Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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]