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    Re: Trombone Kamal Prototype
    From: George Huxtable
    Date: 2009 Jun 5, 21:46 +0100

    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  george{at}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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