A.2.2.11 Tracking Considerations1
A.2.2.11Tracking Considerations:
We used theground tracking code for this analysis. The code provides anunderstandingof our signal projection capabilities forour telecommunications system design.The code works by using trajectory data and a simplified signal theory in order to calculate a ground signal path and coverage area for the system. The signal analysis will tell us and where the listening stations need to be in order to pick up the signal that is being broadcast from the launch vehicle.
For the simplified signaltheory we make a few initialassumptions. First, we assume that the Earth is spherical in shape. Second, we assume that the area where the signal intercepts the Earth is circular. Third, we neglect any antenna mounting errors or design issues.Fourth, we neglect any atmospheric anomalies which may refract or turn the signal, an example of which being clouds.
Fig. A.2.2.11.1shows the propagation of a directional and omnidirectional antenna. The telecommunications system design uses a cluster of directional antennas. However as stated in section A.2.2.2 of this report, we can assume the cluster of directional antennas to propagate as an omnidirectional antenna.Therefore we will be using the omnidirectional antenna to perform the ground tracking analysis. Finally, to perform this analysis we use one additional assumption. We assume the propagation from an omnidirectional antenna to be spherical in shape. Fig. A.2.2.11.2 defines the signal geometry that we use to perform our analysis.
Fig. A.2.2.11.1:Antenna assumptions.
(Timothy Lorenzana)
Fig. A.2.2.11.2: Signal cone geometry.
(Timothy Lorenzana)
Eq. A.2.2.11.1 defines the variable θ in Fig. A.2.2.11.2
(A.2.2.11.1)
where h is the altitude of the launch vehicle, and S is a line from the origin of the signal to the point of contact where the maximum path length of the signal touches the Earth. The path length is a constant and was determined from the link budget analysis in section A.2.2.3 of this report.
Eq. A.2.2.11.2 defines the radius of the circle where the signal touches the Earth
(A.2.2.11.2)
where r is the radius of the circle where the signal touches the Earth, and S is a line from the origin of the signal to the point of contact where the maximum path length of the signal touches the Earth.
Combining Eq. A.2.2.11.1 and Eq. A.2.2.11.2, we get Eq. A.2.2.11.3 defined below
(A.2.2.11.3)
where r is the radius of the circle where the signal touches the Earth, S is a line from the origin of the signal to the point of contact where the maximum path length of the signal touches the Earth, and h is the altitude of the launch.
In order to plot the signal propagation where the signal intercepts the Earth, a conversion constant is needed. The conversion constant converts between kilometers and degrees. the conversion constant is calculated using Eq. A.2.2.11.4 defined below
(A.2.2.11.4)
where c is the conversion constant in kilometers per degree, and REarthis the radius of the Earth in kilometers.
The longitude coordinate of the signal position is calculated using Eq. A.2.2.11.5 below
(A.2.2.11.5)
where x is the longitude coordinate in degrees,r is the signal coverage radius in kilometers,γis a vector which ranges from 0 to 360 degrees, and c is the conversion constant in kilometers per degree.
The latitude coordinate of the signal position is calculated using Eq. A.2.2.11.6 below
(A.2.2.11.6)
where y is the latitudecoordinate in degrees,r is the signal coverage radius in kilometers,γ is a vector which ranges from 0 to 360 degrees, and c is the conversion constant in kilometers per degree.
The longitude and latitude coordinates of the signal position, x and y respectively, are then added to the ground track longitude and latitude coordinates. Adding the two coordinates together will result in a signal path that will change as the launch vehicle ascends. The ground distance covered during vehicle ascent is then calculated by subtracting the position when the vehicle reaches orbit from the position when the vehicle is released from the balloon.
The longitude and latitude coordinate of the signal position, x and y respectively, are then added to the ground track longitude and latitude coordinates. Adding the two coordinates together will result in a signal path that changeswhen the launch vehicle moves.
The signal coverage area is approximated using Eq. A.2.2.11.7 below
(A.2.2.11.7)
where A is the approximated signal coverage area in square kilometers, and rn is the final signal coverage radius in kilometers.
These equations result in the information needed to determine a ground track analysis.
A ground track for the 200gpayload launch vehicle is shown in Fig. A.2.2.11.3. A ground track for the 1kg payload launch vehicle is shown in Fig. A.2.2.11.4.A ground track for the 5kg payload launch vehicle is shown in Fig. A.2.2.11.5.
Fig. A.2.2.11.3:Track from balloon release to orbit for 200g payload launch vehicle.
(Timothy Lorenzana)
Fig. A.2.2.11.4:Track from balloon release to orbit for 1kg payload launch vehicle.
(Timothy Lorenzana)
Fig. A.2.2.11.5:Track from balloon release to orbit for 5kg payload launch vehicle.
(Timothy Lorenzana)
The blue outlineviewed in Fig. A.2.2.11.3, Fig. A.2.2.11.4, and Fig. A.2.2.11.5represents the North, the South, and the Central Americas. The red line in
Fig. A.2.2.11.3, Fig. A.2.2.11.4, and Fig. A.2.2.11.5 represents the ground track from balloon release until the launch vehicle reaches orbit. The distance from blueuntil red in Fig. A.2.2.11.3, Fig. A.2.2.11.4, and Fig. A.2.2.11.5 represents the drift distance covered by the balloon. The green circles in Fig. A.2.2.11.3, Fig. A.2.2.11.4, and Fig. A.2.2.11.5 represents the signal coverage areas at arbitrary instances in time. Since the signal coverage areas are quite large and overlap extensively, the total coverage area for each launch vehicle are approximated as the initial coverage area.
Most notably in Fig. A.2.2.11.3, Fig. A.2.2.11.4, and Fig. A.2.2.11.5, the final signal coverage area contains the entire ground track. This means that only one ground station is necessary to cover the entire ascent of the launch vehicle. Existing ground tracking station locations were researched. However due to time constraints no optimization concerning the ground station location was performed. In order to receive from the vehicle during ascent, any location within the initial green circle is assumed to an adequate ground station location. Costs concerning the tracking station are discussed in appendix 9.2.1.1.
Table A.2.2.11.1 below gives the balloon drift distance from ground release until each launch vehicle separates from the balloon.
Table A.2.2.11.1 Balloon Drift DistanceLaunch Vehicle Payload / Drift Distance / Units
200 g / 120.74 / km
1 kg / 120.45 / km
5 kg / 121.74 / km
Footnotes: Balloon drift is discussed in another section of this report.
Table A.2.2.11.2 below gives the ground distance covered for each of the launch vehicles ascent.
Table A.2.2.11.2Ground Distance CoveredLaunch Vehicle / Ground Distance / Units
200 g / 236.10 / km
1 kg / 355.16 / km
5 kg / 215.12 / km
Footnotes:The 1kg payload launch vehicle takes longer to reach orbit, thus the ground distance covered is larger than its counterparts.
Since each of the altitudes at which the launch vehicle separates from the balloon, the signal coverage area is approximated equally for each vehicle. The approximate signal coverage area is presented to be 78,536,000 km2.
Author: Timothy Lorenzana