Friday, January 11, 2019

The Wright Brothers #6

Competitors of the Wright brothers experimented with alternatives to circumvent the Wright brothers' patent. Foremost was Glenn Curtiss, who invented ailerons ("little wings") instead of wing warping for flight control. (Curtiss also pioneered in attaining more speed.) The Wright brothers sued for patent infringement, starting a years-long legal conflict. Curtiss's company obtained patents, too. Until he died from typhoid in 1912, Wilbur took the lead in the patent struggles.

David McCullough's book devotes little space to the patent wars. McCullough says nothing about how the patent war ended. Wikipedia has an article devoted to them, which says the following. It was ended by the U.S. government. By 1917 the two major patent holders, the Wright Company and the Curtiss Company, had effectively blocked the building of new airplanes, which were desperately needed as the United States was entering World War I. The U.S. government pressured the industry to form a cross-licensing organization (a patent pool), the Manufacturer's Aircraft Association.

All aircraft manufacturers were required to join the association, and each member was required to pay a comparatively small blanket fee (for the use of aviation patents) for each airplane manufactured; of that the major part would go to the Wright-Martin and Curtiss companies, until their respective patents expired. This arrangement was designed to last only for the duration of the war, but the patent war did not resume later. Orville had sold his interest in the Wright Company to a group of New York financiers in 1915 and retired from the business. The "patent war" came to an end. The companies merged in 1929 to form the Curtiss-Wright Corporation, which still exists.

Tuesday, January 8, 2019

The Wright Brothers #5

The Wright brothers continued their experiments with powered flight after the one at Kitty Hawk in December, 1903. They did longer flights with more control of the aircraft, attaining 24 miles in October, 1905. They got a patent approval in 1906. Their fame grew slowly initially. The American press and government expressed little interest. The U.S. goverment wanted drawings and descriptions enough to enable construction, but the brothers refused. Their fame did grow rapidly after Wilbur did demonstrations in France in 1907-8.

Wilbur lost control and crashed a plane in 1905 with minor injury. Orville did, too. They flew little for about two years, trying to commercialize their invention. In September, 1908 Orville crashed a plane and was badly injured, with multiple broken and fractured bones. His passenger was killed.

They formed the Wright Company in 1909. They sold their patents to the company for $100,000 and also received one-third of the shares in a million dollar stock issue and a 10 percent royalty on every airplane sold. With Wilbur as president and Orville as vice president, the company set up a factory in Dayton and a flying school/test flight field at Huffman Prairie, Ohio; the headquarters office was in New York City.

Saturday, January 5, 2019

The Wright Brothers #4

Especially helpful to the Wright brothers were Octave Chanute, a civil engineer, builder of bridges, railroads, and gliders and Samuel Pierpoint Langley, astronomer and head of the Smithsonian. Langley, with help of Smithsonian funding, had helped create a pilotless "aerodrome."

Other experimenters in controlled flight were Sir George Cayley, Sir Hiram Maxim, Alexander Graham Bell, and Thomas Edison. In France the government spent a considerable amount of money on a steam-powered flying machine built by Clement Ader, who gave the word avion, airplane in English, to the French language. Along with the cost of experiments, the risk of failure, injury, and death, there was the inevitable prospect of being mocked as a crank, a crackpot, often for good reason. The experimenters served as a continual source of popular comic relief.

Among the material supplied by the Smithsonian to the Wright brothers was Pierre Mouillard's Empire of the Air, which exalted the wonders of flying creatures. Wilbur took up bird watching on Sundays, observing what Mouillard preached. The dreams of Wilbur and Orville had taken hold. They would design and build their own experimental glider-kite, building on what they had read, observed of birds in flight, and spent considerable time thinking. They became familiar with aeronautical terms such as equilibrium, lift, pitch and yaw. Equilibrium was all-important to them. Wilbur's observations of birds and how they adjusted their wings to maintain balance inspired him to the idea of building a glider with "wing warping" or "wing twisting." This made an immensely important and original advance to their goal.

Wednesday, January 2, 2019

The Wright Brothers #3

For a few weeks each year in 1900-02 the Wright brothers experimented with gliders at Kitty Hawk, North Carolina. Wikipedia has greater detail about the gliders. Kitty Hawk had a small population, the men were mostly fishermen, and the living conditions were uncomfortable and often harsh. It  was quite a journey to get there. However, the Wright brothers chose this place due to the fairly steady wind conditions and the sand bars which afforded the best landing surface.

After their 1901 visit to Kitty Hawk they built a small wind tunnel. It was only six feet long and four feet square, but their experiments with it and numerous wing shapes greatly increased their understanding of flight.

They went again to Kitty Hawk in 1903. This time they had a biplane with motor and propellers. Their long-time bicycle shop employee Charlie Taylor became an important part of the team, building their first airplane engine in close collaboration with the brothers. On December 17, 1903 they made the first controlled, sustained flight of a powered, heavier-than-air, fixed wing aircraft. Their fundamental breakthrough was their invention of three-axis control, which enabled the pilot to steer the aircraft effectively and to maintain its equilibrium.

Sunday, December 30, 2018

The Wright Brothers #2

In 1896 Orville Wright got typhoid fever, and he was in bed for several weeks. During this time Wilbur began reading about German glider enthusiast Otto Lilienthal, who was recently killed in an accident. Wilbur read aloud to Orville.

A manufacturer of small steam engines and a mining engineer by training, Lilienthal started gliding as early as 1869, along with his younger brother. He took his lessons from the birds. He thought the "art of flight" was to be found in the arched wings of birds by which they could ride the wind. He had no use for balloons, since they had so little in common with birds. To fly one had to be "initimate" with the wind.

Over the years Lilienthal built many gliders. Most were monoplanes with an arched wing consisting of muslin stretched over a willow frame. As pilot he would wear padded knees, position himself below the wings, and begin by running downhill. He would swing his body and legs for balance and control.

He also had himself photographed in action, taking advantage of newly invented cameras. Photos of him gliding appeared the world over, more so in the United States. A long article in McClure's Magazine, with seven photos, reached the largest audience.

In 1894 Lilienthal crashed but survived. In 1896 he crashed and died. News of Lilienthal's death aroused a great interest in Wilbur Wright. He began reading intensely on the the flight of birds, including the book Animal Mechanism from the family bookshelf. He read Animal Locomotion; or Walking, Swimming, and Flying, with a Dissertation on Aeronautics. For most readers it was too daunting. For Wilbur the book was exactly what he needed. Wilbur drew upon and quoted the book for years. It opened his eyes and started him thinking in new ways. Orville recovered from his illness and read the same works.

The automobile appeared and gained popularity. For Wilbur it lacked appeal. His sight was upward.

Friday, December 28, 2018

The Wright Brothers #1

The Wright Brothers is a book by David McCullough. It's widely known that the Wright brothers had a bicycle shop, which they opened in 1893, before venturing into flying.

The following is an amusing historical note about bicycles.

"Bicycles had become the sensation of the time, a craze everywhere. (These were no longer the "high wheelers" of the 1870s and '80s, but the so-called "safety bicycles," with two wheels the same size.) The bicycle was proclaimed a boon to all mankind, a thing of beauty, good for the spirits, good for health and vitality, indeed one's whole outlook on life. Doctors enthusiastically approved. One Philadelphia physician, writing in The American Journal of Obstetrics and Diseases of Women and Children, concluded from his observations that "for physical exercise for both men and women, the bicycle is one of the greatest inventions of the nineteenth century."
     Voices were raised in protest. Bicycles were proclaimed morally hazardous. Until now children and youth were unable to stray very far from home on foot. Now, one magazine warned, fifteen minutes could put them miles away. Because of bicycles, it was said, young people were not spending the time they should with books, and more seriously that suburban and country tours on bicycles were "not infrequently accompanied by seductions."
     Such concerns had little effect. Everybody was riding bicycles, men, women, all ages and from all walks of life. Bicycle clubs sprouted on college campuses and in countless cities and towns, including Dayton" (p. 22).

Saturday, December 15, 2018

Approaching Infinity

The title is the title of a book by Michael Huemer, which I read most of, but not all. It’s good in parts. It addresses infinity in several ways. He presents many paradoxes involving infinity and gives his solutions for some of them. He discusses Cantor’s diagonal arguments (see my previous post for one). He doesn’t seem to wholly agree with them, but he doesn’t argue against them either.

He does challenge Cantor concerning Galileo’s paradox. “The puzzle is that there is a compelling argument both that the two sets are equally numerous (the one-to-one correspondence argument), and that one set is larger than the other (for the squares are a proper subset of the natural numbers). Cantor embraces the first of these arguments and rejects the second. His only justification for this is fiat: he proposes to simply define the relations ‘equal to’, ‘greater than’, and ‘less than’ using the one-to-one correspondence criterion.
     Of course, one could not consistently brace both of the arguments Galileo mentions, since they entail contradictory results. But Cantor’s decision to embrace only the one-to-one correspondence argument is not the only alternative. One could embrace the proper-subset argument while rejecting the one-to-one correspondence argument. Or one could, like Galileo, reject both arguments and hold that ‘greater than’, ‘less than’, and ‘equal to’ relations do not apply to pairs of infinite sets. Cantor does not argue for his alternative over the others” (6.9.4).

Huemer did not say one could embrace the proper subset argument for comparing the integers and the rationals.

The weakest parts of the book in my opinion were about the empty set and geometric points.

Huemer misses the strongest reason for having the concept of an empty set. The two major operations on sets are union and intersection. The first forms a new set by combining the members of two or more sets. The second forms a new set by identifying the common members of two or more sets. Say we have set A = {1, 2, 3} and set B = {3, 4, 5}. The intersect of A and B is {3}. But what if B = {4, 5, 6}? Then A and B have no common members. In other words, the intersect of A and B is nothing, i.e. the empty set { }, often symbolized as {∅}. In other words, the empty set is needed to make defined operations complete. It is similar to a need for the number zero, for example 5 – 5 = 0.

Huemer is frustrated with geometric points. He says they are unimaginable, because they have size zero, yet they are supposed to be the building blocks of other geometrical objects (11.2).

I regard the building block perspective as from the wrong direction. Start with 3-dim space, e.g. a cube. Then disregard one dimension to get 2-dim space (a square plane), disregard another dimension to get 1-dim space (a line), and finally to 0-dim space (a point). Alternatively, each intersection of two lines of the square is a point.

Later in the book there is a section (14.6.3) about points as locations. He does not have any arguments against this view, but he doesn’t endorse it either and says he doesn’t understand it. 

In my opinion it is the best view. We often hear people say things like how to get from point A to point B. More concretely it might mean driving a route from one location, such as a town, to another location, another town. In the context of geometry, a point is a location in Cartesian or polar coordinates. For example, the point (2,3) in 2-dim Cartesian coordinates means 2 units to the right of the origin (0, 0) or y-axis and 3 units above the x-axis. Of course, Euclid’s Elements did not have this perspective, since Cartesian coordinates were invented much later.