Flight Theory

Flight, taught properly, years before the first lesson.

The one subject where a teenager will happily work through thermodynamics, because they want to know whether the aeroplane leaves the runway. Taught one to one by a rocket engineer.

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A child who wants to fly is told, for years, to wait.

Seventeen for a licence, in America, in Britain and across Europe. Sixteen even to hold a student pilot certificate. So the waiting becomes what waiting usually becomes: a thousand hours in a simulator, a hundred videos, and a parent who cannot tell whether this is a career or a phase.

There is one thing a fourteen year old can start tonight, and it happens to be the half that flight schools charge two hundred dollars an hour to teach badly, in an aircraft, with the engine running. The physics of the wing. The weather. The machine. The instruments, and the specific way each one lies. The judgement.

A student who arrives at flight training already fluent in this is not simply better prepared. They are a different kind of student, and an instructor can tell inside an hour.

Taught one to one, weekly, on a shared whiteboard, by an engineer who has used this physics for real work. A written note after every class and a report to you every fortnight. The same practice, the same standard and the same person as every other subject here.

How it is taught

Why does the same aeroplane need almost half as much runway again in Phoenix in July as it does in Manchester in January?

One question, answered three times. This is not a syllabus. It is what one idea looks like at three different ages, and it is the clearest way to show how a student would be taught rather than tell you.

Grades 5 to 8

It is not the wings. It is the air.

A wing is pushed up because it pushes air down. If there is less air in each cubic metre, the wing has to move faster before there is enough of it to push, and moving faster takes runway. The propeller has the same problem, and so does the engine, which is why the effect is far larger than anyone expects.

Air thins when it is hot, and it thins when you climb. Pilots combine both into one number: the altitude the aeroplane believes it is at.

density altitude ≈ pressure altitude + 120 × (OAT - standard temperature)

Phoenix Sky Harbor sits at about 1,135 feet. On a 45 degree Celsius July afternoon the air is roughly 32 degrees warmer than standard. Manchester sits at about 257 feet, and on an 8 degree January morning the air is roughly 6.5 degrees colder than standard.

Phoenix    1,135 + (120 × 32.2) ≈ 5,000 ft

          Manchester   257 - (120 × 6.5) ≈ -520 ft

The aeroplane in Phoenix believes it is a mile above the sea before it has begun to move. This is arithmetic, negative numbers and rates of change. It does not feel like any of them.

Grades 9 to 12

Derive it, then argue with it.

Lift depends on air density, on the square of speed, on wing area and on the lift coefficient.

L = ½ ρ v² S C_L

At the instant of lift off, lift equals weight. Wing area is fixed. The aeroplane is rotated to a fixed attitude, so the lift coefficient is fixed too. Everything on the right except density and speed is therefore constant, which gives

v_LOF ∝ 1 / √ρ

Ground roll is approximately the lift off speed squared over twice the mean acceleration. The numerator goes as one over density. And for a normally aspirated piston engine with a fixed pitch propeller, thrust falls roughly in proportion to density as well, so the denominator does too.

s = v_LOF² / 2a ⇒ s ∝ 1 / σ² where σ = ρ / ρ₀

In the standard atmosphere the density ratio is about 0.862 at 5,000 feet and about 1.015 at minus 520 feet. So the student rearranges and finds the answer.

s_PHX / s_MAN = (1.015 / 0.862)² ≈ 1.39

Thirty nine per cent more runway. Same aeroplane, same weight, same pilot, same technique.

Then the argument starts. The relationship is a square, which is why a pilot who is thirty per cent wrong about the air is nearly seventy per cent wrong about the runway, and why hot and high accidents are a category rather than a coincidence. A student who has felt that square close on them understands proportionality in a way no worksheet delivers.

Beyond the theory

The model is not what a pilot uses. That is the lesson.

No pilot computes a ground roll from first principles before taking off. They read the performance chart in the aircraft handbook, because the real aeroplane also has a propeller whose efficiency changes, a runway that may slope, a surface that may be wet grass, and a wind that may be doing something other than what the forecast said.

The derivation exists to make the chart intelligible, not to replace it. Learning when to trust your own model, and when the professional's table beats it, is the actual transferable skill, and it is the one this subject teaches better than almost any other.

Figures are standard atmosphere first order values and elevations are approximate. The aircraft's published performance chart is always the authority.

What is taught

Seven modules, in the order an aeroplane actually makes sense.

Law is taught last, on purpose. A rule learned after the physics is understood is a rule that is remembered. A rule learned first is a fact to be forgotten.

Principles of Flight

Why a wing works, why it stops working, and why a stall has nothing at all to do with speed.

Aircraft Systems

The engine, the propeller, the fuel, the electrics. What fails, and exactly what the pilot sees when it does.

Instruments

What every dial is actually measuring, and the specific way each one lies to you.

Meteorology

The sky as a fluid. Reading a real forecast, and deciding honestly whether today is a day to go.

Performance and Loading

The arithmetic that decides whether the runway in front of you is long enough this afternoon.

Human Performance

Illusions, hypoxia, workload, and what it takes to make a good decision with a clock running.

Air Law and Procedures

The shape of the sky, and the reason behind every line drawn through it.

What your child studies is decided after the assessment, not before it.

There is no fixed syllabus on this page because there is no fixed syllabus in the practice. Two students in the same grade, in the same week, are usually working on different things. The plan is written after I have watched your child work, it is shared with you before the first class, and it is revised every term.

Where it fits

Grades 5 to 12 Taught within any programme Or as a standing class each month Feeds AP Physics C, A-Level Mechanics and IB Physics Project work at Grades 9 to 12

This is ground theory: the classroom half of learning to fly. The flying itself comes later, at a flight school, when a student is old enough.

How every family begins

Begin with an assessment.

Seventy five minutes: forty five with your child, working real problems, and thirty with you. Within forty eight hours you receive a written assessment of your child's reasoning: what they understand, what they only appear to understand, and what I would do about it. Yours to keep, whatever you decide.

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