When modeling the aircraft motion it is advisable to choose a particular model of the Earth, depending both on the task and on the required accuracy of calculation. The article describes various models of the Earth, such as the flat Earth with a plane-parallel field of gravity, spherical and non-rotating Earth with a plane-parallel field of gravity, spherical and non-rotating Earth with a central gravitational field, spherical and non-rotating Earth, taking into account the polar flattening of the Earth, spherical Earth based compression and polar daily rotation. The article also considers the influence of these models on the motion of the selected aircraft.
To date, there is technical equipment to provide highly accurate description of the Earthshape, gravitational field, etc. The improved accuracy of the Earth model description results in more correct description of the trajectory and motion parameters of a ballistic missile. However, for short ranges (10-20 km) this accuracy is not essential, and, furthermore, it increases time of calculation. Therefore, there is a problem of choosing the optimal description of the Earth parameters.
The motion in the model of the Earth, which takes into account a daily rotation of the planet and polar flattening, is discussed in more detail, and the geographical latitude impact on coordinates of the points of fall of a ballistic missile is analyzed on the basis of obtained graphs.
The article individually considers a problem of the wind effect on the aircraft motion and defines dependences of the missile motion on the parameters of different wind loads, such as wind speed and height of its action.
A mathematical model of the missile motion was built and numerically integrated, using the Runge-Kutta 4th order method, for implementation and subsequent analysis.
Based on the analysis of the calculation results in the abovementioned models of the Earth, differences in impact of these models on the parameters of the aircraft motion are revealed. Analysis of different wind loadings allowed us to derive dependences of the coordinates of the points of fall of a ballistic missile on the wind speed and its height of its action. Taking into consideration these differences and deviations will enable improvement of missile accuracy.