Bicycle radar corner reflector

Published

April 29, 2024

This is a simple trihedral corner reflector for a bicycle that can be 3D printed.

Corner reflector mounted on bicycle rack

Car radar frequencies

Legacy automotive radar operates at 24 GHz, while modern systems operate at 77 GHz (Schneider 2005), (Wenger 2005).

Radar cross section

The radar cross-section (RCS), \(\sigma\), of a trihedral corner reflector \[ \sigma = \frac{4 \pi a^4}{3\lambda^2} \] where \(a\) is the length of one side of the cube, and \(\lambda\) is the wavelength of the radar (Doerry 2008).

Code

from IPython.display import display, Markdown
from matplotlib import pylab as plt
import numpy as np
from scipy.constants import speed_of_light

def db10(x):
    return 10.0*np.log10(np.abs(x))

def lin10(x):
    return 10**(x/10.0) 

def wavelength(freq_hz):
    return speed_of_light / freq_hz # meters

def rcs_corner(a_mm,freq_hz):
    # size of corner reflector edge
    # a = 80 # mm
    a_mm /= 1000 # convert to meters

    wavelen = wavelength(freq_hz)

    sigma = 4 * np.pi * a_mm**4 / 3 / wavelen**2 # sq meters
    return sigma

# size of corner reflector edge
a = 80 # mm
frequency = 77e9 # Hz
sigma = rcs_corner(a,frequency)

reflector_efficiency = 0.5

sigma_dbsm = db10(sigma) + db10(reflector_efficiency)

At 77 the RCS is 7.5275861 dBsm, assuming an efficiency of 0.5.

Increase in detection distance

The free space path loss in one direction is \[ \frac{P_r}{P_t} = \left(\frac{4\pi d}{\lambda}\right)^2 \] where \(d\) is the detection distance, \(\lambda\) is the wavelength and \(\frac{P_r}{P_t}\) is the ratio of power received to transmitted. For a radar the signal must propagate out and back, so the path loss is twice the one way path loss or \[ \frac{P_r}{P_t} = 2\left(\frac{4\pi d}{\lambda}\right)^2 \]

The RCS of a cyclist from behind is between -7 and 5 dBsm (European Automobile Manufacturers Association 2018).

Code

target_dbsm = np.array([-7.0, 5.0])
total_dbsm = db10(lin10(target_dbsm) + lin10(sigma_dbsm))
increase_db = total_dbsm - target_dbsm
print(f'Increase in RCS [dbsm] {increase_db}')

Increase in RCS [dbsm] [14.67806647  4.45543625]

So the RCS with the addition of the corner reflector is between 14.6780665 and 4.4554362 dBsm.

Increase in detection distance

Code

d_increase = np.sqrt(lin10(increase_db)/2.0 ) / 4 / np.pi / wavelength(frequency)
print(f'Increase in detection distance [meters] {d_increase}')

Increase in detection distance [meters] [78.31563684 24.13887205]

References

Doerry, Armin W. 2008. “Reflectors for SAR Performance Testing - Second Edition.” SAND2014-0882. Sandia National Laboratories. https://www.osti.gov/biblio/1204079.

European Automobile Manufacturers Association. 2018. “Bicyclist Target ACEA Specifications.” European Automobile Manufacturers Association. https://www.acea.auto/uploads/publications/Bicyclist_target-ACEA_specifications.pdf.

Schneider, Martin. 2005. “Automotive Radar-Status and Trends.” In German Microwave Conference, 144–47. https://duepublico2.uni-due.de/servlets/MCRFileNodeServlet/duepublico_derivate_00014581/Paper/5_3.pdf.

Wenger, J. 2005. “Automotive Radar - Status and Perspectives.” In IEEE Compound Semiconductor Integrated Circuit Symposium, 2005. CSIC ’05. IEEE. https://doi.org/10.1109/csics.2005.1531741.