physbound

Calculate maximum monostatic radar detection range and validate range claims.

Computes the radar range equation R_max = [P_t * G^2 * lambda^2 * sigma / ((4*pi)^3 * S_min * L)]^(1/4) for a monostatic radar (same antenna for transmit and receive). Validates that claimed detection ranges do not exceed the theoretical maximum. Catches the common fourth-root fallacy where LLMs incorrectly state that doubling transmit power doubles radar range (it only increases range by a factor of 2^(1/4) = 1.19x).

Use this tool when you need to:

• Calculate the maximum detection range of a radar system

• Validate whether a claimed radar detection range is physically achievable

• Determine minimum detectable signal power for a radar receiver

• Check if radar performance claims account for the R^4 path loss

• Verify that RCS assumptions are reasonable for the target class

Returns both human-readable summary and machine-readable JSON with all intermediate values. Returns a PhysicalViolationError dict if any input violates physics or the claimed range exceeds R_max.

Args: peak_power_w: Peak transmit power in watts (must be > 0) antenna_gain_dbi: Antenna gain in dBi (same antenna for TX and RX) frequency_hz: Operating frequency in Hz (must be > 0) rcs_m2: Radar cross section of the target in m^2 (must be > 0) system_noise_temp_k: System noise temperature in Kelvin (default: 290K) noise_bandwidth_hz: Receiver noise bandwidth in Hz (default: 1 MHz) min_snr_db: Minimum required SNR in dB for detection (default: 13 dB, Swerling I) claimed_range_m: Optional claimed detection range to validate against R_max (meters) num_pulses: Number of integrated pulses for integration gain (default: 1) losses_db: Total system losses in dB (default: 0)