A.2.2.10 Tracking Considerations
pg. 1
Tracking Considerations:
The ground tracking code was written by Timothy Lorenzana for the purpose of graphical
representation of our ground track signal projection capabilities of the designed
telecommunications system. The computational computer language used was MATLAB.
The code works by using trajectory data and simplified signal theory in order to calculate
a ground signal path and coverage area for the system.
Simple Signal Theory
For this we assume that the Earth is spherical in shape and area where the signal
intercepts the Earth is assumed to be circular. We also assume that the signal is always
being directed towards the Earth throughout its flight while neglecting any antenna
mounting errors or design issues. We also neglect any atmospheric anomalies which may
refract or turn the signal, an example of which being clouds. Our design uses a directional
antenna and we assume the projected signal to be cone shaped. Next we used our Signal
Theory and described the simple geometry seen in Fig. 2.2.10.1. From here we are able to
derive the position and signal coverage area as a function of altitude.
Fig. 2.2.10.1: Signal cone geometry.
(Timothy Lorenzana)
Author: Timothy Lorenzana
A.2.2.10 Tracking Considerations
pg. 2
The radius (r) of the signal coverage is calculated using Eq. (2.2.10.1) below.

r  h tan( )
2
(2.2.10.1)
Where r is the radius in kilometers, h is the altitude in kilometers, and γ is the signal beam width angle in
degrees.
The conversion constant (const.) between kilometers and degrees is calculated using Eq.
(2.2.10.2) below.
const. 
2REarth
360
(2.2.10.2)
Where const. is the conversion constant in kilometers per degree, and REarth is the radius of the Earth in
kilometers.
The longitudal coordinate (x) of the signal position is calculated using Eq. (2.2.10.3)
below.
x  r cos( ) / const .
(2.2.10.3)
Where x is the longitudal coordinate in degrees, r is the signal coverage radius in kilometers, θ is a vector
which ranges from 0 to 360 degrees, and const. is the conversion constant in kilometers per degree.
The latitudal coordinate (y) of the signal position is calculated using Eq. (2.2.10.4) below.
y  r sin(  ) / const.
(2.2.10.4)
Where y is the latitudal coordinate in degrees, r is the signal coverage radius in kilometers, θ is a vector
which ranges from 0 to 360 degrees, and const. is the conversion constant in kilometers per degree.
The signal coverage area (A) is calculated using Eq. (2.2.10.5) below.
A  r 2
(2.2.10.5)
Where A is the signal coverage area in square kilometers, and r is the signal coverage radius in kilometers.
Author: Timothy Lorenzana
A.2.2.10 Tracking Considerations
pg. 3
SB-HA-DA-DA
A complete ground track for the small payload launch vehicle is seen in Fig. 2.2.10.2
Fig. 2.2.10.2: Orbit ground track for SB-HA-DA-DA
(Timothy Lorenzana)
The blue outlines in Fig. 2.2.10.2 represent the Earth’s continents while the red line
shows the ground track for a complete orbit that was achieved. The ground track from
ignition (balloon release at 30km) to orbit (300km) is shown in Fig. 2.2.10.3.
Fig. 2.2.10.3: Track from balloon release to orbit for SB-HA-DA-DA
(Timothy Lorenzana)
Author: Timothy Lorenzana
A.2.2.10 Tracking Considerations
pg. 4
The blue outline viewed in Fig. 2.2.10.3 represents the United States East coast. The red
line represents the ground track from balloon release at 30km until the small payload
launch vehicle reaches orbit at 300km. The green circles represent the signal coverage at
arbitrary instances in time. Although the signals coverage area seems small in
comparison to the land mass, the coverage area is still quite large. An area of
94,247.78km2 is represented by the green circle to the furthest right. Most importantly
from this plot, the final signal coverage area does not contain the entirety of the ground
track. This means that more than one ground station is necessary to cover the entire
ascent of the launch vehicle. Costs concerning the tracking stations are discussed in the
appendix.
Tracking Costs:
Purdue University hosts a ground station located at Purdue’s Airport
Author: Timothy Lorenzana