Bill Hawkins wrote: > OK, there are serious sources of error in making a one-time > solar transit measurement. > > What I propose is a differential method, a favorite of > instrument makers to reduce errors. This is possible > because the equation of time makes a correction of only > one percent or so. > > A steady platform with a single axis of motion is > turned by a precision synchronous motor driven by a > frequency derived from a cesium standard. This provides > a fixed reference rotation speed. > > Use a mirror mounted so that it turns on the horizontal axis > and is in turn turned on the vertical axis by the accurate > frequency. Use a simple sun-tracking servo to keep the image > of the sun on a mirror attached to a galvanometer assembly. > > Use an analog servo to generate a current that will keep the > solar image from the galvo centered horizontally on a target. > Use high frequency dithering to improve accuracy. Filter the > galvanometer current to remove the dither and measure it with > a computer. Use math tricks to subtract the equation of time, > looking for a drift rate at a frequency much less than one > cycle per day, but larger than the drift rate of the standard. > > Systematic errors in the instrument should be revealed. If they > are temperature dependent, they can be compensated. The stability > of the mounting for the apparatus becomes a problem over long > periods of time. Perhaps ways can be found to compensate can be > found, but I can't think of something that doesn't require a > stable reference platform. > > The fact is, no other physical property can be measured to the > same accuracy as frequency, because atomic motion provides a > stable reference. > > The question is, then, can long-term averaging remove the small > errors in measuring the position of the sun relative to a > rotating reference platform? > > If this is feasible, where can I find a Maxwell clamp? Google > can't find one. > > Regards, > Bill Hawkins > > > > _______________________________________________ > time-nuts mailing list > time-nuts@febo.com > https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts > > The accuracy of a solar meridian transit measurement can be significantly improved if the position of the sun is continuously measured starting a short time before until a short time after the meridian transit. A least squares fit to the sequence of positions can then be used to derive an accurate time for the actual transit. This can be done without using any moving components if the position sensor and associated optics have a sufficiently wide field of view.
A Maxwell clamp is a variant of the well known Kelvin clamp kinematic mount. The classical Kelvin clamp employs 3 ball feet on one part which mate with a hole (ideally a 3 sided prismatic hole) a slot (V-groove) and a flat on the other part. The Maxwell variant employs 3 radial V grooves instead of the hole, slot and plane. If the axes of the 3 grooves don't meet at a common centre then differential rotation occurs during differential expansion between the mated parts. However this rotation is repeatable and can in principle be measured and corrected for. Friction should be low in a kinematic mount. Suitable kinematic mount components are available from: http://www.precisionballs.com For heavier loads quasi-kinematic mounts such as spherolinders can be used: http://www.g2-engineering.com/spherolinder.html If a suitable kinematic mount is used, two parts with different thermal expansions can be repeatedly mated whilst maintaining relative alignment to a small fraction of an micron. With suitable components nanometer repeatability can be achieved. For even higher stability with permanently mounted parts, 3 flexures can be used to mate 2 components with differing thermal expansions. Well designed flexure mounts can have higher stability than kinematic mounts because friction is absent. Integral flexures are used in moving stages with nanometer repeatability. http://www.physikinstrumente.com/en/index.php Whilst it is relatively easy to generate a precise frequency it is extremely difficult and expensive to make a platform that rotates with runout of not more than an arcsecond. Roller bearings are inherently unsuitable, preloaded pairs of angular contact ball races are considerably better. Air bearings can be good enough but tend to be expensive. A kinematic bearing design with extraordinary accuracy is possible. Driving such a platform without destroying its inherent precision through the drive coupling can be problematic. Backlash in gear reduction systems can also be a problem unless suitable preloads are used. Periodic and other errors in gears can also be problematic unless the errors are repeatable, so they can be measured. Drag from electrical cables connecting between the rotating platform and its fixed base can also be problematic. You really need an angular position encoder with subarcsecond resolution and accuracy mounted on the rotating platform to allow most of the vagaries of the drive system to be eliminated. Such encoders are not cheap. With an encoder one can also use feedback to improve the accuracy of the rotation speed of the platform. For small rotations flexure pivots or integral flexure equivalents thereof can be used. In principle one could use a pair of star trackers to monitor variations in the angular orientation of the instrument mount with respect to the stars. An accuracy of around 1 arc second in determining the tilt, tip and rotation of the plinth. Although such measurements can only be made at night, with suitable insulation the movements of a well designed plinth would tend to be slow. Bruce _______________________________________________ time-nuts mailing list time-nuts@febo.com https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts