Reflection Propagation Law of Electromagnetic Waves in U-Shaped Roadway

To address the complex and space-constrained characteristics of underground coal mine roadways, this study proposes an electromagnetic wave reflection model based on the mirror image method. A U-shaped roadway model was designed and a relay node was established at the center of the roadway to simplify calculations. The point normal vector method was used to calculate the equations and boundary ranges of eight reflection planes. The valid reflection paths were determined by calculating the mirror points, counting the number of reflection lines, and evaluating their validity. The sensitivity of the number of valid reflection lines to the positions of the transmitting and receiving points relative to the corners was determined, and the reflected field strength at the receiving point was calculated. Its sensitivity to variables such as the distance between the relay node and the receiving point, antenna transmitting frequency, relative dielectric constant of the roadway walls, and width of the U-shaped roadway was studied. The simulation results showed that the number of valid reflection lines decreased with increasing distance from the transmitting and receiving points to the corners. The horizontal position of the transmitting point has a higher effect on the number of effective reflection lines than the vertical position, while the transmitting and receiving points are favorable for electromagnetic wave propagation when they are located in the center of the roadway. As the distance between the relay node and the receiving point increases, the reflection field strength attenuation at the receiving point will decrease with a larger roadway width, a smaller relative permittivity of the roadway walls, and a lower transmitting frequency of the antenna.