MAC optimization context model

1. Overview

Manages MAC optimization including longitudinal balance (MAC range constraints) and lateral balance constraints for aircraft weight distribution.

1. Dependent Contexts

Aircraft
Stowage
Mean Aerodynamic Chord (MAC)

2. Concepts / Entities

1. MAC Range

Defines allowable MAC percentage range based on total weight.

$m i n M A C_{w e i g h t}$ : Minimum MAC percentage at given total weight.

$m a x M A C_{w e i g h t}$ : Maximum MAC percentage at given total weight.

2. Longitudinal Balance

Longitudinal balance constraints ensuring MAC is within allowable range per flight phase.

$m a c R a n g e$ : MAC range.

$t o r q u e$ : Torque data.

3. Lateral Balance

Lateral balance constraints for wide-body aircraft ensuring symmetrical loading.

$t o r q u e$ : Lateral torque data.

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.

4. Predicates

This context does not define independent predicates.

5. Sets

This context does not define independent sets; its balance limits range over positions and flight phases.

6. Intermediate Values

This context does not define independent intermediate values.

7. Assertions

This context does not define independent assertions.

8. Constraints

1. Longitudinal Balance Limit

[CN]: 纵向平衡限制

Description: MAC percentage must be within allowable range per flight phase.

s . t . m i n M A C_{w e i g h t} \leq m a c \leq m a x M A C_{w e i g h t}, \forall p h a s e \in F l i g h t P h a s e s

2. Lateral Balance Limit

[CN]: 横向平衡限制

Description: Lateral torque must be within allowable range (wide-body only).

s . t . | l a t e r a l T o r q u e | \leq m a x L a t e r a l T o r q u e

3. Horizontal Stabilizer Limit

[CN]: 水平安定面限制

Description: Horizontal stabilizer position must match MAC.

s . t . s t a b i l i z e r P o s i t i o n = f (m a c), \forall p h a s e \in F l i g h t P h a s e s

9. Objective Function (if applicable)

Minimize MAC deviation from target range.

min | m a c - m a c T a r g e t |

10. Algorithm References

This context does not define an independent algorithm reference.

11. Ubiquitous Language

Term	Symbol	Definition
MAC Range	`MACRange`	Allowable MAC percentage range
Longitudinal Balance	`LongitudinalBalance`	Fore-aft weight balance
Lateral Balance	`LateralBalance`	Left-right weight balance
Horizontal Stabilizer	`HorizontalStabilizer`	Tail horizontal stabilizer

12. Design Decisions

Decision	Alternatives	Rationale
MAC range modeling	Linear vs Piecewise linear	Piecewise linear is more accurate

13. Change Log

No context-specific change entries are recorded on this page.

MAC optimization context model ​

1. Overview ​

1. Dependent Contexts ​

2. Concepts / Entities ​

1. MAC Range ​

2. Longitudinal Balance ​

3. Lateral Balance ​

3. Variables ​

1. Decision Variables ​

2. Auxiliary Variables ​

4. Predicates ​

5. Sets ​

6. Intermediate Values ​

7. Assertions ​

8. Constraints ​

1. Longitudinal Balance Limit ​

2. Lateral Balance Limit ​

3. Horizontal Stabilizer Limit ​

9. Objective Function (if applicable) ​

10. Algorithm References ​

11. Ubiquitous Language ​

12. Design Decisions ​

13. Change Log ​