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 ``` ATI's Appendix of Defense Related Terms and Formulas ```

 Metric Prefixes Multiple Prefix Symbol Multiple Prefix Symbol 10-1 deci- d 10 deca- da 10-2 centi- c 102 hecta- h 10-3 milli- m 103 kilo- k 10-6 micro- μ 106 mega- M 10-9 nano- n 109 giga- G 10-12 pico- p 1012 tera- T 10-15 femto- f 1015 peta- P 10-18 atto- a 1018 exa- E

 Greek Alphabet Name Symbol Name Symbol Alpha A, a Nu N, n Beta B, b Xi X, x Gamma G, g Omicron O, o Delta D, d Pi P, p Epsilon E, e Rho R, r Zeta Z, z Sigma S, s Eta H, h Tau T, t Theta Q, q Upsilon U, u Iota I, i Phi F, f Kappa K, k Chi C, c Lambda L, l Psi Y, y Mu M, m Omega W, w

 International System (SI) Units Quantity Unit Symbol Quantity Unit Symbol length meters m force Newton mass kilogram kg energy Joule time seconds s pressure Pascal Pa temperature Celsius oC power Watt W temperature Kelvin- K frequency Hertz Hz

 Physical Constants Constant Symbol Value Nominal Speed of Light c 3x108 m/s Stefan-Boltzmann's constant σ 5.67x10-8 W/m2 . K4 Planck's constant h 6.63x10-34 J . s Density of Dry Air ρ 1.2929 Kg/m3 Nominal Speed of Sound (air) ν 343 m/s

 Geometry Circumference Area Volume circle of radius "r" 2πr πr2 sphere of radius "r" 2πr 4πr2 (4/3) πr3

 Conversion Factors Convert Multiply by Convert Convert Multiply by Convert → → ← ← Ounces 0.028 Kilograms Knots 1.151 MPH 35.28 0.869 Pounds 0.454 Kilograms Knots 0.5144 m/s 2.205 1.9438 Feet 0.305 Meters Degrees 1.745x10-2 Radians 3.28 57.296 Statute Miles 1609.3 Meters m2 104 cm2 6.2x10-4 10-4 Statute Miles 0.869 Nautical Miles m2 10.764 ft2 1.151 9.29x10-2 Nautical Miles 1851 Meters in2 6.944x10-3 ft2 5.4x10-4 144 Nautical Miles 6076.41 Feet Kelvin = ˚Celsius + 273 1.645x10-4 ˚Celsius = (˚Fahrenheit - 32) x (5/9)

 Exponents & Logarithms Logarithm to base b Properties of Logarithms Natural Logarithm

Wave Properties

Case

Equation

Variables

Dispersion Relationship

υ = velocity of propagation in medium (m/s)

f = frequency (Hz)

λ = wavelength (m)

Refractive Index

n = refractive index (unitless)

c0 = speed of light in vacuum (m/s)

c = speed of light in medium (m/s)

Snell's Law

ni = refractive index of incident medium

nt= refractive index of transmitting medium

θi = angle of incidence

θt = angle of  refraction

Interference

Constructive

Destructive

(in deg)

Ep = electric field at point P (volts/m)

Eo = maximum electric field strength (volts/m)

Δϕ = phase angle shift between two sources

Δx = path length difference (m)

λ = wavelength of carrier (m)

 For f = 240 to 120 deg (Constructive interference) For f = 120 to 240 deg (Destructive interference)

Doppler Shift (fD)

fD = Doppler shift (Hz)

vLOS = velocity in the line-of-sight (LOS) (m/s)

λ = wavelength (m)

Relative Velocity Along Line of Sight (v LOS)

v 1 = velocity of transmitter (knots)

v 2 = velocity of target (knots)

θ1 = angle between transmitter hdg and LOS

θ2 = angle between target hdg and LOS

 Signal to Noise Case Equation Variables Signal to Noise S = signal level (W) N = noise level (W) S/N = signal-to-noise (unitless) SNR = signal-to-noise ratio (dB) Receiver Sensitivity Smin = minimum signal for detection (W) MDS = minimum discernable signal (dBm)

 Antennae Case Equation Variables Optimum Antenna Length (Ground Plane Dipole) λ = wavelength (m) L = length of antenna (m) Optimum Antenna Length (Free Space Dipole) λ = wavelength (m) L = length of antenna (m) Diffraction Theory qnn = null-null beamwidth (radians) L = antenna array length (m) l = wavelength of carrier (m) d = aperture (m) Beamwidth Approximation (θ-3dB or f-3dB) f-3dB = elevation beamwidth ½ power point                 (radians) q-3dB = azimuth beamwidth (½ power point                 (radians) k =antenna shape  proportionality constant use k = 1.02 (circular antenna) else k= 0.88 (linear, parabolic, ect.) l = signal wavelength (m) W = width of the antenna array (m) H = height of the antenna array (m) Effective Antenna Area Ae = effective antenna area (m2) ρa = antenna efficiency (unitless decimal) A = antenna area (m2) Directive Gain Gdir = directivity gain (unitless) ϕ = vertical beamwidth (radians) θ = horizontal beamwidth (radians) Power Gain G = power gain (unitless) λ = signal wavelength (m) Ae = effective antenna area (m2) k = 0.88 (linear) or 1.02 (circular) Power Gain G = power gain (unitless) ρ = antenna efficiency (unitless) Gdir = directive gain (unitless) Power Gain (dB)   These relationships also apply to directive gain GdB = power gain (dB) G = power gain (unitless)