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    Re: Amplitudes
    From: George Huxtable
    Date: 2010 Jun 2, 21:02 +0100

    Jeremy tells us of his observations of amplitudes. Amplitude is the angular 
    difference of a body from due East (when rising) or West (when setting).
    
    Amplitude tables were provided in all the textbooks, and were used to 
    determine the true bearing of a body, on rising or setting, to compare with 
    its compass bearing, and so determine compass error.
    
    What was tabulated was not quite the amplitude at the moment of rising as 
    we would conventionally understand it, but at the moment when the true 
    altitude of the centre of the body was exactly zero degrees. In which case, 
    the table of amplitudes was completely symmetrical, between Summer, when 
    the declination was an the same hemisphere as the observer, and the 
    amplitude was in the opposite hemisphere ; and Winter, when the signs of 
    latitude and declination were opposite, and again, the amplitude was 
    opposite to the sign of the declination. This stratagem allowed the 
    amplitude table to be listed over just a single quadrant of lat and dec, so 
    it was very compact.
    
    Usually, it was applied to sunrise and sunset. Jeremy wrote- "As George 
    notes, this is not the visible horizon, but some  arc-minutes off of the 
    visible horizon depending on the body ...  I was never taught, or have I 
    read, to take into  account any height of eye when taking the measurement 
    (dip correction)."
    
    Neither have I seen the effect of dip treated in any text, but when 
    observers are perched as high as on Jeremy's 100-foot bridge, its effect 
    may not be negligible.
    
    Let's look at it from first principles, and think about it in terms of 
    zenith angle, from the vertical above your head, to avoid the ambiguities 
    in what we mean by the horizon, and "horizontal".
    
    We are looking for the moment when the Sun's centre has a zenith angle of 
    exactly 90�, so presuming a diameter of 32', the true direction of its 
    lower limb will be 90� 16' from the zenith. From a height of eye of 100 
    feet, the dip will be 9.7', so it's at 90� 9.7' from the zenith. So the 
    Sun's lower limb would be be 6.3' below the visible horizon, if there were 
    no refraction in the path to the eye.
    
    Next we need the low-altitude refraction corrections page A3 from the 
    Almanac (stars/planets column), to find what apparent altitude, above the 
    visible horizon, gives rise to a true altitude, above that dipped horizon, 
    of -6.3'. That table isn't laid out well for answering our question, but it 
    tells us that for an apparent altitude of +24', the refraction correction 
    is -29.3', so resulting in a true altitude of -5.3'. And that an apparent 
    altitude of 21' corresponds, in the same way, to a correction of -29.8', so 
    to a true value of -8.8'. So the best interpolated estimate we can make is 
    that corrected for refraction, the lower limb of the sun should appear to 
    be floating above the apparent horizon by 23', which is nearly 
    three-quarters of the Sun's diameter. I would be pleased if someone else 
    would cross-check my numbers.
    
    That differs, quite a bit, from the rule that Jeremy has been assuming, 
    that the gap between lower limb and horizon should be just one-third of the 
    Sun's diameter, and I wonder if it might be part of the reason why he has 
    found amplitudes to be disappointingly inaccurate.
    
    Of course, bearing by amplitudes is by no means an exact science, because 
    of the major uncertainties in predicted refraction that can occur over the 
    hundreds of miles of low-angle air-path. That's why a guess of the Sun's 
    altitude, rather than a proper sextant observation, suffices. It's 
    certainly to be expected that a proper sextant observation for altitude, 
    when the Sun has risen above the dangerous zone of 5� altitude, and then a 
    proper azimuth calculation, would be more precise, if less handy.
    
    George.
    
    contact George Huxtable, at  george@hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    ----- Original Message ----- 
    From: 
    To: 
    Sent: Wednesday, June 02, 2010 12:26 AM
    Subject: [NavList] Amplitudes
    
    
    | George brought up an interesting topic in a previous post about measuring
    | amplitudes.  Over the years I have found amplitudes to be far easier to
    | shoot and reduce by hand than azimuths, but less accurate as well.  I 
    have
    | taken azimuths within an hour or two of a amplitude of the same body and 
    had
    | different compass errors which should not have existed, and in all cases, 
    I
    | tend  to believe the azimuth over the amplitude.
    |
    | Amplitudes are shot when the center of the body is on the celestial
    | horizon.  As George notes, this is not the visible horizon, but some 
    arc-minutes
    | off of the visible horizon depending on the body.  (To be fair,  you may
    | shoot the body when the center on the visible horizon, but a correction 
    needs
    | to be applied which increases as you and the body get further from  the
    | equator.)  I was never taught, or have I read, to take into  account any 
    height
    | of eye when taking the measurement (dip correction).
    |
    | I was taught to observe the Amplitude of the sun when the lower limb was
    | 1/3 of the sun's diameter above the visible horizon.  I was also told 
    that
    | stars and planets are observed when 1 sun's diameter above the visible
    | horizon,  and the moon when the upper limb is on the visible horizon.
    |
    | I have shot amplitudes of the sun, moon, and two planets.  Shooting  the
    | moon on the celestial horizon is quite the challenge, but it does  work. 
    It
    | is the only body that I prefer to shoot on the visible  horizon.  Planets 
    are
    | very difficult because they tend to disappear into  the haze of the 
    horizon
    | below about 2 degrees of altitude.  I have never  been able to shoot an
    | amplitude of a star because even mighty Sirius disappears  before 
    reaching
    | amplitude height.  The sun is the easiest body to observe  but you need 
    to watch
    | out for "amplitude clouds" as we called them.  Those  were clouds forming
    | as the earth cooled and obscured the sun from view as  it decended.
    |
    | For reduction, I have tended to avoid the tables due to the need to
    | interpolate.  While interpolation is not difficult, it is far more  time 
    consuming
    | than a straight calculation.  I find it far easier to just  use the 
    formula
    | as even a basic user of any calculator with trig functions can  pull it 
    off
    | with little trouble.
    |
    | The other major advantage of amplitudes over azimuths is not needing 
    exact
    | time as the only almanac entry is declination which tends to change 
    slowly
    | enough to require little time accuracy.
    |
    | While I still shoot amplitudes at every opportunity, I rely on azimuths 
    as
    | my preferred method of compass correction at sea.
    |
    | Jeremy
    |
    | 
    
    
    
    
    

       
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