MAC context model

1. Overview

Computes Mean Aerodynamic Chord (MAC) percentage, longitudinal/lateral torque, CLIM, and index for each flight phase from aircraft and stowage data.

1. Dependent Contexts

1. Aircraft
2. Stowage

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2. Concepts / Entities

1. Torque

Computes longitudinal torque, lateral torque, CLIM, and index per flight phase from load, fuel, fuselage, and formula data.

$longitudinalTorqu{e}_{phase}$ : Longitudinal torque per flight phase.

$lateralTorque$ : Lateral torque (wide-body only).

$clim$ : CLIM (Center of Gravity Index Moment).

$inde{x}_{phase}$ : Index per flight phase.

2. MAC

Computes MAC percentage as a linear intermediate symbol from torque index and total weight.

$mac$ : MAC percentage, linear intermediate symbol.

3. Horizontal Stabilizer

Horizontal stabilizer position and limits for balance computation.

$key$ : Horizontal stabilizer identifier.

$points$ : Horizontal stabilizer data points.

$limit$ : Horizontal stabilizer limit.

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3. Variables

1. Decision Variables

This context reuses decision variables from the stowage context and does not define independent decision variables.

2. Auxiliary Variables

This context does not define independent auxiliary variables.

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4. Predicates

This context does not define independent predicates.

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5. Sets

This context does not define independent sets; the intermediate values range over the aircraft's positions and flight phases.

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6. Intermediate Values

1. Longitudinal Torque

Description: Longitudinal torque per flight phase, composed of load torque, fuel torque, fuselage moment, and liferaft moment.

$$longitudinalTorqu{e}_{phase}=\sum _{j\in J}loadLongitudinalTorqu{e}_j+fuelWeigh{t}_{phase}\cdot fuelAr{m}_{phase}+dow\cdot balancedArm+liferaftWeight\cdot liferaftArm$$

2. MAC Percentage

Description: Mean Aerodynamic Chord percentage, computed from torque index and total weight.

$$mac=\frac{inde{x}_{TakeOff}}{tow}\cdot 100\mathrm{\%}$$

For each phase $p$, the phase index is derived from the corresponding torque and aircraft formula. The exact coefficient and unit conversion are supplied by Formula and the aircraft model; the displayed equations are the contract-level expansion, not a replacement for those typed coefficients. MAC is an intermediate consumed by the balance and airworthiness contexts, not an independent decision variable.

7. Assertions

Every referenced phase has a valid fuel/fuselage formula and every arm, weight, and index uses the aircraft's configured compatible units. A phase with no required formula is not silently treated as a zero torque phase.

8. Constraints

This context exposes derived symbols only. Balance and envelope constraints are registered by mac_optimization and airworthiness_security; defining MAC does not add a solver row by itself.

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9. Objective Function (if applicable)

This context does not define an independent objective function.

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10. Algorithm References

No independent algorithm document; phase formulas are supplied by the aircraft Formula model and MAC aggregation.

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11. Ubiquitous Language

Term	Symbol	Definition
Torque	Torque	Force times arm distance
Mean Aerodynamic Chord	MAC	Wing mean aerodynamic chord length
Horizontal Stabilizer	HorizontalStabilizer	Tail horizontal stabilizer
CLIM	CLIM	Center of gravity index moment

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12. Design Decisions

Decision	Alternatives	Rationale
MAC computation formula	Linearized vs Non-linear	Linearization facilitates optimization model solving

13. Change Log

Version	Change	Reason
1.1	Clarified phase scope, units, and downstream constraint ownership	Distinguish intermediates from active balance limits