cueFlash

Glossary of AERO230 Formulae

Start Studying! Add Cards ↓

Created by Rasori

Deck Info

Description

Tags

Recent Users

Basic Electromagnetism
Wavevector
k = 2*pi / lambda
= 2*pi * f / c

lambda = wavelength
f = frequency
c = speed of light




Decibels
two formats!
Power(dB) = 10 log10 (Power)
Power dBm = 10 log10 (Power(dBm))
Area dBsm = 10 log10 (Power(dBsm))

E(dBmicroV/meter) = 20 log10 (E(microV/meter)



Radar Equations
Antenna Gain
Gr = Gt = ?

Gr = 4pi Ae / lambda^2 = Gt

Ae = Antenna effective area
lambda = wavelength


Radar Equations
Gain transmitted
Gt = 4pi / (dTHETA dPHI)

dTHETA = angular beamwidth vertical
dPHI = angular beamwidth horizontal


Radar Equations
Vertical Beamwidth
general / circular?

general:
dTHETA = lambda / 2a
circular:
dTHETA = 1.02 * lambda/2a

lambda = wavelength
a = aperture radius





Radar Equations
Power Received
Pr = (Pt Gt Gr lambda^2 sigma Ls) / ((4pi)^3 R^4))

Pt = power transmitted
Gt = transmitter gain
Gr = receiver gain
lambda = wavelength
sigma = RCS radar cross section
Ls = Loss factor (0.3 - 0.5)
R = range







Radar Equations
Radar Noise
N = k T0 B F
k = Boltzmann's Constant
= 1.38 * 10 ^(-23)J/K
T0 = temperature
B = bandwidth
F = "noise figure"




Radar Equations
Signal-to-Noise Ratio
SNR = Pr/N =
(Pt Gt Gr lambda^2 Ls) / ((4pi)^3 R^4 N)

Pr = Power received
N = Noise
Pt = Power transmitted
Gt = Gain transmitted
Gr = Gain received
lambda = wavelength
Ls = loss factor (0.3 - 0.5)
R = range









Radar Equations
Range Resolution
(rough)

dR = 0.8*c*t0

c = speed of light
t0 = pulse duration


Radar Equations
Range accuracy
dR = c / (2B sqrt(2SNR))

c = speed of light
B = bandwidth
SNR = signal-to-noise ratio



Radar Equations
Doppler Shift
fd = 2 vr / lambda

vr = radial velocity
lambda = wavelength


Radar Equation
frequency (bandwidth)
fBW = 1 / t0

t0 = pulse length

Radar Equations
Range and Max Range
R = c * tr / 2
Rmax = c / 2fPRF

c = speed of light
tr = time to recieve
fPRF = pulse repetition frequency




Radar Equations
Two dopplers
Integration time
Frequency error
Radial Velocity error



tint = 1/dfd
df = 1/(tint sqrt(2SNR))
dvr = lambda / (2tint sqrt(2SNR))

tint = integration time
dfd = difference between doppler shifts
df = frequency error
SNR = signal-to-noise ratio
dvr = radial velocity error
lambda = wavelength








Radar Equations
Radar Cross Section (RCS)
Summation of many scatterers

sigma = sum(sqrt(sigma-m) e^(j phi-m)

sigma = RCS
sigma-m = RCS of individual scatterer
phi-m = 2-way phase difference



Radar Equations
Phased Array Radar
phi / 2 pi = (d sin(theta)) / lambda

phi = phase difference between elements
d = distance between elements
lambda = wavelength



Radar Equations
Phased Array Radar
Gain GaTHETA

GaTHETA = abs(EaTHETA)^2 / N^2
= (sin^2(N pi (d/lambda) sin(theta)) / (N^2 sin^2(pi (d/lambda) sin(theta)))

EaTHETA = field intensity pattern
N = number of antennae in array
d = distance between antennae
lambda = wavelength





Radar Equations
Synthetic Aperture Radar
cross-range resolution

dcr = R lambda / 2a

R = range to target
lambda = wavelength
a = antenna radius



Radar Equations
Synthetic Aperture Radar
cross-range resolution to a

dcr = lambda / 2thetaB = 2a/2 = a

lambda = wavelength
thetaB = beamwidth


Inertial Navigation Systems
Ring Laser Gyro
df = 4 A omega / (L lambda)

A = path area
omega = rate of rotation
L = path length
lambda = wavelength (laser average, in this case)




Inertial Navigation Systems
Fibre Optical Gyro
dPHI = (8pi A N omega)/(c lambda)

A = path area
N = number of turns
omega = rate of rotation
c = speed of light
lambda = wavelength





Intertial Navigation Systems
Schuler Frequency
theta..
and T


theta.. = (a - g sin(theta)) / Re = (a - gtheta) / Re

a = acceleration reading
gsin(theta) = horizontal error due to earth's rotation
Re = radius of the earth
gtheta = horizontal error again

T = 4pi sqrt(Re/g) = 84 minutes






Radio Navigation Systems
LORAN
D = sqrt((x-x1)^2 + (y-y1)^2) - sqrt((x-x2)^2 + (y-y2)^2) = c*td

D = distance
x1,y1 / x2,y2 = fixed points
x, y = observer point
c = speed of light
td = time delay





Imaging Systems
angular resolution
dTHETA = theta / N

dTHETA = angular resolution
theta = field of view (rads)
N = number of pixels



Imaging Systems
Rayleigh Criterion
dTHETA = 1.22lambda / D

lambda = wavelength
D = aperture diameter


Imaging Systems
Johnson Criteria (3)
Rd = (dX/3)/dTHETA
Rr = (dX/7)/dTHETA
Ri = (dX/11)/dTHETA

Rd = Range of Detection
Rr = Range of Recognition
Ri = Range of Identification
dX = Critical Dimension (smallest of height/width/length)
dTHETA = angular resolution







Air Data Sensors
Pitot tube Airspeed
Indicated versus true?

Q = .5 rho V^2 = Pt - Ps

Q = dynamic pressure
rho = air density
V = airspeed
Pt = total pressure
Ps = static pressure

Indicated is without temperature reading







Add Cards

You must Login or Register to add cards