Radar Physics Simulator

Radar systems operate by transmitting electromagnetic pulses and measuring the returned echo. The maximum detection distance is governed by the radar range equation: P_r = (P_t * G² * λ² * σ) / ((4π)³ * R⁴), where R is the distance and σ is the target's radar cross-section. The R⁴ dependency arises because the power density decays as 1/R² on the outward path, and the reflected wave decays as 1/R² on the return path.

Radar fires a single pulse of radio waves and reads the returning echo three ways at once. The delay before it comes back gives distance (R = c·Δt/2, halved because the pulse makes a round trip); the strength of the echo tells you whether the target is even detectable; and any shift in its frequency reveals how fast the target is closing or receding. Takeaway: light is so quick that a target 150 km away answers in under a millisecond.

MTI radar rejects ground clutter by ignoring echoes whose frequency doesn't change from pulse to pulse. But a target flying at a blind speed — where its Doppler shift lands on an exact multiple of the PRF — looks frozen between pulses and gets filtered out along with the hills. These speeds follow v = n·λ·PRF/2; with λ = 0.1 m and PRF = 1000 Hz the first is 50 m/s. Real radars hop their PRF to close the gaps.