To estimate the wing loading, a constraint analysis is exploited in which flight equitation is simulated based on the modes and missions of the flight. Along with the four listed steps, a statistical method is employed to estimate the FWMAV weight for a well-defined mission. This developed methodology is very beneficial by giving guidelines for the design of efficient bio-inspired FWMAVs. Unable to display preview. Download preview PDF. Skip to main content. Advertisement Hide. A novel methodology for wing sizing of bio-inspired flapping wing micro air vehicles: theory and prototype.
Original Paper First Online: 17 November This is a preview of subscription content, log in to check access. Fenelon, M. Theory 45 , — Google Scholar. Abdelkefi, A. Klingebiel, K. Hassanalian, M.
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Meccanica 51 , 1—18 CrossRef Google Scholar. Sibilski, K. Acta Polytech. Michelson, R. In: Encyclopedia of Aerospace Engineering. Georgia Institute of Technology, Atlanta Sladek, N. Pfeiffer, A. Bionic Eng. Whitney, J. Nguyen, Q. DeLaurier, J. Orlowski, C. Anderson, M. Greenewalt, C. In: Smithsonian Miscellaneous Collections, vol. Smithsonian Institution, Washington Google Scholar. Pennycuick, C. Avian Biol. Rayner, J. Fluid Mech. Norberg, U. B Biol. Tucker, V. Lighthill, J. In: Wu, T. Swimming and Flying in Nature, vol. Spedding, G. Beng, T. I shall show in subsequent chapters that despite the minimal amount of input information that Flight needs about the bird, the programme predicts a surprisingly wide variety of measures of flight performance.
The reader who wishes to test the accuracy of these predictions against field or laboratory observations need only enter the bird's mass, wing span and wing area into the programme, and run it. Rudimentary as these measurements may be, they are unfortunately not to be found in the traditional morphometrics of ornithology, and they cannot be reliably determined from museum specimens. The definitions come from aeronautics, not from ornithology, and are given in Boxes 1. These procedures are not difficult or arduous, but they may be unfamiliar to some biologists, and they need to be carefully followed.
The concept of lean mass is not used in Flight. This is an obsolete term that refers to everything that is not fat, including the flight muscles. It was originally conceived as a constant baseline against which other masses, including the fat mass, could be compared, but this became untenable when it was realised that large quantities of protein from the flight muscles are consumed during long migratory flights, and smaller amounts from the airframe.
These changes are predicted in Flight 's migration calculation. Flight considers that a bird's empty mass consists of three components, the flight muscle mass , the fat mass and the airframe mass , which is the mass of everything else in the body, that is not flight muscles or consumable fat.
All three components are reduced by substantial amounts in the course of a long migratory flight, for different reasons, and this is represented in the computation. The total mass of everything that the bird has to lift just weigh the bird , including any hardware such as rings and radio transmitters. This dates from the early development of Flight , when birds carrying heavy loads of food in their crops happened to be a subject of special interest.
The starting fat fraction is directly related to the distance a migrating bird can fly before it runs out of fat, and this not the fat mass as such is the number that is needed to represent the stored fuel energy in migration calculations Chapter 8. The combined wet mass of the wing depressor and elevator muscles of both sides. In birds, these are the pectoralis and supracoracoideus muscles.
Note that as a bird takes on or consumes fat, it also builds up or consumes its flight muscles. The flight muscle mass is greater when a bird is fat than when it is thin, but the flight muscle fraction varies much less, whether the bird is fat or thin. The mass that is left after subtracting the fat mass and the flight muscle mass from the empty mass.
The airframe is perceived as the basic structure of the bird, which has to carry the engine flight muscles and the fuel fat , although actually a small part of the airframe also gets consumed on migratory flights. The three mass fractions change progressively during a long migratory flight, but they always add up to First enter the empty mass.
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This is what you get by weighing the bird with its crop empty. If the effects of carrying a crop load are not important to your calculation, you can consider the crop contents to be part of the airframe. In that case set m crop to zero the default , and set m empty to the mass that you get by weighing the bird, including any crop contents. Next, enter the fat mass. The programme will automatically calculate and enter the fat fraction.
Alternatively, if you enter the fat fraction first, the programme will calculate and enter the fat mass. Likewise, enter either the flight muscle mass or preferably the flight muscle fraction. To fatten up a computer bird, first enter a higher value for the empty mass, then increase the fat mass by a lesser amount because additional flight muscle mass is added as well as fat.
Modelling the Flying Bird.
This is not taken care of automatically by the programme. In some circumstances it is possible to estimate the fat fraction from measurements of body mass alone, without resorting to carcase analysis Chapter 8, Box 8. The only two wing measurements that are required by Flight are the wing span and the wing area.
In addition, there are a number of related variables that are mentioned in the text and calculated by the programme, whose definitions are given below. A bird's wing span is the most important morphological variable for flight performance calculations. It is the distance from one wing tip to the other, with the wings at full stretch out to the sides, that is, with the elbow and wrist joints fully extended Figure 1. This usage occurs in both the aeronautical and the ornithological literature, and is liable to cause major misunderstandings and errors.
Hoping to minimise this problem, I denote wing span by capital B in this book, thus breaking with both traditions. The wing area, denoted by S wing, is essentially the area that supports the bird's weight when it is gliding. It is defined as the area, projected on a flat surface, of both wings, including the part of the body between the wings Figure 1.
Why include part of the body? Because the bird is supported in normal gliding flight by a zone of reduced pressure which extends from one wing tip to the other. There is no gap in the middle Figure 1. Measuring the wing area is more complicated than measuring the span, more stressful for the bird and harder to do repeatably.
On the other hand, this is a less critical measurement. The wing area is important in gliding performance, because it determines gliding speeds, and also the minimum radius of turn for circling in thermals. However, minor changes in the wing area have only a small effect on performance in flapping flight Spedding and Pennycuick, Chord is an aeronautical term that dates from the nineteenth century, when people built thin wings, with cross sections that were arcs of circles.
Modern aircraft wings are not thin arcs in cross section, but the chord is still the distance from the leading edge of the wing to the trailing edge, measured along the direction of the air flow Figure 1. Ornithological readers will be aware that this term was borrowed at some time in the past for use in bird morphometrics, and assigned a meaning that is unrelated to its aeronautical definition, and of no use for flight performance calculations of any kind. The conventional aeronautical definition of chord is the only one used in this book.
The chord of a particular wing, unlike its span, does not have a unique value unless the wing is rectangular, which is unusual. Most wings have a maximum root chord where the wing joins on to the body, and taper to a smaller tip chord , with the chord diminishing along the span. A few flying animals butterflies have negative taper, meaning that the tip chord is greater than the root chord.
The mean chord c m , which does have a unique value for the wing, is the ratio of the wing area S wing to the wing span B :. Flight calculates the mean chord internally, and uses it for calculating Reynolds numbers Chapter 4, Box 4. The aspect ratio R a is the ratio of the wing span to the mean chord, and it expresses the shape of the wing:.
Wing area is somewhat troublesome to measure Box 1. If a few wing areas are measured among a sample of birds of the same species, they can be used to get an estimate of the aspect ratio, which may be assumed to be constant for the species. This means that the wings are assumed to be all of the same shape, though not necessarily the same size. Then, if a bird's span has been measured, the aspect ratio can be used to estimate its area by inverting Equation Flight will accept either the wing area or the aspect ratio for input.
If supplied with one, it will calculate and enter the other automatically, so long as the wing span has already been supplied. The tail is an accessory lifting surface in birds, and is more analogous in its function to a flap than to the horizontal tail of conventional aircraft. Birds' tails have been represented as an expandable delta wing, behind the main wing Thomas, This is not included in Flight as most birds only deploy and use their tails at low speeds that are below the range covered by the calculations, and besides, the theory is somewhat conjectural.
The tail is usually furled at normal cruising speeds, from the minimum power speed up, and may then be assumed to contribute no lift. Figure 1. The wing span is the distance from wing tip to wing tip, and the wing area is the projected area of both wings, including the body between the wing roots grey. These measurements are made with the wings fully extended.
It is important that the elbow joint is locked in the fully extended position. The chord, which varies from point to point along the wing, is the distance from the leading edge of the wing to the trailing edge, measured along the direction of the relative air flow. B A gliding bird's weight is balanced by the pressure difference between the lower and upper surfaces, multiplied by the wing area.
The area of reduced pressure above the wings accounts for most of this pressure difference, and it continues across the body. This is why the area of the body between the wing roots is included in the wing area. There are two ways to measure the wing span, both of which are quick and easy to do on a live bird, with minimal stress. For a small bird, with both wings in good condition, place the bird on a flat surface, the right way up not on its back.
Stretch both wings out to the sides as far as they will go, with the tips on the surface, and check that the elbow and wrist joints are in their fully extended positions. Place markers, just touching each wing tip. Then fold the wings up, remove the bird, and measure the distance between the markers. This is the only option if one wing is damaged.
Stretch the good wing out as above, and use a tape measure to determine the distance from the backbone to the wing tip. Double it to get the span. The measurement is made from the body centre line not the shoulder joint to the wing tip. The centre line is easy to locate by feeling for the neural spines of the vertebrae, which stand up from the backbone as a sharp ridge.
It is important to make sure that the elbow joint is fully extended, by pushing it gently forward until it locks. The wing area is measured in two stages. First make a tracing of one wing not forgetting to measure the wing span , and then measure the area from the tracing.
A wing tracing that is not accompanied by a wing span measurement is completely useless, and cannot be used for measuring wing area. The best idea is to write all the data about the bird, including the span, directly on the wing tracing. Wings of small birds can be traced in a sketchbook that opens flat, while a roll of parcel paper is good for large birds. Put the drawing surface at the edge of a table, and hold the bird with one wing spread on the drawing surface, and its body beside the table edge, but not actually on it Figure 1.
Spread the wing straight out to the bird's side, with the elbow and wrist joints fully extended. Find the elbow joint quite close in to the side of the body , and push it gently forwards until it locks in the fully extended position. Then draw the outline of the wing, following in and out of the indentations between the flight feathers.
This results in a partial wing , which is incomplete open at the inner end. First complete the partial wing tracing by drawing a straight line across the open end, parallel to the body centre line. This is the wing root line. Its exact position is not critical, so choose a position that gives a realistic root chord defined in Box 1. The first job is to measure the area of the partial wing. Of course, there are digital ways of doing this, and it may be worth the trouble of setting one up, if you have hundreds of small wings to measure. If you have to measure occasional warblers, ducks, pelicans etc.
Number the lines along all four edges. Print the grid out on acrylic sheet as used for overhead transparencies, and check that the line spacing is indeed what it is supposed to be. Lay the grid over your wing tracing, aligning one edge with the wing root line, as shown in Figure 1. Line up the leading edge of the wing so that it roughly corresponds with one of the horizontal grid lines.
Starting from the left edge of the grid in Figure 1. If the filled parts of columns 11 and 12 were flipped over, they would fit in the unfilled parts of columns 9 and 10, making two complete squares beyond column 8. That makes 10 filled squares for the first row of the partial wing row 3.
Row 4 has a bit more than 11 filled squares, and row 5 has a bit less than 11, so count them as 11 each. Row 6 has about 8 filled squares, and all the small parts of the trailing edge in row 7 add up to about 1 filled square. That makes 41 filled squares in all for the partial wing. That is ample precision for the wing area measurement. In practice, 0. Although the squares in Figure 1. You have to extend the root end of the wing to the centreline, by adding a root box.
First measure the root chord on the tracing, along the wing root line which you marked in. Then measure the partial wing length , which is the distance from the wing root line to the tip of the longest primary. The area of the root box is therefore 1. You can now work out the wing area as follows:. The best place to do this little calculation is on the tracing, right beside the partial wing. An aspect ratio near 7 means that the wing is shaped about like the one in Figure 1.
If we had got a ridiculous aspect ratio of 70 or 0. Notice that the measured wing area is not very sensitive to the exact position where you draw the wing root line, to complete the partial wing.
If you move the wing root line outwards a bit, you get a smaller partial wing, but this is compensated by a bigger root box, and vice versa. Little or no subjective judgement is required by this method of measuring wing areas, and it is consequently very repeatable between different observers. The wing area is a less critical measurement. If you have a measured value, then enter it in square metres.
The programme will automatically calculate the aspect ratio, and display it in the box. Check that it is a believable value, and if not, look for wrong units or spurious factors of 10 in the entered wing span and area. Sometimes you have a good value for the wing span essential , but no measured wing area. In that case, you can enter the aspect ratio, if you can guess it from other birds that you have measured, whose wings are similar in shape.
The programme will then calculate and enter the wing area. The root end of the wing is left open at a point that is representative of the root chord. The root box extends the wing root to the centre line backbone , and the combined area is then doubled to get the total wing area see Box 1. The programme will be misled by numbers that mean something different from what it assumes, which is not unusual for numbers identified by the same names in the ornithological literature.
It serves no useful purpose for a field or laboratory observer to collect infinitely detailed statistics on variables that do not affect flight performance, and then get wing spans and areas which do from bird field guides, museum specimens or published figures from authors who neglected to define exactly what their measurements mean. Body mass is straightforward, but the manner in which the programme subdivides it Box 1. In particular, the concept of lean mass is not used in this book or in Flight , because its use in migration studies is obsolete and misleading.
Mass fractions are defined in Box 1. Bats, pterosaurs and even mechanical ornithopters can be described by their mass, wing span and wing area, and Flight will predict their performance, interchangeably with birds. The reader should not be intimidated by the number of variables that can be adjusted, or by the somewhat arcane nature of some of them. The defaults will do for most practical purposes, but if one such variable a drag coefficient for instance is suspected to be the source of an observed discrepancy, it is easy to change the value systematically through several programme runs, keeping all other values the same.
The results can be saved as an Excel Workbook, in which the results of each run are saved as a new Worksheet, together with the input from which they were generated. The meanings of those variables that are accessible to the user, and the effects and implications of tweaking their values, are explained in later chapters, and in Flight 's online manual.
Besides the three morphological variables that describe the bird, Flight also requires values for two further variables only that describe the environment in which the bird flies. These are the acceleration due to gravity and the air density, both of which have a major effect on Flight 's performance predictions. These variables are discussed in Chapter 2, with methods of entering values into Flight.
A default value is used for gravity, but this can be changed by the reader who wants to simulate flight elsewhere than here on earth.
Optimal flight speed in birds
Air density is often overlooked or ignored by biologists, although not by pilots, who are acutely aware of its effects on flight performance. These effects also apply to birds, and it is essential to supply a realistic value. There is no default value for the air density, and Flight will not run until the user selects one of a number of options. For example, the programme will calculate and enter the air density if the user supplies measured values of the ambient pressure and temperature, or it will calculate a hypothetical value that corresponds to a specified height in the International Standard Atmosphere Chapter 2.
In physiology, if you want an estimate of the rate of fuel consumption, then you have to measure it directly, or else measure something that you hope is proportional to it, like the rate of oxygen consumption. The result comes out in whatever units happen to be inscribed on the apparatus, such as watts, British Thermal Units per hour, calories per minute or even millilitres of oxygen per hour. If you only have to deal with one type of quantity, an arbitrary choice of units is fine for collecting statistics fodder, and may even serve for very basic calculations, but that is not Flight 's approach.
The programme does not get its power estimates from regressions based on data of this type; in fact it does not use regressions at all. Instead, it estimates the power from other variables with other dimensions, basically the force that the wings apply to the air, and the speed with which they move. The force in turn comes from the rate at which momentum mass times speed is added to the air flowing over the wings.
Flight then goes on to assume that the power estimated from force times speed must be accounted for by the rate of consumption of fuel energy. The calculation does not depend on any direct measurements of power as such. Unnatural as it may seem to many biologists, no statistics are involved. The vast literature about measured rates of energy consumption in birds gets barely a mention in this book, because total fuel consumption is the end result of all processes that consume energy. A statistical summary of measurements of this type, on some particular bird, can be used to predict the energy consumption of the same bird, but cannot be transferred to other birds, flying under other conditions.