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    Re: Sextant Arc Calibration : FIRST LIGHT
    From: Brad Morris
    Date: 2014 Mar 21, 21:16 -0400

    Hello Frank

    Thanks for the encouragement, I was beginning to think it was just Bill and myself who were concerned.

    You asked (in general), how I will prove I am measuring something and not just noise?  That's an easy one!  The Autocollimator has a range of measurement of 30 arc minutes, which is divided into 3600 directly indicated parts of 0.5 arc seconds each.  Align the AC to the index mirror and zero the AC.  Move the sextant mirror by 10 arc minutes and observe the AC.  Yes, 10 arc minutes.  So it really is measuring angles and not noise.

    The AC was last calibrated in 2012, used in 2012 to certify other machinery accuracy and repeatability, and then it sat on a shelf from then until now.  Their PhD's were required to review my equipment (Ultradex & AC), my process, equations, measurements and results; as these are key to overall machine performance.  We passed with flying colors and sold off the multimillion dollar machine. 

    The equipment is in good working order!

    Your point about repeatability is spot on.  If you look at the graphical data, you will see that there are many angles in which measurements are repeated to within a very few arc seconds, albeit with some large outliers.  The woobly wooden structure is the issue here.  The first light announcement was to show the method and some preliminary results.  Not to show final results.  That woobly wood is a POS.

    Once I move to a concrete floor, granite surface plates and structural metal members (as discussed in my response to Bill) I have confidence that the results will be stellar.  How confident?  I have been used this type of equipment to certify servo axes for accuracy and repeatability since the 1980's.  That includes the design of the servo system and the brackets & devices used in the metrology.  The sextant is a precision rotary device, just as the servo systems were.  I just never had the $40K to plunk down on the AC and Ultradex.  That's been resolved.

    I do have a question that you can help me with.  How parallel must the telescope be to the arc?  What is the collimation required?  Is there some sort of equation that defines the tolerance?  I ask because this drives the flatness requirement to the granite surface plate.  In my notes to Bill, I described a method using the AC and a Starrett Croblox Reflecting Cube.  It depends on the surface plate flatness.  So I should get a surface plate good enough to do the collimation as well


    On Mar 21, 2014 7:00 PM, "Frank Reed" <FrankReed{at}historicalatlas.com> wrote:

    Hi Brad,

    Looks really interesting. I hope you can get it working.

    As with any of these means of estimating arc error, you have a problem to consider: how will you prove that you're measuring something? How will you test your accuracy? Repeatability is probably the place to start. Try this with one sextant on two days and see if you get the same results --or at least close. Oddly enough, you really need a sextant with some substantial arc error so that you will have some guaranteed signal above the noise. After repeatability, you'll need to find way of proving that the system itself isn't producing some sort of bias. For example, a (hypothetical) misalignment of some sort might lead to an apparent arc error from the system rather than the individual instruments. For example, suppose the measuring system introduces a bias of 0.5'*(angle/90°)^2. That is, it's proportional to the square of the measured angle, and at 90° the bias is half a minute of arc. As long as any such bias is stable, you would probably be able to detect it after accumulating data on something like a dozen different instruments. And of course that complicates matters quite a bit... You would almost need to open a laboratory to test sextants just to get the data to prove that you CAN open a laboratory to test sextants.


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