## 3 Theoretical Analysis and Simulation Model of Temperature Error
### Aerodynamic Heat  
Based on the Joule and radiant heat simulation analysis above, the sensor scheme was determined, and further optimization of the sensor arrangement was carried out based on the aerodynamic heat analysis of the model. The positive work of air compression on the front of the object causes aerodynamic heat, making it more prominent at the front. Still, the parts around the object also have airflow disturbances that create a specific temperature difference. Therefore, we used ANSYS software to analyze the aerodynamic heat of the radiosonde and sensor to explore the distribution of the aerodynamic heat field [17]. Our analysis created a cuboid flow field surrounding the sensor to establish a fluid boundary. The boundary conditions were determined by selecting the mathematical model. The K-epsilon standard model was selected for the turbulence model, and the SIMPLE algorithm was used to solve the pressure field and velocity field. We determined the boundary conditions by selecting the mathematical model. Specifically, we chose the K-epsilon standard model for the turbulence model and used the SIMPLE algorithm to solve the pressure and velocity field. In this study, the sensor's geometric model's unstructured meshes were generated using the ICEM meshing software. To balance the calculation amount and accuracy, we set the size of the airfield outside the sensor to \(10\) mm \(\times\)\(10\) mm \(\times\)\(15\) mm. Additionally, we positioned the sensor in the middle of the front end of the fluid area. The overall calculation model is shown in Figure 4. To set the boundary conditions, the left end of the front end of the air domain was the velocity inlet boundary, the left end was the pressure outlet boundary, the four sides were the pressure far-field boundary, and the outer surface of the sensor was set as the fixed wall boundary.  
The high-speed movement of the sensor in near space will compress the front air. This positive pressure will cause the gas to compress and deform, and the gas will move toward the center under the action of external forces. Therefore, the sensor will act positively on this part of the gas, raising the temperature. Aerodynamic heat generated on rockets and other aircraft exceeds 1000 K [40, 41]. In the simulation of the sensor falling with the radiosonde by ANSYS software, it was found that this aerodynamic heat can make the gas temperature rise by tens or even hundreds of degrees. The magnitude of aerodynamic heat is related to the rate of descent of the object, i.e., to the relative flow rate of air. Additionally, the atmospheric pressure affects the specific heat capacity of air and the size of aerodynamic heat. First, the thermal field distribution of the radiosonde and sensors was studied by simulating the aerodynamic heat field distribution at different altitude locations during the radiosonde's descent for sensor placement. Then, its effect on the aerodynamic heat of the radiosonde and sensor was studied by setting various air pressures (\(5\times 10^{0}\) Pa, \(5\times 10^{1}\) Pa, \(5\times 10^{2}\) Pa, \(5\times 10^{3}\) Pa, \(5\times 10^{4}\) Pa, and \(5\times 10^{5}\) Pa) and relative air flow rates (\(100\) m/s, \(150\) m/s, \(200\) m/s, \(250\) m/s, and \(300\) m/s). To reduce the computational effort, we simplified the whole model from a three-dimensional model to a two-dimensional model.  
We studied the effects of different air pressures and relative air flow rates on the aerodynamic heat of the radiosonde or sensor.  
Figure 4: Sensor and airflow field model.  
The aerodynamic heat error model is shown in Equation (13):  
\[T_{c}=0.5\times\rho V^{3}A_{s}c_{P} \tag{13}\]  
where \(T_{c}\) is the aerodynamic heat correction error, \(\rho\) is the air density, \(V\) is the relative air velocity, \(A_{s}\) is the reference area of the sensor, and \(c_{P}\) is the air isobaric specific heat capacity.