## 3 Mission Operations
### Flight Predictions
#### 3.2.2 Modeling of the Horizontal Motion  
The horizontal motion is modelled assuming that the \(x\) and \(y\) components of the HAB velocity are equal to the \(x\) and \(y\) components of winds. The \(x\) component is along the local parallel while the \(y\) component is parallel to the local meridian. Magnitudes of these winds' components, often referred to as \(U_{v}\) and \(U_{u}\), are made available for any location in the world by meteorological services, such as the American National Oceanic and Atmospheric Administration (NOAA), with resolution of \(1^{\circ}\) or \(0.5^{\circ}\). If \(\Delta_{t}\) is the integration time set by the simulator, the horizontal displacements can be computed as follows:  
\[\begin{array}{lcl}\Delta_{x}&=&V_{x,W}\ \Delta_{t}\\ \Delta_{y}&=&V_{y,W}\ \Delta_{t}\end{array} \tag{6}\]  
while the changes of latitude and longitude are:  
\[\Delta_{lat}=\text{asin}\left(\frac{V_{x,W}\ \Delta_{t}}{r_{e}}\right) \tag{7}\]  
\[\Delta_{long}=\text{asin}\left(\frac{V_{y,W}\ \Delta_{t}}{r_{e}\ \ \text{cos}(lat)}\right) \tag{8}\]  
where \(r_{e}\ \text{cos}(lat)\) is the radius of the circle relative to the parallel with the considered latitude.  
The predictor turned out to be fairly accurate if precisely tuned. Table 1 shows the displacement between predicted and actual landing sites for the five flights carried out (ISM-HAB #1 to ISM-HAB #5). The actual ground distance values are shown along with the percentage of the total distance traveled. Figure 9 shows the simulated trajectory and the real trajectory for a typical flight.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Mission** & **ISM-HAB \#1** & **ISM-HAB \#2** & **ISM-HAB \#3** & **ISM-HAB \#4** & **ISM-HAB \#5** \\ \hline Landing displacement with & 1.2 km & 5 km & 2.9 km & 8 km & 3 km \\ respect to prediction & \(-14\%\) & \(-6\%\) & \(-10\%\) & \(-6\%\) & \(-4\%\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Predictor errors.  
* ISM-HAB#1: The balloon payload included only the tracking systems and the dynamics package. Burst altitude was about 10 km lower than expected. The reason for the early burst was later traced to the accumulation of ice on the balloon during ascent through a thick layer of clouds.
* ISM-HAB#2: Full payload, including the RF measurement system. No RF measurement was recorded due to a software glitch. Once again, the balloon suffered from an early bursting, traced back to accumulation of ice due to launch in bad weather, with ground-level rain.
* ISM-HAB#3: The flight was a complete success. A 1080p camera was placed on the base plate, producing excellent pictures (Figure 10b).
* ISM-HAB#4: This launch worked perfectly as far as the recording of measurements was concerned; however, the balloon was inflated insufficiently due to a failed helium bottle. The initial lifting force was lower than optimal, resulting in a very slow ascent rate. The balloon spent a considerable amount of time inside strong lateral winds and landed about 140 km further than expected, making recovery more complex.
* ISM-HAB#5: For the final launch, transmission from a ground station was received on the balloon, allowing to verify the proper working of the tracking and antenna pointing models.