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George,

You asked at what angle do I hold the Trombone Kamal. That angle is 90
degrees so that the inverse tangent is equal to the inches on the
kamal over the inches from the tape measure. You will aslo find out if
you make one of these that the tape measure likes being at 90 degrees
making maintaining this angle a little easier. For piloting purposes
the Trombone Kamal will be limited to 22.5 degrees off the bow and
forward of the beam. Determining the 45 degree angle can be done with
a 45/90 chart plotting triangle and a length of electric tape to
permanently mark the 45 angle on the cockpit coming.

Greg

On Jun 5, 1:46�pm, "George Huxtable"  wrote:
> In various postings, Greg Rudzinski has described his Trombone Kamal. It's a
> simple and portable device, with some snags. Those snags should be, at
> least, assessed and discussed. Let me try to put it in perspective.
>
> It compares, as Frank has pointed out, with the cross-staff, the standard
> altitude instrument for Western navigation from the beginning of the 16th
> century until it was gradually supplanted by the backstaff in the 17th.
>
> Greg has produced a version of the cross-staff that uses modern material,
> light-absorbing white plastic, to protect the user from being blinded by the
> Sun, an all-too-common fate of navigators in those days. It's also adapted
> to measuring �smaller angles that the conventional cross-staff would. But
> clearly, in writing "Relative bearings, doubling the angle on the bow, and
> distance off by vertical angle are piloting applications that can also be
> performed by the Trombone Kamal.", Greg must have bigger angles in mind,
> even if his recent tests have been limited to angles up to 13�. What angular
> range does he propose will be usable?
>
> Greg hasn't (yet) told us at what angle his plastic plate should be held. It
> doesn't matter (much) for his present small angles, but it will become more
> important as angles increase. Should it be held vertical, at right angles to
> the observer's sight-line to the horizon? Or perhaps, tilted, at
> right-angles to the sight-line to the Sun? One of these two it seems, if the
> angle is to be derived from the arc-tan of the ratio of the two lengths, as
> Greg suggests.
>
> But the cross-staff manages rather better than that, by having the two vanes
> of the transom projecting equally up and down from the staff, with the
> horizon at the end of one, and the Sun at the end of the other. That implies
> that the transom is automatically tilted from the vertical by just half the
> altitude of the Sun, and the instrument departs from linearity according to
> the tan of half the altitude; not the tan of the altitude. That in itself
> doubles the angular range before the blow-up of the tan scale makes the
> instrument impossible to use. How, with large altitudes, will Greg get the
> observer to hold his plastic plate at the correct angle, however he chooses
> to specify that angle? That tilt will matter, as the angles increase.
>
> The next problem, which Greg's trombone shares with the cross-staff, is with
> the human eye. To see an object with any acuity of vision, it needs to be
> imaged on the fovea, right at the centre of the retina. That's why you can't
> read a line of text without your eye scanning along it bit by bit: just try
> it! Even at the small altitudes that Greg was observing, the Sun's limb and
> the horizon can't both be placed on the fovea at the same time. The eye has
> to flicker in direction between the two, however subconsciously.
>
> That's the basic problem at the heart of all such instruments; that the eye
> can't look in two directions at the same time. If you draw a diagram of the
> geometry of the two light-paths, you will see that they cross, not at the
> lens at the front of the eye, or the centre of the retina at the back, but
> at the centre of rotation of the eyeball, as it flickers between one
> sight-line and the other. So, the dimension that needs to be measured, if
> the tan formula is going to work, is between the cross-piece (or plastic
> plate) and the centre of the eyeball. Not a practical proposition,
> obviously, but what is the best that can be done? There's a notch in the
> edge of the skull-bone, just close to the side of the eye, which isn't far
> from a plane drawn through the centre of the eyeball. Just the spot where
> the user of a cross-staff would press the end of the staff. There was much
> argument, then, about whether different individuals should shave off a
> suitable amount from the staff, appropriate to their own eye-socket
> dimensions.
>
> All that Greg says about this is "trombone the tape-measure out, until
> pressed below the eye". This is a vital factor in setting the calibration,
> and the way errors vary with angle. It therefore needs to be specified
> somewhat more closely, if Greg is to approach the precision of a
> cross-staff's stick, when it's tailored to suit the individual's eye-notch.
>
> And then, Greg's device calls for the use of a 10-inch slide rule to convert
> its readings into angles. I expect that the accuracy available from a slide
> rule wouldn't degrade, significantly, the limited accuracy of such a device.
> But really, in this aspect, the cross-staff wins, hands-down, on
> convenience, being direct-reading. You read the angle straight off, marked
> on one of a number of scales, each dependent on the chice made from a range
> of transoms of varying lengths.
>
> Wher Greg wins is in the convenience of madern plastic material for cutting
> down danger from scorching of the retina. There were tricks the cross-staff
> user would use to limit that danger. The earliest users would try to cover
> the Sun with the top of the vane, always measuring to its upper limb, just
> allowing a sliver to glint past. Later, a piece of smoked glass would be
> added at the top of the vane. But commonly, the cross-staff was used for
> twilight observations of the Pole star, and for Sun observations only, the
> backstaff was introduced, which must have done a lot to reduce the
> prevalence of one-eyed navigators..
>
> So, to sum up: the trombone, as an observing instrument, definitely shows
> promise, and with further development might eventually rival the
> capabilities previously achieved in the sixteenth century.
>
> George.
>
> contact George Huxtable, at �geo...@hux.me.uk
> or at +44 1865 820222 (from UK, 01865 820222)
> or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
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