### I. Introduction

### II. Proposed Method to Estimate Dynamic RCS of Rotating Propellers

### 1. Dynamic RCS of a Single Propeller

*S*

^{CW}(

*t*) and

*E*

^{i}are the scattering matrix of the CW rotating propeller and the incident electric field, respectively. Instead of rotating the propeller, if the incident azimuth angle,

*φ*

_{inc}, is rotated in the direction opposite to the rotation direction of the propeller, thus keeping the incident elevation angle,

*θ*

_{inc}, fixed, the same scattered field as Eq. (1) can be obtained by

### 2. Dynamic RCS of Multiple Propellers

*O*, of the reference coordinate is the center of the drone, and the nth propeller and the radar are located at

*T*

_{n}and

*P*

_{1}, respectively. If the radar, which faces the head of the drone, is far from the drone, then the backscattered field at the far-field can be approximated as

*n*th single propeller when the center of the propeller is located at the origin

*O*, and

*θ*

_{P1}and

*φ*

_{P1}are the elevation and azimuth angles of the incident field from

*P*

_{1}, respectively, where

*φ*

_{P1}= 0 because of the radar located in the heading direction. Here,

*⇉*

_{n}is the position vector of the

*n*th propeller’s center, and

*k̄*is the wave number vector for the operating frequency,

*f*, and is defined as

### 3. Dynamic RCS of Multiple Propellers in the Azimuth Plane

*P*

_{1}to

*P*

_{2}by changing only the azimuth angle from

*φ*

_{P1}to

*φ*

_{P2}while maintaining the elevation angle,

*θ*

_{P1}. The incident and scattered angles is included in

*k̄*of Eq. (4). If only the wave vector

*k̄*is updated with the moved observation point, the initial direction of the propellers is directed toward

*P*

_{2}, as shown in Fig. 4(a). This is because the changed angle information is not updated to the scattered field of each propeller, so the initial direction of the propellers is toward the incident wave direction. However, the desired direction of the propellers should be the heading direction as shown in Figs. 3(b) and 4(b). In order to update the changed angles into the scattered field, it is not necessary to recalculate the backscattered field, but only to change the rotation starting angle of

*φ*

_{obs}is the angle between

### III. Results and Discussion

### 1. Single Propeller

*θ*−

*θ*and

*φ*−

*φ*polarizations), the backscattered fields of the CW and CCW propellers are identical, while the fields of with cross-polarization (

*θ*−

*φ*and

*φ*−

*θ*polarizations) are inverse of each other because of their mirror-symmetric shape and rotation in opposite directions. Their polarimetric characteristics can be used to derive the backscattered field from the other propellers by simply calculating the backscattered field of only one propeller. Therefore, with more propellers, the time for calculating the backscattered field can be reduced.

### 2. Multiple Propellers of Ascending Drone

*φ*

_{P2}= 70°. Compared to the front-looking case of Fig. 8(a), the dynamic RCS pattern is considerably changed. However, the back-scattered spectrum is similar. The first peak frequency is also 313.3 Hz, as shown in Fig. 9(b), which means the rotation frequency can be successfully obtained from the frequency-domain of the dynamic RCS.