Download Mapping flight lines is a technically challenging process of

FLIGHT MAPPING USING ANGULAR MEASUREMENTS
By Andrew Francis [email protected]
Please circulate this work, I would be pleased to hear feedback and suggestions,
positive or otherwise!
ABSTRACT
I describe a simple method for estimating distances of known objects from their size
using optics with angular measurement scales (reticules). I propose that this method
may be used at very least to train distance awareness and suggest that optics which
contain reticules are very useful instruments because they also contain very
accurate and easily read compasses. I have used these methods to estimate
overall distances of birds and invite other observers to experiment with the methods
and to provide feedback on their effectiveness.
I outline some principles for
evaluating the quality of optics in general. I have also developed an Excel spread
sheet to aid the mapping of flight lines using a table of bird sizes and some
trigonometric methods, I am happy to provide this to any interested parties.
INTRODUCTION
Mapping flight lines is a technically challenging process of “guestimation”. As a
fieldworker I would like some means of calibrating my distance estimates against
calculated measurements. In the past I have done this largely using a GPS or by
pacing out distances but what I am proposing are a variety of methods the simplest
of which doesn’t require any trigonometry. More elaborate methods that include
trigonometry are, in theory, simple to employ if you gather data in the field and
perform the calculations later, perhaps using a spread sheet like the one I have
produced and can make available on request.
This document is a work in progress and I intend to circulate this to any fieldworkers
who are willing to try it out and to provide feedback on the method’s successes and
failures or for suggestions of how I might re-write this document to make it easier to
read.
If the methods described ultimately fail as a method of mapping bird flight lines I will
continue to hold that the basic method is at very least an excellent way of getting
to know the distances of those objects in one’s view shed which are not marked on
maps but are of consistent or estimable dimensions e.g. static animals, fences and
trees. It may also be employed to estimate the dimensions of objects (e.g. pylons)
that are of known distances – something else that may be of use to ornithological
fieldworkers trying to map birds by height band.
Estimation of total distance - without concern for what components of a bird’s
distance are vertical (as required for height-banding) and horizontal distances (as
required for mapping) - does not require trigonometry because small angles are
close to the values obtained by multiplying them with their sine function as would be
required for trigonometric calculation. This allows us to use a very simple equation;
distance (in Metres) = size (in mm)/angle (in milliradians or ‘mil’).
(I will write more of mil later – they are not a measurement familiar to most of us but
have a clear advantage over degree scales).
For birds which are known to be at low altitude (for instance birds which intervene
between the observer and fairly low objects such as hedges) an estimate of overall
distance will closely approximate that of horizontal distance allowing us to map such
birds easily.
For birds at higher elevation things are more complicated and a trigonometric
solution may be in order. To do so we must record a variety of data for each flight
and perform some calculation after the flight has passed.
WHY NOT USE A LASER RANGEFINDER?
Why not indeed! Laser rangefinders are phenomenal bits pieces of equipment and
some also record elevation angles. I have seen an internet clip of a very expensive
pair of Bausch and Lomb binocular rangefinders picking out a deer at nearly 1600m.
I would be very interested to hear from fieldworkers who use laser rangefinders. My
reasons for confining my study so far to the old fashioned angular method are: 1) I
am sceptical about how well laser rangefinders can pick up small animals at large
distances. 2) I am concerned that there may be risk of injuring the sight of wild
animals 3) I am tight-fisted and aware that rangefinders with large ranges are
expensive. I am aware that many laser rangefinders also have scales for angular
measurements which would allow them to measure distances of objects of known
size even if they are out of laser range. It would be interesting to compare distance
measurements obtained by each method, especially where map measurements
could be used to verify them.
MEASURING ANGLES AND BEARINGS
For accuracy we will be using optics, either a pair
of ‘marine’ type binoculars or monocular,
equipped with a compass and a reticule. Bear in
mind that most marine binoculars have separate
focussing for each eyepiece which makes them
less useful for bird-watching.
‘Marine’ type
binoculars have a built in compass and reticule
that is superimposed over the field of visions of one
of your eyes. An optical compass is a very useful
piece of equipment even before we consider the
benefits of a reticule – they make it very easy to
record the positions of animals relative to a vantage point and easier to remain
aware of a bird’s position where there is no distinctive background in view. Many
compasses only work up to a certain elevation, they tend to get stuck with
increasing elevation. I am not familiar with digital compasses but they may be free
from these constraints.
The reticule (or graticule) is a transparent piece of glass that is finely etched and
placed at one of the focal planes of the optical instrument so that it is in focus along
with the target image. Angular measurements are typically either in Mils or
Milliradians (our preferred unit of measurement for the purpose) or in degrees and
minutes. The compass below usually gives bearings in degrees. Traditionally the
reticule was formed from spider silk (from the grey recluse spider!) and the word
‘reticule’ comes from the same route as “reticulation” and means ‘netting’ in Latin.
THE METHOD
WHILST WE ARE WATCHING A FLIGHT:
we need ascertain the following:
Bearing
at 15 second increments
Elevation above the horizon
at 15 second increments
Angle subtends in our field of vision by the bird at 15 second increments
(as ascertained using a reticule).
Number
Whilst the birds are close enough.
Species
Whilst the birds are close enough.
Although we may know the species immediately we should consider bearing,
elevation and angle first (before the number and species of the birds) as the birds
may be too distant to identify and count initially and we do not want to lose flight
line data whilst we are unsure even if they are target species.
Recording data in a rigid order, time and time again, helps in developing the
automatic habits we need to record bird flights.
Conveniently the three datum
that are to be collected at 15 second increments (Bearing, Elevation and Angle)
and the two that are gathered for the entire flight (Number and Species) spell out
the mnemonic “BEANS”. All we need to add to this is the time and date; time is
important but only needs to be approximate and ascertained after the flight has
passed.
Elevation can be difficult to assess and requires good knowledge of local
geography, particularly if you are watching from a high vantage point. It may be
beneficial to study maps carefully and if there are distinctive areas such as crags or
lines of forests at similar heights in order to assess a height line.
WHEN THE FLIGHT HAS LEFT OUR FLIGHT ZONE:
We can calculate the bird’s distance and height
Distance (Metres) = Size(mm) /Angle (Mil or miliradians)
Mnemonic = DSA (like “Driving Standards Agency”). Remember what the units are;
you will get some pretty wacky figures if you fail to multiply sizes to mm (not the most
instinctive unit of measurement). We can estimate the size of a bird if we know its
species (and sometimes its sex) and the angle subtended in radians we took from
the reticule.
Miliradians are a unit which are not familiar to most people but are used by firearms
enthusiasts and sailors. There are 6283 Miliradians in 360 degree circle so 1 degree is
equivalent to 17.453 Mil. These are unwieldy numbers because they are calculated
from pi π. Miliradians are the desired unit of measurement because 1 Mil is closely
equivalent to 1m at 1000m. This makes it much easier to calculate distances using
this unit than to do so using degrees.
As mentioned before, the distance of the bird is usually very largely horizontal from
the observer and so usually approximates closely to its overall distance from the
observer. If this is not the case and the elevation of the bird is quite high then you
will have to use trigonometry to calculate the horizontal distance of the bird from the
observer.
If you have to use trigonometry and are uncomfortable with it then you email me
and I can send you an Excel spread sheet which uses the relevant equations.
FINISHING OUR MAPPING
You should now have bearings and horizontal and vertical displacements from the
observer for each 15 second increment. You can now plot the flight line on the
map. Remember that the bearings you will have obtained from your binoculars or
rangefinder are not based on grid north and you will have to add a correction
angle as marked on maps but, as of May 2013 about 2 degrees. The British
Geographical Survey have a website which gives correction angles depending on
your location; they ask for email address but the calculator works without it.
http://www.geomag.bgs.ac.uk/data_service/models_compass/gma_calc.html.
You will be able to tell from the contours how high or low the land is at each plotting
point in relation to the position of your vantage point. This difference will need to be
added or subtracted from the altitude of your vantage point. This will yield a height
over the land for your target at each 15 seconds.
Now all you need to do is to join the dots. Some flight lines (e.g. those of geese on
migration) are very direct, others, such as Hen Harriers hunting, are very circuitous.
The length of the lines linking each carefully plotted point will influence the collision
risk of birds. There will inevitably be errors in this process and this will remain a very
subjective area for dealing with circuitous flights.
SOME FURTHER COMMENTS ON PRACTICE
Secondary species generally
outnumber target species.
Large birds like gulls are good
to practice on because they
are more likely to subtend
reasonably
measureable
angles.
Elevations may
sometimes exceed what our
optics can measure from the
horizon. Sometimes we may
need to measure these
angles
based
on
the
dimensions subtended by our
own hands compared to the
objects we are viewing. To
the left is a figure to show
some ball-park figures for Mil
measurements.
It is good to become familiar
with measurement of objects
which have fairly consistent
dimensions
e.g.
sheep
(750mm height), Cars (about
4000mm long), single tracks of
roads (each about 2500mm)
Deer
Fences
(2,000mm),
plantation
conifers
(15,000mm), Pylons (variable but typically 35,000mm) and wind turbines (80,000mm
to hub) etc. Larger objects yield smaller errors and can allow us to infer the ranges
of birds associated with more accurately.
You may wish to keep a list of lengths and wingspans of target species (and
secondary ones for practice). I have prepared a quiz in Excel for the learning of
some of these figures. For low angle flights and with a bit of practice at mental
arithmetic it may sometimes be possible to plot flight lines in the field knowing these
figures.
CHOICE OF OPTICS
As discussed already most compass and reticule containing binoculars are called
marine binoculars, have separate focussing for each eye and are of a fairly low
power (typically 7x). A result of the lower power is that the human eye is better able
to accommodate focussing at different distances (i.e. has a greater “depth of
field”) and so less refocusing is required than would be for a 10x pair. The wide
objective lenses typically associated with such optics and their low powers tend to
give wide fields of view. Low powers are also more suited to rolling decks as failure
to steady higher magnifications causes more apparent blurring and nausea on high
seas. I am doubtful that these methods would be suitable for marine work as it is
quite hard enough to line up birds with graticule measures when on stationary land
let alone on the sea.
An idea of the brightness of the image in poor light may be obtained by dividing the
objective lens diameter by the magnification. To the left is a diagram which shows
the names of the
parts of binoculars.
If you hold a pair of
binoculars with the
objective
lenses
facing the floor you
will be able to
make out a pupil of
light
in
the
eyepieces. This is
known as the exit
pupil. In poor light
the human pupil
expands to let in
more light. At the
point where the
human
pupil
is
wider than the exit pupil our binoculars are limiting our light gathering capacity. For
young people pupils can expand to 7mm or so. Older people’s eyes are less able to
expand and so exit pupils wider than 5 or 6mm may offer no advantage. An exit
pupil of 4mm or more is a minimum requirement. If you are in any doubt whether you
would benefit from a larger exit pupil (and the extra weight of glass!) you can
always ask an optician to measure your pupils in the dark.
Exit Pupil = Objective Lens diameter / magnification e.g. 50mm/7 = 7.14mm
Our needs differ slightly from those of seafarers because a higher power reduces the
amount of error in our angular measurements of bird lengths and wingspans. This
would favour a magnification of about 10x (around the limit of comfortable hand
held support) although doing so would require larger (and heavier) objective lenses
to give equivalent low light performance and higher magnifications yield smaller
fields of view and may reduce our chances of using the vertical reticule to measure
elevation.
Any decent optical equipment will come fully multi-coated with anti-reflective
coatings. These are responsible for the purple, blue, green or (typically on cheap
nasty instruments) red blooms that you can see on the lenses. These bloomings
increase the amount of light transmitted within the binoculars and reduce the
amount that bounces around inside the instrument which, in strong light create haze
and in low light make the image gloomier. Most optics these days are multi-coated,
that is to say that several layers of coatings, with different refractive properties, have
been added to maximise light transmission. The quality of coating varies widely but
most instruments are slightly biased towards transmitting red light compared to blue
light so poor lighting tends to give a yellow or red bias to image colour.
Decent optical instruments are well corrected for what is called chromatic
aberration. Chromatic aberration is the property of lenses to change the angles of
different colours of light by different amounts leading to what is known as dispersion.
The result of dispersion is that different frequencies of light are focussed at different
planes and the contrast of the image is reduced. Chromatic aberration is most
apparent when looking at silhouetted objects. Very expensive models may be built
from what are known as low dispersion materials which bend the different colours of
light more equally. These tend to be referred to as ED (extra low dispersion) or
fluorite models.
The compromise of different magnifications and optical qualities is a matter of
personal choice and availability. As with all optics you get what you pay for
although it is the case that a law of diminishing returns seems to apply and the
improvement of quality per increase in price gets smaller the more you pay. In
general terms I would suggest that the old fashioned Porro Prism (kinked) designs,
yield better value for money as they have fewer optical surfaces from which light
can be reflected and should transmit more light. The most expensive ‘flagship’
models are almost invariably roof prisms. They are more compact and can be held
hold with the arms under the binoculars which is a more stable configuration than
that required for most (but not all) porro prisms where the arms are out to the side.
The downside is that they are more complicated to manufacture and some require
use of phase correction coatings and semi-silvered mirrors which reduce light
transmission relative to equivalent quality porro prisms.
Rather than jumping in with both feet and committing to supporting the (generally)
greater weight of marine binoculars in favour of their own binoculars some observers
might wish to ease themselves in by purchasing a moderately priced monocular
which they can keep with them along with their favoured binoculars. I have seen a
marine “Seago” 8x42 monocular on sale for only 50 pounds. I do not know how
good it is but it looks like the slightly more expensive Celestron Oceana 8x42 which I
bought for 80 pounds My only complaint is that I prefer to use both eyes for
observation if I can.
In summary here is how to test binoculars or monoculars:
1)
2)
3)
4)
Ignore the brand name and assess the image on its merits without prejudice.
Are they a comfortable weight to hold (may be for a long time)
Are they a suitable colour (not the deliberately garish yellow models).
Is the focussing separate for each eye (unfortunately this is the norm for
marine binoculars) or is there a single focus.
5) Is the focussing smooth and easy and how much of it is required to go from
close to distant.
6) What is the field of view like? Field of view is often measured in degrees or in
metres per 1000m, these are easy to convert for the purposes of comparison.
7) Check out silhouetted objects for contrast-reducing colour fringes (chromatic
aberration).
8) The periphery of the field tends to be less sharp than the interior, how much of
the field of view is of lower quality and how much less so.
9) How bright is the image. In bright daylight where the exit pupil is smaller than
the human pupil the quality of the light transmission of the lenses and light
reflection of the prisms will have the most influence on light-transmission.
10) How well do the optics perform when held towards strong light (being careful
not to actually look at the sun!). Most images will go milky and loose contrast
because of reflected light that failed to transmit properly. Very good optics
will have less of these problems due to good light absorption by matt black
surfaces within the instrument.
11) How large is the exit pupil? An exit pupil of at least 4mm is recommended.
12) Does the compass stick?
13) Does the reticule have suitable gradations in horizontal and vertical axes? Are
they in Mil or are you prepared to work in degrees?
For further information on optics I would recommend reading the articles and
review on the allbinos page where the expertise is stunning. Their article on
colour rendering was of great interest to me and each review demonstrates
every detail you might look for in evaluating optical goods by real experts.
http://www.allbinos.com//160.1-articleColour_rendering_in_binoculars_and_lenses.html
SOME CAVEATS IN THE METHODOLOGY
Before inviting criticism of the methods in question I will outline what I know to be
potential problems:


The angular distances subtended by birds at distance are typically very small
and most optics with this facility are low-powered (7x) which does not make
the process as easy as you might hope. High powered optics are harder to
stabilise.
It can be difficult to estimate total wingspan angle or length angle for birds
moving in straight lines at an angle that is not perpendicular to the observer.
This is even harder for birds which are circling.




Elevation is very hard to estimate. As for all bird flight line surveying the
problem of establishing an eye line to measure against will require a strong
knowledge of each vantage point view-shed. Some laser rangefinders have
built in inclinometers these could be of very great use.
Traditional marine-binocular style compasses jam at moderate elevations.
To measure angular distances with a reticule an observer needs to support
their optics very well, this could be difficult for rapidly flying birds or impossible
for birds observed from boats.
Some obervers may think it’s harder to record “BEANS” than the more
traditional method.
Any solutions to some or all of these problems or comments on the suitability of
various kinds of equipment would be of interest to me. I would also be interested
to hear if anyone knows of telescope eyepieces fitted with reticules (apart from
the simple cross hairs used in astronomical finder scopes) as the ability to
accurately measure the distances of static birds at great distance could also be
useful.
Andrew Francis [email protected]