Defense Systems Calculators
Radar range, EO/IR seekers, blast overpressure, CEP, and the math the engineering cluster runs on.
- Radar Range EquationMaximum detection range for a monostatic radar from transmit power, gain, RCS, and receiver sensitivity — Skolnik's classic point-target form.R_max = [ Pₜ · G² · λ² · σ / ((4π)³ · S_min · L) ]^¼ , λ = c / f
- RCS vs Detection RangeHow far a radar sees a target given its RCS, or the RCS reduction needed to shrink detection range by a set factor.R_max = [ Pₜ·G²·λ²·σ / ((4π)³·S_min·L) ]^(1/4) , R ∝ σ^(1/4)
- IR Seeker Detection Range (NEP)Noise-limited detection range for a point IR target from radiant intensity, aperture, and detector NEP.R = √( J · τ_atm · τ_opt · A_o / (SNR · NEP) ) A_o = π·D²/4 NEP = √(A_d·Δf)/D*
- Laser NOHD (Nominal Ocular Hazard Distance)Eye-safety standoff range for a CW laser from output power, beam divergence, and exit aperture — the ANSI Z136.1 range-safety number.NOHD = [ √( 4·P / (π·MPE) ) − a ] / θ (P in W, MPE in W/m², a in m, θ full-angle in rad)
- Proportional Navigation Miss DistanceEstimate homing-loop miss distance from a heading error using Zarchan's dimensionless adjoint result.Miss ≈ Vm·sin(HE)·τ · [ (tf/τ)^(N'−1) · e^(−tf/τ) / (N'−1)! ]
- Circular Error Probable (CEP)Convert range and cross-range (bearing) miss-distance sigmas into the 50% circular error probable radius.CEP ≈ 0.5887·(σ_r + σ_b) for σ_min/σ_max ≥ 0.2 , CEP ≈ 0.615·σ_max + 0.562·σ_min otherwise
- Blackbody Radiance (Planck's Law)Spectral radiance, photon flux, Wien peak, and total exitance of a greybody target — the front end of every EO-IR link budget.L(λ) = ε · (2hc²/λ⁵) · 1/(e^(hc/λkT) − 1) M_tot = ε·σ·T⁴ λ_peak·T = 2897.77 µm·K
- Dawes Angular ResolutionSmallest resolvable double-star separation for a given aperture — the empirical bench limit for an optic.R(arcsec) = 116 / D(mm) = 4.56 / D(in) , compare Rayleigh θ = 1.22·λ/D
- Blast Overpressure at Range (Hopkinson-Cranz)Peak incident overpressure from a hemispherical surface burst via Hopkinson-Cranz scaling and the Kinney-Graham correlation — a quick standoff and clearance estimate, not a substitute for UFC 3-340-02 design tables.Z = R / W^(1/3) , Z_eff = R / (1.8·W)^(1/3) (surface burst) , Pso/P₀ = 808·[1+(Z_eff/4.5)²] / √(1+(Z_eff/0.048)²)·√(1+(Z_eff/0.32)²)·√(1+(Z_eff/1.35)²) (Kinney–Graham) , Pr ≈ Pso·[2 + 6·(Pso/Pa)/(Pso/Pa + 7)]
- TNT-Equivalent Blast RangePeak overpressure vs. standoff distance for a surface or free-air TNT charge using scaled distance.Z = R / W^(1/3) , Ps/P₀ = 808·[1+(Z/4.5)²] / √(1+(Z/0.048)²)·√(1+(Z/0.32)²)·√(1+(Z/1.35)²)
- Airy Disk Diffraction RadiusDiffraction-limited spot size and angular resolution for a circular aperture.θ = 1.22 · λ / D , r_Airy = 1.22 · λ · f / D = 1.22 · λ · N
- Gaussian Beam DivergenceFar-field half-angle, Rayleigh range, and spot size for a TEM₀₀ Gaussian beam from its waist.θ = M²·λ / (π·w₀) , z_R = π·w₀² / (M²·λ) , w(z) = w₀·√(1 + (z/z_R)²)