Physics Aerodynamics From Rs Aerodynamic Force

The five forces

Aerodynamics names five canonical force types that act on a flying body: lift, drag, thrust, weight, and moment. Lift holds the aircraft up, drag resists its motion through the air, thrust pushes it forward, weight pulls it down, and moment is the twisting tendency that rotates the body around its center of gravity. These five are the standard working set in any flight mechanics course, and the Recognition Science framework's machine-checked library of formal theorems defines them as an inductive type with exactly five constructors.

The library proves that the number of these force types is five, by a direct computation on the definition. It also proves one equilibrium statement: at the cruise condition, the recognition cost J evaluated at the value 1 equals 0. In the framework, recognition cost is a forced, not chosen, price that reality pays for each recognition event, and its value at unity is zero by definition. The cruise equilibrium is then the statement that lift balances drag at the level where this cost vanishes.

The framework does not derive the physical laws of flight. It does not prove that lift equals drag in any real atmosphere, nor does it compute a lift coefficient or a drag polar. The declaration certifies a structural fact: the framework's own model of aerodynamics recognizes exactly five force types, and one formal identity holds at the cruise point. The connection between this formal model and the measured behavior of actual wings remains a modeling choice, not a proved theorem.

theorem aerodynamicForceCount : Fintype.card AerodynamicForce = 5 := by decide

theorem aerodynamicForceCount : Fintype.card AerodynamicForce = 5 := by decide

/-- Cruise equilibrium: J = 0. -/
theorem cruise_equilibrium : Jcost 1 = 0 := Jcost_unit0

What this page does not claim

The declaration does not prove that lift equals drag in any real atmosphere. The declaration does not compute any aerodynamic coefficient or performance number. The framework's model of aerodynamics is a definitional choice, not a derived physical law.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Physics/AerodynamicsFromRS.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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Derived articles

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