Telltale Calibration Report Version 7 6/2 2009 Christina von Holstein-Rathlou(1), Haraldur Pall Gunnlaugsson(2), Jonathan Peter Merrison(2) (1) Niels Bohr Institute, Univ. Copenhagen, Denmark (2) Inst. Physics and Astronomy, Univ. Aarhus, Denmark 1 Document log: 21/5 2007 Initial release Draft composed of the documents in \\VAGROD\hpg\TT_new\analysis\Report which are gathered here in a single document. 25/5/2007 1. corrected edition File collected on \\FLETTE\ Documents and Settings\flette\Desktop\Speciale \Reports 29/6/2007 Called draft and distributed to ASTG as a pdf file. 23/1/2008 Added user manual, notes on TiltImages and dynamics 31/3/2008 Added notes on version 3 compliance with requirements (chapter 11), and more small changes. 11/4/2008 Added much more File accepted by Scott and Deborah version 4_draft detailed description of error contributions based on discussions with Deborah and Scott. Small additions to the Mirror calibration section 10/11/2008 Changed to version 5, version 5 change monitoring removed and put to letter size and sent to Thomas Stein as pdf (HPG) 1/12/2008 Added more in-depth introduction version 6 6/2/2009 Added Appendix (chapter 13) version 7 Content Telltale Calibration Report.................................................1 Version 6...................................................................1 10/11 2008..................................................................1 1 Document log:.............................................................2 Content.....................................................................3 2 Introduction..............................................................5 2.1 The Telltale............................................................5 2.2 Calibration report......................................................5 2.3 Notes on nomenclature...................................................5 3 Tilt Measurements.........................................................6 3.1 Log.....................................................................6 3.2 Introduction............................................................6 3.3 Data....................................................................6 3.4 Data reduction..........................................................8 3.5 Analysis................................................................9 3.5.1 Path of the Telltale..................................................9 3.5.2 Origin of the coordination system....................................10 3.5.3 Mass density integrals...............................................12 3.5.4 Stiffness constant...................................................12 3.5.5 Updated Stiffness Constant...........................................15 3.6 Summary of Excel functions.............................................15 3.7 Summary and Conclusions................................................16 4 Oscillation Measurements.................................................16 4.1 Log....................................................................16 4.2 Data reduction.........................................................17 4.3 Analysis...............................................................20 4.4 Results................................................................21 4.5 Frequency response.....................................................22 5 Wind Tunnel Measurements.................................................23 5.1 Log....................................................................23 5.2 Introduction...........................................................23 5.3 Data...................................................................23 5.4 Wind tunnel calibration................................................24 5.5 Data reduction.........................................................25 5.6 Analysis...............................................................27 5.7 Model of the Telltale..................................................28 5.8 Excel functions........................................................30 5.9 Modeling of parameters for wind tunnel.................................31 5.9.1 Density, rho.........................................................31 5.9.2 Viscosity, mu........................................................31 6 Tilt Images..............................................................32 6.1 Data...................................................................32 6.1.1 Catalog of image data................................................35 6.2 First analysis of Tilt-Images..........................................35 6.2.1 Introduction.........................................................35 7 Telltale Mirror calibration..............................................35 7.1 Introduction...........................................................35 7.2 Items calibrated.......................................................35 7.3 Description of the calibration.........................................36 7.3.1 Targets and images...................................................36 7.4 Analysis...............................................................37 7.4.1 Color target.........................................................37 7.4.2 Alignment target.....................................................37 7.5 Data...................................................................37 7.6 Results................................................................37 7.6.1 F001.................................................................37 7.7 Conclusions............................................................39 8 ATLO imaging.............................................................39 8.1 Data...................................................................39 8.2 Files in "Telltale_install"............................................39 9 Evaluation of PIT images of the Telltale from post ORT7..................42 9.1 Table of images........................................................43 9.2 Visual inspection......................................................45 9.2.1 Ratio='N/A' SC344EFF896256365_00000R4M1.jpg..........................45 9.2.2 Ratio=12 SC344EFF896256546_00000R4M1.VIC.............................46 9.2.3 Ratio=3.0 SC344EFF896256274_00000R4M1.JPG............................47 9.2.4 Ratio=5, SC344EFF896256093_00000R4M1.VIC.............................48 9.2.5 Ratio=9.0 SC344EFF896256451_00000R4M1.JPG............................49 9.3 Conclusions from visual inspection.....................................50 10 Interpretation of data from Mars........................................50 10.1 Using the model of the Telltale.......................................50 11 Error estimates and compliance with Payload requirements................51 11.1 Image errors..........................................................51 11.2 Zero wind position....................................................52 11.3 Lander tilt error.....................................................53 11.4 Calibration errors....................................................53 11.5 Summary...............................................................53 12 Telltale user manual....................................................54 12.1 Introduction..........................................................54 12.2 IDL analysis..........................................................54 12.3 Excel analysis part 1.................................................57 12.4 Excel wind analysis (part 2)..........................................58 13 Appendix: Conversion of LTST to LMST using CHRONOS data.................60 2 Introduction 2.1 The Telltale The Telltale wind indicator is a mechanical anemometer designed to operate on the Martian surface as part of the meteorological package on the NASA Phoenix lander. It consists of a lightweight cylinder suspended by Kevlar fibers and is deflected under the action of wind. Imaging of the Telltale deflection allows the wind speed and direction to be quantified and image blur caused by its oscillations provides information about wind turbulence. The Telltale will primarily support surface operations by documenting the wind conditions to improve the efficiency of sample delivery to instruments on the lander deck. During the latter stages of the mission the Telltale investigation will focus on meteorological studies. 2.2 Calibration report This is the seventh version of the Telltale calibration report. At this stage there are several known shortcomings: 1) Not all wind tunnel data has been analyzed, especially the data recorded under 45deg rotation are causing problems. As this data will unlikely change the results obtained, they will probably not be used. 2) Tilt Images are still in the process of being analyzed. This analysis is done with the tools being developed for landing operations (see section 12), that consequently are changing. The main conclusion here is a model that can be applied with the appropriate set of parameters to determine deflections on the surface of Mars and the tools necessary to extract the needed parameters from the images. New versions of this report are expected when people ask for them, and the one produced before landing will be called final. 2.3 Notes on nomenclature There has been some misunderstanding in what actually is called the "Telltale". In this report, the "Telltale" is always the active part of the instrument, consisting of the Kapton tube and Kevlar threads (see Fig. 1). When referring to the whole instrument, we use the term "Telltale Assembly" or "Telltale Experiment". 3 Tilt Measurements 3.1 Log File (folders) Where Description tilt2.pro C:\IDL\tilt on \\FLETTE IDL source code used for all tilt3.pro 070329_b14#1analysis.xls C:\Desktop\Speciale\Tilt Excel folder used on \\FLETTE for analysis b14_1analysis_4.xls C:\hpg\TT_new\analysis\Tilt Should be the last Excel on \\VAGROD analysis file Telltale_addin.xla C:\Desktop\Speciale\Analyse Excel addin file, which on \\FLETTE contains the functions used in analysis 3.2 Introduction The aim of the tilt measurements is manifold. First, one needs to determine the path of the Telltale, or the average position of the Kapton part relative to an origin of a coordination system for further analysis. The tip of the screw has been selected as the origin of the coordination system, and all variables are taken relative to that. Second, a coordinate system is found which is better suited for describing the movement of the Telltale. This coordinate system is also used to calculate the stiffness of the Kevlar fibers. 3.3 Data The Tilt data consists of images taken of the Telltale attached to a screw and tilted at an angle theta' perpendicular to the direction of the camera. This angle is defined positive in the case illustrated in Fig. 1. Fig. 1: Definition of the tilt angles; theta' is here positive while theta is negative. Also shown are the directions in the two coordinate systems made use of in the data reduction. The angle theta is defined from the direction of the Kevlar screw towards the Kapton part of the Telltale from an effective hanging point (x0', y0') that is found in the analysis. The data is taken for different orientations phi of the screw as defined in Fig. 2. Fig. 2: (Left) Definition of the orientation of the screw for theta' = 0 deg in the calibration data. The angle phi is here positive. (Right) Definition of the beta angle on Mars. The angle phi is used to catalog our calibration data and results, and can be related to the directions of interest in Mars data. Here one should note, that we record a property of the Telltale in directions phi + 90deg (theta > 0) and phi - 90deg (theta < 0). If one observes the Telltale under the angle beta on Mars, this should be related to the observation directions phi as: phi = 219.2 deg - beta, for theta > 0 And phi = 39.2 deg - beta, for theta < 0 For each orientation of phi, of the order of 40 images were taken for different tilt angles theta'. The convention used was to start at high theta' (~pi/2), move to negative theta' (~-pi/2) and then back again. The scale of the images (mm/px) was determined by making use of the known size of the Telltale holder (width = 24.79 mm, height = 25.12 mm) marked A in Fig. 1. The raw data is stored under ...\Tilt\b14#1\o on various hard drives containing the raw data from the Telltale calibration. In some cases, additional datasets exists, and these are labeled with a "b". 3.4 Data reduction The pictures were analyzed with IDL routines in tilt2.pro and tilt3.pro which run a number of tasks/subroutines described below. The original data consists of images taken of the Telltale holder with the Telltale and screw fastened to it as seen in Fig. 1. The first task is to determine the position of the screw tip in each picture by zooming in on the screw and using the mouse to choose the five points in the screw indicated in Fig. 3. Going counterclockwise the designations are Top Left (TL), Bottom Left (BL), Tip (of screw), Bottom Right (BR) and Top Right (TR). Fig. 3: Blow-up of Fig. 1. The points to be chosen are designated by white points. For each image, the screw's angle, theta', with respect to vertical is determined from the vectors going from the top point to the bottom point on either side of the screw. The final angle is the average of the angles between vertical and the vectors from the right and left side respectively. To determine the position of the Kapton part of the Telltale a box is centered on the Telltale in the first picture in a series of tilt pictures as seen in Fig. 4. The average background intensity, B_ave, is calculated from the three sides that do not include the Kevlar threads, i.e. the left, right and bottom side. B_ave is subtracted from the picture within the box thus giving the background zero intensity and ensuring that only the Telltale and the Kevlar thread has a non-zero intensity. The calculations are performed in the blue color only. Fig. 4: An example of how the box should be placed in the Tilt pictures. The curves indicate the weighted averages in x and y, showing the final positions of and . To obtain the (x, y) coordinates of the Telltale in the image, a weighted average of the intensities is calculated by summing the intensities by columns in the x-direction and rows in the y-direction, multiply by the column or row number and dividing by the summed intensity. This approach was chosen since the uneven shape of the Telltale makes it impossible to choose corners as done with the screw. For subsequent pictures in the dataset, the user chooses the center point for the box, which should coincide with the center of the Telltale. IDL runs the calculations and the coordinates obtained for a dataset of pictures is written to ...\Tilt\o\o(b).txt. This file is subsequently written to an Excel file for further analysis. 3.5 Analysis 3.5.1 Path of the Telltale It turned out that it was possible to describe the position of the Kapton part in a simple way in the (x', y') coordinate system defined in Fig. 1. All possible positions of the Kapton part of the Telltale can be described on a circle with origin at (x'0, y'0) and radius R. This furthermore allows us to determine the position of the Telltale with a single parameter theta defined as the angle relative to the y' axis as illustrated in Fig. 5. The angle theta is positive counter-clockwise from the y' axis. Fig. 5: Definitions of quantities used in the analysis of Tilt data. The angle theta as illustrated in the figure is positive. The circle of radius R has a centre in the point (x'0, y'0). The angle theta will be used to determine deflection or position of the Telltale. It is possible to define this angle in different ways, but the following convention has been applied in all cases: theta is the angle from the y' axis to the position of the Kapton part of the Telltale, with the origin at (x'0, y'0), positive in the counter-clockwise direction. 3.5.2 Origin of the coordination system From each dataset (same phi), we find the x0', y0' and R in pixel coordinates. The length of the Telltale L = R + y0' should be a constant if the scale of the images is the same. We needed to scale the series (in mm/pixels) since there was a small movement of the camera due to replacement of memory cards and batteries. This scale was found by using the Telltale holder but is not as accurate as the scale found by using the calculated values of L. By scaling the L values we find the average distance of L in mm, and in the end used that value to scale each dataset. We find the mean L distance to be 28.1(2) mm. In regard to the x0' parameter, if it is observed under a specific orientation phi, it is also possible to imagine that this observation is made from the behind under phi + 180 deg, but then the value -x0' is observed. Fig. 6 shows the value of x0' as a function of orientation, where this feature has been used. Fig. 6: x0' as a function of orientation phi. The error bars do not take into consideration errors in determination of the screw tip, and must be underestimated. This data has been analyzed in terms of a sine function x0' = A * sin(phi -phi0) that simulates how this parameter should vary upon orientation. The results are A = 1.6(1) mm and phi0 = 157(4) deg. This can be viewed as the Telltale is shifted 1.6(1) mm in the direction given by beta = -28(4) deg. We would thereby expect the Telltale to be shifted -0.73 +/- 0.13 mm as viewed by the SSI. The variation in R is shown in Fig. 7 in the same way, except that the sign is the same regardless of the Telltale being viewed under phi or phi + 180 deg. Fig. 7: R as a function of orientation phi. The data has been simulated using a sin square function R = R0 + A * sin^2(phi - phi0) and we find A = 2.2(3) mm, phi0 = 70(4) deg and R0 = 22.3(2) mm. This means that there is an axis where the R is greatest, and/or smallest. The greater radius is at phi = 70(4) deg +/- 90 deg, and the small radius perpendicular to that. Relative to the SSI, the short axis will be at beta = -31(4) deg and 149(4) deg and the greater axis at beta = 59(4) deg and -121(4) deg. The variation in y0' is bound by the variation in R, and not presented here as such. 3.5.3 Mass density integrals Before we can calculate the Kevlar Stiffness, an introduction to the mass density integrals that enter the energy equations has to be made. They are defined as rho^(i) = Integral [ l^i rho(l) dl Where rho(l) is the density along the length of the Telltale. From the construction data this is known with reasonable accuracy. Table 1: Mass densities of the Telltale determined from construction data. Part Length (mm) Mass density (mg/mm) Kevlar fibers 24.14 0.04498 Kapton + glue 2.4 4.542 Kapton 4.58 0.205 90% of the mass is situated in the gluing of the Kevlar to the Kapton. The length here is significantly different from the length L above, found to be 28.1(2) mm. However, the centre of the Kapton part is at 27.63 mm, which is in fair agreement with the above. For constant levels of rho_i and l_i, the mass integrals can easily be evaluated as: rho^(1) = Sum i=1 to 3 [ 1/2 * rho_i (l_i^2 - l_i-1^2) And rho^(1) = Sum i=1 to 3 [ 1/2 * rho_i (l_i^3 - l_i-1^3) using the parameters given in Table 2. Table 2: Parameters for the F014 Telltale No. l (mm) rho (mg/mm) 0 0 N/A 1 R-3.49 (mm) 0.04498 2 R-1.09 (mm) 4.542 3 R+3.49 (mm) 0.205 The Excel function "MI(i as integer, R as double)" in the Telltale_addin.xla workbook add-in, calculates the mass integral pho^(i) for the F014 Telltale in SI units. 3.5.4 Stiffness constant To avoid confusion, the parameters involved are shown in Fig. 8. Fig. 8: Definitions relevant to the calculation of stiffness constants. For an infinitely stiff Telltale, theta will always be zero. For an infinitely soft Telltale, the Kapton part will hang in the direction of gravity and theta = -theta'. The gravitational energy of the Telltale is described by: U_G = rho^(1)(phi) * g * (1 - cos(theta' + theta)) using the sign rules represented in Fig. 8. The mass integral rho^(1) is taken from the (x0',y0') position, which depends on the orientation phi. The Kevlar fibres try to make the angle theta as small as possible. This contribution can be represented by a power expansion. U_K = A_K^(0)|theta| + A_K^(1)theta^2 + A_K^(2)|theta^3| + A_K^(3)theta^4 +... The first term will not contribute to a force and the energy in minimized when 0 = d(U_K + U_G)/dtheta = 2A_K^(1)theta + 3A_K^(2)theta|theta| + 4A_K^(3)theta^3 + rho^(1) (phi) * g * sin(theta' + theta) Rewriting this we have: 0 = a_1theta + a_2theta|theta| + a_3theta^3 + sin(theta' + theta) which has to be solved numerically in terms of three parameters a1, a2 and a3 that are: a_1 = 2A_K^(1) / [rho^(1)(phi) * g] a_2 = 3A_K^(2) / [rho^(1)(phi) * g] a_3 = 4A_K^(3) / [rho^(1)(phi) * g] The hysteresis is added directly to the model and end points removed from the analysis. In the analysis performed here, two of the three a_i terms should be enough to describe the Telltale in details, thus a_2 has been set to zero. The graphs used are drawn relative to the gamma = theta + theta' angle that gives a better information on the quality of the fit. As an example Fig. 9 shows a typical hysteresis curve obtained. Fig. 9: Example of a hysteresis curve for the Telltale, obtained under phi = 135 deg. Before it is possible to determine the parameters from the analysis, the mass density integrals have to be solved. It turns out that the variation predicted in this formula, is not enough to show the variation in a_1. This can be understood in terms of the physics of the fibers. Under angles that show additional stiffness, the radius of motion is correspondingly shorten, and this is exactly what is observed. Fig. 10: The value of A_K^(1) as function of orientation angle. The data has been analyzed in terms of a model A_K^(1) = alpha * sin^2(phi -phi0) + beta where the parameters for alpha = (3.8 +/- 0.7)*10^-7 J and beta = (3.5 +/- 0.4)*10^-7 J where found and phi0 was restricted to follow the dependence for the radius. As one can expect, the stiffness is greatest where the circular motion has the shortest radii. The value of A_K^(3) shows no significant dependence on orientation, and a general value was found to be A_K^(3) = (1.40 +/- 0.36)*10^-7 J. 3.5.5 Updated Stiffness Constant It turns out from the wind tunnel experiments that the variation in stiffness along the length of the Telltale is not as prominent as suggested by the Tilt measurement data. If the 90 deg point is dropped from the analysis, it turns out that a much smoother result is obtained, that is in much better correspondence with the wind tunnel measurements. As a part of this, the data was re-examined and refitted. The model for the Stiffness constant was altered slightly to A_K^(1) = alpha * {sin^2(phi-phi0)^-0.5} + beta to easier express what it the combination between average and variation. Table 3: Updated stiffness constants based on wind tunnel data. Parameter\Method All points Excluding 45 deg (and 270 deg) alpha (3.86 +/- 0.71)*10^-7 J. (2.40 +/- 0.91)*10^-7 J. beta (5.47 +/- 0.25)*10^-7 J. (4.98 +/- 0.32)*10^-7 J. In the version 1 calibration data, we apply alpha = 1.50 * 10^-7 J. In this re-examination the value for the other A_K^(3) = (8.5 +/- 4.2)*10^-8 J 3.6 Summary of Excel functions Table 4 shows the Excel functions defined in this section: Table 4: Excel function defined in this section. Function Excel function Comments pho^(i)(R) MI(I,R) R given in mm, Output in SI untits A_K^(i) AkMod(Phi) Phi given in degrees, output in SI units (J) R(phi) Rmod(Phi) Phi given in degrees, output in mm. 3.7 Summary and Conclusions The Telltale selected for Flight is considerably different from earlier versions of Telltales, especially in the respect that it is not a relatively long tube. This has meant that the results are worked out differently than was described in the Telltale CDR and earlier versions of the CCC report. The main findings are listed below: a. The path of the telltale can be described well using a circular motion around an effective binding point that varies in height with orientation b. With this binding point shifted away from the screw direction, there is no offset in the position of the Telltale. c. The stiffness can be described as a power law, that leads to some complications with respect to the formulas d. Excel functions with the main findings have been made to allow for easier evaluation of data. 4 Oscillation Measurements 4.1 Log File (folders) Where Descr. Osc.pro \\VAGROD\IDL\OSC IDL source code used for all AVI \\VAGROD\IDL Package used to read in .MOV Preview_b.xls \\VAGROD Excel file used to read in data \TT_new\analysis\osc Osc.xls \\VAGROD Excel file used to anaslyze profiles \TT_new\analysis\osc Telltale.xla \\FLETTE Excel file with routines for solving \Desktop\Speciale\Analysis diff. equation 4.2 Data reduction The films were analyzed with IDL routine osc, that runs a number of tasks/subroutines described below. The first task is to determine when a single drop starts and ends and determine the frame numbers where a drop starts and ends. Here one enters the frame number to take a look at, and enters a negative number to accept. Fig. 11 shows an example when a oscillation is about to be set into motion. Fig. 11: First frame of an oscillation measurement. The program then takes the average of the first 30 frames to work with. This averages out some of the JPEG compression features, and gives a picture of the position of the Kapton part during the first second. The value of 30 frames has been determined empirically, as using too few does not give a good picture of the position of the Kapton part, and too many overemphasize the low angle oscillations. Fig. 12 shows an example of the obtained average. Fig. 12: Image obtained after averaging the first 30 frames of the oscillation film in the blue color. Due to low contrast, and varying background illumination, it is difficult to determine exactly where the active unit is. The user is prompted for ten points outside the Kapton part, a background model (plane intensity) is fitted to the image intensity of these points and a new picture generated that is scaled to enhance the position of the Kapton part. Fig. 13 shows an example of the generated image Fig. 13: The same as Fig. 12, but the background illumination has been scaled to make the Kapton part of the Telltale better visible. The user is then prompted for the points on the circles that define the upper edge of the Kaption foil and the lower edge. These are fitted two circles with the same origin, and used to determine that origin point where from the angle is determined, and the two radii in pixel coordinates. This data can in principle be compared to Tilt data, but is probably of less quality. It is not important how accurately this is done, as it will not affect the rate of damping nor the timing of the damping. Fig. 14 shows an illustration of what is determined. Fig. 14: Same as Fig. 13, indicating areas that are enhanced for the image analysis. Profiles of the average image intensity are then obtained along the angle determined by the origin found above. This is done by finding an average of pixels that lie within the area defined by theta - Deltatheta /2 < theta < theta + Deltatheta /2 and R_2 < R < R_1. Deltatheta was chosen such that a profile extending from theta = -pi/2 to pi/2 would consist of 200 points. The data obtained for all frames is written to a text file that is subsequently written into an Excel file for further analysis. Fig. 15 shows, as an example, the five first profiles obtained from the analysis of a film. Fig. 15: Profiles of the Kapton part obtained in the first five frames. A lowering of intensity is observed moving from the left to right. The profiles obtained are masked by the gradient in the background illumination, but still it is possible to follow the movement of the active unit along this background. To enable further analysis, all the profiles are normalized to maximum intensity. Fig. 16: Same as Fig. 15 but the profiles have been normalized to the maximum intensity in all frames. All profiles have to be studied in detail, in order to see how to perform the automatic analysis of them. From the data displayed above, it is clear that the data at theta > 1.2 rad. cannot be used, and one has to require normalized intensity < 0.9 to get meaningful analysis. In some cases, individual profiles may have to be altered. This gives the oscillation profile, as illustrated in Fig. 17 and the standard deviation in the angle as illustrated in Fig. 18. Fig. 17: Example of a drop profile. Fig. 18: Example of a standard deviation of the angular determination. The standard deviation can be reduced to velocity of the Kapton part and applied into the analysis, but this has not been done at this stage. 4.3 Analysis The drop data is analyzed in terms of Lagrangian with a Raleigh's dissipation function d/dt (dL/dthetadot) - dL/dtheta + dF/dthetadot = 0 Where L = T - U and F is Raleigh's dissipation function. Here we have for the kinetic energy T = rho^(2) * thetadot^2 / 2 The potential energy comes from two sources, the gravity, U_G, at theta'= 0 and the Kevlar fibres U_K U_G = rho^(1) g (1 - cos theta) U_K = A_K^(1)theta^2 + A_K^(3)theta^4 And Raleigh's dissipation function is written F = 0.5 c thetadot^2 where c is the damping constant. The equation of motion yields: 0 = D thetadotdot + sin theta + a_1 theta + a_3 theta^3 + C thetadot Where D = rho^(2) / [ rho^(1) g ] C = c / [ rho^(1) g ] and the parameters a_1 and a_3 are defined as in the Tilt section. 4.4 Results The model described above, was programmed and the final version was Damp_5 in the Telltale xla file. The last optimization can be found in osc.xls under \\GIBTAM\hpg\TT_new\analysis\osc". In the geometry tested, the value of D is calculated to 2.25*10^-3 s^2, and there was not found any reason to not use this value. The value of C showed the following pressure dependence indicated in Fig. 19. Fig. 19: Pressure dependence of the damping parameter C. The pressure dependence is similar to data obtained of test units (see CDR files for comparison). This shows that the damping of the atmosphere is only of the order of 7*10^-4 s. 4.5 Frequency response Having access to the dynamical model described above, it is possible to add a small AC (alternate current) term, and look at the frequency response. This is shown for terrestrial vacuum and Martian air in Fig. 20. This has not been calculated for all tilt angles, but the natural frequency increases of the order of ~10-20% at high tilt angles. Fig. 20: Frequency response of the Telltale under the conditions indicated. From this data, it will be possible to estimate that any smearing (or Deltanu) is ~7 times amplified at 3 Hz. 5 Wind Tunnel Measurements 5.1 Log File (folders) Where Descr. b14_routine.pro, C:\IDL\AVI on \\FLETTE IDL source code for analysis screw.pro, Fit_Image.pro Telltale_addin.xla C:\Desktop\Speciale\Anlysis Add-in package for Excel on \\FLETTE with wind speed calibration data Theta_b14#1_p8.xls, C:\Desktop\Speciale\Analysis\WTC\p

Excel files with Theta_b14#1_p11.xls, on \\FLETTE data analysis Theta_b14#1_p14.xls, Theta_b14#1_p20.xls C:\hpg\TT_new\analysis\WTC \\VAGROD Diverse files 5.2 Introduction The most important data from the calibration of the Telltale is the wind tunnel data. Here the deflection of the Telltale was measured as a function of wind speed under several different conditions. The greatest danger in these measurements was the risk of contamination, as the wind tunnel is by definition a dusty environment. However, by careful cleaning and limitations in wind speeds and pressures, it is possible to maintain a dust free environment. During the measurements, the dust content in the wind tunnel was measured using a Laser Doppler Anemometer (LDA). Not a single particle was counted (actually 16 particles are needed to make a LDA measurement) The wind speed is controlled by the frequency applied to the motor driving the fan in the wind tunnel. The wind tunnel is calibrated (i.e. relationship between motor frequency and wind speed) using and dust in suspension. For these reasons, the wind tunnel was calibrated after the Telltale calibrations were finished. 5.3 Data The wind tunnel data consists of a number of datasets of 35 sec films showing the Telltale in the wind tunnel at all combinations of 4 different pressures, P, and 8 different orientations, phi. For every combination 14 pre-chosen wind tunnel frequencies, f, were filmed for 35 sec giving a total of 32 datasets with 14 movies each. There are 30 frames per second giving us 1050 frames per film. Due to loss of camera settings when changing the camera battery, about half of the datsets are focused, and the other half are unfocused. An example can be seen in Fig. 21. Fig. 21: LEFT: focused picture from the wind tunnel. The white box shows the cut used for finding the origo. RIGHT: unfocused picture from the wind tunnel. The movies are stored in QuickTimeTM format (end with *.MOV) and are stored under ...\WTC\b14#1\p

\o on various hard drives containing the raw data from the Telltale calibrations. 5.4 Wind tunnel calibration At each setting used in the measurements of the Telltale, dust was injected into the wind tunnel. During the 8 mbar calibration, however, a bearing broke, which meant that the wind tunnel calibration took much longer than anticipated, as a different types of bearings were applied. The calibration has been given in the Telltale_addin.xla with the function: Function Hz2vV2(ByVal p As Double, ByVal f As Long) As Double Which gives the wind speed in m/s when applied the pressure p in mbar (integer) and f in Hertz (integer). Fig. 22 shows the calibration profiles. Fig. 22: Wind tunnel calibration profiles. The 20 mbar curve appears to have a kink, but this is probably correct as the derived tilt curves become smooth with this calibration. 5.5 Data reduction The Telltale datasets were analyzed with IDL routines in b14_routine.pro, screw.pro and Fit_Image.pro which do two things. The first program uses the box described in Sec. 3.4 to find the position of the Telltale in all 1050 frames of a film. The other programs find the angle of the screw, theta', and the position of the origo for the (x', y') coordinate system (the tip of the screw). This is done by fitting the small image in the white box shown in Fig. 21 to a calculated average picture of 100 frames from a movie. When fitting, the program ignores the Kevlar string because of its fluctuating position (see Fig. 23) and all fitting is done using the blue pictures. The fitting itself is accomplished by choosing an initial position for the origo, which the program then adjusts along with the magnification, blurriness, rotation and several intensity parameters for the smaller picture. The program returns the fitted parameters mentioned above, whereof we use the position of origo and rotation for further analysis. An example of a fit can be seen in Fig. 23. Fig. 23: BOTTOM LEFT: The white area is not used in the fit. BIG PICTURE: A fitted average picture, with the white box overlain to show the little picture that is fitted to the big picture. For each folder the programs are run and all data is saved in *.txt files under ...\WTC\b14#1\p

\o. This data is subsequently written to an Excel file for further analysis. In version 1 of the calibration report, it has not been possible to reduce all movies. This is due to the fact that in many films, there have been difficulties in determining the screw position accurately due to reflections etc. Table 5 lists the available data. As the quality of the model obtained with this partial data has proven to be excellent, it is unlikely that the remaining data will ever be analysed. Table 5: Datasets available in version 1 of the calibration report marked with an "X". Pressure (mbar) Orientation, phi (deg) 8 11 14 20 0 X X X 45 90 X X 135 X X X 180 X X X 225 X X 270 X X X X 315 X X X X 5.6 Analysis The first step concerns theta'. The rotation angle, r, is given by the program and expresses the angle through which the small image was rotated in the clockwise direction in order to make the fit. By definition theta' is thus equal to -r. The second step involves finding the Telltale angle, theta, which is complicated by the matter that we are using definitions both from the wind tunnel and tilt analysis. These two systems do not use the same scale, and thus a scaling constant, alpha, is introduced in the calculations. Fig. 24: Definitions used in determining theta x_T = alpha x0 + alpha R sin theta y_T = alpha y0 - alpha R cos theta The position of the Telltale, (xT, yT) come from the data reduction of the wind tunnel data and is transformed from the (x, y) to the (x', y') coordinate system. x0, y0 and R come from the Tilt analysis and are scaled in relation to the wind tunnel data. Dividing the equations with each other and rearranging gives: cos theta + (yT/xT) sin theta = y0/R - (x0/R)(yT/xT) or in vector form: [1, yT/xT] * [cos theta, sin theta] = y0/R - (x0/R)(yT/xT) The left side is the cross product between two vectors which, through the cosine formula, is related to the angle between them, and is called Phi. In a common coordinate system, each of the vectors have an angle with the first axis, which are, respectively, xi, and theta. xi is defined as: xi = tan^-1 (yT/xT) Geometry shows that the Telltale angle, theta, can be calculated as: theta = xi - Phi for xi > 0 and theta = xi + Phi for xi < 0 Fig. 25 shows a series of average deflection angles at different air pressures. Fig. 25: Average deflection of the Telltale (averaged over available orientations) for different pressures. The Excel files used for data analysis were named Theta_b14#1_p

.xls and are located in ...\Analysis\WTC\b14#1\o. 5.7 Model of the Telltale We set up a model of the energy of the Telltale as: U = U_G + U_K + U_W Where U_G is the gravitational part, U_K the Kevlar part and U_W the wind contribution. As found previously we write: U_G = rho^(1)(phi) g (1 - cos(theta' + theta)) U_K = A_K^(1)theta^2 + A_K^(3)theta^4 The wind contribution U_W should be divided into drag part U_D and a lift part U_L. The drag potential energy onto a cylinder of width D and length L, that tilts in the wind can be written U_D = [C_D(Re)L^2Drhov^2]/4 * |[theta/2 + sin(2theta)/4 - pi/4]| Where C_D(Re) is the drag coefficient, depending on the Reynolds number Re = D rho v / mu The useful range of wind velocities for the Telltale is 1-10 m/s, meaning Reynolds numbers up to ~62. The lift part can be written in a similar way with the identical pre-factor but a different angular dependence. Since the Telltale is far from being an ideal cylinder, lift has to be taken into consideration. We use a generalized function for the wind contribution since the lift part is not expressed as easily as the drag part. U_W = C_1 * C_D(C_2 rho v / mu) * rho v^2 * f(theta) Where C_1 and C_2 are fitting variables. In SI units, C_1 should be larger than 5*10^-8 m^3, and C_2 around 4*10^-3 m. To find the minimum, one needs to differentiate with respect to the angle, and solve. An empirical way is used to find f(theta) instead of using theory. When solving for the angle theta, one applies dU/dtheta = 0 ==> d(U_G+U_K)/dtheta = -C_1 * C_D(C_2 rho v / mu) * rho v^2 * df(theta)/dtheta Since U_G and U_K are known, we can obtain the quantity df(theta)/dtheta. It turns out, that it followed closely an expression given by df(theta)/dtheta = -B + A * e^(-k theta) Where A, B and k are some parameters. This quantity can not be determined apart from a scaling factor (included in C_1), so we optimized all profiles assuming df(theta)/dtheta = -1 + a * e^(-k theta) Having analysed all profiles under different orientations, it turned out that the deflection did not show as prominent variation in orientation as suggested by the Kevlar stiffness constant. This lead to a re-examination of that data. The final set of parameters obtained is given in Table 6. Table 6: Calibration constants for the F014 telltale Parameter Value C1 (m^3) 3.46(6)*10^-7 C2 (m) 4.12(24)*10^-3 a 0.628(38) k 18.3(13) A series of Excel functions make use of these constants, to predict the position of the Telltale. A comparison between model and data from the wind tunnel is shown in Fig. 25 Fig. 26: Example analysis of a deflection angle profile. The data is taken at 20 mbar under phi = 315 deg. 5.8 Excel functions A great number of Excel functions have been fabricated for these purposes. A list of the important functions is given below Table 7: Functions defined in the Telltale_addin.xla. The most important function is the UtSolve3 function used to predict the position of the Telltale. Parameter Excel function Comments U_G (theta) Function UG(ByVal theta As theta given in radians, and mgl = Double, ByVal mgl As Double) rho^(1)g where can be calculated As Double with the Excel function MI(1,R), where R is in mm. U_K (theta) Function UKevlar(ByVal theta theta given in radians. As Double, ak1 As Double, ak2 As Double) As Double theta <=> Function UtSolve3(ByVal mgl As Parameters as defined above. The dUt/dtheta Double, ByVal ak1 As Double, function delivers theta in radians. ByVal ak2 As Double, ByVal C1 As Double, C2 As Double, aa As Double, kk As Double, v As Double, rho As Double, my As Double) As Double All the energy functions exist also in differentiated form with the same parameterization but the name of the function is then with an added "d" e.g. UKevlar -> UKevlard. 5.9 Modeling of parameters for wind tunnel The parameters used in the wind tunnel are the wind velocity v measured in m/s, Pressure P measured in mbar, and orientation of the Telltale, phi. The orientation should give the value of the parameters A_K's and R. 5.9.1 Density, rho The pressure gives indirectly the density rho of the medium. The Excel function AirDens(P [mbar]; T [degC]) calculates the density in kg/m^3 for dry air. Using the assumption that the atmosphere on Mars is an ideal CO2 gas, the density on Mars can be calculated using the formula: rho_MARS = 0.5366 P [mbar]/T [K]. 5.9.2 Viscosity, mu We apply Sunderland's formula (Crane, 1988) for the viscosity; mu = mu0 * [(0.555T0 + C)/(0.555T + C)] * (T/T0)^1.5 Where C and T0 are, respectively, the Sunderland's constant and the reference temperature. The values are taken from "http://www.lmnoeng.com/Flow/GasViscosity.htm" that is based on the CRC catalogue. These are the same values applied by Nilton Renno in his description of sample delivery experiments for the Phoenix mission. The XLS function my_mars(T) calculates the viscosity in SI units when given the temperature in K. 6 Tilt Images 6.1 Data Tilt images were obtained using three cameras with the geometry shown below Fig. 27: Schematic image of the setup used for Tilt Images. The Telltale assembly is mounted on a rig that can be rotated in all different positions, thereby giving all possible tilt angles of the active unit by making use of the gravity pull. The cameras labeled C1 and C2 take pictures of the assembly to document the orientation and position of the active part of the Telltale. The C3 camera takes images in a position that should resemble the right eye of the SSI. The description of the images is given below: Camera Format C1 JPG 1632x1224 taken with a JVC Everio G Series hard disc camcorder. Images always labelled "PIC_.jpg", size usually ~ 600 kB C2 TIF 3264x2448 taken with a Nikon 8800. Images always labelled "DSCN.tif", size 23520 kB C3 JPG 3264x2448 taken with a Nikon 8700. Images always labelled "DSCN.jpg", size ~ 2600 kB The data is stored under "...\TiltImag\\o