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Air Data SensorsPitot tube AirspeedIndicated versus true?
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Q = .5 rho V^2 = Pt - PsQ = dynamic pressurerho = air densityV = airspeedPt = total pressurePs = static pressureIndicated is without temperature reading
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Radar EquationsVertical Beamwidthgeneral / circular?
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general:dTHETA = lambda / 2acircular:dTHETA = 1.02 * lambda/2alambda = wavelengtha = aperture radius
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Radar EquationsPower Received
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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
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Radar Equationfrequency (bandwidth)
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fBW = 1 / t0t0 = pulse length
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Radar EquationsTwo dopplersIntegration timeFrequency errorRadial Velocity error
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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
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Inertial Navigation SystemsFibre Optical Gyro
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dPHI = (8pi A N omega)/(c lambda)A = path areaN = number of turnsomega = rate of rotationc = speed of lightlambda = wavelength
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Intertial Navigation SystemsSchuler Frequencytheta..and T
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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
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Radar EquationsDoppler Shift
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fd = 2 vr / lambdavr = radial velocitylambda = wavelength
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Radar EquationsPhased Array RadarGain GaTHETA
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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
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Radar EquationsRange and Max Range
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R = c * tr / 2Rmax = c / 2fPRFc = speed of lighttr = time to recievefPRF = pulse repetition frequency
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Imaging SystemsJohnson Criteria (3)
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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
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Imaging SystemsRayleigh Criterion
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dTHETA = 1.22lambda / Dlambda = wavelengthD = aperture diameter
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Imaging Systemsangular resolution
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dTHETA = theta / NdTHETA = angular resolutiontheta = field of view (rads)N = number of pixels
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Radar EquationsRadar Cross Section (RCS)Summation of many scatterers
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sigma = sum(sqrt(sigma-m) e^(j phi-m)sigma = RCSsigma-m = RCS of individual scattererphi-m = 2-way phase difference
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Basic ElectromagnetismWavevector
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k = 2*pi / lambda= 2*pi * f / clambda = wavelengthf = frequencyc = speed of light
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Inertial Navigation SystemsRing Laser Gyro
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df = 4 A omega / (L lambda)A = path areaomega = rate of rotationL = path lengthlambda = wavelength (laser average, in this case)
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Radar EquationsSynthetic Aperture Radarcross-range resolution
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dcr = R lambda / 2aR = range to targetlambda = wavelengtha = antenna radius
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Radio Navigation SystemsLORAN
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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
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Radar EquationsRange Resolution(rough)
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dR = 0.8*c*t0c = speed of lightt0 = pulse duration
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Radar EquationsSignal-to-Noise Ratio
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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
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Radar EquationsGain transmitted
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Gt = 4pi / (dTHETA dPHI)dTHETA = angular beamwidth verticaldPHI = angular beamwidth horizontal
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Radar EquationsSynthetic Aperture Radarcross-range resolution to a
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dcr = lambda / 2thetaB = 2a/2 = alambda = wavelengththetaB = beamwidth
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Radar EquationsAntenna GainGr = Gt = ?
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Gr = 4pi Ae / lambda^2 = GtAe = Antenna effective arealambda = wavelength
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Radar EquationsRadar Noise
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N = k T0 B Fk = Boltzmann's Constant = 1.38 * 10 ^(-23)J/KT0 = temperatureB = bandwidthF = "noise figure"
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Radar EquationsRange accuracy
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dR = c / (2B sqrt(2SNR))c = speed of lightB = bandwidthSNR = signal-to-noise ratio
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Decibelstwo formats!
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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)
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Radar EquationsPhased Array Radar
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phi / 2 pi = (d sin(theta)) / lambdaphi = phase difference between elementsd = distance between elementslambda = wavelength
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