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radar_range

Calculate maximum radar detection range using the radar range equation and validate if claimed ranges are physically achievable by accounting for R^4 path loss.

Instructions

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)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
peak_power_wYes
antenna_gain_dbiYes
frequency_hzYes
rcs_m2Yes
system_noise_temp_kNo
noise_bandwidth_hzNo
min_snr_dbNo
claimed_range_mNo
num_pulsesNo
losses_dbNo

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault

No arguments

Behavior4/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

With no annotations provided, the description carries full burden and does an excellent job disclosing behavioral traits. It explains the specific equation used, mentions error handling ('Returns a PhysicalViolationError dict if any input violates physics'), describes the return format ('Returns both human-readable summary and machine-readable JSON'), and warns about common misconceptions ('Catches the common fourth-root fallacy'). The only minor gap is not explicitly mentioning rate limits or authentication requirements.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is well-structured and appropriately sized for a complex tool with 10 parameters. It front-loads the core purpose, then provides usage guidelines, return behavior, and detailed parameter explanations. While comprehensive, every sentence earns its place by adding necessary information for this technical domain tool.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness5/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the tool's complexity (10 parameters, physics calculations), no annotations, but with an output schema, the description is remarkably complete. It covers purpose, usage scenarios, behavioral traits, parameter semantics, and return behavior. The output schema handles return values, so the description appropriately focuses on what the tool does rather than output structure.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters5/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

With 0% schema description coverage and 10 parameters, the description provides comprehensive parameter semantics beyond the bare schema. It explains each parameter's meaning, units, constraints ('must be > 0'), and default values. The description fully compensates for the schema's lack of documentation, adding crucial context about physical meaning and validation requirements.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool's purpose with specific verbs ('calculate', 'validate') and resources ('maximum monostatic radar detection range', 'range claims'). It explicitly distinguishes this tool from potential siblings by focusing on the radar range equation and validation, unlike tools like 'noise_floor' or 'shannon_hartley' which address different RF concepts.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines5/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description provides explicit usage guidelines with a bulleted list of five specific scenarios when to use this tool ('Calculate the maximum detection range', 'Validate whether a claimed radar detection range is physically achievable', etc.). It also implicitly distinguishes from siblings by focusing on radar-specific calculations rather than general noise or link budget analysis.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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