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Dip by backsight.

Some time ago we discussed the dip of the horizon
on the old list, and a possibility of measuring dip
by a back sight was mentioned. After a recent hint
from Frank J., that modern sextants do permit back
sights under certain conditions, I worked the details.
The method should also work if you want to determine
the hight of a mountain while standing on the peak,
if you see the horizon in all directions.

It is a common opinion that uncertainty of the dip is the major
factor affecting the accuracy of altitude measurements.
Both Schufeldt and Russian theorists recommend to use dipmeters.
However I have never seen a dipmeter "alive" or on e-bay.
So the method using only ordinary sextant might be of some
interest.

The method is applicable if two conditions are satisfied:
a) The Sun altitude is more than 60 d.
(If your sextant measures angles up to 140 d, as SNO-T
does, you can use Sun at smaller altitudes down to 40).
b) You can see the horizon under the Sun and in the opposite direction.

Here are the simple steps.

1. Measure the Sun altitude in the usual way, say lower limb,
and record the time of the observation. Let the altitude be H1 and time T1.

2. Put your sextant arm at approximately 180d minus altitude
you just measured. Turn back to the Sun and take a back sight.
Measure the upper limb. It will LOOK LIKE LOWER LIMB through
your sextant: you will see the Sun touching the horizon from above,
if your scope is a straight one. Let the altitude by back sight
be H2 and time T2.

3. Compute the dip by the formula:
DIP=90d-(H1+H2)/2-SD+TC.
Here H1 and H2 are your altitudes, both corrected for the IC.
SD is the Sun semidiameter from the almanac.
TC is a "time correction" computed by the formula
TC=(T2-T1)cos(LAT)cos(DEC)sin(LHA)/cos(H1),
where T2-T1 is the elapsed time between the observations,
translated into ANGULAR units. (So if the elapsed time is 2 min 3 sec,
you use (15 times 2)+3/4=30'.8 as T2-T1.
The quantities LAT, DEC and LHA have the usual meaning.
The TC correction is positive after noon and negative before noon.
(The formula takes this into account automatically)
DIP is always negative.

The time between observations has to be measured very accurately, as you do
with ordinary Sun sights.

Unfortunately I have neither Sun nor horizon at this moment to test the method.
Will appreciate any comments and especially test results.

Alex.

   

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