top header
top gradation HOME top vertical line top vertical line top vertical line top vertical line top vertical line top vertical line top vertical line menu gray
spacer


ATI's Appendix of Defense Related Terms and Formulas

Share |

 

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 radians)

(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

-3dB or f-3dB)

f-3dB = elevation beamwidth power point (radians)

q-3dB = azimuth beamwidth ( 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)


 

Radar

Case

Equation

Variables

Basic Radar Range

R = Radar range

c = speed of light (m/s)

Δt = round trip time for pulse (s)

Minimum Range (Rmin)

PW = Pulse Width (s)

c = speed of light (m/s)

Maximum Unambiguous Range (Runamb)

c = speed of light (m/s)

PRT = Pulse Repetition Time (s)

Range Resolution (Rres)

c = speed of light (m/s)

PW = Pulse Width (s)

PCR = Pulse Compression Ratio (unitless)

[simplified] Maximum Radar Range (Rmax)

Pt = peak transmitter power (W)

G = power gain (unitless)

Ae = effective antenna area (m2)

σ = radar cross section (m2)

Smin = minimum signal for detection (W)

RADAR Line of Sight Range (RLOS)

RLOS = range tangential to the horizon (km)

HT = height of targer above surface (m)

HR = height of RADAR above surface (m)

Duty Cycle

PW = Pulse Width (s)

PRF = Pulse Repetition Frequency (Hz)

PRT = Pulse Repetition Time (s)

Pavg = average power (W)

Ppeak = peak power (W)

Number of Target

Returns (N)

θ-3dB = beamwidth (radians)

PRF = Pulse Repetition Frequency (Hz)

Ω = antenna scan rate (rad/sec)

FMCW Range (RFMCW)

c = speed of light (m/s)

T = period of frequency sweep (s)

Δf = instantaneous frequency diff (Hz)

f2 = frequency sweep, upper (Hz)

f1 = frequency sweep, lower (Hz)

Phase Shift (ΔΦa,e) (element-to-element)

Δϕa,e = phase shift (radians)

λ = wavelength (m)

e = elevation element number

a = azimuth element number

de = elevation element spacing (m)

da = azimuth element spacing (m)

α = elevation angle (degrees)

ε = azimuthal angle (degrees)

Cross Range Resolution

(Rcross)

q-3dB = azimuth beamwidth ( power point (radians)

λ = wavelength (m)

R = range to target (m)

k = antenna shape proportionality constant

L = length of array (m)


 

Electronic Warfare

Case

Equation

Variables

Self-Screening Burnthrough range

(Rburnthru)

Rburnthru = Range at which radar signal echo equals EA signal at the radar (m)

Ppeak = radar peak power (W)

Gr = radar directive gain (dimensionless)

σ = target radar cross section (m2)

PBW = jammer power per noise bandwidth (W/MHz)

Gj = jammer antenna gain (dimensionless)

B = radar receiver noise bandwidth (MHz)

C = minimum J/S ratio for target obscuration (dimensionless)

Stand-off Burnthrough range

(Rburnthru)

Rburnthru = Range at which radar signal echo equals EA signal at the radar (m)

Ppeak = radar peak power (W)

Gr = radar directive gain (dimensionless)

σ = target radar cross section (m2)

PBW = jammer power per noise bandwidth (W/MHz)

Gj = jammer antenna gain (dimensionless)

B = radar receiver noise bandwidth (MHz)

C = minimum J/S ratio for target obscuration (dimensionless)

Rj = range from radar to jammer

Pulsed Bandwidth approximation

BW-3dB = bandwidth of the receiver at the power points

PW = pulse width of transmitted pulse