EarTh HOrizon Sensor Preliminary Design Review
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EarTh HOrizon Sensor Preliminary Design Review Team Noah Buchanan Matthew Busby Matthew Cirbo Taylor Dean Jesse Keefer Patrick Klein Thomas Konnert Cole Oppliger Neal Stolz Customers Joe Breno Randy Owen Advisor Dr. John Farnsworth Outline • Background – Motivation – CONOPS and FBD – Baseline Design • Critical Elements – Sensor Feasibility – Algorithm Feasibility – Testing Feasibility • Summary Outline 7/12/2016 Background CPE: Sensor CPE: Algorithm University of Colorado Aerospace Engineering Sciences CPE: Testing Summary 2 Motivation Outline 7/12/2016 • Increase in number of small satellites • Sun sensors are too inaccurate • Star trackers are too expensive • Surrey’s customers desire a Goldilocks solution Background CPE: Sensor CPE: Algorithm University of Colorado Aerospace Engineering Sciences CPE: Testing Summary 3 Requirements • FR.1: ETHOS shall be able to make observations of a simulated Earth. • FR.2: ETHOS shall receive raw data from the sensor and return the attitude displacement vector. • FR.3: ETHOS shall integrate with a simulated spacecraft bus. 7/12/2016 University of Colorado Aerospace Engineering Sciences 4 Nadir Vector Mission Profile Roll Axis Error (-) 7/12/2016 University of Colorado Aerospace Engineering Sciences 5 Coordinate Frame • Any part of the Earth outside the cyan cone is not visible from spacecraft Produced Using Systems Tool Kit (STK) 7/12/2016 University of Colorado Aerospace Engineering Sciences 6 Coordinate Frame • Nadir Vector: Points from spacecraft to Earth Center 7/12/2016 University of Colorado Aerospace Engineering Sciences 7 Coordinate Frame Top-down view 7/12/2016 University of Colorado Aerospace Engineering Sciences View 1 8 Coordinate Frame Top-down view View 1 Rotate about Nadir Vector 7/12/2016 University of Colorado Aerospace Engineering Sciences 9 Coordinate Frame Top-down view View 1 Rotate about Nadir Vector View 2 7/12/2016 Defining the nadir vector as a frame axis removes angular displacement about 1 axis from calculations 10 Coordinate Frame 1 2 2 1 3 3 1 Top-down view • Remaining 2 axes must be perpendicular to nadir vector 7/12/2016 Orbitalside view University of Colorado Aerospace Engineering Sciences 3 2 Orbitalnormal view 11 Coordinate Frame 3 1 2 2 1 1 2 Top-down Orbitalview side view • Remaining 2 axes must be perpendicular to nadir vector • For convenience, direct one axis along sensor’s FOV 7/12/2016 3 3 University of Colorado Aerospace Engineering Sciences Orbitalnormal view Three Axes: In-Sensor: Roll Cross-sensor: Pitch Nadir: Yaw 12 Baseline Design • Single IR (8 – 14 μm) Camera integrated into housing • Test stand with angled mount • Scaled steel Earth disk • Heater below disk • Coated wood plane to provide IR intensity difference 7/12/2016 University of Colorado Aerospace Engineering Sciences 13 CONOPS Inclinometer: Measure Test Bed Angles ETHOS Metal Plate - Simulate view of Earth Heat-pad - Raise temperature of simulated Earth Computer and Power Supply 7/12/2016 Side-view of test setup University of Colorado Aerospace Engineering Sciences Background (Wood) - Room temperature 14 CONOPS Two degree of freedom (DOF) Gimbal Centered IR Image No attitude error in pointing Top-down view of test setup 7/12/2016 University of Colorado Aerospace Engineering Sciences 15 CONOPS Two degree of freedom (DOF) Gimbal Centered IR Image No attitude error in pointing Top-down view of test setup 7/12/2016 Off-point IR Image Attitude error in pointing - Error returned - Compared to inclinometer data University of Colorado Aerospace Engineering Sciences 16 Command and Data Handling Displacement Vector 17 Critical Project Element #1 SENSOR Outline 7/12/2016 Background CPE: Sensor CPE: Algorithm University of Colorado Aerospace Engineering Sciences CPE: Testing Summary 18 CPE: Sensor Functional Requirement FR.1 ETHOS shall be able to make observations of a simulated Earth. Design Requirements DR.1.1 ETHOS shall make observations from simulated orbital altitudes of 250-750 km. DR.1.2 ETHOS shall be fixed and non-rotating. Baseline Design Preassembled infrared camera with optical lens 7/12/2016 University of Colorado Aerospace Engineering Sciences 19 Camera Aspect Ratio • Requirement for perturbations of ±40° in both axes (DR.1.2.1) – Square image provides uniform change in both axes and that both axis meet the requirement • Typical image sizes have set aspect ratios – 3:2 • Usually only used with 35 mm film – 16:9 • Widescreen for television and some cameras – 90° by 50.6° – 4:3 • Typically used in common cameras • Most square ratio of options • IR cameras found with this aspect ratio – 90° by 67.5° FOV 7/12/2016 University of Colorado Aerospace Engineering Sciences 20 Field of View of Pixels • A matrix is created from the pixels of the camera view • Field of view (FOV) is the amount visible in each direction – Each pixel is a portion of the FOV 90° 67.5° 7/12/2016 University of Colorado Aerospace Engineering Sciences 21 Pixel Accuracy • A pixel outputs a value of intensity that is registered from the optics 4 Pixels Simulated Horizon 4 Pixels • This value is considered to occur at the very center of the pixel – Max error: Horizon is considered in the middle of the pixel giving 2 error scale 2 7/12/2016 University of Colorado Aerospace Engineering Sciences 22 Pixels Required • Pixel error is found by the following: πΉππ 1 πππ₯ππ πππππ = ∗ πππ₯πππ 2 • Max error cannot exceed 0.5° accuracy (DR.2.2.1) • Pixel requirements for common FOV below: 7/12/2016 Axis Field of View Minimum Pixels Needed 50° 71 67.5° 96 90° 128 University of Colorado Aerospace Engineering Sciences 23 Realistic Pixel Analysis • Using a camera with 320 x 240 for 4:3 aspect ratio: FOV 1 ∗ = pixel error pixels 2 90° 1 ∗ = 0.199° 320 2 67.5° 1 ∗ = 0.199° 240 2 7/12/2016 University of Colorado Aerospace Engineering Sciences 24 Field of View • 250 km altitude • Angled 74.5° from Nadir (ρ) • 750 km altitude • Angled 63.5° from Nadir (ρ) View of earth from spacecraft [2] 7/12/2016 University of Colorado Aerospace Engineering Sciences 25 STK Representation Dark blue represents Satellite path and FOV Cyan is the view of a 90° by 67.5° camera Systems Tool Kit (STK) simulation 7/12/2016 University of Colorado Aerospace Engineering Sciences 26 Simulated Images Neutral Image of Horizon 90° by 67.5° Pitch Displacement of ±40° 7/12/2016 Roll Displacement of ±40° University of Colorado Aerospace Engineering Sciences 27 Conclusion: Sensor • Field of View – 4:3 typical aspect ratio • 90° by 67.5° field of view with this aspect ratio – Capable of ± 40° disturbance in each axis • Pixel – Minimum pixels needed in a 90° by 67.5° FOV is 128 by 96 to meet 0.5o error from each pixel – Cameras with pixel error of 0.199o in each axis are readily available 7/12/2016 University of Colorado Aerospace Engineering Sciences 28 Critical Project Element #2: ALGORITHM Outline 7/12/2016 Background CPE: Sensor CPE: Algorithm University of Colorado Aerospace Engineering Sciences CPE: Testing Summary 29 CPE: Algorithm Functional Requirement FR.2 ETHOS shall receive raw data and return the displacement vector. Design Requirements DR.2.1 ETHOS should post process raw data from the sensor. DR.2.2 ETHOS shall determine the attitude displacement vector from a simulated Earth. Baseline Design Gradient threshold edge detection with least square curve fitting University of Colorado Aerospace 7/12/2016 Engineering Sciences 30 Algorithm Flowchart 7/12/2016 University of Colorado Aerospace Engineering Sciences 31 Edge-detection • Conventional Edge Detection Filters – Useful in many applications – Computationally inefficient • Simple Gradient Threshold Method – Specific to horizon detection – Computationally efficient 7/12/2016 University of Colorado Aerospace Engineering Sciences 32 Gradient Threshold Flowchart 7/12/2016 University of Colorado Aerospace Engineering Sciences 33 Gradient Threshold Example Curve Fitting • The horizon line can be approximated using a best fit line • Best fit line is found using least squares method 7/12/2016 Horizon approximation University of Colorado Aerospace Engineering Sciences 35 Attitude Determination • A best fit line is fit to the horizon using least squares method • The proportional line perpendicular to the best fit line is used to calculate pitch (δ) and roll (φ) πΏ= π= 7/12/2016 π₯π2 + π¦π2 tan−1 π₯π π¦π University of Colorado Aerospace Engineering Sciences 36 Algorithm Testing Neutral Image of Horizon 90° by 67.5° 7/12/2016 University of Colorado Aerospace Engineering Sciences 37 Conclusion: Algorithm • Edge Detection: – A simple gradient threshold method may be used to detect edges. • Curve Fitting: – Linear least squares method will provide equation of horizon line. • Attitude Determination: – Attitude displacement is readily calculated from the best fit line. 7/12/2016 University of Colorado Aerospace Engineering Sciences 38 Critical Project Element #3: TESTING Outline 7/12/2016 Background CPE: Sensor CPE: Algorithm University of Colorado Aerospace Engineering Sciences CPE: Testing Summary 39 CPE: Testing Functional Requirements FR.1 ETHOS shall be able to make observations of a simulated Earth. FR.2 ETHOS shall receive raw data from the sensor and return the displacement vector. Design Requirements DR.1.1 ETHOS shall make observations from simulated orbital altitudes of 250-750 km. DR.2.2 ETHOS shall determine the displacement vector from observations of a simulated Earth Baseline Design Test stand with angled mount and a scaled, heated, steel Earth disk with wood plane to provide IR difference. 7/12/2016 University of Colorado Aerospace Engineering Sciences 40 Testing: Scaling • A flat disk will simulate the Earth • Only half of a disk will be needed • Disk radius of 50 cm – Requires sensor heights from 14 to 25 cm to simulate 250 to 750 km altitude 7/12/2016 University of Colorado Aerospace Engineering Sciences π H π πππ π 41 Testing: Scaling • Basic Calculations (Assume Perfect Sphere) π» π = π»π‘ππ π‘ π πππ π H = π π − π π π π = sin−1 π π X π π : π ππππ’π ππ πΈπππ‘β π π : π ππππ’π ππ πππ‘πππππ‘π 7/12/2016 π H (π, π) π π π π EARTH University of Colorado Aerospace Engineering Sciences 42 Testing: Scaling Scaled Results With Rdisk : 50cm X (km) H (km) Rdisk (cm) Htest (cm) π (o ) 6628 1735 490 50 14 74.2 7128 2848 1420 50 25 63.5 Rs (km) π H (π, π) X π π π π EARTH 7/12/2016 University of Colorado Aerospace Engineering Sciences 43 Materials • • Needs: • Replicate IR spectrum • Emissivity difference between “Earth” plate and background • Materials: • Highly emissive and thermally conductive front plate • Low emissivity and thermally nonconductive back plate • Rounded edge Steel and wood are the chosen testing materials 7/12/2016 Material Emissivity Conductivity (W/mK) Aluminum .40 204-250 Steel (weathered/oxidized) .80-.88 12.10-45.00 Wood .85-.90 .09-.20 Wood (w/Yellow Paint) .33 .09-.20 University of Colorado Aerospace Engineering Sciences 44 Planck’s Law • Appropriate testing temperatures can be found by rearranging Planck’s Law • Coated Wood: – Twood = 20o – 26 oC (ε = 0.33) – λ = 9.92 to 9.72μm • Desire a wavelength of 8μm with steel: – Tsteel = 89.7ΛC (ε = 0.80) • Silicone heater: •L(T): Spectral Radiance •h: Planck’s Constant •c: Speed of Light •κ: Boltzmann’s Constant •λ: Wavelength Min. Spectral Radiance(L) of Earth: 5.74 W/m2sr [3] Wein’s Law: l = – Up to 260 oC 7/12/2016 βπ π π π= π π2 ln πΏ 2β 5 − 1 π University of Colorado Aerospace Engineering Sciences b T 45 Testing: Apparatus ρ 7/12/2016 Simulated Altitude Mount Angle, ρ 250 km 750 km 74.54o 63.48o • 1 initial angle for each simulated altitude (250 and 750 km) • Inclinometer attached to sensor mount – Provide angular position of sensor for comparison – Max of 0.14o degrees of error • Ball-joint connection for 2 axis control • Adjust sensor from initial positon and compare to inclinometer data University of Colorado Aerospace Engineering Sciences 46 Displacement of Sensor ρ 7/12/2016 Pitch • Attitude adjusted to desired angle • Inclinometer outputs adjusted angles • Inclinometer angles and ETHOS angles compared University of Colorado Aerospace Engineering Sciences 47 Conclusion: Testing • Scaled Earth: • 0.5 m disk of steel • Heated to 89.7 oC • Coated wood behind disk at room temp (20 – 26 oC) • Test Mount • Ball Joint for 2 degree of freedom rotation • Inclinometer to measure test mount’s angular displacement • Plate to connect ball joint with sensor • Sensor is 14 – 25 cm above disk 7/12/2016 Angular Error Source Error Magnitude (o) Pixel* 0.199 Inclinometer 0.140 Mounting Angle 0.100 Model Earth Size/Distance Placed 0.019 Max Slew Rate (3 o/s)* 0.050 Velocity Error* 0.030 Total+ 0.270 *Based on Tamarisk 320 IR Camera +Added in quadrature University of Colorado Aerospace Engineering Sciences 48 SUMMARY Outline 7/12/2016 Background CPE: Sensor CPE: Algorithm University of Colorado Aerospace Engineering Sciences CPE: Testing Summary 49 Summary of Feasibility • CPE 1 - Sensor – Feasible to capture an image of the Earth horizon with a pixel error of 0.199° using a 320x240 pixel image • CPE 2 - Algorithm – Feasible to determine displacement from raw sensor image • CPE 3 - Testing – Feasible to scale the Earth horizon for altitudes of 250 to 750 km and replicate Earth’s IR emissivity with a total angular error of 0.268° 7/12/2016 University of Colorado Aerospace Engineering Sciences 50 Studies Still Needed • Sensor – Select sensor model • Algorithm – Select, build, and implement algorithm • Testing – Finalize decision on materials and plate size, and design testing apparatus • Electronics – Identify microcomputer with sufficient capability – Select suitable voltage regulator and power board 7/12/2016 University of Colorado Aerospace Engineering Sciences 51 Questions? 7/12/2016 University of Colorado Aerospace Engineering Sciences 52 References [1]Peterson, David. "Your Camera’s Settings: Aspect Ratio Selector." Digital Photo Secrets. Digital Photo Secrets, 2014. Web. 8 Oct. 2014. [2] Larson, W., & Wertz, J. (Eds.). (1999). Space Mission Analysis and Design (3rd ed., Vol. 8). Microprose. [3] Van Rensburg, H., “An Infrared Earth Horizon Sensor for a LEO Satellite,” Masters Thesis, Department of Electrical Engineering, University of Stellenbosch, Matieland, South Africa, 2008. [4] Thomas, J., and Wolfe, W., “Spacecraft Earth Horizon Sensors,” NASA, SP-8033, Langley, Virginia, December 1969 [5]http://www.mpoweruk.com/solar_power.html [6]http://www.udel.edu/Geography/DeLiberty/Geog474/geog474_ energy_interact.html 7/12/2016 University of Colorado Aerospace Engineering Sciences 53 BACKUP SLIDES 7/12/2016 University of Colorado Aerospace Engineering Sciences 54 Budget Equipment and Structure 29.80% Sensor Electronics 55.90% Testing Equipment 10.40% 3.90% 7/12/2016 Margin University of Colorado Aerospace Engineering Sciences 55 Mass Budget 22.91% 7.08% 59.95% 10.06% Housing Camera Microcomputer Margin 7/12/2016 University of Colorado Aerospace Engineering Sciences 56 Volume Budget 7.55% 3.38% 7.95% Housing Camera 81.12% Microcomputer Margin 7/12/2016 University of Colorado Aerospace Engineering Sciences 57 Power Budget 18.17% 43.83% Camera 38.00% Microcontroller Margin 7/12/2016 University of Colorado Aerospace Engineering Sciences 58 Projected Costs Equipment and Structure Sensor Electronics Item Cost ($) Infrared Camera Housing Materials Miscellaneous Testing Equipment Item Cost ($) 2620.00 75.00 100.00 Microcomputer Data Storage (32GB SD Card) Power Board Power Regulation Components Miscellaneous (e.g. wires) Total 2795.00 80.00 30.00 15.00 20.00 50.00 Total 195.00 Item Cost ($) Steel Heating Pad Wood Paint Inclinometer DAQ Miscellaneous 100.00 120.00 20.00 20.00 100.00 60.00 100.00 Total 520.00 Total Budget Percent of Cost ($) Total (%) Equipment and Structure 2795.00 Electronics 195.00 Testing Equipment 520.00 Total 3510.00 Allowed Budget Margin Margin Percent 7/12/2016 79.6 5.6 14.8 100 5000.00 1490.00 29.8 University of Colorado Aerospace Engineering Sciences 59 Camera Options Single Camera Multiple Cameras Pros Cons Pros Cons Higher Resolution More Expensive Cost Less More complexity Less Complexity Higher Risk Less Risk Lower resolution Less error 7/12/2016 More Error University of Colorado Aerospace Engineering Sciences 60 Example of Pre-assembled Camera Configurations 7/12/2016 University of Colorado Aerospace Engineering Sciences 61 Data from Pixels Data produced from an image of 320 x 240 pixels of various pixel depth 7/12/2016 Pixel Size Size of Image 8 bit 76800 bytes (76.8 Kbytes) 16 bit 153600 bytes (153.6 Kbytes) 24 bit 230400 bytes (230.4 Kbytes) 32 bit 307200 bytes (307.2 Kbytes) University of Colorado Aerospace Engineering Sciences 62 Curve Analysis Derivation Sin π = cos π= π πΈ π πΈ +π» π πΈπ· = D sinπ π»′ = D cosπ D = π πΈ tan π 7/12/2016 University of Colorado Aerospace Engineering Sciences 63 Curve Analysis Derivation FOV half angle πΉππ π= 2 Angles to widths of FOV πΌ1 = π − π πΌ2 = π + π 7/12/2016 University of Colorado Aerospace Engineering Sciences 64 Curve Analysis Derivation 2D height of curve π = π πΈπ· (1 − cos π½) Length of half of curve π = π· sin π 7/12/2016 University of Colorado Aerospace Engineering Sciences 65 Curve Analysis Height of viewable curve P = N sinπ Height of one pixel βπππ₯ = π (ππ’ππππ ππ πππ₯πππ )/2 Number of pixels in P π ππ’ππππ₯πππ = βπππ₯ 7/12/2016 University of Colorado Aerospace Engineering Sciences 66 Simulation of Disturbances 90° Vertical FOV 67.5° Horizontal FOV Pitch: -40° to +40° perturbation 7/12/2016 Roll: -40° to +40° perturbation University of Colorado Aerospace Engineering Sciences Pitch & Roll 67 Backup: Software Requirements • • • • • 7/12/2016 Return the nadir vector from the sensor data Monitor input current and voltage Store 200 minutes of telemetry data Flag “stale” data that did not update Output the data via CAN bus University of Colorado Aerospace Engineering Sciences 68 Backup: Software Health Data • Input current and voltage are controlled via a power distribution board (PDB) • ADC and a current sensor will provide this data to the MCU 7/12/2016 University of Colorado Aerospace Engineering Sciences 69 Backup: Software Data Storage • External storage (SD card) will be attached to the MCU • Assuming single precision 200 minutes ~ 0.5 MB 7/12/2016 University of Colorado Aerospace Engineering Sciences 70 Backup: Software Data Storage • Input and Voltage saved at 0.5 Hz • displacement vector (two elements) saved at 5 Hz • Single precision (32 bits) [(2 numbers)*(0.5 Hz) + (2 numbers)*(5 Hz)] *(200 minutes)*(60 seconds/minute)*(32 bits/number) = 528 kB 7/12/2016 University of Colorado Aerospace Engineering Sciences 71 Least Square Derivation - Backup [3] 7/12/2016 University of Colorado Aerospace Engineering Sciences 72 Testing - Backup Slide • BOTE Calculations (Assume Perfect Sphere) Equation of Circle π 2 + π 2 = π π2 Y = π π2 − π 2 Tangent of Circle −π π′ = π π2 − π 2 Slope of a line π π −π m= 0−π 0 = π − π′ π π − π π 0= + 0−π π π2 − π 2 Distance Formula π = (0 − π)2 −(π π − π)2 7/12/2016 Since d, Re, & Rs are known: Solve for X & Y University of Colorado Aerospace Engineering Sciences 73 Testing - Backup Slide 7000 Earth 250km Alt 750km Alt 6000 Distance [km] 5000 4000 3000 2000 1000 0 7/12/2016 -7000 -6000 -5000 -4000 -3000 -2000 Distance [km] -1000 University of Colorado Aerospace Engineering Sciences 0 1000 74 Error Analysis-Backup Slide • Pixel Error* – 0.199o • Inclinometer Error – 0.14o total • 0.1o in each axis ο 0.12 + 0.12 = 0.14π • Mounting Angle, ρ – 0.1o • Model Earth Size/Distance Placed from Sensor – 0.02o • Max Slew Rate (3 o/s)* – 0.050o • 3 0/s / 60 Hz = 0.050o • Velocity Error – 0.03o • Total Error: 0.270o D.R. 2.2.1 – Independent Sources ο Add in quadrature 7/12/2016 University of Colorado Aerospace Engineering Sciences 75 Model Earth Size/ Distance Place error π • π = tan−1 ππππ π • πΏπ = • πΏπ = π πππ π π ππ₯ π πππππ π πΏπ = • πΏπ = 0.02π 2 + π π ππ¦ π ∗ πΏππππ π ππ πππ 2 2 ππ πππ +ππππ π • 7/12/2016 ∗ πΏπ₯ 2 + πππ πππ + πΏππππ π = 1.5 ππ πΏππ πππ = 1.5 ππ + … π 2 ∗ πΏππππ π 2 ∗ πΏπ¦ π ∗ πΏππ πππ ππππ π 2 2 ππ πππ +ππππ π 2 2 ∗ πΏππ πππ University of Colorado Aerospace Engineering Sciences 76 Project Element: Power Management Design Requirements DR.3.2.3 – Consume no more than 5 Watts DR.3.2.4 – Accept an input voltage between 22 V and 34 V Design Implication • Step-down voltage regulator to generate usable output voltage for imaging and processing equipment • Supply current limited to 227 mA at 22 V and 5 Watts 7/12/2016 University of Colorado Aerospace Engineering Sciences 77 Voltage Regulators 1. Linear Regulators • Fixed output voltage by adjusting voltage divider network • Difference between input and regulated voltages dissipated as heat Pros: Cheaper Cons: Excess heat, Lower efficiency 2. Buck Converter • Switch operates at high frequency to control the current flow Pros: Greater efficiency Cons: Complexity, More expensive 7/12/2016 University of Colorado Aerospace Engineering Sciences 78 Available Buck Converters Microcomputer Voltage: Vout = 5 V π·π’π‘π¦ πΆπ¦πππ = 7/12/2016 πππ’π‘ πππ Input Voltage: 22 V < Vin <34 V Dmin = 15% Dmax = 23% Model Vin (V) Vout (V) Duty Cycle (%) Max Supply Current (mA) ISL 8115 2.97 – 36 0.6 – 5 10 – 90 - ISL 8107 9 – 75 1.2 – 75 ≤ 100 - LT1934 3.2 – 34 3.3 – 5 ≤ 83 250 LT3470 4 – 40 1.25 – 16 10 – 90 160 ADP 2442 4 – 40 0.6 – 36 5 – 95 2 L7985 4.5 – 38 0.6 - 38 ≤ 100 3500 A5974D 4 – 36 1.235 – 35 ≤ 100 4100 University of Colorado Aerospace Engineering Sciences 79 Spectral Distribution of Earth [4] 7/12/2016 University of Colorado Aerospace Engineering Sciences 80 Spectral Distribution of Sun [5] 7/12/2016 University of Colorado Aerospace Engineering Sciences 81 Earth Vs. Sun Spectrum Distribution [6] 7/12/2016 University of Colorado Aerospace Engineering Sciences 82 Solar Interference [4] 7/12/2016 University of Colorado Aerospace Engineering Sciences 83 Exposure Time Error 7/12/2016 University of Colorado Aerospace Engineering Sciences 84 Exposure Time Error • Expected frame rate is 60 Hz -> exposure time of 0.12 seconds • Velocity at 250 km is ~ 7.75 km/s • Angular error of 0.03° • Error should be accounted for by subtracting out of total error, since testing will be static 7/12/2016 University of Colorado Aerospace Engineering Sciences 85
