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Every aircraft diagram in your physics book shows four arrows: lift, weight, thrust and drag. The idea that a flying machine should be thought of this way, with a wing to hold it up and a separate push to keep it moving, goes back to an English landowner, George Cayley. This post sets out what he actually wrote in 1809, works through his own numbers as a Class 11 resolution of forces problem, and ends with what you can borrow from how he worked.
Who was George Cayley?
The Science Museum Group's record describes Sir George Cayley, sixth baronet, as an aeronautical designer born in Scarborough, Yorkshire, on 27 December 1773, who died in 1857. The museum holds a small silver disc, one inch across, engraved with an early design of his for a glider and dated 1799. It also holds a model of his first model glider, from 1804.
What did Cayley publish in 1809?
In November 1809, Nicholson's Journal of Natural Philosophy, Chemistry and the Arts printed his essay "On Aerial Navigation". You can read it in the 1809 volume 24 scan on the Internet Archive. Cayley's letter is dated Brompton, 6 September 1809. He wrote because the journal had reported a Viennese watchmaker, Jakob Degen, raising himself into the air.
Three things in it still matter to a physics student:
He split the air's force into two parts. Watching a bird glide with still wings, he drew the total force of the air on the wing and resolved it into "the force that sustains the weight of the bird" and "the retarding force" that slows it down. Today we call these lift and drag.
He stated the problem in one line. "The whole problem is confined within these limits, viz. To make a surface support a given weight by the application of power to the resistance of air."
He measured. He dismissed strapping wings to a person's arms, then tested a flat square foot on a whirling arm about five feet long, over runs of 600 feet. He reports 4 ounces of resistance at 11.538 feet per second and 8 ounces at 17.16 feet per second.
NASA's history of wind tunnels, taken from the book Wind Tunnels of NASA, calls this separation of propulsion and lift Cayley's major contribution: use an engine for forward motion and let the motion develop lift through the wings.
How does Cayley's own example work out?
Cayley gave a full example. A flat sail of about 200 square feet meets the air at 6 degrees, moving at about 35 feet per second. The total air force on it is 200 pounds, acting perpendicular to the sail. Find the pull needed to keep the machine moving. This is resolution of vectors, section 3.5 of the NCERT Class 11 chapter Motion in a Plane.
The sail is tilted 6° from the flight path, so the force perpendicular to it is tilted 6° from the vertical.
Vertical part (lift): 200 × cos 6° = 200 × 0.9945 = 198.9 lb.
Horizontal part (drag): 200 × sin 6° = 200 × 0.1045 = 20.9 lb.
In steady level flight the forces balance, so the pull (thrust) must equal the drag: about 21 lb.
Cayley's own answer was "a tension of about 21 pounds". In SI units, 200 lb-force is about 890 N and 20.9 lb-force about 93 N. The lift is 198.9 ÷ 20.9 = 9.5 times the drag, which is his point: a small push holds up a much larger weight. He also noticed that 198.9 lb is about 1.1 lb short of 200, and suggested throwing out a little ballast.
You can also check his whirling arm data against the rule that air resistance grows roughly with the square of speed. The speed ratio is 17.16 ÷ 11.538 = 1.487, and 1.487² = 2.21. His measured force ratio was 8 ÷ 4 = 2. That is close but not exact, which is what real data looks like.
What mistakes do students make with lift and drag?
Making the engine hold the plane up. In level flight thrust balances drag and lift balances weight. NASA's four forces page says it directly: the job of the engine is to overcome drag, not to lift the airplane.
Swapping sine and cosine. Draw the angle. If the sail is 6° from the horizontal, the force perpendicular to it is 6° from the vertical, so lift uses cos 6° and drag uses sin 6°.
Thinking steady flight needs a net force. If speed and height are constant, the forces are balanced, and Newton's first law applies. NASA notes that an aircraft with balanced forces cruises at constant velocity.
Assuming lift always points straight up. Lift is perpendicular to the flight direction, so it tilts when the aircraft climbs or banks.
If resolving forces still trips you up, our post on common errors with vectors walks through the habits that cause them. When you get the right answer but are unsure why each step follows, the Fermi Problem Library has a step-by-step solver that explains the reasoning rather than printing an answer.
What can a student take from Cayley's way of working?
State the problem in one sentence. His "support a given weight" line turned a vague dream into a physics question.
Break a force into parts that do different jobs. Once lift and drag were separate, each could be studied.
Measure, and report what you measured. He gave speeds to three decimal places and the length of each run.
Check against simple models. He set his results beside earlier measurements, such as Smeaton's figure of one pound on a square foot at 21 feet per second.
About a century later the Wright brothers made the first powered flight after testing their own lift data against published tables.
Next time you draw a free body diagram for an aircraft or a kite, label which force does which job before you write a single equation.
