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# Mathematical simulation of aircraft background-target environment above sea level

https://doi.org/10.38013/2542-0542-2021-2-42-47

### Abstract

The developed software model environment allows to estimate the power characteristics of background radiation. A method of this model implementation makes it possible to obtain solar radiation indicatrices taking into account scattered radiation from the water surface. The high level of versatility of the model environment enables us to make calculations for any aircraft under different conditions of the water surface in several spectral ranges.

#### For citations:

Riazantceva V.A.,
Steshenko K.N.,
Nikeev D.D.,
Gavrilov E.V.
Mathematical simulation of aircraft background-target environment above sea level. *Journal of «Almaz – Antey» Air and Space Defence Corporation*. 2021;(2):42-47.
https://doi.org/10.38013/2542-0542-2021-2-42-47

## Introduction

Aircraft radiation makes a major contribution to spatial energy distribution when simulating background-target environment. Now, there are some studies devoted to calculations and simulation of aircraft engine radiation characteristics [1], [2], along with developed methods of complete analysis of spatial energy distribution [3]. Research efforts in this field provide quite accurate estimation of aircraft radiation, though for comprehensive estimation of the background-target environment we should take into account radiation from background objects (water surface, scattered radiation in fog or cloudy conditions). Despite available studies that give detailed description of calculation of parameters of radiation reflected from water surface [4] and scattered radiation characteristics in fog and cloudy conditions [5], [6], software implementation with consideration to both aircraft and background radiations has not yet been developed. Therefore, a unified multipurpose tool for specified calculations needs to be created.

## Calculation method

This study is a follow-up of paper [7] which proposes a model that allows to determine aircraft radiation characteristics. In our study, we represent a new model accounting for background radiation, including reflections from water surface.

Solar radiation is supposed to make a major contribution to background radiation. Solar radiation spectrum I(λ, T) is assumed to correspond to radiation of an absolute black body with the temperature of 6000 K [8] and calculated using the Planck formula:

(1)

where h – Planck constant, с – light velocity in vacuum, k – Boltzmann constant; Т – temperature, λ – wavelength.

The specific feature of calculation of background radiation above water surface is that it requires simulation of radiation scattered by fogs and mists. Parameters of radiation that has passed through a layer of aqueous aerosols drastically differ from parameters of radiation that has passed through the atmospheric layer consisting of gas molecules only. Hence, they require specific calculation. Scattering of solar radiation by aqueous aerosols is considered as per the Mie theory and formulas (2) and (3) described in [9]:

where Q_{экст}, Q_{рас} – coefficients of extinction efficiency and radiation scattering by aerosols, respectively, to be calculated using Mie coefficients a_{n}, b_{n}; аnd x – parameter defining the ratio of aerosol particle size to radiation wavelength.

Another important factor contributing to the final radiation distribution is radiation reflection from the water surface. In a computational model, the water surface is divided into surface elements, and the resulting reflection is calculated as the sum of reflections from each element. Reflection of each surface is supposed to be the Lambertian reflection, with the reflection coefficients calculated by the Fresnel formulas (4) [8]:

where r_{||}, r _{┴} – longitudinal and lateral components of reflected wave amplitude, τ_{||}, τ_{┴} – longitudinal and lateral components of propagated wave amplitude, α_{1} – incident angle, α_{2} – angle of reflection, n_{1} – refractive index of medium with light propagated before reflection, n_{2} – refractive index of medium with light propagated after reflection.

The use of surface elements of variable size allows to take into account different grades of water surface swell during simulation. Fig. 1 illustrates an example of water surface formation.

**Fig. 1.** An example of the water surface divided into polygons for reflection calculation (green, red and blue lines are the axes of Cartesian coordinate system)

In order to demonstrate the simulation results, there is an option for visualization of the resulting radiation.

Reflection coefficients were calculated to take into account the intensity of light reflected from different types of water surfaces in several optical ranges. Obtained results (Fig. 2) are used for further simulation of the background-target environment.

## Results

The method described in [7] is used to plot the indicatrix of radiation reflected from the water surface. Variable parameters are the observation angle and the water surface state that can be estimated on a ten-grade scale. Fig. 3 shows the spectrum of solar radiation that has reached the water surface, with account for absorption by the atmospheric air and aerosols in the visible and near IR ranges. Absorption of atmospheric gases corresponded to absorption of standard atmosphere and was calculated using the HITRAN data base [10]. Fig. 4 illustrates a plotted indicatrix in the visible range at the sunlight incident angle of 60°. At one-grade water surface swell, the indicatrix is considered sufficiently smooth, and therefore, reflection occurs at the angle of 60 degrees. At observation angles of 30° and 60°, radiation scattering is close to uniform scattering (Fig. 4а, c). At observation angle of 40°, the preferred axis corresponding to the reflection angle appears (Fig. 4b). At five-grade swell, the water surface is severely distorted and flares appear randomly, therefore no preferred direction of radiation is observed as shown in Fig. 4 (d–f).

**Fig. 3.** Spectra of solar radiation reaching water surface with account for absorption by the atmospheric air and aerosols, in the range of: а) 0.3–1.0 µm, b) 2–6 µm, c) 8–14 µm

**Fig. 4.** Dependence of reflected radiation distribution on azimuth at different angles of observation point: а) 30°, b) 40°, c) 60° at 1-grade water surface swell, d) 30°, e) 40°, е) 60° at 5-grade water surface swell

Fig. 5 shows the resulting spectrum of reflected radiation making a major contribution to the background-target environment with the target located above the sea surface. These spectra are determined for nonspecular reflection from the sea surface at the observation angle of 45°, at the distance of 1 km from the surface of reflecting element.

**Fig. 5.** Spectra of solar radiation reflected by water surface, in the range of: а) 0.3–1.0 µm, b) 2–6 µm, c) 8–14 µm

## Conclusion

The software environment which makes it possible to estimate power characteristics of background radiation depending on the observation angle was developed.

The developed software environment is very flexible and allows to conduct calculations with water and solid surfaces being in different states. The developed software environment can be used for creating optoelectronic systems.

## References

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10. The HITRAN molecular spectroscopic database. https://hitran.org

### About the Authors

**V. A. Riazantceva**Russian Federation

**Riazantceva Valentina Aleksandrovna** – Software Engineer of the 3rd category, Directorate for Optoelectronic Systems.

Science research interests: investigation of physical processes in discharge, optics.

St. Petersburg

**K. N. Steshenko**Russian Federation

**Steshenko Kirill Nikolaevich** – Head of General Software Sector, Directorate for Optoelectronic Systems.

Science research interests: remote optical research methods, gas-dynamic calculations of aircraft, spatial modelling of physical processes.

St. Petersburg

**D. D. Nikeev**Russian Federation

**Nikeev Dmitriy Dmitrievich** – Head of Software Department, Directorate for Optoelectronic Systems.

Science research interests: mathematical modelling of physical processes, generation and distribution of infrared radiation.

St. Petersburg

**E. V. Gavrilov**Russian Federation

**Gavrilov Egor Valerievich** – Deputy General Director – Deputy General Designer.

Science research interests: development of optoelectronic systems.

St. Petersburg

### Review

#### For citations:

Riazantceva V.A.,
Steshenko K.N.,
Nikeev D.D.,
Gavrilov E.V.
Mathematical simulation of aircraft background-target environment above sea level. *Journal of «Almaz – Antey» Air and Space Defence Corporation*. 2021;(2):42-47.
https://doi.org/10.38013/2542-0542-2021-2-42-47