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    Polhemus computer
    From: Gary LaPook
    Date: 2008 Jul 15, 04:12 -0700

    
    Gary LaPook writes:
    
    The Polhemus computer provides a convenient way  to plot celnav fixes 
    and this posting will show how you use it for this purpose. The other 
    side of the computer is used for in flight celnav and I will leave a 
    discussion of that use for later.
    
    The first step in plotting a celnav fix is plotting the assumed 
    positions for each body and I will use the data from the "3-Star 
    Fix-'Canned Survival  Problem'" thread for this example.
    
    Figure 1 shows the standard way of making a plotting sheet. A line is 
    drawn from the center at the same angle above above the horizontal that 
    is the same as the latitude of the center of the plotting sheet, in this 
    case, 34 degrees. The dividers are set to the difference in longitude 
    from the center meridian (in this case 119º 15') to the longitude of the 
    A.P. The first A.P. plotted is for Vega which is 119º 06.9' which is 
    7.9' east of the center meridian so the dividers are set to represent 
    7.9 as measured on the center meridian scale which I have multiplied 
    four times to make the scale of the plotting sheet larger so the 
    dividers were set to 31.6 and placed along the diagonal line. From this 
    point you go straight down and place the mark for the A.P. (an inverted 
    "V") on the central parallel of latitude.
    
     Figure 2 shows the other two A.P.s plotted as well.
    
    Figure 3 shows the base of the Polhemus computer which a vertical grid 
    marked in units, an unmarked horizontal grid and a surrounding azimuth 
    scale. ( On my computer I have added two scales near the center of the 
    grid for calculating the "motions" for in flight use and these scales 
    should be disregarded for this discussion..)
    
    Figure 4 shows the transparent plotting surface that is mounted on the 
    central pivot of the base which has three vertical and three horizontal 
    lines lines forming a square and spaced to occupy 15 units on the 
    vertical scale on the base unit. (The plotting surface also has scales 
    marked along the lines but we will not make use of these tic marks.)
    
    Figure 5 shows the plotting disk mounted on the base with the true index 
    set at 56º which lines up the numbered central line on the base 34º 
    above the horizontal and this causes the computer to be set in the 
    equivalent manner as the plotting sheet in figure 1. We use a similar 
    procedure and go straight down from 7.9 on the scale and place the Vega 
    A. P. on the horizontal line.
    
    Figure 6 show the the other A.P.s plotted with the A.P. for Spica 
    plotted up from 7.9 since the A.P. is 119º 22.9 which is 7.9 west of the 
    center meridian; and Pollux plotted up from 24.1 representing 119º 39.1'.
    
    Figures 7 through 12 show the plotting of the Spica line on the plotting 
    sheet using an aircraft plotter and the '"flip-flop" method. Figure 7 
    shows the plotter's edge passing through the Spica A.P. and set to the 
    azimuth of 170.5º, the azimuth of Spica.
    
    Figure 8 shows the dividers set to a scaled intercept of 12.9 NM and set 
    along the straight edge with one leg on the A.P.. Holding the dividers 
    in place the the plotter is slid up so that the 270º mark on the plotter 
    scale is against the other leg of the dividers which is shown in figure 9.
    
    Now carefully holding that leg and the plotter in place you move the leg 
    that had been at the A.P. so that is is on the reference line on the 
    other side of the azimuth scale on the plotter so that now the dividers 
    is at right angles to its previous position as shown in figure 10.
    
    Carefully holding the dividers in place you slide the plotter out and 
    reposition it with the straight edge against the two divider legs so now 
    the straight edge is in position to draw the Spica LOP as shown in 
    figure 11 and 12.
    
    Figure 13 shows the complete fix after carrying out the same steps for 
    the other bodies.
    
    We will now go through the same process on the Polhemus computer. Figure 
    14 shows the true index set to 58º which is the azimuth of Vega. Figure 
    15 shows the A.P. for Vega which is at 5.5 on the base grid. Since the 
    Vega intercept is .5 away we move away from 58º half of a NM and trace 
    the LOP on top of the "5" grid line as shown in figures 15 and 16.
    
    
    Figure 17 shows the true index set to 170.5º which is the azimuth of 
    Spica. We then count down (away) 12.9 NM from the Spica A.P. (which is 
    the "V" located on the "1" grid line, actually the "10" line which we 
    are scaling as "1") and trace the Spica LOP on top of the "14" line as 
    shown in figure 18. Figure 19 shows the Vega and Spica LOPs with the 
    plotting disk set to show north as up.
    Figure 20 shows using the same procedure being used to plot the Pollux 
    line with an intercept of 13.6 away from an azimuth of 290º.
    
    Figure 21 shows the completed fix with the plotting disk set to north up.
    
    After carefully plotting these two examples I decided to go for "time." 
    I started over again with a fresh plotting sheet and an erased Polhemus 
    plotting disk. It took 2 minutes and 10 seconds to plot the three A.P.s 
    on the plotting sheet; an additional 1 minute 25 seconds to plot the 
    Vega LOP; an additional 1 minute 30 seconds to to plot the spica LOP; 58 
    seconds more to plot the Pollux LOP and finally another 40 seconds to 
    derive the fix for a total time of 6 minutes and 45 seconds. The fix is 
    34º 13'N, 119º 16.5' W. This is shown in figures 22 and 23.
    
    I then did the same exercise on the Polhemus computer. It took 22 
    seconds to plot the three A.P.s; 40 seconds to plot the first LOP; 28 
    seconds for the second LOP; 18 seconds for the third LOP; then 41 
    seconds to derive the fix for a total of just 2 minutes and 29 seconds 
    which is 4 minutes and 16 seconds faster than using the traditional 
    plotting sheet. The fix is 34º 12.5'N, 119º 16' W a half  mile south and 
    a half mile east of the fix as plotted on the traditional plotting 
    sheet. This is shown in figures 24 and 25.
    
    gl
    
    
    
    
    
    
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