### Coorapid n° 12118

Now this object is quite something ... It is a Coorapid, developed by Leander Avanzini. A lot has already been written about the Coorapid in the Historische Bürowelt periodical, from the international federation of historic office equipment (www.ifhb.de). The article by Detlef Zerfowski can be found in issue 121, and on Detlef’s website. The model I bought came with all of its documentation, and a wooden cabinet of which the top and one side was broken. Luckily, I know a great wood restorer, who made the cabinet as new, which also means that the machine can now be kept dust-free. This seems to be the earliest known serial number, and at the same time the most complicated form of Coorapid - the one with two angle microscopes, and a division in normal (360) degrees and in gradians, where a full circle is 400°. But we’re getting ahead of ourselves.

Essentially, this machine, if you can call it that, is a two-dimensional lookup or conversion table, that allows to convert polar coordinates, characterized by an angle and a distance, to rectangular coordinates, characterized by two perpendicular coordinates in the same base, x and y. Polar coordinates are often used in surveying, because you can traverse from point to point, measuring the angle of the new traverse against the previous one, and measuring the distance to the next point by a measuring chain - or at least that is how they did it a century ago. This gives you polar coordinates, but for using a map, it is a bit easier to just have the relative rectangular coordinates. Also calculating areas is a bit easier that way, so conversion between polar and rectangular coordinates was an important part of survey work.

Now - how wuld you do this in practice ?

If you start at the origin, and you measure the angle alpha against the direction of the x-axis, then measure the distance d, you will end up at the point a, with polar coordinates (d, alpha). To convert this location to rectangular coordinates (x,y), what one needs to do is to calculate

x = d . cos(alpha), and

y = d . sin(alpha)

So this calculation would have involved looking up the sine and cosine of alpha in a table, and making two multiplications of d with these two numbers.

Avanzini thought you could do this much easier by building essentially a scale model of the 2-d rectangular and polar coordinate system, with a rotating table that can be set to any angle, and a sliding distance measure, that can be set to a scale distance. Then you just look at the map at the position where you ended up, and read off the rectangular coordinates of the spot. Or, if necessary, vice versa. This is the Coorapid. The trick is to do it as accurately as possible, and to bring the angle measurements and distance measurements in line with the movable map of rectangular coordinates. The reading of angle, distance and map position is done with microscopes, each with marks, scales and cross-hairs. The Coorapid is calibrated in the factory for the origin of the map to coïncide with the centre of rotation of the map. If the position of the glass plate on which the rectangular coordinate map is engraved is disturbed, and its coordinate centre is no longer in the centre of rotation of the instrument, it may be quite a challenge to restore it. Hence, I have not disassembled the glass plate to replace the water-damaged paper underneath. This is only there to provide contrast anyway.

So how does it work ? First of all , the microscopes need to be adjusted in such a way that for a distance of zero, you end up at the origin. For obtaining this, there are adjustment screws on the sides of the microscopes, so you can calibrate the axes and have the microscope crosshairs point at where you want them. First, let’s look at the contraption and point out some names of things.

There are 4 microscopes - the ones on the left are the “angle microscopes” - they are used to look at the scales with either degrees (the bottom microscope) or gradians (the top microscope). You also see the plug labeled “360” and “400”, which is used to provide 6V to the little lamps that illuminate these scales. Only one at a time can be lit, and it prevents msireading the scales. There is a course setting window at the front, which can be adjusted to read either degrees or gradians.

If the little blind is flipped to cover the 360° scale, the 400 gradian scale is revealed on the right.

So that is two microsopes down, two to go. The middle microscope is the distance microscope. There is a course distance scale in the rectangular window on the carriage. The scale runs from 0 to 20, or 0 to 200m, although it can of course in turn be scaled if necessary.

The table with the map can be rotated by reaching under the edge into the finger holds, and spinning it manually. Once the course setting has been made, the knob at the front is turned to lock the table into a micrometer screw, and it can further be adjusted up while looking through the angle microscope.

This is what you would then see. The fine nonius is part of the microscope, the wide divisions between 30 and 31 are part of the scale. You can tell the long line of the nonius (on the left) is between 30 and 31, more sepcifically it is past the 2nd of 6 divisions, so this means 30°20’. Now looking at the nonius, the 20’ mark is just past the second mark on the nonius, so that makes it 22’. And then it is possible to see that it is a little before half of the distance between the 2nd and the 3rd division on the nonius. So let’s call that 30° 22’ 20”. An error of about 10” should be obtainable in this way.

Let’s look at the distance microscope now. This is the setting of the course scale:

And this is what it looks like under the distance microscope. We know we are between 17 and 18, now we look for the hairline coinciding with the nonius scale:

From this image, we read 170 (17 on the course scale) + whatever we read in the nonius, in this case 7.23 - so 177,23m. An error of 2 to 3 cm should be manageble to obtain.

Now, the procedure for adjustment is detailed in the manual. The first step is to accurately set the angle scale to zero with the angle microscope.

Then do the same with the distance microscope.

Now we finally take our first look through the coordinate microscope, and this is what we see.

We seem to pretty much bang on zero - the miroscope has provision to rotate the crosshairs to bring them parallel to the markings on the map, like so:

If however the location of the map would not be accurately equal to zero, the fine adjustment of the distance is turned to make the vertical marking on the map pass exactly through the origin. Next, the adjustment screw for the coordinate map microscope is turned to make the horizontal mark also pass exactly though the origin. Now we switch our eye to the distance microscope. Because of the adjustment made with the distance screw, the scale will have moved. It is returned to exactly 0 with the correction screw on the distance microscope. With both scales now on 0 and the origin corresponding exactly, the distance is now set to 190m

We look through the coordinate microscope, and twist the crosshairs to coincide with the lines on the map.

It is obvious how to read the coordinates off the map now - the base number is the “Y+19” on the left of the screen. The horizontal scale in the crosshairs reads exactly 0. If this would not be the case, the distance adjustment screw should be used to place the vertical line exactly through 0 on the horizontal scale. The angle micrometer at the front is used to place the horizontal line exactly on the 0 of the vertical scale. Now finally, with all this accomplished, the correction screw for the angle microscope is adjusted until the angles scale is also returned to exactly 0.

The Coorapid is now adjusted.

Let’s try and use it to see whether we can do coordinate transformations. Set 30°22’30” into the angle - first with the course scale:

...then with the fine scale

This is what we see at first, so we lock the map to the micrometer at the front, and slowly turn the micrometer screw to bring the 0 mark of the nonius up through 30° and 20’ to the second mark of the nonius -22’ and then to exactly half of the next division, 30”.

Now we shift our attention to the distance mciroscope - we want to set 177.25m, so we start at 17, towards the 18

And then we adjust the mark on the nonius to 7.25 as well as we can.

Looking at the map, we can now see this:

Starting horizontally from the left, we see that the crosshairs are past the x+14 section, into the x+15 section - this means 150+ meters. Looking at where the mark intersects the crosshairs, we find 152.92m (the last 2 is an estimate - the actual microscope is much sharper than the picture). Starting from the top for y, we see that the crosshairs are in the last section of y+8, so 80+ meters, but not 90+. The crosshairs are at 9.62m, so in total y+89.62m.

Now lets see how well we did ... we find the sine of 30°22’30” to be 0.50566, and the cosine of the same angle to be 0.86273. Plugging these into the formulae above, we obtain:

x= 177.25 x 0.86273 = 152.92m

y= 177.25 x 0.50566 = 89.63m

That is a pretty good 4 significant digit accuracy, I would say.

Let’s try another one - convert an angle of 56°13’10” and distance of 126.82m to rectangular coordinates ?

Looking through the coordinate microscope:

Rotating the crosshairs:

...and reading x=70.52m, y=105.41

calculating with the sine and cosine gives us :

x=70.51 and y=105.40 - not bad, a 1-2cm accuracy! Now we’ll finish up with some more pretty pictures of the instrument:

One slightly odious remark that remains to be made with respect to this machine, is that the pictures of the crosshairs of the coordinate microscope above have all been edited by me. I am sure technical reasons can be made up as an excuse for it, if you try to engrave scales with a certain unit length with marks that are equal to the unit length, and you also need an actual crosshair at the origin, that you end up with the symbol of the Third Reich in the center of your coordinate transformation device microscope crosshairs. For a Linz pair of inventors and a construction firm with its seat in Vienna, in 1948, only three years after the end of the second World War, the failure to rectify this situation rather seems to point to a certain political conviction of those who were involved in building and selling it, rather than a mere oversight - otherwise the insensitivity on display is simply mind-boggling. It bothered **me**, on my very first look though the coordinate microscope, 76 years after the fact.