##### AERO230 Formulae
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#### Complete list of Terms and Definitions for AERO230 Formulae

Terms Definitions
Air Data SensorsPitot tube AirspeedIndicated versus true? Q = .5 rho V^2 = Pt - PsQ = dynamic pressurerho = air densityV = airspeedPt = total pressurePs = static pressureIndicated is without temperature reading
Radar EquationsVertical Beamwidthgeneral / circular? general:dTHETA = lambda / 2acircular:dTHETA = 1.02 * lambda/2alambda = wavelengtha = aperture radius
Radar EquationsPower Received Pr = (Pt Gt Gr lambda^2 sigma Ls) / ((4pi)^3 R^4))Pt = power transmittedGt = transmitter gainGr = receiver gainlambda = wavelengthsigma = RCS radar cross sectionLs = Loss factor (0.3 - 0.5)R = range
Radar Equationfrequency (bandwidth) fBW = 1 / t0t0 = pulse length
Radar EquationsTwo dopplersIntegration timeFrequency errorRadial Velocity error tint = 1/dfddf = 1/(tint sqrt(2SNR))dvr = lambda / (2tint sqrt(2SNR))tint = integration timedfd = difference between doppler shiftsdf = frequency errorSNR = signal-to-noise ratiodvr = radial velocity errorlambda = wavelength
Inertial Navigation SystemsFibre Optical Gyro dPHI = (8pi A N omega)/(c lambda)A = path areaN = number of turnsomega = rate of rotationc = speed of lightlambda = wavelength
Intertial Navigation SystemsSchuler Frequencytheta..and T theta.. = (a - g sin(theta)) / Re = (a - gtheta) / Rea = acceleration readinggsin(theta) = horizontal error due to earth's rotationRe = radius of the earthgtheta = horizontal error againT = 4pi sqrt(Re/g) = 84 minutes
Radar EquationsDoppler Shift fd = 2 vr / lambdavr = radial velocitylambda = wavelength
Radar EquationsPhased Array RadarGain 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 patternN = number of antennae in arrayd = distance between antennaelambda = wavelength
Radar EquationsRange and Max Range R = c * tr / 2Rmax = c / 2fPRFc = speed of lighttr = time to recievefPRF = pulse repetition frequency
Imaging SystemsJohnson Criteria (3) Rd = (dX/3)/dTHETARr = (dX/7)/dTHETARi = (dX/11)/dTHETARd = Range of DetectionRr = Range of RecognitionRi = Range of IdentificationdX = Critical Dimension (smallest of height/width/length)dTHETA = angular resolution
Imaging SystemsRayleigh Criterion dTHETA = 1.22lambda / Dlambda = wavelengthD = aperture diameter
Imaging Systemsangular resolution dTHETA = theta / NdTHETA = angular resolutiontheta = field of view (rads)N = number of pixels
Radar EquationsRadar Cross Section (RCS)Summation of many scatterers sigma = sum(sqrt(sigma-m) e^(j phi-m)sigma = RCSsigma-m = RCS of individual scattererphi-m = 2-way phase difference
Basic ElectromagnetismWavevector k = 2*pi / lambda= 2*pi * f / clambda = wavelengthf = frequencyc = speed of light
Inertial Navigation SystemsRing Laser Gyro df = 4 A omega / (L lambda)A = path areaomega = rate of rotationL = path lengthlambda = wavelength (laser average, in this case)
Radar EquationsSynthetic Aperture Radarcross-range resolution dcr = R lambda / 2aR = range to targetlambda = wavelengtha = antenna radius
Radio Navigation SystemsLORAN D = sqrt((x-x1)^2 + (y-y1)^2) - sqrt((x-x2)^2 + (y-y2)^2) = c*tdD = distancex1,y1 / x2,y2 = fixed pointsx, y = observer pointc = speed of lighttd = time delay
Radar EquationsRange Resolution(rough) dR = 0.8*c*t0c = speed of lightt0 = pulse duration
Radar EquationsSignal-to-Noise Ratio SNR = Pr/N =(Pt Gt Gr lambda^2 Ls) / ((4pi)^3 R^4 N)Pr = Power receivedN = NoisePt = Power transmittedGt = Gain transmittedGr = Gain receivedlambda = wavelengthLs = loss factor (0.3 - 0.5)R = range
Radar EquationsGain transmitted Gt = 4pi / (dTHETA dPHI)dTHETA = angular beamwidth verticaldPHI = angular beamwidth horizontal
Radar EquationsSynthetic Aperture Radarcross-range resolution to a dcr = lambda / 2thetaB = 2a/2 = alambda = wavelengththetaB = beamwidth
Radar EquationsAntenna GainGr = Gt = ? Gr = 4pi Ae / lambda^2 = GtAe = Antenna effective arealambda = wavelength
Radar EquationsRadar Noise N = k T0 B Fk = Boltzmann's Constant = 1.38 * 10 ^(-23)J/KT0 = temperatureB = bandwidthF = "noise figure"
Radar EquationsRange accuracy dR = c / (2B sqrt(2SNR))c = speed of lightB = bandwidthSNR = signal-to-noise ratio
Decibelstwo 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 EquationsPhased Array Radar phi / 2 pi = (d sin(theta)) / lambdaphi = phase difference between elementsd = distance between elementslambda = wavelength