Lightning Effects and Structure
Analysis Tool (LESAT)
Steve Peters
410-273-7722
steve.peters@survice.com
www.survice.com
What Is LESAT?
• LESAT - Lightning Effects Structure Analysis
Tool
– Computational methodology implemented in MATLAB
to analytically predict actual transient current levels
and voltages on aircraft wiring and structural
elements.
– Assists designers in protecting aircraft against the
indirect effects of lightning strikes.
– Implements the methodology used successfully for
MH-47 lightning analysis.
Outline
•
•
•
•
•
•
Motivation
Objectives
Methodology
Results
Conclusions and Future Work
Questions?
Motivation
• Lightning is a severe threat (up to 200 kA peak).
• More reliance on electronic systems.
• Technology evolution from metallic aircraft
structure to composite structure.
• High cost aircraft-level testing and hazardous
aspect of experiments in laboratories.
Objectives
• Input system geometry in a CAD format.
• Circuit analysis approach - apply Kirchhoff’s
laws to obtain linear equations that can be
solved in matrix form.
• Predict induced currents and voltage drops on
wiring and structural elements.
Lightning Indirect Effects Waveform
• MIL-STD-464C Severe Stroke in both Time and
Frequency Domains
I s  I 0 ( e  t  e   t )
I 0  218810A
  11354s 1
  647265s 1
Why Kirchhoff Rather Than Maxwell?
• Since the source frequency is very low, we have a
Quasi-static (near steady state) situation.
• Dimensions of the conducting network are much
smaller than the wavelength.
• Tool gives good results for aircraft dimensions up to ¼
the wavelength of the maximum frequency.
1 
10
Drawing not to scale
  300m
c  f
c 3x108 m / s
 
 300m
f
1MHz
Code Analysis Methodology
Read Geometry
& Electrical
Characteristics
From Mesh
Files
Calculate
Laplace
Responses
Break Up
Structure Into
Linear
Segments
Calculate
Frequency
Domain
Impulse
Response for
Each Branch
Calculate Time-Domain
Solutions (Induced
Currents and Voltages)
Compute
Resistances
Compute
Impedance
Matrix
Plot
Results
Calculate
Self & Mutual
Inductances
Compute
System of
Linear
Equations
Input Geometry
Example Mesh Geometry Input for a Structure
• Input system CAD geometry as a series of mesh files used to represent skins,
pylons, and other routed cabling and electrical equipment inside the aircraft.
Fundamental Resistance Data
Line/Cable
Resistivity Ω/m
1.
Lines/Cable Resistivity is measured
in Ohms per meter ρ – to get Ohms
use: Rc = ρL
2.
Skin/Mesh Resistivity is measured in
Ohms per square ρ – to get Ohms
use: Rskin = ρL/W
3.
Bulk Resistivity is measured in Ohmmeters ρ – to get Ohms use:
Rbulk = ρL/(WH)
4.
Equivalent resistance for a branch
use:
RADIUS
LENGTH
SKIN RESISTIVITY Ω/□
R = Rbulk X Rskin/(Rbulk + Rskin)
BULK RESISTIVITY Ω-m
LENGTH (L), WIDTH (W), THICKNESS (H)
Attachment Points
lightning
attachment
point
lightning
detachment
point
Model
• Circuit Approach: The airframe is represented by an
equivalent R,L circuit network.
z
I1
Piece of the mesh
has 5 nodes and 4 branches.
B
D
M12
A
M12
L1
R1
R4
M12
L4
R2
I2
C
y
M23
L2
3D representation
Each branch is a
resistive, mutually
inductive circuit
element.
Code calculates
mutual inductances
x
R3
L3
M34
Kirchhoff’s Laws are enforced:
(Rn  jLn )I n  j M nk I k  (En1  En 2 )  0
k
I  0
bk
b connected
to node k
Five-Branch Four-Node Circuit Example
System of linear equations
Is
E1
I L1(jω)
Z11
I1
Z22
I2
I4
Z55
Z44
Z33
Z13 I1  Z 23 I 2  Z33 I 3  Z34 I 4  Z35 I 5
 0,
Z14 I1  Z 24 I 2  Z34 I 3  Z 44 I 4  Z 45 I 5
I L2(jω)
E3

 I3
- I3
 I1
E 2E 3
 E 3 E 4
E 2
E 4
 0,
 0,
 I s ,
I2
 I2
I3
Is
 0,
 0,
I1
E2
E 4
Z12 I1  Z 22 I 2  Z 23 I 3  Z 24 I 4  Z 25 I 5  E 1 E 2
Z15 I1  Z 25 I 2  Z35 I 3  Z 45 I 4  Z55 I 5
I5
E4
Z11 I1  Z12 I 2  Z13 I 3  Z14 I 4  Z15 I 5  E 1
 I5
 I4
 I4
 0,
 Is ,
 I5
 0.
Matrix Notation
 Z
 topology

topology T   I   0 
 E   I 
0
   s 
Ax = b
Number of
Branches
Number of
Nodes
A
Number of
Branches
Number of
Nodes
Z
TopologyT
x
b
I
0
Physics
(square
matrix)
=
Input
Topology
0
E
Is
Output
Reduction To Transformed Currents
Ax  b
 Z 11 Z 12 Z 13 Z 14 Z 15

 Z 12 Z 22 Z 23 Z 24 Z 25
 Z 13 Z 23 Z 33 Z 34 Z 35

 Z 14 Z 24 Z 34 Z 44 Z 45
 Z 15 Z 25 Z 35 Z 45 Z 55

1 0 0 0
 1
 0 1
1 0 1

 0 0 1 1 0
 1 0 0  1  1

1
1
0
0
0
0
0
0
0
0  1   I1 
 
1
0 0 I2 
1  1 0 I3 
 
0
1  1 I4 
1
0  1 I5  
 
0 0 0   E1 
0 0 0  E 2 
 
0 0 0  E 3 
0 0 0   E 4 
0
System reduces to:
branches – (nodes – 1)
transformed currents.
 0

 0
 0

 0
 0

  Is
 0

 Is
 0

























Z11 Z12 Z13 Z14 Z15
1 0
Z12 Z 22 Z 23 Z 24 Z 25 0 1
Z13 Z 23 Z 33 Z 34 Z 35 0
0
Z14 Z 24 Z 34 Z 44 Z 45 0
0
Z15 Z 25 Z 35 Z 45 Z 55 0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0   I1  
0   I 2  


1  I3  
  
0 I4  

0   I5  
  
0   E4  
0   E2  
  
0   E3  
Z 44 Z 45   I 4   Z 34 
Z Z
  I    Z 
55
 45
  5   35 
0 
0 

0 

0 
0 

0 
0 

1 
Solution for Multiple Frequencies
Solution for a specific branch
current at each frequency.
Sn ( jk )  S n Re al ( j )  jS n Im ag ( j )
1  n  # of branch currents
1  k  24
k  2f k
j  s
Branch Current Laplace Transform –
represents the frequency-domain
Transfer function between the
Injected lightning current and the
current of the “victim” component.
bnm s
Sn (s)  ao  
m 1 c s
nm
Time-Domain Solution
I (t )  I o e  t  I o e   t
Lightning Time Dependence
Lightning Laplace Transform
Frequency Domain Transfer Function
Branch Current Laplace Response
Io
Io
I( s)  0 I (t )e dt 

 s  s

 st
bnm s
Sn (s)  a o  
m 1 c s
nm
J n s   Is Sn ( s )
Io 
bnm s 
 Io
J n ( s )  I( s )Sn ( s )  

ao  



m 1 c


s


s
s


nm 
Branch Current Time Dependence


 bnm 
 bnm 
 t
J n (t )  I o e ao   m
 I o e  ao   m



c

1

c

1




nm
nm
 t
 bnm   I o
I o   ct
  m   

e

 cnm   cnm  1  cnm  1
nm
Note the addition of the purely resistive part ao
Cable Inside A Conducting Box
•
•
•
•
•
•
•
Rectangular
volume of material
with dimensions
(13.6m x 2.5m x
2.5m).
Skin Thickness:
1.6mm
Bulk Resistivity:
2.65x10-8 Ohmmeters
Skin Parallel Mesh
Resistivity:
1.35x10-4 Ohms/sq
Skin Perpendicular
Mesh Resistivity:
1.35x10-4 Ohms/sq
Cable Resistivity:
1.728x10-15
Ohms/meter
Cable Radius:
2.54cm
Results for Aluminum Conducting Box
• Blue curve represents
cable current and voltage
drop on cable for blue
bolt strike location.
• Magenta curve
represents cable current
and voltage drop on cable
for magenta bolt strike
location.
Driving
Waveform
Conclusions and Future Work
• Validation: compare calculated results to
experimental data.
• Apply methodology to:
– Ground systems
– Buildings
– Electromagnetic Pulse (EMP) excitation
• Relate predicted Lightning Effects to
structural damage.
Questions?
Steve Peters
410-273-7722
steve.peters@survice.com
www.survice.com