1. Factors Affecting EFW Boom Mounting Accuracy Paul Turin UCB/SSL

2. Boom Geometry Errors The accuracy of the EFW electric field measurement is in part dependant on the geometry of the EFW booms on the spacecraft. Types of geometric errors are: –Boom placement on spacecraft SPBs: –Sensitive only to translation of wire hinge point caused by: –Boom bolt pattern location –Rotation of boom on bolt pattern –Translation of boom on bolt pattern –Boom mounting planes not parallel to SC XY plane AXBs: –Coaxiality of AXB housing to SC Z axis –Boom straightness SPBs – not a factor as wires fall on radial lines naturally AXB boom-to-mount runout AXB whip-to-boom runout –Spin Axis Errors CG offset Principal axis tilt

3. SPBs: Effective Axes and Effective Center The EFW XY measurements are sensitive to the angle between opposite pairs of spin plane sensors. The angle between these axes is defined not by the boom wires themselves, but by lines between opposite pairs of sensor spheres. We define these as the effective axes. The angle between the effective axes is the effective angle. Where these imaginary lines cross is the effective center of the measurement, and this moves away from the CG as the result of several effects. Both non-right effective angles and effective center shifting cause phase errors in the EF measurements. The former causes a phase shift due to the spacecraft spin, and the latter due to relative motion between the spacecraft and the E-field wave. These effects are not separable and are cumulative. The effective angle is less sensitive to hinge point changes than are the individual wires, due to the effective axes being approximately twice the wire length.

4. SPB Placement Errors SPB Error Budget Allocation The science requirement is to know the electric field to within 1 deg in X and Y, taking into account all sources of error. Keeping the probable magnitude of other sources in mind, a 0.1 deg error was allocated to the effective angle due to mechanical placement errors for the SPBs. This allocation may be revisited as the relative error contributions become better known, with a direct impact on the positioning tolerance for the EFW booms. Hinge point translations The SPBs are sensitive only to translations of the hinge point (where the wire exits the boom unit) in a plane normal to the wire because the wire is effectively limp and will lie on a radial line (from the actual spin axis) originating at the metering wheel regardless of small rotational errors of the boom about that point. Translations in the radial direction have no effect. Translations in the Z direction have less effect than translations normal to the radial and in the XY plane, as will be shown. Wire Hinge Point (for small angles) Metering Wheel Spacecraft Radial Direction

5. SPB Specific Cases SPB hinge point translations can stack up in different ways and cause different kinds of effects. To investigate sensitivity to these different types of positional errors, in each case I set the effective axis error to the total position budget of 0.1 deg and looked at the corresponding SPB mounting tolerance required to achieve this. The effect of this movement is shown for different directions on the layouts below. Offset in Z Because the boom wires remain parallel to the XY plane, offsetting the SPBs in the Z direction has little effect on the angle between the effective axis and the spin axis. A combined offset of opposite booms of 5.35” (.136m) is req’d to generate a 0.1 deg angle error. Effective Axis

6. One SPB Offset in XY Plane If three booms are perfectly located, one boom must be offset.138” (.0035m) in the tangential direction to generate a 0.1 deg effective axis angle. Offset exaggerated for clarity

7. Worst-Case SPB Offsets in XY Plane If all four booms are off the same amount in the worst configuration (a flattened X as shown), they must be offset by.036” (.0009m) to generate a 0.1 deg effective axis angle. Since this is the smallest offset of the in- plane cases it is the worst case, and we will look at the boom mounting positional tolerance required to generate a.036” hinge point offset and hold the effective angle error to 0.1 deg. The booms can both translate and rotate on their mounting bolts due to mounting hole clearance, as well as rock side-to-side due to their mounting planes not being parallel to the SC XY plane. We will look at the worst case of each to bound the problem. Offsets exaggerated for clarity Effective Aves are coincident with wires in this case

8. Worst-Case Translation of Boom on Bolts Here the a SPB is translated against its mounting bolts, taking in to account reasonable minimum bolt-to- hole clearances, and the position tolerance on the bolt hole pattern is adjusted to yield a hinge-point offset from the theoretical location matching the.036” offset from the previous page. This results in a TP requirement of 0.060”. Note that this is the tolerance of the four-bolt pattern to the SC coordinate system – the tolerance within the pattern needs to be something like 0.005” TP. This case assumes the boom mounting surface is perfectly flat and parallel to the SC XY plane. Deviations from these conditions must be accounted for as shown later in “SPB Mounting Plane effects”. View of the SPB bolt hole pattern in XY plane

9. Worst-Case Rotation of Boom on Bolts Here the a SPB is rotated against its mounting bolts, again taking in to account reasonable minimum bolt- to-hole clearances, and the position tolerance on the bolt hole pattern is adjusted to yield a hinge- point offset from the theoretical location matching the.036” offset from the previous page. This results in a TP requirement of 0.129”. This is looser than the translation case because the hinge point is located within the bolt pattern. Thus, translation is a tighter requirement. View of the SPB bolt hole pattern in XY plane

10. SPB Mounting Plane effects In addition to the bolt pattern location, both the mounting surface flatness and coplanarity with the SC XY plane effect the SPB hinge point location. To avoid excessive boom structure distortion, we would like to set the flatness tolerance to 0.005” between 0.5” dia. areas surrounding the bolt holes. Since as previously noted the effective angles are not sensitive to hinge point location in the SC radial and Z directions, what we care about is keeping it located between two parallel planes as for the greatly simplified boom shown at right. As the mounting surface tilts about a radial axis, the hinge point swings side to side as shown by the red arrows. The tolerance zone is defined by the two red planes as shown, and from the “Worst-Case SPB Offsets in XY Plane” page, these are 2x.036” = 0.072” apart if we assume the bolt pattern is located perfectly on the surface. The corresponding parallelism tolerance on the mounting plane (represented by the parallel green planes), taking into account the hinge point height and feet spacing, is 0.023”. Of course, the location of the hinge point in this tolerance zone is also affected by the bolt pattern true position on the plane, so both of these contributors must be considered. Radial Direction Hinge Point Mounting Feet Mounting Base Simplified Boom Model

11. Boom Straightness SPB Wires –not a factor as the wires fall on a radial line naturally (from the spin, not geometric axis). The wires are effectively limp on the scale we care about. AXB –Due to its relatively short length, the inherent AXB measurement accuracy is low compared to the SPBs and so its positional sensitivity is less critical than the SPBs. The science requirement is to know the electric field to within XXX deg in Z. 1 deg is allocated for the mechanical error. Of this, 0.8 deg is taken up by the worst-case stackup of deployed straightness, Whip/Stacer runout, bending due to centripetal acceleration, and thermal bending. This leaves 0.2 degrees for alignment of the AXB tube to the spacecraft axis, and the translates to a concentricity tolerance of 0.039”.

12. Spin Axis Errors Despite best efforts in spin balance, there will be some difference between the spacecraft Z geometrical axis and the spin (principle) axis. There needs to be a budget for both angular and CG offsets. CG Offset The direction the SPB wires point is not only a function of the boom position on the spacecraft, but also of the location of the SC CG, as this determines the location of the spin axis and hence the origin of the radial lines that the wires lie upon. With perfect boom placement, causing a effective angle of 90.1 deg takes a CG offset of 42mm or 1.65”. This also generates an effective center offset of between 64.2” (1.63m) and 80.7” (2.05m) depending on the offset direction. The phase shift due to offsets of less than XXX are considered negligible. Effective Center Path of Effective Center as the CG offset azimuth varies

13. Spin Axis Tilt The EF measurement is sensitive to spin axis tilt – 0.1 deg of tilt translates into a 0.1 deg error in the Z axis component of the E field (top right figure). However, if the actual spin axis is known (via star tracker or other measurements), then the effect is much less pronounced. It takes a spin axis tilt of 4 deg to generate an effective angle of 0.1 deg from the actual spin axis (bottom right figure). The uncertainty in the spin axis angle knowledge adds directly to this error.

14. What do we do with all of this? A proposal for boom alignment I initially had hoped that the boom positioning requirements would be loose enough that we could avoid any alignment measurements and adjustments during the spacecraft structure build up and instrument installation. While the tolerance budget looks to be loose enough to allow installation of the booms without any alignment checks (with bolt hole slop minimized), alignment of the boom mounting brackets on the spacecraft will likely be necessary. I propose that SSL provide a alignment fiducial with tight-fitting bolts a and a tooling ball (or cube), something like the one shown on the “SPB Mounting Plane effects” page. APL would then mount it to the SPB bracket and shim the mount until the hinge point (tooling ball center) is within a lateral tolerance zone of 0.060” (0.072” – 0.012” for the bolt clearance). As this is critical only in one direction, shimming should not be too difficult. The relative contributions of mounting pattern offsets and mounting plane tilts will not matter since rotations of the boom are not important as long as the hinge point is in the right place. This alignment, if performed during the SC structure buildup before any heavy equipment (such as the battery) is installed, might avoid concerns about 1g release of structural sag as well. 1g sag would also cause deflections mainly in the Z direction, to which we are not sensitive. The panel that the boom brackets are mounted to need to be pinned or otherwise have their mounting repeatable if they are to be removed at any time after the initial alignment. This plan would allow boom installation and removal without realignment, as will be required for restowing the booms after deployment during EMC, to be done without any rechecking of the boom alignment. The issue of errors due to spin axis tilt needs to be addressed. If we are going to count on accurate knowledge of the spin axis offset rather than tight control of it, then the ability to measure the offset magnitude with the ADCS needs to be determined.