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Technical Methodology & Regulatory Source Hierarchy

Technical Calculation Methodology & Source Standards

At Aeroway (aeroway.org), we treat flight calculations as deterministic engineering models rather than informal rules of thumb.

To maintain mathematical integrity and transparency, every tool, guide, and benchmark on the platform is governed by this public methodology framework.

1. Four Mathematical Classifications

Every calculation model on Aeroway is explicitly tagged with one of four architectural classifications:

Class 1: Exact Mathematical Models

  • Definition: Closed-form mathematical physics that are exact within the stated geometric and thermodynamic assumptions.
  • Examples:
    • Runway Crosswind Decomposition: $XW = W \cdot |\sin(\text{WD} - \text{Runway})|$
    • Navigational Wind Triangle: Law of Sines crab angle $\text{WCA} = \arcsin\left(\frac{W \cdot \sin(\theta)}{\text{TAS}}\right)$
    • Time-Speed-Distance kinematics: $D = S \times T$
  • Boundary: Theoretical kinematics. Real-world flight remains subject to micro-scale gusts, pilot control lag, and sensor measurement tolerances.

Class 2: Standardized International Reference Methods

  • Definition: Implementations directly codified by international treaties or national civil aviation authorities.
  • Examples:
    • ICAO Doc 7488/2: Standard Atmosphere geopotential pressure and temperature lapse rates up to 20 km (65,617 ft).
    • ICAO Doc 8168 & FAA AIM Table 7-3-1: Sub-zero cold-temperature altimetry error corrections.
    • FAA TERPS (Order 8260.3F): Obstacle departure climb gradients and required climb profiles.

Class 3: Empirical Polynomial & Chart Digitizations

  • Definition: High-order polynomial regressions derived from empirical flight test tables and aerodynamic monographs.
  • Examples:
    • Tetens and Goff-Gratch saturation vapor pressure equations for humid air density.
    • POH/AFM takeoff ground roll quadratic weight scaling exponents ($S_{g} \propto W^2$).

Class 4: Cockpit Heuristics & Rules of Thumb

  • Definition: Linear first-order approximations historically used by pilots for in-flight mental math.
  • Examples:
    • 120-ft density altitude rule: $\text{DA} \approx \text{PA} + 120 \times (\text{OAT} - \text{ISA})$
    • 3:1 descent profile rule: $\text{Distance} \approx 3 \times \Delta\text{Altitude} / 1000$
    • 60:1 wind crab rule: $\text{WCA} \approx XW / (\text{TAS} / 60)$
  • Aeroway Rule: Heuristics are never presented as exact models. Every heuristic is analyzed alongside its mathematical divergence from the exact closed-form equation.

2. Regulatory & Authority Hierarchy

When selecting technical references, Aeroway adheres to a strict six-tier hierarchy of authority: