Flying is one of humanity's greatest achievements, especially considering that nearly every early attempt began with someone looking at a bird and reaching the dangerously incomplete conclusion, "I can probably do that." Birds had feathers, hollow bones, specialized muscles, millions of years of evolution, and an instinctive understanding of air currents. Humans had bedsheets, wooden planks, questionable carpentry, and friends willing to push them off buildings. The gap between those two engineering programs was enormous, although history shows that optimism can hide an astonishing amount of missing mathematics.The science of flying begins with air, a substance that seems like nothing until you try to move through it at several hundred miles per hour. Air has mass, pressure, temperature, density, and a talent for becoming extremely opinionated around wings. Shape a wing correctly, move it fast enough, and the air helps lift an airplane into the sky. Shape it incorrectly, move it too slowly, or attach it to something built in a garage by a man who refuses to read instructions, and the air files an immediate objection.
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