fandomhigh | Aviation & Avionics, Thursday September 18, Period 2

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Aviation & Avionics, Thursday September 18, Period 2

Murdock was sitting at the desk, giving lots of pets and scritches to a dog. An Afghan Hound to be precise.

"Morning class," Murdock chirped as the students filed in. "We've got a bit to cover today, so let's get started, okay?"

Abby Irene just settled herself quite like the lady she was and watched as Murdock went about his class instruction.

(ocd ~~coming~~ up! AbbyIrene!doggie modded with permission)

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As you do.

Chat with your classmates, doodle, make paper airplanes, gawk at the dog in class...etc.

Murdock has quite a bit to cover today.

He'll be busy petting and scritching Abby Irene some more.

"How does flight work?" Murdock paced in front of the chalkboard, thumping a piece of chalk against a finger. "It's simple, really. Just a matter of ratios." And he began scrawling figures and equations on the board as he talked.

"The wings of a Boeing 747 (http://en.wikipedia.org/wiki/Boeing_747) have a surface area of 5500 square feet, and they can lift 800,000 pounds into the air. This means they have a carrying capacity of 145 pounds per square foot. Now, for an example let's say a 5x7 foot waterbed weighs 2000 pounds and we want to set it up in a room that's 35 square feet. Wow, that's a big room," he muttered. "At that ratio, the floor must be able to carry 57 pounds per square foot. That's almost half the loading on the Boeing's wings."

"A 747 burns 12,000 liters of fuel per hour. Midway on a long intercontinental flight, the plane weighs approximately 300 tons (300,000 kilograms, 660,000 pounds). The 12,000 liters of fuel it burns each hour weighs about 10,000 kilograms (22,000 pounds) because the specific gravity of the fuel is about 0.8 kilogram per liter. This means that a 747 consumes roughly 3 percent of its own weight each hour."

"'Carrying capacity', as it's referred to, depends on a number of factors;" he turned toward the class and ticked off a few fingers, "wing size, airspeed, air density, and the angle of the wings with respect to the direction of flight. The role of wing size is straightforward," he said, waving the chalk around, before returning to the chalkboard, "a wing's aerodynamic lift L is proportional to its surface area S. In practice, S is defined as the surface area measured from a full-scale photograph of the wings taken from above. The relation between L and S is simple enough; a wing twice as large can carry twice as much weight. Easy right?" he grinned back at them.

"However, the relation between lift and airspeed is less straightforward. If we call the airspeed V , for velocity and the air density d, then the mass flow of air around the wings is proportional to d times V." Which he wrote out as dV. "According to a version of Newton's Second Law of Motion, the force generated by the airflow around the wings is proportional to V times dV ." That also went on the chalkboard, dV^2. "If one flies twice as fast," and he moved his hands around at various angles, trying to demonstrate this, "with the same wings at the same angle in the air stream, the lift is 4 times as great. And if one flies at an altitude of 12 kilometers (39,000 feet) where the air density is only one-fourth its value at sea level, one must fly twice as fast to sustain the same weight."

"Now let's look at the angle between the wing and the airflow," he continued, turning back to the classroom. "This is known as 'angle of attack'. If you stick your hand out the window of a moving car, keeping your hand level, you feel only air resistance. But turn your wrist, your hand wants to move up or down. That is aerodynamic lift. But as you increase the angle of your hand," and he moved his own hand around, "you start generating more resistance while losing much of the lift. The angle of attack can be changed by a set of wings to fit a certain circumstance. Nose up, with a high angle, for flying slowly; nose down when speeding. In long-distance cruising, 6 degrees is a reasonable average."

"Since wings have to support the weight of the craft, the lift L must equal the weight W. The lift is proportional to the wing area S and to dV^2, and so is the weight." He wrote W=0.3 dV^2S. on the board. "Now, you're probably wondering where the 0.3 comes from. That's also simple, it's related to the angle of attack in long-distance flight, for which the average value of 6 degrees has been adopted."

"Clear and consistent definitions for the units in which d, V, and S are expressed are needed. The best way to ensure consistency is to express S in square meters, V in meters per second, and d in kilograms per cubic meter. The rules of physics then require that the weight W in the equation be given in kilogram-meters per second squared. This frequently expressed in newtons. A newton is slightly more than 100 grams (3.6 grams)."

"A Boeing 747 has a wing area of 5500 square feet (511 square meters) and flies at a speed of 560 miles per hour (900 kilometers per hour; 250 meters per second). At an altitude of 12 kilometers (40,000), where the air density is only one-fourth its sea-level value of 1.25 kilograms per cubic meter, V = 250 meters per second, and S = 511 square meters." He scrawled all that out on the board as well. "Then we calculate from the equation that W must equal 2,990,000 newtons. And because a newton is about 100 grams, this corresponds to roughly 300,000 kilograms, or 300 tons. Which just happens to be the weight of a 747 at the midpoint of an intercontinental flight."

"So," he put the chalk down and spun to face the class, brushing his hands together to get the chalk dust off, "we now see how it all comes back to work together. Right?" he grinned. "Questions?"

Ooh science!

Let me know if if your brain has imploded now. Mine has. :D

Jack Burton!

There was a dog in class. Jack took notes and wondered if the dog was scritchable. Well, one way to find out. "Here boy," he said, softly.

*re-explodes brain to proper density and volume*
that ^2 makes me miss my TI-85.

Naomi Wildman

Naomi listened carefully to the lecture and took detailed notes.

Anemone

Anemone was making faces at all the math, but she was taking notes as quickly as she could.

Hee! I actually borrowed that idea from work. Since databases also can't handle subscript. :)

Cindy Mackenzie

Abby Irene just turned her head up a bit, clearly in a manner to indicate that she was in fact, not a boy.

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Aviation & Avionics, Thursday September 18, Period 2

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