Overview
ISO 1151-3:1989 - "Flight dynamics - Concepts, quantities and symbols - Part 3: Derivatives of forces, moments and their coefficients" defines the conventions and terminology for first‑order partial derivatives used in flight dynamics. The standard covers direct, specific, normalized and coefficient derivatives of forces and moments (and related quantities) as they appear in Taylor‑series representations of small variations. It is restricted to first‑order terms and assumes a rigid aircraft (many definitions remain applicable to flexible aircraft; aerolastic effects require additional treatment).
Key topics
- Scope and definitions
- Partial derivatives with respect to independent variables (aircraft motion relative to air, control surface deflections, etc.).
- Clarifies that derivative values depend on the chosen set of independent variables.
- Classes of derivatives
- Direct derivatives: partial derivatives of force/moment components w.r.t. independent variables; assembled in derivative matrices (R for forces, Q for moments).
- Specific derivatives: direct derivatives scaled by inertial properties (e.g., divided by mass or multiplied by inverse inertia matrix) to yield accelerations or angular accelerations.
- Normalized derivatives: direct derivatives divided by aerodynamic reference quantities (reference force/moment, reference speed, area, length, density) to produce non‑dimensionalized sensitivity terms.
- Coefficient derivatives: derivatives of aerodynamic coefficients (treated in the same framework).
- Matrix notation and conventions
- Component ordering, axis system conventions (right‑handed, positive rotations defined), and matrix element organization are specified to ensure consistent use across analyses.
- Reference/normalization quantities
- Defines reference force, moment, speed, angular speed and acceleration used for normalization of derivatives.
Applications and users
ISO 1151-3 is directly applicable to:
- Aerospace and flight dynamics engineers performing stability, control and handling‑qualities analysis.
- Flight test engineers deriving linearized models from measured force/moment responses.
- Aircraft design teams who need consistent derivative definitions for simulation, control law design and certification documentation.
- Researchers and educators in aerodynamics and flight mechanics who require standard notation and normalization conventions.
Practical uses include linear model derivation for trim and small perturbation analysis, control system synthesis, and comparison of aerodynamics data across datasets or suppliers.
Related standards
- ISO 1151-1: Aircraft motion relative to the air
- ISO 1151-2: Motions relative to the Earth
- ISO 1151-4: Parameters used in the study of aircraft stability and control
- Other parts of ISO 1151 (5–7) cover measurements, geometry and flight envelopes
Using ISO 1151-3 ensures consistent terminology and non‑dimensionalization for flight dynamics, derivatives of forces, moment derivatives, and aerodynamic coefficient reporting across engineering and testing workflows.
Open preview (PDF)Flight dynamics — Concepts, quantities and symbols — Part 3: Derivatives of forces, moments and their coefficients
