This article reflects the results of the investigation of an aircraft speed comparator operating features above the sea surface. The structure of the sea surface is considered, the method of modeling the water surface and the radio signal reflected from it is indicated. The results of full-scale tests and the results of mathematical simulation of the flight of an aircraft over the sea surface are given.
Introduction
The sea waves are divided into the following types for convenience: wind waves - waves in the area of acceleration. Waves arise under the influence of atmospheric influences nascent waves - grow over time under the influence of wind force, until they become developed developed waves - waves that occur when the wind operates at a great distance and for a fairly long time swell - waves outside the acceleration region gravitational waves - a wavelength of more than 2.5 cm, damp for a long time, propagate in the direction specified by the wind capillary waves - a wavelength of less than 2.5 cm, quickly damp, the wind depends relatively weakly
Common elements for waves are (Figure 2) [
The widest distribution and application was the representation of the agitated sea surface, as a probabilistic random process. While modeling sea waves, the statistics of wave elements are the most interesting.
( ) [ ( ) ] ( ) [ ( ) ] where: – is the average wave height
The motion of reflecting elements of the sea surface is determined by different types of currents: tidal currents, drift current of the surface layer of water under the action of the local wind, trade-stable currents, for example, the Gulf Stream. In addition, in the case of wind waves in the water surface, orbital motion of the reflecting particles occurs, a moving foam forms on the sea surface, water splashes fly.
The speed of tidal currents, caused by the attraction of the mass of water by the Moon and the Sun, strongly depends on the place and relief of the surrounding land. In some narrow straits this speed can reach several kilometers per hour. In the open ocean, the tidal current does not exceed 0.2 km / h.
The drift current on the seas and oceans is caused by friction forces when the wind affects the elements of the water
surface. The experimental value of the wind coefficient Vdr in the middle latitudes, according to the data given in [
The main effect on the offset of the frequency of the signal reflected from the sea surface is caused by the orbital motion of the reflecting particles of the water surface. As is well known, in the case of wave motion, the water particles in the deep sea move along orbits close to the circles with steady waves (Fig. 3). These circles lie in planes perpendicular to the crests of the waves. Velocity of motion The velocity of motion of a particle along the orbit Vorb at a wave period
It should be noted that practically the particle velocity is not the same at different sites and reaches the maximum value at the crest of the wave.
The orbital motion of particles leads to frequency modulation of the reflected signal and to the spreading of the spectrum if the reflection from different parts of the wave is the same.
Figure 4 shows the experimental dependence of the velocity Vx of the total orbital and drift currents on the wind speed. where Vorb, U - are expressed in km / h, and the coefficient depends on the wind speed, increasing with its grow. Seawave,ball 1 2 3 4 5
Vorb , m/s 0,3750,750,971,261,57 While modeling, the sea surface, its corresponding height (hv), length (Lв) and the period (Тв) of the wave are specified (Table 1). The basic direction of wave propagation (θ) is also selected.
According to [
According to [
On the basis of (1) for each facet k its current coordinates Xk (t), Zk (t) and Hk (t) are calculated in time. The displacement of a particle is determined by the sum of the displacements introduced by each of the N waves.So the current coordinate of the facet k along the H axis:
- random initial phase of wave i; is the coordinate of the facet k along the axis of motion of the wave i: ( ) ( )
In addition to the oscillation of particles along the vertical axis H, movements along the X and Z axes also take place due to the orbital motion, which also represent oscillatory processes: ( )
( ( )
∑ ( ) ∑ ( ) ( ) ( ) ( ) Fig. 6 shows the vibrational displacements of particles based on the orbital motion and without taking into account. In accordance with the geometry of the problem, the transmitting system emits a probing signal, which is a rectangular pulse signal of unit amplitude with a duration of T. As the sounding signal directs at various times, different surface areas will be illuminated.
The resulting diffraction field of scattering of the radar scene is generally determined by coherent summation of the local scattering fields of individual elements belonging to different surface elements.
When modeling the radar signal reflected from the surface under consideration, the position of each facet and its slope on the surface were taken into account. For this, the plane of the water surface at each site is approximated by the five nearest points.
Assuming that A 0 , the equation can be written in the form
then we can have
According to the method of least squares, the values of the parameters b, c and d are chosen so that the value ∑ ( ) takes the smallest value.
In accordance with the theory of extrema, the parameters b, c and d are found from the condition that the following partial derivatives
Taking into account the notation introduced, the system of equations takes the form ∑ ∑ ( ( ∑
( ∑
∑ ∑ ∑ ∑ ∑ ∑ ∑
∑ ∑ ∑ ∑ ) )
) ∑ ∑ ∑ ∑ ∑
( { ( (
) ) ) ⃗ *
+ ⃗ *
+ (
⃗ ⃗ |⃗ | |⃗ | ) Modeling of the aircraft flight at the altitude of 100 m above the water surface with various wave parameters was carried out. The longitudinal component of the ground speed Vx was set at 200 m / s, transverse Vz = 0 m / s.
The results of the simulation are the values of the velocity components measured by the correlation meter during the flight of the aircraft, shown in Figures 10 and 11.
The data presented, obtained by calculation, confirm some influence of the orbital current on the readings of the correlation speed meter.
From the simulation results in Fig. 10, 11 it follows that, when flying over the sea surface, the measured values of the longitudinal velocity component differ from the reference velocity by an amount commensurate with the orbital velocity of the sea surface particles motion. In this case, the direction of wave relative to the direction of flight determines the sign of the introduced measurement error.
It was established that the orbital motion of the elements of the water surface introduces a systematic error (on the orthodrome) in the measurement of the velocity components. The value of the error depends on the parameters of the wave and its direction.