Finite-difference time-domain modeling of ultra-high frequency
antennas on and inside the carbon fiber body of a solar-powered electricvehicleKatherine Han1, Paul Freeman2, Hai-Yue Han3, Jacob Hamar4, James F. Stack, Jr.5
1

School of Chemical, Biological, and Environmental Engineering
Oregon State University, Corvallis, OR 97331, USA
2

School of Electrical Engineering and Computer Science
Oregon State University, Corvallis, OR 97331, USA
3

Inspired Light, Llc., Corvallis, OR 97330

4

School of Mechanical, Industrial, and Manufacturing Engineering
Oregon State University, Corvallis, OR 97331, USA
5

Remcom, Inc.
315 S. Allen St., Suite #416, State College, PA 16801, USA

This paper was presented at ACES 2013, the annual conference of the Applied
Computational Electromagnetics Society

Abstract - Finite-difference time-domain
simulations are performed on a 900 MHz band
antenna inside and outside the carbon fiber bodyof a solar-powered electric vehicle. Data are
analyzed to determine the optimal antenna
placement for transmission to a receiving antenna
located toward the rear of the solar vehicle.
Modeling data are compared to experimental
results. Computational fluid dynamics are used todetermine acceptability of external antenna
placement. It is found that the ideal antenna
would be inside the vehicle’s body and oriented
vertically, but that the portion of the bodysurrounding the antenna must be constructed of anon-conductive material.
Index Terms - FDTD, vehicle antenna modeling,
antenna CFD

I. INTRODUCTION
Since the first World Solar Challenge in 1987
student groups and others from around the world
have been designing, building, and racing solarpowered electric vehicles. These vehicles,
primarily one-person, three-wheeled vehicles aredesigned to travel during the daylight hours for
one to two weeks across 1200 to 2400 miles while
only charging their batteries from their solar
array. During this race the solar vehicle is flanked
in front and back by lead and chase vehicles inorder to protect the solar vehicle.
Radio communication, both audio andtelemetry data, is required between these vehicles
to enhance safety and racing strategy. The
telemetry receiving antenna is usually locatedbehind the solar vehicle in the chase vehicle.
Over the last two decades radio and cell
phone communication in passenger vehicles has
been studied by several types of modeling andexperimentation [1]. Applications from modelingand experimentation include installing miniatureprinted magnetic phonic crystal antennas into
vehicular platforms and studying the effects ofsignal bounce and attenuation on vehicles inurban environments [2, 3]. Modeling methods
have included method of moments (MoM) [4-8],
geometric theory of diffraction (GTD) [9], finiteintegration (FI) [10, 11], and finite-differencetime-domain (FDTD) [12]. All of these methods
require significant computer resources to solve
and report the field strength or gain patterns andpolarization information of antenna signals
within or around a vehicle. FDTD is a simple andaccurate approach to a differential numericalsolution of Maxwell’s curl equations [13]. The
FDTD method allows simulation of complex
geometric shapes, uses no linear algebra, isaccurate and robust, treats impulsive or nonlinear
behavior naturally, is a systematic approach tomodeling, and is becoming increasingly powerful
as computing resources improve [13].
The FDTD method was first described in1966 by Yee [14]. This research proposed what is
now known as the Yee cell, a method of gridding
a physical model in order to solve alternately forthe electric and magnetic fields in the modelingspace as the simulation steps through time. Thismethod is a numerical solution to Maxwell’s curl
equations, which describe the behavior of theelectric and magnetic fields of EM radiation in
one, two, or three dimensions. Until recently mostthree dimensional simulation methods, including
FDTD, were too computationally demanding tosimulate large models. However, advances inpersonal computing technology have enabled
highly accurate modeling of complicatedstructures in three dimensions.
This study uses Remcom’s XF 7.3.0 software
to simulate the electromagnetic fields around the2012 Oregon State University solar vehicle
resulting from a 900 MHz band antenna. Antenna
placement is explored. The goal of theinvestigation is to determine the optimal antenna
placement for data transfer to the chase vehicle
during the solar vehicle competitions. To
determine effects of antenna location on vehicle
efficiency, all simulations with external antenna

locations are also analyzed for aerodynamic
effects using computational fluid dynamics.
II. METHODSFDTD simulations were carried out using
Remcom’s XF 7.3.0 software. A PEC monopole
antenna with a center frequency of 915 MHz wasmodeled to represent the antenna of the FLC910E
Ethernet radio from Data-Linc Group. The solar
vehicle body, titanium frame, and human driver
were modeled in XF, with the vehicle bodymodeled as a thin carbon fiber shell with aconductivity of 2 x 105 S/m [15]. The antenna was
fed with a 50 ohm voltage source excited at 915
MHz. Outer boundary conditions were all set toperfectly matched layer (PML) conditions withseven absorbing layers. Far field sensors wereused to detect realized gain. Realized gain is thegain of the antenna reduced by impedancemismatch losses. This allows for a consistent,
qualitative comparison of system performance
between potential antenna locations. Solidworks
Flow Simulation 2013 was used to perform thecomputational fluid dynamics (CFD) for 50 mph
air flow. A computational domain that is 80
meters long, 20 meters wide and 6 meters tall was
setup with a velocity opening in the front of thevehicle, a ground plane with moving air below thevehicle and environment (1 atmosphere at STP)
pressure openings on the remaining sides of thecar. The vehicle was located 30 meters from thefront of the opening, centered width wise, andwas placed 6 inches above ground for groundclearance.
Experimental results were obtained byrecording signals around the frequencies ofinterest (900-912 MHz) for five seconds of datausing a Terratec T Stick software defined radio.
The software defined radio antenna was oriented
vertically for all vertical antenna positions andhorizontally for all horizontal positions.
Measurements were taken at twelve evenly
spaced locations around the car, fifteen feet fromthe center of the vehicle. The vehicle and allantennas were in the center of a field away fromany other buildings or significant metal objects.
Normalized average power was computed foreach data point by

𝐴 2

𝑃 = 10𝑙𝑜𝑔 ([ ]) ,(1)where P is the normalized average power at aparticular XY point and antenna position, A is theamplitude of the FFT under those conditions, andN is the normalization factor, or the average
amplitude of the FFT of all twelve XY points forthe top vertical antenna position.
𝑁

III. RESULTS
Six different antenna positions were analyzed
for their gain patterns (see Figure 1). The “InsideBack” position is the location of the antennaduring the 2012 American Solar Challenge.
“Inside Front” is a proposed internal position forimproving gain toward the receiver. The “Top”
and “Back” positions are proposed external
positions that are likely to improve the gain but
could potentially increase aerodynamic drag.
Both horizontal and vertical orientations areanalyzed at these external locations. Verticallypolarized realized gain plots were analyzed foreach antenna location in the XY, YZ, and XZ
planes (Figures 2, 3, and 4). Special attention was
paid to transmission toward the rear of thevehicle, as that is the location of the receiving
antenna in the chase vehicle during highway
races. To address concerns of increased
aerodynamic drag due to antenna placement
outside the vehicle, computational fluid dynamics(CFD) was performed on the vehicle with andwithout external antennas. For EM safety

analysis, SAR data is considered for each antenna
position.

Fig. 1. Locations of antenna in and on thesolar vehicle body. Positions “Inside Back” and“Inside Front” are inside the body and are bothvertical antennas. Positions “Top” and “Back”
are outside and are analyzed for both vertical andhorizontal antennas. Colors of the numbers in thisfigure correlate to the colors of the lines in
Figures 2, 3, and 4.

Fig. 2. XY cut of a theta-polarized realized gain plot for six antenna positions.
Realized gain was analyzed for antennas
located inside the solar vehicle’s body. “InsideBack” is the antenna placement during the 2012
American Solar Challenge and “Inside Front” isa proposed improved antenna location that iscloser to the windshield (see Figure 1), bothmodeled in a vertical orientation. It was foundthat for both internal antenna locations the signal
strength toward the rear of the vehicle wassignificantly attenuated when observing both the
XY and YZ realized gain plots compared toexternal antenna locations (see red and blue lines
in Figures 2 and 4, respectively). In the XZ gain
plot the Inside Back antenna displays a null at 270
degrees (toward the right of the vehicle; see
Figure 4), which may explain some of thecommunication difficulty when the car is racing
on a track and the receiver is stationary.
Transmission in all directions of the XY plane isimportant during track races. The internalantennas were both found to have relatively highgains toward the top of the vehicle (see Figs. 3
and 4).
In an attempt to increase signal strength
toward the rear of the vehicle, vertically-oriented
antennas were modeled at the top of the vehicle
and the center back of the vehicle (see Figure 1).
These vertical external antennas both showedsignificantly increased gain toward the right andleft of the vehicle, with the Top antenna being thestrongest transmitter (see the solid green line in
Figures 2 and 3).

Fig. 3. YZ slice of theta-polarized realized gain plot for the six antenna positions.
With the prediction that they would cause lessaerodynamic drag than vertical antennas, horizontal
antennas in these two external locations weremodeled for their signal gain and aerodynamics.
Computational fluid dynamics (CFD) modeling
was performed on the bare solar vehicle body aswell as the body with each of the four externallylocated antenna positions. It was found that allantenna positions had negligible drag impact on the
car at 50 mph, as determined by CFD. Also, as seenin the dotted lines of Figure 2, the signal gain in the
XY direction for a horizontally polarized antenna is
not as strong as for the vertically polarized

antennas, making horizontal antennas doubly
undesirable.
SAR data were analyzed to determine theenergy absorbed by a 147 lb human phantom in thedriver’s seat for each antenna position. All externalantenna locations resulted in no energy absorbed.
The Inside Front and Inside Back positions
produced peak absorption of 4 and 2 mW/kg,
respectively (both averaging about 2 mW/kg). If the
carbon fiber backing on the seat is removed theenergy absorbed from the antenna located in the
Inside Back location increases to a peak 1 g average
SAR of 170 mW/kg.

Fig. 4. XZ slice of theta-polarized realized gain plot for the six antenna positions.
Experimental results were obtained using asoftware-defined radio. To make the modeling
results more comparable to the experimental
results, modeling results were reported for thepolarization that matches the transmitting antennaorientation; theta polarized data are reported forvertical antenna positions and phi results arereported for horizontal antenna positions (see Fig.
5A). Experimental results were obtained with thereceiving antenna in the same orientation as thetransmitting antenna in or on the car. As seen withthe modeling results, external vertical antenna
positions were by far the strongest locations, withthe overall strongest transmitting position being the
top vertical (see Fig. 5B). Although we had
expected that the inside antenna positions would beleast powerful we found that the positions with thelowest transmission were the inside front andoutside back horizontal. The top horizontal antenna
position performed better than expected. The
location of the antenna during the 2012 American

Solar Challenge, the inside back, was found to be a
mediocre position, a stronger performer at allmeasured locations in the XY plane than the inside
front, but generally weaker than external verticalantennas.
IV. DISCUSSION
The telemetry antenna modeled in this study isrequired to transmit data between the solar vehicle
and its chase vehicle, which is located toward thesolar vehicle’s rear during cross country races andanywhere in the XY plane during track races. Six
antenna positions were studied to assess their signal
strength and aerodynamic drag for purposes ofchoosing the best antenna position and orientation
for racing conditions. The optimal antenna position
would be one where the signal strength is hightoward mainly the rear but also the sides and frontof the vehicle and the aerodynamic drag is not
significantly increased.

It was found that although externally placed,vertical antennas are most effective at transmitting
signal toward the rear of the vehicle. The body ofthe solar vehicle is designed to hold the solar array,
contain the driver and electronics, and have as little
aerodynamic drag as possible. This is done byminimizing both the frontal cross sectional area andlow pressure regions on the back side of any
structures in the vehicle. The antenna modeled here

does not appear to contribute a detectable amountof drag by Solidworks 2013 Flow Simulation.
Experimental studies have shown that vehicle
antennas typically produce approximately 1N ofdrag force, which would be approximately 23W ofpower loss [16]. Although this is a significant
amount of drag in solar car racing (23 W of dragcould decrease average speed by 0.5 or 1 mph), it is
not accurately detectable using CFD.

Fig. 5. XY slice of realized gain from modeling (A) and normalized average power from experimental
measurements (B).
Modeling and experimental results suggest thatthe proposed internal antenna position, “Internal
Front,” was not any better for transmission in the
XY plane than was the original “Internal Back”
position. Experimental results confirmed that, infact, the “Internal Front” position was a worse
location for the transmitting antenna than “Internal
Back.”
Simulations suggest that horizontal positioningof the antenna on the outside of the vehicle wasfound to improve neither the aerodynamics nor thesignal transmission in the XY plane, which is theplane of interest to receivers at ground level. The
signal transmission of a horizontal antenna is
expected to be reduced in the horizontal direction.
The two horizontal antenna positions modeled did
show a higher gain toward the +z axis (above thevehicle), but this information is only useful if one

were interested in detecting the signal from thespace above the vehicle. Experimental results in the
XY plane indicate that horizontal orientation of theantenna in the back of the vehicle is highly
discouraged, while a horizontal antenna on the topof the vehicle produced higher than expected signal
strength.
Discrepancies between modeled and simulated
results could come from several factors. In thesimulation the car was modeled in free space,
without ground underneath, while duringexperiments the car was in a field. The simulation
did not include every component currently on thecar; there are several electronic and some small
mechanical systems that were not practical tosimulate.
SAR data indicate that all antenna locations arevery much below the FCC safety limit of 1600

mW/kg peak 1 g averaged SAR (80 mW/kg wholebody average SAR). The carbon fiber seat back had
a significant effect on energy absorbed by thedriver; removal of the seat back increased the peakenergy by more than 40x, resulting in an energy
absorption that is about 10% of the FCC limit. Thus
the internal configuration of the vehicle could affectthe safety of the antenna, especially if multiple
antennas are to be considered.
It is concluded that two of the proposed antenna
positions will satisfy both of the design constraints
of increased XY transmission and low aerodynamic
drag compared to the original placement used in the2012 American Solar Challenge. Future
improvements of the vehicle would include
incorporating a vertical antenna inside the body ofthe vehicle but in an area that is free of conductive
carbon fiber. Other solutions to explore areantennas incorporated into the composite structureof the car’s body surrounded by non-conductive
materials. The simulation and modeling data arefound to be in enough agreement to help thedesigners engineer better communications in futurerevisions of the vehicle.
ACKNOWLEDGEMENT
Special thanks to Remcom, Inc. for theirsupport of the Oregon State University Solar
Vehicle Team and their assistance with this paper.
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Katherine Han is currently a Ph.D.
student in the School of Chemical,
Biological, and Environmental
Engineering at Oregon State
University. She is a co-founder of
the OSU Solar Vehicle Team andhas served as graduate student
president in her department. Kat is currently the lab
manager for the Oregon Process Innovation Center.

Jacob Hamar is currently a juniorof mechanical engineering at
Oregon State University. He is
working as a controls engineer at
Daimler Trucking North America
and is co-captain of the Oregon
State University Solar Vehicle
Team. Jacob’s interests include water desalination,
aerospace and energy technology.

Paul Freeman is a senior incomputer science at Oregon State
University.
His
educationemphasizes cognitive science,
artificial intelligence, computer
ethicsandgoal-directedcomputation. He is a member ofAmerican Mensa, the Upsilon Pi Epsilon honor society
for Computing and Information Disciplines, and theOSU Solar Vehicle Team. He has worked as a software
engineering intern for Intel and Garmin AT. Whileattending classes, Paul works as a teaching assistant for
freshman level computer science students. In addition tohis computer science background, Paul earned an
Associates of Applied Arts in Graphic Design at
Portland Community College.

James F. Stack, Jr. received aB.S.
degreeinelectricalengineering from the Pennsylvania
State University in 2001 and an
M.E.
degreeinsystems
engineering from the Pennsylvania
State University in 2010. He has worked for Remcom,
Inc. since 2000 where he currently manages theapplications engineering department. His researchinterests include high performance computing(SSE/AVX vectorization, GPGPU, MPI and threading)and using optimization techniques to achieve novel RF
structures.

Dr. Hai-Yue Han received his
Ph.D. in electrical engineering at
Oregon State University. He is aco-founder of the Oregon State
University Solar Vehicle Team andhas built three solar powered cars at
OSU. He currently works as thelead balance of systems engineer at Inspired Light.