CoCalc Shared FilesASYS 631 - Spacecraft Engineering / Homework-04-Lab-03-MOI / HW04_Lab03MOI.sagewsOpen in CoCalc with one click!
Author: Jordan Ziegler
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########### General Use Constants ########### mu_E_km = 3.98601e5; mu_E1 = 1.; #Mu for Earth in km^3 s^-2 #Mu for Earth in canonical units mu_S_km = 1.32715e11; mu_S1 = 1.; #Mu for Sun in km^3 s^-2 #Mu for Sun in canonical units R_E_km = 6378.1366; R_E1 = 1.; #Earth radius in km #Earth radius in canonical units pii = RealField(30)(pi); #Pi to a certain precision SiderealDay_s = 86164.09054; #Sidereal day in seconds SiderealYear_s = 365.25636*SiderealDay_s; #Sidereal year in seconds AU_km = 1.49599e8; #Astronomical Unit in km AU_m = 1.49599e11; #Astronomical Unit in m c = 299792458; #Speed of light in m/s k = 1.38064852e-23; #Boltzmann constant in SI units def RF(r): #Give me a friggin number return RealField(30)(r) def degToRad(degree): #Give degrees, get radians return degree*2*pi/360 def radToDeg(radian): #Give degrees, get radians return radian*360/(2*pi) #############################################
########### MOI Lab Constants ########### M_sr = 680.1e-3; #Measured Mass of the steel ring in KKgrams M_gpc = 386.7e-3; #Measured Mass of the gray plastic cylinder in Kgrams M_slac = 715.3e-3; #Measured Mass of the "SLA Cylinder" in Kgrams Ixx_sr = 1912.2; #Calculated Ixx of steel ring Kg-mm^2 Ixx_gpc = 703.6; #Calculated Ixx of gray plastic cylinder Kg-mm^2 Ixx_slac = 1090.5; #Calculated Ixx of SLA cylinder Kg-mm^2 Iyy_sr = 1912.2; #Calculated Iyy of steel ring Kg-mm^2 Iyy_gpc = 703.6; #Calculated Iyy of gray plastic cylinder Kg-mm^2 Iyy_slac = 1090.5; #Calculated Iyy of SLA cylinder Kg-mm^2 Izz_sr = 3602; #Calculated Izz of steel ring Kg-mm^2 Izz_gpc = 1209.3; #Calculated Izz of gray plastic cylinder Kg-mm^2 Izz_slac = 1950.4; #Calculated Izz of SLA cylinder Kg-mm^2 Do_sr = 150; #Measured Outer diameter of steel ring in mm Do_gpc = 152; #Measured Outer diameter of gray plastic cylinder in mm Do_slac = 152; #Measured Outer diameter of "SLA cylinder" in mm DI_sr = 142; #Measured INNER diameter of steel ring in mm DI_gpc = 0; #Measured INNER diameter of gray plastic cylinder in mm DI_slac = 138; #Measured INNER diameter of "SLA cylinder" in mm WT_sr = 4; #Measured Wall thinkness of steel ring in mm WT_gpc = 0; #Measured Wall thinkness of gray plastic cylinder in mm WT_slac = 7; #Measured Wall thinkness of SLA cylinder in mm h_sr = 50; #Measured Height of steel ring in mm h_gpc = 51; #Measured Height of gray plastic cylinder in mm h_slac = 42; #Measured Height of "SLA Cylinder" in mm ###########################################
########### MOI Lab Question 1 ########### #The steel ring: MOI_sr_xx = MOI_sr_yy = (M_sr/16)*( Do_sr^2 + DI_sr^2 ) + (M_sr*h_sr^2)/12; MOI_sr_zz = (M_sr/8)*(Do_sr^2 + DI_sr^2); print 'The MOI of the steel ring about x and y is: ', MOI_sr_xx, 'kg mm^2'; print 'The MOI of the steel ring about the z axis: ', MOI_sr_zz, 'kg mm^2'; #The plain cylinder (gray plastic cylinder): MOI_gpc_xx = MOI_gpc_yy = (M_gpc*Do_gpc^2)/16 + (M_gpc*h_gpc^2)/12 ; MOI_gpc_zz = (M_gpc*Do_gpc^2)/8; print '\nThe MOI of the gray plastic cylinder about x and y is: ', MOI_gpc_xx, 'kg mm^2'; print 'The MOI of the gray plastic cylinder about the z axis: ', MOI_gpc_zz, 'kg mm^2'; #differences / errors for steel ring: Error_sr_xx = 100*abs(MOI_sr_xx - Ixx_sr)/MOI_sr_xx; #% error for the steel ring about x or y (against measured) Error_sr_zz = 100*abs(MOI_sr_zz - Izz_sr)/MOI_sr_zz; #% error for the steel ring about z (against measured) print '\nThe error % for the steel ring about X or Y: ', Error_sr_xx; print 'The error % for the steel ring about Z axis: ', Error_sr_zz; #differences / errors for plastic cylinder: Error_gpc_xx = 100*abs(MOI_gpc_xx - Ixx_gpc)/MOI_gpc_xx; #% error for the plastic cylinder about x or y (against measured) Error_gpc_zz = 100*abs(MOI_gpc_zz - Izz_gpc)/MOI_gpc_zz; #% error for the plastic cylinder about z (against measured) print '\nThe error % for the plastic cylinder about X or Y: ', Error_gpc_xx; print 'The error % for the plastic cylinder about Z axis: ', Error_gpc_zz;
The MOI of the steel ring about x and y is: 1955.17415000000 kg mm^2 The MOI of the steel ring about the z axis: 3626.97330000000 kg mm^2 The MOI of the gray plastic cylinder about x and y is: 642.212025000000 kg mm^2 The MOI of the gray plastic cylinder about the z axis: 1116.78960000000 kg mm^2 The error % for the steel ring about X or Y: 2.19797044677580 The error % for the steel ring about Z axis: 0.688543805933176 The error % for the plastic cylinder about X or Y: 9.55883300378874 The error % for the plastic cylinder about Z axis: 8.28360149485632
########### Homework Question 1 ########### P_transmit_w = 2; #Transmit power of satellite in watts P_transmit_dB = 10*log(P_transmit_w/1, 10); #Transmit power of satellite in dB referenced to 1 w G_sat_dB = 8; #Satellite antenna gain in dB Loss_f = 1; #Antenna loss/gain as a fraction Loss_dB = 0; #Antenna loss/gain as dB G_sat_rat = 10^(8/10); #Satellite antenna gain as fraction EIRP = P_transmit_w*G_sat_rat*Loss_f; EIRP_dB = 10*log(P_transmit_w,10) + G_sat_dB; print 'EIRB as a fraction is: ', RF(EIRP); print 'EIRB in dB is: ', RF(EIRP_dB);
EIRB as a fraction is: 12.619147 EIRB in dB is: 11.010300
########### Homework Question 2 ########### f = 2.2e9; #Carrier freq in hz wavelength = c/f; #Wavelength of carrier freq alt = 400e3; #Altitude in meters (given as 400km) Ls = (4*pii*alt/wavelength)^(-2); Ls_dB = 10*log(Ls,10); #In dB print 'Free Space Loss L_s: ', Ls; Ls_dB
Free Space Loss L_s: 7.3494753e-16 -151.33744
########### Homework Question 3 ########### G_rec_dB = 20; #Receiver gain in dB G_rec_rat = 10^(20/10); #Receiver gain as fraction Tnoise = 1000; #Receiver noise temp in kelvin GT_Ratio = G_rec_rat/Tnoise; GT_Ratio_dB = G_rec_dB - 10*log(Tnoise,10); print 'Receiver G/T ratio: ', GT_Ratio; print 'Receiver G/T dB: ', GT_Ratio_dB;
Receiver G/T ratio: 1/10 Receiver G/T dB: -10
########### Homework Question 4 ########### R = 2e6; #Data rate given in bps EbNo_rat = EIRP*Ls*G_rec_rat*(1/k)*(1/Tnoise)*(1/R); EbNo_dB = EIRP_dB + Ls_dB + G_rec_dB - 10*log(k*Tnoise,10) - 10*log(R,10) print 'EbNo as ratio: ', RF(EbNo_rat); print 'EbNo in dB: ', RF(EbNo_dB);
EbNo as ratio: 33.587153 EbNo in dB: 15.261732
########### Homework Question 6 ########### M_prop_dry = 5; #Mass of dry propulion system in kg M_without_prop = 1000; #Mass without propulsion system DeltaV_req = 500; #Total delta-v required for lifetime in m/s Orbit_Alt = 600; #Orbit altitude in km Thrust = 200; #200N thrust Isp = 220; #Isp in seconds M_0 = M_prop_dry + M_without_prop; #Total Mass of system without propellant g = 9.81; #Graviational acceleration near Earth surface M_p = M_0*(e^(DeltaV_req/(Isp*g)) - 1) print 'Propellant mass required: ', M_p, 'kg'; print 'Total system mass: ', M_p + M_0, 'kg';
Propellant mass required: 262.012902906327 kg Total system mass: 1267.01290290633 kg
########### Homework Question 7 ########### HT_Isp = 1500; #Hall thruster Isp in seconds HT_Thrust = 50e-3; #Hall thruster thrust in N HT_Thruster_mass = 2; #Hall thruster mass in kg HT_PwrSys_mass = 10; #Hall thruster power system mass in kg HT_Tank_mass = 3; #Hall thruster tank mass in kg HT_M_0 = HT_Thruster_mass + HT_PwrSys_mass + HT_Tank_mass + M_without_prop; #Mass of system (including hall thruster) without propellant HT_M_p = HT_M_0*(e^(DeltaV_req/(HT_Isp*g)) - 1); print 'HT Propellant mass required: ', HT_M_p, 'kg'; print 'Total system mass: ', HT_M_p + HT_M_0, 'kg';
HT Propellant mass required: 35.0812535988290 kg Total system mass: 1050.08125359883 kg
########### Homework Question 9 ########### mdot_hyd = Thrust/(g*Isp); #Mass flow rate for the hydrazine system hyd_time = M_p/mdot_hyd; #Burn time for the hydrazine system print 'Burn time for full delta V of hydrazine system: ', hyd_time, 'seconds'; print ' ', hyd_time/60, 'minutes'; print ' ', hyd_time/60/60, 'hours'; print ' ', hyd_time/60/60/24, 'days'; print ' ', hyd_time/60/60/24/365, 'years'; mdot_hall = HT_Thrust/(g*HT_Isp); hall_time = HT_M_p/mdot_hall; print '\nBurn time for full delta V of hall system: ', hall_time, 'seconds'; print ' ', hall_time/60, 'minutes'; print ' ', hall_time/60/60, 'hours'; print ' ', hall_time/60/60/24, 'days'; print ' ', hall_time/60/60/24/365, 'years';
Burn time for full delta V of hydrazine system: 2827.38123526217 seconds 47.1230205877029 minutes 0.785383676461715 hours 0.0327243198525714 days 0.0000896556708289629 years Burn time for full delta V of hall system: 1.03244129341354e7 seconds 172073.548902256 minutes 2867.89248170427 hours 119.495520071011 days 0.327384986495921 years
########### Homework Question 10 ########### mission_life = 4*SiderealYear_s; #Mission life in seconds (4 years) percent_mx_life_hyd = hyd_time/mission_life*100; percent_mx_life_hall = hall_time/mission_life*100; print '% mission life hydrazine: ', percent_mx_life_hyd, '%'; print '% mission life hall : ', percent_mx_life_hall, '%';
% mission life hydrazine: 0.00224595104041468 % % mission life hall : 8.20127320712797 %