Laws of Conservation

Laws of Conservation

Aerodynamic problems are often solved using conservation laws as applied to a fluid continuum. In many basic problems, three conservation principles are used:

• Continuity: If a certain mass of fluid enters a volume, it must either exit the volume or change the mass inside the volume.
• Conservation of Momentum: Application of Newton's second law of motion to a continuum.
• Conservation of Energy: Although energy can be converted from one form to another, the total energy in a given system remains constant.

Let`s aerodynamics !

Continuity assumption of aerodynamics

Continuity assumption of aerodynamics

Gases are composed of molecules which collide with one another and solid objects. If density and velocity are taken to be well-defined at infinitely small points, and are assumed to vary continuously from one point to another, the discrete molecular nature of a gas is ignored.

The continuity assumption becomes less valid as a gas becomes more rarefied. In these cases, statistical mechanics is a more valid method of solving the problem than continuous aerodynamics. The Knudsen numbercan be used to guide the choice between statistical mechanics and the continuous formulation of aerodynamics.

History Aerodynamics

History

A drawing of a design for a flying machine by Leonardo da Vinci (c. 1488). This machine was an ornithopter, with flapping wings similar to a bird, first appeared in his Codex on the Flight of Birds in 1505.

Images and stories of flight have appeared throughout recorded history, such as the legendary story of Icarus and Daedalus.Although observations of some aerodynamic effects like wind resistance (a.k.a. drag) were recorded by the likes of Aristotle,Avicenna,Leonardo da Vinci and Galileo Galilei, very little effort was made to develop governing laws for understanding the nature of flight prior to the 17th century.

In 1505, Leonardo da Vinci wrote the Codex on the Flight of Birds, one of the earliest treatises on aerodynamics. He notes for the first time that the center of gravity of a flying bird does not coincide with its center of pressure, and he describes the construction of an ornithopter, with flapping wings similar to a bird.

Sir Isaac Newton was the first person to develop a theory of air resistance, making him one of the first aerodynamicists. As part of that theory, Newton believed that drag was due to the dimensions of a body, the density of the fluid, and the velocity raised to the second power. These beliefs all turned out to be correct for low flow speeds. Newton also developed a law for the drag force on a flat plate inclined towards the direction of the fluid flow. Using F for the drag force, ρ for the density, S for the area of the flat plate, V for the flow velocity, and θ for the inclination angle, his law is expressed below. F = ρSV²sin²(θ)

Unfortunately, this equation is completely incorrect for the calculation of drag (unless the flow speed is hypersonic). Drag on a flat plate is closer to being linear with the angle of inclination as opposed to acting quadratically. This formula can lead one to believe that flight is more difficult than it actually is, and it may have contributed to a delay in human flight.

A drawing of a glider by Sir George Cayley, one of the early attempts at creating an aerodynamic shape.

Sir George Cayley is credited as the first person to identify the four aerodynamic forces of flight - weight, lift, drag, and thrust, and the relationship between them.Cayley believed that the drag on a flying machine must be counteracted by a means of propulsion in order for level flight to occur. Cayley also looked to nature for aerodynamic shapes with low drag. One of the shapes he investigated were the cross-sections of trout. This may appear counterintuitive, however, the bodies of fish are shaped to produce very low resistance as they travel through water. Their cross-sections are sometimes very close to that of modern low drag airfoils.

These empirical findings led to a variety of air resistance experiments on various shapes throughout the 18th and 19th centuries. Drag theories were developed by Jean le Rond d'Alembert, Gustav Kirchhoff, and Lord Rayleigh. Equations for fluid flow with friction were developed by Claude-Louis Navier and George Gabriel Stokes. To simulate fluid flow, many experiments involved immersing objects in streams of water or simply dropping them off the top of a tall building. Towards the end of this time period Gustave Eiffel used his Eiffel Tower to assist in the drop testing of flat plates.

Of course, a more precise way to measure resistance is to place an object within an artificial, uniform stream of air where the velocity is known. The first person to experiment in this fashion was Francis Herbert Wenham, who in doing so constructed the first wind tunnel in 1871. Wenham was also a member of the first professional organization dedicated to aeronautics, the Royal Aeronautical Society of the United Kingdom. Objects placed in wind tunnel models are almost always smaller than in practice, so a method was needed to relate small scale models to their real-life counterparts. This was achieved with the invention of the dimensionless Reynolds number by Osbourne Reynolds. Reynolds also experimented with laminar toturbulent flow transition in 1883.

By the late 19th century, two problems were identified before heavier-than-air flight could be realized. The first was the creation of low-drag, high-lift aerodynamic wings. The second problem was how to determine the power needed for sustained flight. During this time, the groundwork was laid down for modern day fluid dynamics and aerodynamics, with other less scientifically inclined enthusiasts testing various flying machines with little success.

A replica of the Wright Brothers' wind tunnel is on display at the Virginia Air and Space Center. Wind tunnels were key in the development and validation of the laws of aerodynamics.

In 1889, Charles Renard, a French aeronautical engineer, became the first person to reasonably predict the power needed for sustained flight. Renard and German physicist Hermann von Helmholtz explored the wing loading of birds, eventually concluding that humans could not fly under their own power by attaching wings onto their arms. Otto Lilienthal, following the work of Sir George Cayley, was the first person to become highly successful with glider flights. Lilienthal believed that thin, curved airfoils would produce high lift and low drag.

Octave Chanute provided a great service to those interested in aerodynamics and flying machines by publishing a book outlining all of the research conducted around the world up to 1893. With the information contained in that book and the personal assistance of Chanute himself, the Wright brothers had just enough knowledge of aerodynamics to fly the first powered aircraft on December 17, 1903, just in time to beat the efforts of Samuel Pierpont Langley. The Wright brothers' flight confirmed or disproved a number of aerodynamics theories. Newton's drag force theory was finally proved incorrect. The first flight led to a more organized effort between aviators and scientists, leading the way to modern aerodynamics.

During the time of the first flights, Frederick W. Lanchester,Martin Wilhelm Kutta, and Nikolai Zhukovsky independently created theories that connected circulation of a fluid flow to lift. Kutta and Zhukovsky went on to develop a two-dimensional wing theory. Expanding upon the work of Lanchester, Ludwig Prandtl is credited with developing the mathematics behind thin-airfoil and lifting-line theories as well as work with boundary layers. Prandtl, a professor at Gottingen University, instructed many students who would play important roles in the development of aerodynamics like Theodore von Kármán and Max Munk.

As aircraft began to travel faster, aerodynamicists realized that the density of air began to change as it came into contact with an object, leading to a division of fluid flow into the incompressible and compressible regimes. In compressible aerodynamics, density and pressure both change, which is the basis for calculating the speed of sound. Newton was the first to develop a mathematical model for calculating the speed of sound, but it was not correct until Pierre-Simon Laplace accounted for the molecular behavior of gases and introduced the heat capacity ratio. The ratio of the flow speed to the speed of sound was named the Mach number after Ernst Mach, who was one of the first to investigate the properties of supersonic flow which included Schlieren photography techniques to visualize the changes in density. William John Macquorn Rankine and Pierre Henri Hugoniot independently developed the theory for flow properties before and after a shock wave. Jakob Ackeret led the initial work on calculating the lift and drag on a supersonic airfoil. Theodore von Kármán and Hugh Latimer Drydenintroduced the term transonic to describe flow speeds around Mach 1 where drag increases rapidly. Because of the increase in drag approaching Mach 1, aerodynamicists and aviators disagreed on whether supersonic flight was achievable.

A computer generated model of NASA's X-43Ahypersonic research vehicle flying at Mach 7 using acomputational fluid dynamics code.

On September 30, 1935 an exclusive conference was held in Rome with the topic of high velocity flight and the possibility of breaking the sound barrier.Participants included von Kármán, Prandtl, Ackeret, Eastman Jacobs, Adolf Busemann, Geoffrey Ingram Taylor, Gaetano Arturo Crocco, and Enrico Pistolesi. The new research presented was impressive. Ackeret presented a design for a supersonic wind tunnel. Busemann gave perhaps the best presentation on the need for aircraft with swept wings for high speed flight. Eastman Jacobs, working for NACA, presented his optimized airfoils for high subsonic speeds which led to some of the high performance American aircraft during World War II. Supersonic propulsion was also discussed. The sound barrier was broken using the Bell X-1 aircraft twelve years later, thanks in part to those individuals.

By the time the sound barrier was broken, much of the subsonic and low supersonic aerodynamics knowledge had matured. TheCold War fueled an ever evolving line of high performance aircraft. Computational fluid dynamics was started as an effort to solve for flow properties around complex objects and has rapidly grown to the point where entire aircraft can be designed using a computer.

With some exceptions, the knowledge of hypersonic aerodynamics has matured between the 1960s and the present decade. Therefore, the goals of an aerodynamicist have shifted from understanding the behavior of fluid flow to understanding how to engineer a vehicle to interact appropriately with the fluid flow. For example, while the behavior of hypersonic flow is understood, building a scramjet aircraft to fly at hypersonic speeds has seen very limited success. Along with building a successful scramjet aircraft, the desire to improve the aerodynamic efficiency of current aircraft and propulsion systems will continue to fuel new research in aerodynamics.

Welcome to the Beginner's Guide to Aerodynamics

Welcome to the Beginner's Guide to Aerodynamics
What is aerodynamics? The word comes from two Greek words: aerios, concerning the air, and dynamis, which means force. Aerodynamics is the study of forces and the resulting motion of objects through the air. Judging from the story of Daedalus and Icarus, humans have been interested in aerodynamics and flying for thousands of years, although flying in a heavier-than-air machine has been possible only in the last hundred years. Aerodynamics affects the motion of a large airliner, a model rocket, a beach ball thrown near the shore, or a kite flying high overhead. The curveball thrown by big league baseball pitchers gets its curve from aerodynamics.

Aerodynamics and Hydrodynamics of the Marine Life and Uses for AI, UAVs, Robotics, and the Future

Aerodynamics.

Air has 750 times less density as the oceans, yet so many of the same principles apply there as well. We are quite familiar with marine life and the performance abilities of sharks, dolphins, penguins, fish, alligators, etc. Mankind is quite fascinated by marine life and often tries to use these observations to create devices to serve him.

A Great White Shark can swim 7 times as fast as the Olympic swimmers in Athens taking the gold this year, yet it is not even close to being the fastest in the water. Powerful, yes indeed, but the need for speed limits its abilities to catch some of its favorite meals. Luckily humans are not one of them, as much as JAWS I, II and III would have you believe. The Great White Shark swims at about 25 mph. Squids can move through the water at 20 mph. The Blue Shark has been clocked in short bursts at 43 mph yet its average cruising speed in open water is between 17.7 and 24.5 mph. The Make Short Fin can travel at 10 times its body length per second, which is quite fast and amounts to over 46 mph at top speed. It can accelerate at 45 feet per second/ per second, faster than a rock can fall or a human accelerates after he departs a perfectly good airplane in search for an adrenaline rush to achieve sense of purpose. A human can swim at 5.04 mph, but only for short distances and you have to be a Mark Spitz or Michael Phelps to it for very long.

As good as these super star athletes are, they are no match for evolution, without modification. You might be happy to know that a barracuda will catch you and nibble before a great white shark will catch you in open water, they can swim at 27 mph, one of the fastest, well and hungriest fish in the water. Mammal Sea Life is quite adapted; Sea Lion 25 mph, Common Dolphin 24.7, Gentoo Penguin 17, Blue Whale 29.76, Bottle Nose Dolphin 17 mph. Many of the fish eaten by the marine life of prey are also quite adapted for instance the Pacific Salmon can swim at 14 mph. Then there are the flying fish, those, which leap out of the water and become airborne, thus proving that there is a similarity between the two realms. The flying fish flies at 35 mph and has been known to fly right into a boat, for an easy catch. The Leaping Albacore Tuna leaps at 40 mph great sushi no doubt, the Yellow Fin Tuna at 46.35, the Sword Fish 60 mph and the Sail Fish at 68 mph. Here is a claim from Barbados that a flying fish was clocked at 55 mph?

Well maybe, but not if Hurricane Ivan has anything to say about it because if that fish pops out of the water it is liable to be doing some 135 mph within a few feet of leaving the waters surface and might be airborne for quite a while too? Now that would certainly be a new record.

Does this mean we might also wish to look at Fish and Sea Life Evolution in the aerodynamic designs of aircraft, UAVs, Blimps and Olympic Swim Gear? Yes, this is one of the points of this dialogue. Does this mean we should look at aviation designs for submarine, AUVs, ship hulls and underwater submersibles? Should we also be designing underwater bases for aircraft, spacecraft and double use vessels? Flying AUVs, which become UAVs? Designing flying torpedoes, Mechanical Fish and MAVs, which look like the flying fish photo too? Yes, it does. If you made a mechanical fish what good would it be? Hunting water mines, data relays, additional net-centric communication unit?

If nature can do these things, so can we and we have been constantly re-designing and bettering natures methods. If an eagle has 3-4 better times the eye sight and can see, react and adapt while in-flight that quickly, yet has less of a brain to coordinate all the data yet has also developed triple the reflex or response time, should we be looking into how this is done? For instance does an Eagle use some sort of visual frame bursting, for instance it knows the type of fish it likes to eat which tastes good and is the right weight and size and when it sees this it’s brain fills in the details and it’s eyes only focus on the slight variations of motion and detail so it knows where to pick it up at and how best to snatch it out of the water? We know that our brains use up about 45% of the brain capacity in visual cognition. What does the Eagle do with all the many flights and all that data for it’s memory, it cannot possibly store it all, does it have a Random Access Memory Data dump like when you windows computer crashes? Does it only save the frames and basic shapes and let the eyes fill in the rest of the details each time? We should test this as it is important to know.

We know the human brain can be fooled often enough when something appears to be close to something we are familiar with. What can we learn from these birds besides their aerodynamics. Is it possible to play optical tricks on an Eagle? For instance make a small AUV, which mimics a salmon fish? Will the Eagle be fooled by this? Old Eagle eyes, or will the Eagles excellent eye sight trigger another wave in it’s brain, as if to ask itself; “Hey something is fishy about that fish?” Would such a thought from an Eagle significantly activate it’s brain for a second look, before diving upon it’s prey? It appears in humans this does activate an additional brain wave.

Since Eagles do not flock are do they communicate and navigate, migrate using ELF, entangled brains with other eagles? Only their immediate families from the same mother or nest? This too would be of value for determining AI for robotic UAVs as part of the net centric warfare situation.

As we look at Artificial Intelligence models perhaps we should be looking at other species, which seem to be able to do more with less. Less brain capacity, yet still think. Perhaps we ought to dump the ego into thinking that mankind is the only animal which can reason and adapt on this Planet, we have significant proof of other animals here doing quite fine in the thinking region. If we open our minds we may find other species may in fact supercede our abilities in many aspects. Is the future of robotics going to the birds with regards to UAVs and MAVs as the needs of mankind and the competitiveness of the species looks towards innovation as the ultimate contest and in our speed to achieve we find ourselves bettering hundreds of thousands of years of evolution with breakthrough after break through?

Robots to really assist us must have some fuzzy logic capabilities at minimum and to be most effective they must also have some artificial intelligence capabilities to serve our needs, as mankind has no end in sight to the tasks it wishes to assign to robotic apparatuses.

Press-on will solve all that mankind desires. There are clues everywhere and one might ask what is taking us so long anyway, where would you like to go today? We need to ratchet up the thinking here and move forward in this arena.