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

10^{2}

hecta

h

10^{3}

milli

m

10^{3}

kilo

k

10^{6}

micro

μ

10^{6}

mega

M

10^{9}

nano

n

10^{9}

giga

G

10^{12}

pico

p

10^{12}

tera

T

10^{15}

femto

f

10^{15}

peta

P

10^{18}

atto

a

10^{18}

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

^{o}C

power^{}

Watt

W

temperature^{}

Kelvin

K

frequency^{}

Hertz

Hz

Physical
Constants

Constant

Symbol

Value

Nominal Speed of Light

c

3x10^{8} m/s

StefanBoltzmann's constant

σ

5.67x10^{8}
W/m^{2} . K^{4}

Planck's constant

h

6.63x10^{34}
J . s

Density of Dry Air

ρ

1.2929 Kg/m^{3}

Nominal Speed of Sound
(air)

ν

343 m/s

Geometry


Circumference

Area

Volume

circle of radius
"r"

2πr

πr^{2}


sphere of radius
"r"

2πr

4πr^{2}

(4/3) πr^{3}

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

m^{2}

10^{4}

cm^{2}

6.2x10^{4}

10^{4}

Statute Miles

0.869

Nautical Miles

m^{2}

10.764

ft^{2}

1.151^{}

9.29x10^{2}

Nautical Miles

1851

Meters

in^{2}

6.944x10^{3}

ft^{2}

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)
c_{0} = speed of light in vacuum (m/s)
c = speed of light in medium (m/s)

Snell's
Law


n_{i} = refractive index of incident medium
n_{t}= refractive index of transmitting
medium
θ_{i} = angle of incidence
θ_{t} = angle of refraction

Interference

Constructive
Destructive
(in radians)
(in deg)

E_{p} = electric field at point P (volts/m)
E_{o} = 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 (f_{D})


f_{D}
= Doppler shift (Hz)
v_{LOS} = velocity in the lineofsight (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)
θ_{1}
= angle between transmitter hdg and LOS
θ_{2}
= 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 = signaltonoise (unitless)
SNR = signaltonoise ratio (dB)

Receiver
Sensitivity


S_{min} = 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


q_{nn}
= nullnull 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


A_{e}
= effective antenna area (m^{2})
ρ_{a}
= antenna efficiency (unitless decimal)
A
= antenna area (m^{2})

Directive
Gain


G_{dir}
= directivity gain (unitless)
ϕ
= vertical beamwidth (radians)
θ
= horizontal beamwidth (radians)

Power
Gain


G
= power gain (unitless)
λ
= signal wavelength (m)
A_{e}
= effective antenna area (m^{2})
k
= 0.88 (linear) or 1.02 (circular)

Power
Gain


G
= power gain (unitless)
ρ
= antenna efficiency (unitless)
G_{dir}
= directive gain (unitless)

Power
Gain (dB)
These
relationships also apply to directive gain


G_{dB}
= 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 (R_{min})


PW
= Pulse Width (s)
c
= speed of light (m/s)

Maximum
Unambiguous Range (R_{unamb})


c
= speed of light (m/s)
PRT
= Pulse Repetition Time (s)

Range
Resolution (R_{res})


c
= speed of light (m/s)
PW
= Pulse Width (s)
PCR
= Pulse Compression Ratio (unitless)

[simplified]
Maximum Radar Range
(R_{max})


P_{t}
= peak transmitter power (W)
G
= power gain (unitless)
A_{e}
= effective antenna area (m^{2})
σ
= radar cross section (m^{2})
S_{min}
= minimum signal for detection (W)

RADAR
Line of Sight Range (R_{LOS})


R_{LOS}
= range tangential to the horizon (km)
H_{T}
= height of targer above surface (m)
H_{R}
= height of RADAR above surface (m)

Duty
Cycle


PW
= Pulse Width (s)
PRF
= Pulse Repetition Frequency (Hz)
PRT
= Pulse Repetition Time (s)
P_{avg}
= average power (W)
P_{peak}
= 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
(R_{FMCW})


c
= speed of light (m/s)
T
= period of frequency sweep (s)
Δf
= instantaneous frequency diff (Hz)
f_{2}
= frequency sweep, upper (Hz)
f_{1}
= frequency sweep, lower (Hz)

Phase
Shift (ΔΦ_{a,e})
(elementtoelement)


Δϕ_{a,e} = phase shift
(radians)
λ
= wavelength (m)
e
= elevation element number
a
= azimuth element number
d_{e}
= elevation element spacing (m)
d_{a}
= azimuth element spacing (m)
α = elevation angle
(degrees)
ε = azimuthal angle (degrees)

Cross
Range Resolution
(R_{cross})


q_{3dB} = azimuth beamwidth (½ 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

SelfScreening
Burnthrough range
(R_{burnthru})


R_{burnthru}
= Range at which radar signal echo equals EA signal at the radar (m)
P_{peak}
= radar peak power (W)
G_{r}
= radar directive gain (dimensionless)
σ
= target radar cross section (m^{2})
P_{BW}
= jammer power per noise bandwidth (W/MHz)
G_{j}
= jammer antenna gain (dimensionless)
B
= radar receiver noise bandwidth (MHz)
C
= minimum J/S ratio for target obscuration (dimensionless)

Standoff
Burnthrough range
(R_{burnthru})


R_{burnthru}
= Range at which radar signal echo equals EA signal at the radar (m)
P_{peak}
= radar peak power (W)
G_{r}
= radar directive gain (dimensionless)
σ
= target radar cross section (m^{2})
P_{BW}
= jammer power per noise bandwidth (W/MHz)
G_{j}
= jammer antenna gain (dimensionless)
B
= radar receiver noise bandwidth (MHz)
C
= minimum J/S ratio for target obscuration (dimensionless)
R_{j}
= range from radar to jammer

Pulsed
Bandwidth approximation


BW_{3dB}
= bandwidth of the receiver at the ½ power points
PW
= pulse width of transmitted pulse

