## 4 Results and Analysis
### Dynamics: Acceleration, Spin, Oscillations  
Accelerations were measured in the sensor body frame during all the mission duration with a sampling frequency of 15 Hz. The \(x\) and \(y\) axes correspond to horizontal accelerations, while the \(z\)-axis to the vertical acceleration (so that its average value is \(-1\) g). The graph for the entire flight (Figure 18a) clearly shows the accelerations due to pre-launch handling; the ascent phase, characterized by a visible decrease in acceleration with increasing altitude and decreasing atmospheric density, and the balloon burst, followed by the turbulent descent phase that ends with the landing, with a sudden crash acceleration of up to almost 2.5 g.  
By plotting the \(x\)-axis acceleration graph with respect to altitude (Figure 18b), it is noticeable that the amplitude of acceleration undergoes a significant decrease from about 12 km of altitude upwards, except for a brief turbulence around the altitude of 16 km. To get a better understanding of the dynamics at high altitude, a signal composed of 4000 samples was extracted, corresponding to 274 s of flight close to the bursting altitude. The sample was then processed with a MATLAB script: first, de-trending was performed in order to assess the real amplitudes of the oscillations. De-trending was implemented by interpolating the signal with a low-order polynomial and then subtracting it from the original raw signal. Then, the high-frequency noise, which is typical of MEMS accelerometers, was removed with an exponential binomial filtering. The result was a periodic signal, with 35 peaks with values of 1.8 \(\times\) 10\({}^{-3}\) g and an average period of 5.82 s (Figure 19a). This is very close to the period of a pendulum in vacuum with a chord length equal to the distance between the balloon and the payload, showing that at altitudes  
Figure 17: Horizontal speed during flight ISM-HAB #3: (**a**) during ascent and (**b**) during descent. Figure 18: Gondola dynamics: (**a**) acceleration along the three body axes during the whole flight, and (**b**) acceleration along the \(x\)-axis as a function of altitude. above 23-24 km, the gondola essentially behaves like a free pendulum, unperturbed by atmospheric drag. For the \(z\)-axis, a similar analysis shows that the vertical motion follows a similar pattern but with amplitude peaks of up to 0.08 g (Figure 19b). As values were very similar for all flights, we conclude that during motion in near space, our sounding balloons exhibit an acceleration along the vertical body axis about 40 times larger than the acceleration on the horizontal axes. This is believed to be due to the coupling of buoyancy with the intrinsic elasticity of the natural rubber balloon. No method is presently available to suppress or compensate these vertical oscillations. If confirmed in future experiments, this issue shall be taken into account for future utilization of the HABs for applications where a stabilized platform is needed, such as astronomical observation or optical communications. During the early stages of ascent, the yaw rate is very variable, although almost always in the same direction (Figure 20a). The motion is essentially random and there are no particular trends emerging from the data in the early stages of the ascent. Above 22.5 km, yaw amplitude decays from initial peaks of 40 deg/s to almost zero before burst, while direction reverses regularly. This behavior was also verified by the video recorded buy the onboard camera, showing rotation periods of 8-9 s, consistent with the measured yaw rate. The magnitude of the oscillations suggest that a reaction wheel might be used to stabilize yaw pointing at high altitudes. Figure 19: Acceleration close to burst altitude: (**a**) along \(x\), (**b**) along \(z\). Note the different vertical scale. The sampled interval is 274 s.  
Figure 20: (**a**) Yaw rate as a function of altitude.