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

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 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

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 = 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

A_e = effective antenna area (m²)

ρ_a = antenna efficiency (unitless decimal)

A = antenna area (m²)

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 (m²)

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 (m²)

σ = radar cross section (m²)

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)

f₂ = frequency sweep, upper (Hz)

f₁ = frequency sweep, lower (Hz)

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

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

Self-Screening 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 (m²)

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)

Stand-off 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 (m²)

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