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    HR-1 working re-creation
    From: Gary LaPook
    Date: 2010 Jan 18, 03:59 -0800

    I wrote back in July about my plan to make a working model of the HR-1 
    German model of the Bygrave slide rule using off-the-shelf items to make 
    the locking device that sets the HR-1 apart from the Bygrave. See my 
    prior posts at:
    
    
    http://www.fer3.com/arc/m2.aspx?i=109056&y=200907
    
    http://www.fer3.com/arc/m2.aspx?i=109993&y=200909
    
    I have now accomplished my goal. I have attached twenty eight 
    photographs showing how to do this, but read my prior posts before going 
    further.
    
    Going in numerical order, the first two photos show the 1.500 inch 
    outside diameter tube that I have used for my prior Bygrave re-creations 
    cut off to ten inches that will be used to mount the cotangent scale.
     
    The next photo shows the locking mechanism I had described in my prior 
    posts along with the cotangent tube and a piece of PVC pipe cut to fit 
    inside the cotangent tube to take the compression load of the locking 
    mechanism.
    
    Photo four shows the locking mechanism with the PVC pipe in the 
    assembled position.
    
    Photos five, six and seven show the same now installed inside the 
    cotangent tube.
    
    Photo eight shows a detail of the expanding ring that is used to lock 
    the two tubes together.
    
    The difficulty in making this is finding tubes that are a good tight 
    fit. I found aluminum tubing used for making antennas at:
    
    http://www.dxengineering.com/Products.asp?ID=278&SecID=136&DeptID=43
    
    They have tubing with an outside diameter of 1.625 inches and a wall 
    thickness of .058 inches making the internal diameter 1.519 inches, a 
    good fit on 1.500 inch O.D. tubing. If you could print the cotangent 
    scale directly on the 1.500 tube this would be a good solution but my 
    method requires me to print the scale on paper and mount it on the tube 
    under a plastic sheet for protection making the diameter of the 
    cotangent scale 1.520 inches, too large to fit inside a tube of this size.
    
    The next largest size of tubing in 1.75 O.D., 1.634 I.D., too large for 
    a good fit on the 1.520 diameter cotangent scale.
    
    http://www.dxengineering.com/Parts.asp?ID=2413&PLID=278&SecID=136&DeptID=43&PartNo=DXE-AT1251
    
    Photo nine shows this tubing in line with the cotangent tube.
    
    Photo ten shows my solution to this problem. I decided to bush the inner 
    tube out to fit closely to the cosine, outer, tube. I used five sheets 
    of regular paper, 8.5 by 11 inches (standard paper size in the U.S.), 
    glued with rubber cement (which has the advantage, that if you need to 
    start over, the glue will come off easily) totaling 55 inches wrapped 
    around the tube. The paper is .004 inches thick and the five sheets 
    brought the diameter close enough (considering that the cotangent scale 
    and the plastic sheet would be placed around it) to make a good fit to 
    the cosine tube. Since I wanted to seal the scale from the environment, 
    prior to putting the paper on the tube, I used several sheets of the 
    sticky plastic sheets cut into 1/4 inch wide strips to wrap around the 
    tube near the top to bring the diameter out far enough that the plastic 
    sheet mounted on top of the scale would stick to these layers of plastic 
    thus sealing off the top of the tube and the scale. After mounting the 
    paper I did the same thing at the other  end of the paper this time 
    using 3/4 inch wide strips.
    
    Photo eleven shows the cotangent scale and photo twelve, thirteen and 
    fourteen shows th scale mounted on top of the paper on the cotangent 
    tube and covered with the protective plastic sheet.
    
    Photos fifteen and sixteen show the cosine scale mounted on the larger 
    tube and covered with a plastic sheet. Photos seventeen and eighteen 
    show the cotangent tube being inserted inside the cosine tube.
    
    
    Making the cosine scale presented a bit of a problem. Since the cosine 
    tube has an O.D of 1.750 and the cotangent scale was only 1.520 inches 
    in diameter it was necessary to print the cosine scale at a larger scale 
    than the cotangent scale which was not a problem using Acrobat. However 
    when I tried out the scales a problem presented itself. My printer made 
    the cosine scale wider but also taller so that the pitch of the scales 
    no longer matched. Although it worked this way it caused ambiguity since 
    the cursor would sometimes end up between spirals on the cotangent scale 
    and either answer (higher or lower than the end of the cursor) could 
    have been the correct one. I contacted Dave Walden (the original source 
    for the scales I have been using) and he was able to modify the vertical 
    and horizontal ratios of the cosine scale so that, when printed out wide 
    enough to fit around the tube, the vertical spiral pitch matched the 
    cotangent scale. (Thanks again Dave.)
    
    Photos nineteen and twenty show the two cursors, the cosine cursor 
    pointing to zero and the cotangent cursor on 76 degrees. I again made 
    the cursor  out of clear plastic by first printing the instructions on a 
    sheet of paper, drawing in the cursors and then photocopying this onto a 
    clear plastic sheet made for use in an ink jet printer. I then wrapped 
    it tightly around the cosine scale and held in that position with two 
    pieces of scotch tape on the inside of the cursor tube. I then wrapped a 
    sticky clear plastic sheet around it to protect the printing on the 
    cursor tube and to hold it in shape. I then removed the scotch tape.
    
    Photo twenty-one shows the condensed instructions printed on the cursor 
    tube. The cosine scale is white underneath this section of the cursor 
    tube to enable easier reading of the instructions.
    
    Photo twenty-two shows the "zig-zag" printed on the cursor tube which 
    lines up with the two cursors to guide the user through the computation.
    
    Photo twenty-three and twenty-four show close ups of the cursors 
    pointing to zero on the cosine scale and 76° on the cotangent scale.
    
    Photo twenty-five shows the cursor pointing to 76°on the cotangent scale.
    
    Photo twenty-six shows the tubes extended so that the cotangent cursor 
    can point at 55'.
    
    Photo twenty-seven shows a close up of the cursor pointing to 55' at the 
    bottom of the cotangent scale.
    
    Photo twenty-eight shows the tubes collapsed.
    
    Turning the wing-nut (control knob) one quarter of a turn locks the two 
    tubes together and is an easy manipulation to make. Since the cosine 
    tubing is only .058 inches thick the cosine scale and the cotangent 
    scale are very close together, and to the cursor, minimizing any 
    parallax problem when reading the scales.
    
    I have also attached the modified cosine scale and note that the tick 
    marks go down from the line under the numbers. The cotangent scale is 
    made with the scales posted last March bt Dave Walden for the flat 
    Bygrave at http://fer3.com/arc/img/107501.f2-lapook1.pdf
    
    Also attached is the form for the cursor tube.
    
    The only downside to this model, compared to the prior model I made of 
    the Bygrave, is that it is three times heavier since the locking 
    mechanism and the cosine tube each weigh as much as my original 
    re-creation of the Bygrave.
    
    I demonstrated this HR-1 to Frank, Mike and Greg prior to our flight 
    last Saturday.
    gl
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    

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