝛾𝑎𝑎𝛾𝛾𝑎𝑎−1 𝑃𝑃s𝑃𝑃 − 𝑙𝑙𝑙𝑙 𝐿𝐿𝑃𝑃𝑎𝑎𝑙𝑙𝑙𝑙 1𝛾𝛾 + 1 −𝑀𝑀𝑁𝑁
𝑉𝑉𝑠𝑠 = 𝑓𝑓 𝑃𝑃𝑠𝑠,𝑃𝑃,𝑀𝑀𝑁𝑁
Kennedy Space Center
The model equation is graphed for stainless steel electrodes (γ = 0.02) at various
Mach numbers for air (γa = 1.4) between 0.5 and 3.75 and a gap of 1.3 cm.
Theoretical Comparison
10
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
0.00 0.01 0.10 1.00 10.00 100.00 1,000.00
D
is
ch
ar
ge
 V
ol
ta
ge
 (V
s)
Pd (Torr ⋅ cm)
Comparison of Theoretical Paschen Curves for Various MN
Paschen's Law Mach 1 Mach 1.75 Mach 2 Mach 3.25
Mach 3.5 Mach 3.75 Mach 0.5 Mach 1.5
Kennedy Space Center
Gap: 4.4 cm, Gas: air, Gas velocity: Mach 1.47
A Hypothesized Effective Discharge Path
0
5
10
15
20
25
30
35
40
45
50
0 100 200 300 400 500
Y
 (M
M
)
VELOCITY (M/S)
Velocity  Profi le
Length of velocity profile measured to be
~ 11.7 cm from full scale print.
Wind tunnel velocity profile data
provided by UCF.
11
• From inspection of the model equation,
we can hypothesize an effective electrode
separation
• For air: γa = 1.4. At Mach 1.47 and d =
4.4 cm this gives a value of d’ of 15.48 cm
or only about 25% larger than the
measured value.
• Additional experiments will be needed to
better evaluate this hypothesis.
𝑃𝑃′ = 1 + 𝛾𝛾𝑎𝑎 − 12 𝑀𝑀𝑁𝑁2 𝛾𝛾𝑎𝑎𝛾𝛾𝑎𝑎−1 𝑃𝑃
Kennedy Space Center
• Wind tunnel experiments were performed at the Florida
Center for Advanced Aero-Propulsion (FCAAP) of the
University of Central Florida (UCF)
• An existing wind tunnel was modified to incorporate a
stainless steel electrode plate attached to a movable sting
mount in the test section.
Description of Wind Tunnel Experiments
12
Kennedy Space Center
Description of Wind Tunnel Experiments
13
• The upper portion of the test section
was also made from stainless steel
and acted as the ground plate.
• 1.3 cm was the closest the electrode
could be physically placed to the
stainless steel upper surface.
• The test section was instrumented to
input DC voltage to the electrode,
measure static pressure, Ps, mean
velocity, vxm, and to provide video of
the experiment.
• A high speed camera was used with a
Schlieren system to capture images
of the supersonic shocks around the
electrode.
Kennedy Space Center
Description of Wind Tunnel Experiments
Typical shocks around the electrode.
Mach 3.5
High level schematic of the wind
tunnel experimental setup.
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Kennedy Space Center
Description of Wind Tunnel Experiments
15
• Two types of experiments were performed.
– Under steady supersonic flow, the electrode voltage was ramped
up to observe and record any sparking.
– Preload the electrode to achieve sparking during no-flow
conditions, then turning on the wind tunnel to observe the effects
of the supersonic flow.
• The voltage ramping experiments were difficult
– short duration of steady supersonic flow (< 30 seconds)
– shock reflections between the electrode and the wall of the test
section affected pressure measurements.
– High voltage supply was limited to about 35 kV due to the rating
on the high voltage cabling that could fit through the sting mount.
Kennedy Space Center
Description of Wind Tunnel Experiments
16
• A new instrumented test
section was attached to
the wind tunnel.
– Pressure sensing port
located to more accurately
measure static pressure
between the electrodes.
– Located further down the
tunnel to mitigate air
turbulence.
• Experiments were run at
Mach 1.65 for this test
section.
Kennedy Space Center
• Video data shows sparking quenched by the onset of
supersonic flow consistent with the theoretical model.
• Noted that the shape of the deformation of the spark prior
to quenching is convex in appearance.
Experimental Data
Air flow direction
Sparking Start of supersonic 
flow
Sparking quenched Sparking resumes 
after supersonic flow 
ends
17
Kennedy Space Center
• Two of the eleven Mach 1.65
experiments yielded measurable
sparks during supersonic flow.
• These two data points compare
well to the theoretical model
with both the Mach number and
compressible dynamic pressure
terms.
Experimental Data
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
0.001 0.010 0.100 1.000 10.000 100.000 1000.000
D
is
ch
ar
ge
 V
ol
ta
ge
 (V
s)
Pd (torr ⋅ cm)
Model Equation Comparison to Paschen's Law and Experimental Data 
(Mach 1.65, d = 1.3 cm)
Paschen's Law Vs (Volts)
Model Equation with Mach Number & Comp. Dynamic Pressure Vs (Volts)
Exp. Data Vs (Volts)
18
Kennedy Space Center
• Recent award of a FY 2019 Center Innovation Fund (CIF)
project is continuing this work (project start 3/1/19).
• Theoretical work underway to put the model equation into a
form that includes ambient temperature.
• New wind tunnel experiments under design
– Develop LabView™ control program
– Design and fabricate new wind tunnel test sections to lessen shock
reflections. The upper and lower panels will be the HV electrode and
ground respectively.
– Both voltage ramp and spark quenching experiments planned.
– Gather more velocity profile data to better evaluate the hypothesized
effective discharge distance.
Future Work
19
Kennedy Space Center
• A first approximation theoretical model equation based on
Paschen’s law was developed to account for the effect of
gas flow on the sparking voltage.
• An effective discharge distance due to gas velocity was
hypothesized based the theoretical model and limited wind
tunnel test data.
• Wind tunnel experiments were conducted that gave results
consistent with the prediction of the model equation.
• Further theoretical revision of the model equation and
wind tunnel experimentation via a KSC CIF project are
underway.
Summary
20
Kennedy Space Center
• The authors would like to thank the NASA Science
Innovation Fund (SIF), the Center Innovation Fund (CIF),
and the Kennedy Space Center (KSC) for their support.
• The authors would like to give special thanks to Dr. Carlos
Calle, Mr. Michael Johansen, Mr. James Phillips, and Mr.
Paul Mackey of the Electrostatics and Surface Physics
Laboratory (ESPL) at KSC for their suggestions, reviews,
and helpful comments on this work.
Acknowledgements
21


Revision of Paschen's Law Relating to the ESD of Aerospace Vehicle Surfaces

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