11.3 Mean Aerodynamic Chord (%MAC) Computations & Stability

FAA Aircraft Dispatcher Certificate ADX

Track your progress as you read

Finished sections get a check mark.

1 Chapter 1: Regulations, Certification & Operational Control

1.1 Part 65 Subpart C: Certification, Eligibility & Currency 1.2 Operational Control & Dispatcher-PIC Joint Responsibility 1.3 Domestic, Flag & Supplemental Operations Framework 1.4 Dispatch Release Elements, Signatures & Recordkeeping 1.5 Regulations, Manuals, Crew Qualifications, and Source Control

2 Chapter 2: Atmospheric Physics, Pressure Systems & Fronts

2.1 Atmospheric Structure, Standard Atmosphere & Altimetry 2.2 Air Masses, Frontal Systems & Frontogenesis 2.3 Atmospheric Stability, Lapse Rates & Cloud Formation 2.4 Earth Motion, Regional Weather, Local Winds, and Water Phase Changes

3 Chapter 3: Aviation Weather Hazards & Severe Weather Avoidance

3.1 Structural and Induction Icing: Types, Accretion & Operations 3.2 Thunderstorms, Squall Lines, Microbursts & Low-Level Windshear 3.3 Clear Air Turbulence (CAT), Mountain Waves & Jet Streams 3.4 Low Ceilings, Fog Types & Visibility Restrictions 3.5 Hurricanes, Typhoons, Tornadoes, and Tropical Dispatch Hazards

4 Chapter 4: Weather Observations, Forecasts & Advisories Decoding

4.1 METAR and SPECI Surface Observations: Decoding & Operations 4.2 Terminal Aerodrome Forecasts (TAF): Groups & Timing 4.3 Pilot Weather Reports (PIREP): Coding, Severity & Urgent Alerts 4.4 In-Flight Advisories: AIRMETs, SIGMETs & Convective SIGMETs 4.5 Weather Collection, NWS Facilities, GFA, and EWINS

5 Chapter 5: Aviation Weather Charts & Upper-Air Analysis

5.1 Surface Analysis & Radar Summary Charts 5.2 Constant Pressure Analysis & Winds Aloft (FB) 5.3 Significant Weather Prognostic Charts (SIGWX) 5.4 Satellite Imagery, Moisture-Stability Analysis, and Forecast Integration

6 Chapter 6: Air Navigation, Airspace Architecture & Route Structure

6.1 National Airspace System: Classes, Rules & Special Use 6.2 Ground-Based Navigation Aids & Standard Service Volumes 6.3 Area Navigation (RNAV), GNSS/GPS, PBN & RNP Fundamentals 6.4 En Route Airways, SIDs, STARs & Chart Interpretation 6.5 Earth Coordinates, UTC, Chart Projections, and Flight Instruments 6.6 North Atlantic, Pacific, RVSM, and Global Navigation Differences

7 Chapter 7: Instrument Approaches, Minimums & Airport Operations

7.1 Precision Approach Systems: ILS Categories & Tolerances 7.2 Non-Precision Approaches, RNAV & Decision Minimums (MDA/DA) 7.3 Takeoff Minimums, Lower-Than-Standard & Takeoff Alternates 7.4 Holding Procedures: Patterns, Speed Limits & Timing

8 Chapter 8: Subsonic Aerodynamics & Jet Aircraft Performance

8.1 Subsonic Jet Aerodynamics: Lift, Drag & Flight Regimes 8.2 High-Altitude Flight: Mach Number, Buffet & Coffin Corner 8.3 Transport Turbine Engines: Thrust, Specific Fuel & Bleed Air

9 Chapter 9: Transport Category Takeoff & Landing Runway Analysis

9.1 Takeoff Performance Speeds & Balanced Field Concept 9.2 Takeoff Climb Segments & Obstacle Clearance Gradients 9.3 Landing Performance: Field Lengths, 60% Rule & Contamination

10 Chapter 10: En Route Performance, Driftdown Profiles & ETOPS Operations

10.1 One/Two-Engine-Inoperative En Route Net Profiles & Driftdown 10.2 Extended-Range Operations (ETOPS): Philosophy & Regulations 10.3 ETOPS En Route Alternates: Adequate vs. Suitable & Critical Fuel

11 Chapter 11: Aircraft Weight & Balance, Center of Gravity, and Loading

11.1 Transport Aircraft Structural Weight Limits: Definitions & Rules 11.2 Center of Gravity Computations: Datum, Arm, Moment & Index 11.3 Mean Aerodynamic Chord (%MAC) Computations & Stability 11.4 Payload-Range Analysis, Zero Fuel Weight Tradeoffs & Loading

12 Chapter 12: Destination Alternate Airport Selection & Weather Rules

12.1 Destination Alternate Selection: 91.169 & Part 121 1-2-3 Rule 12.2 Flag & Supplemental Operations Destination Alternate Rules 12.3 Derived Alternate Minimums: 1-Nav and 2-Nav Facility Rules

13 Chapter 13: Part 121 Fuel Planning, Reserves & En Route Re-Release

13.1 Part 121 Domestic Fuel Requirements: Reserves & Calculations 13.2 Part 121 Flag Fuel Requirements: 10% Reserve & Island Rules 13.3 Supplemental Fuel Requirements & Holding Fuel Management 13.4 Redispatch and En Route Re-release Procedures

14 Chapter 14: Transport Systems, Pressurization & MEL/CDL Procedures

14.1 Transport Jet Auxiliary Power, Electrical, Hydraulic & Pneumatic Systems 14.2 Cabin Pressurization, Rapid Decompression & Oxygen Requirements 14.3 Master Minimum Equipment List (MMEL), MEL & CDL Procedures 14.4 Flight Controls, Autoflight, Fuel, Oil, Brakes, and Fire Protection

15 Chapter 15: Hazardous Materials, Duty Regulations & Emergency Procedures

15.1 Dangerous Goods Carriage by Air (49 CFR Part 175) & NOTOC 15.2 Dispatcher Duty Limitations, Rest Requirements & Fatigue 15.3 Emergency Authority, Declaration & Diversion Decision-Making 15.4 NTSB Part 830 Accident Reporting & Wreckage Preservation 15.5 Security, Overdue Aircraft, and FAA Emergency Services

16 Chapter 16: Communications, ATC, and Flight Plan Procedures

16.1 Voice, Data Link, Position Reports, and Lost Communications 16.2 ATC Facilities, Separation, ICAO Flight Plans, and Traffic Management

17 Chapter 17: Human Factors and Practical Dispatch Applications

17.1 Dispatch Resource Management, Human Error, and Risk Decisions 17.2 Manual Flight Planning, PIC Briefing, Flight Watch, and Postflight Closeout

11.3 Mean Aerodynamic Chord (%MAC) Computations & Stability

Key Takeaways Explain This Topic AI

Mean Aerodynamic Chord (MAC) represents the chord of an aerodynamic reference chord used to express longitudinal locations for the actual wing; it does not assert that an imaginary wing has every identical lift/drag characteristic.

Center of gravity position in transport aviation is standardized as a percentage of MAC: %MAC = ((CG Station - LEMAC) / MAC) * 100%.

Operating at the forward CG limit increases longitudinal static stability, but elevates stall speed (Vs), creates excessive horizontal stabilizer trim downwash, produces high trim drag, and degrades cruise fuel efficiency.

Operating at the aft CG limit reduces trim drag and fuel burn, but degrades longitudinal static stability, lightens flight control stick forces, and introduces severe susceptibility to unrecoverable deep stalls in T-tail aircraft.

The flight deck takeoff-trim indication is aircraft-specific (for example trim units or stabilizer angle) and is selected using the approved CG/trim data, ensuring appropriate longitudinal control forces during takeoff rotation and initial climb.

Last updated: October 2026

Mean Aerodynamic Chord (%MAC) Computations & Stability

Quick Summary: Expressing center of gravity strictly in fuselage station inches fails to convey how balance impacts aerodynamic performance across different aircraft models. Transport category aviation standardizes center of gravity as a percentage of the Mean Aerodynamic Chord (%MAC) . An aircraft's location within its certified %MAC envelope directly dictates longitudinal static stability, control stick force gradients, trim drag, cruise fuel economy, and stall recovery characteristics.

1. Aerodynamic Geometry: Why Transport Jets Use %MAC

On a simple rectangular wing, the chord (distance from leading edge to trailing edge) is uniform across the entire span, making aerodynamic balance intuitive. However, modern commercial jet transports feature wings that are swept, tapered, and twisted (washout) . On a swept, tapered wing, the chord length and local aerodynamic center change continuously from the wing root to the wing tip.

To standardize aerodynamic calculations, aeronautical engineers define the Mean Aerodynamic Chord (MAC) :

Mean Aerodynamic Chord (MAC): The chord of an imaginary, untwisted, rectangular airfoil that has the same total area, aerodynamic lift, drag, and pitching moment characteristics as the actual complex three-dimensional wing. Fuselage Centerline

• │ LEMAC (Station in Inches)
• │ ▼
• ──┼──┌───────────────────────┐ ▲
• \ │ │ │ │
• \│ │ │ │ MAC (Length in Inches)
• \ │ Equivalent Mean │ │
• \ │ Aerodynamic Chord │ │
• \│ (Rectangular) │ ▼
• │ │ TEMAC (Station in Inches)
• └───┴───────────────────┘
• Actual Swept Tapered Wing
• Geometric Boundary Stations: LEMAC and TEMAC

Two fixed physical stations locate the MAC along the aircraft's longitudinal axis:

LEMAC (Leading Edge of Mean Aerodynamic Chord): The fuselage station, measured in inches from the reference datum, where the leading edge of the imaginary MAC begins.

TEMAC (Trailing Edge of Mean Aerodynamic Chord): The fuselage station where the trailing edge of the imaginary MAC terminates.

The physical length of the Mean Aerodynamic Chord is the linear distance between these two stations: MAC = TEMAC − LEMAC \text{MAC} = \text{TEMAC} - \text{LEMAC} MAC = TEMAC − LEMAC

Both LEMAC and MAC length are fixed structural constants specified in the aircraft's FAA Type Certificate Data Sheet (TCDS) and Weight and Balance Manual.

2. Mathematical Conversion: Station Inches to %MAC and Vice Versa

Expressing the center of gravity in inches aft of datum provides a physical balance station, but expressing it as a percentage of MAC reveals where the CG sits relative to wing lift.

Converting CG Station to %MAC

To convert an aircraft's center of gravity from station inches into %MAC: % MAC = CG Station − LEMAC MAC × 100 % \%\text{MAC} = \frac{\text{CG Station} - \text{LEMAC}}{\text{MAC}} \times 100\% % MAC = MAC CG Station − LEMAC ​ × 100%

Where:

CG Station \text{CG Station} CG Station = Current calculated center of gravity in inches from datum.

LEMAC \text{LEMAC} LEMAC = Station of the leading edge of MAC in inches from datum.

MAC \text{MAC} MAC = Total chord length of MAC in inches.

Interpretation: If an aircraft's CG is at 25 % MAC 25\%\text{ MAC} 25% MAC , the center of gravity is located exactly one-quarter of the distance aft along the Mean Aerodynamic Chord from its leading edge.

Converting %MAC to CG Station

In dispatch load planning and flight deck operations, it is frequently necessary to convert %MAC back into a fuselage station: CG Station = LEMAC + ( % MAC 100 × MAC ) \text{CG Station} = \text{LEMAC} + \left( \frac{\%\text{MAC}}{100} \times \text{MAC} \right) CG Station = LEMAC + ( 100 % MAC ​ × MAC )

3. Longitudinal Stability Mechanics: CG vs. Center of Pressure (CP)

In flight, an aircraft's static longitudinal stability is determined by the physical separation between its Center of Gravity (CG) and the wing's aerodynamic center or Center of Pressure (CP) . Upward Wing Lift (at CP)

• ▲
• │
• CG │
• ▼ │
• ───[ Weight ]──────┼─────────[ Tail Downforce ]───
• ▼
• <─── Stability Arm ───><─────── Tail Arm ───────>
• The Balancing Couple in Stable Flight

In transport category aircraft, certified loading envelopes place the Center of Gravity forward of the aerodynamic Center of Pressure throughout normal operations:

The downward gravitational force acting through the CG and the upward lift force acting through the CP create a natural, continuous nose-down pitching moment ( W × arm CG-CP W \times \text{arm}_{\text{CG-CP}} W × arm CG-CP ​ ).

To achieve pitch trim equilibrium, the horizontal stabilizer must generate a continuous downward aerodynamic force (often referred to as negative lift or tail downforce).

If an atmospheric gust displaces the aircraft nose upward, airspeed momentarily decays, wing lift decreases, and the natural nose-down couple immediately acts to restore the aircraft to its trimmed pitch attitude. This provides positive longitudinal static stability .

4. Aerodynamic & Performance Consequences: Forward vs. Aft CG Limits

The certified Center of Gravity envelope has two primary boundaries: the Forward CG Limit and the Aft CG Limit . Operating near these limits produces radically different aerodynamic and performance behaviors.

The Forward CG Limit (Controllability / Control Authority Boundary)

When an aircraft is loaded near its forward CG limit, it is extremely nose-heavy:

High Tail Downforce Required: To keep the nose level, the horizontal stabilizer must fly at a high negative angle of attack, generating massive downward aerodynamic force.

Increased Effective Weight: Because the tail is pushing downward, the main wing must generate additional lift equal to the gross weight plus the tail downforce ( L = W + T down L = W + T_{\text{down}} L = W + T down ​ ). The aircraft behaves aerodynamically as if it weighs thousands of pounds more than its physical scale weight.

Higher Stall Speed ( V S V_S V S ​ ): Because the wing must operate at a higher angle of attack to support this extra downward tail load, stall speed increases ( V S ∝ L / W V_S \propto \sqrt{L / W} V S ​ ∝ L / W ​ ).

Severe Trim Drag and High Fuel Burn: The combination of higher wing induced drag and stabilizer trim drag increases total aircraft drag by 1% to 3%, directly burning additional fuel and reducing cruise range.

Elevator Flare Deficiency: During landing, when ground effect reduces downwash and engine thrust is reduced to idle, the flight crew may encounter inadequate upward elevator control authority to flare the aircraft, risking heavy nose-gear first touchdowns.

The Aft CG Limit (Static Stability Boundary)

When an aircraft is loaded near its aft CG limit, it is tail-heavy:

Reduced Tail Downforce and Lower Trim Drag: With the CG close to the Center of Pressure, the nose-down moment is tiny. The horizontal stabilizer requires minimal downward aerodynamic force, and can even carry positive lift. Wing angle of attack decreases, trim drag is minimized, and fuel efficiency improves by 1% to 2% (which is why airline dispatchers often load toward the aft limit for fuel conservation).

Degraded Longitudinal Static Stability: The distance between the CG and the neutral point (the static margin ) is dangerously narrow. When disturbed by turbulence, the aircraft possesses weak restoring pitch forces.

Light Stick Forces and Over-Control Risk: Pitch control forces become exceptionally light and sensitive. A small pilot control input produces a rapid, dramatic pitch displacement, increasing the hazard of pilot-induced oscillations (PIO) or accidental airframe overstress.

Unrecoverable Deep Stall Hazard: In transport aircraft equipped with T-tail empennages (such as regional jets, MD-80/90, and corporate transports), an aft CG stall can lead to a deep stall . In a deep stall, the turbulent, detached wake of the stalled main wing completely immerses the high-mounted horizontal stabilizer and elevator. With zero airflow across the elevator, the crew has zero nose-down pitch authority, making recovery aerodynamically impossible.

5. Comprehensive Comparison Table: Forward CG vs. Aft CG

Operational Characteristic Forward CG (Nose-Heavy) Aft CG (Tail-Heavy) Aerodynamic Physics Governing Behavior

Longitudinal Static Stability High / Strong Weak / Marginally Stable Large vs. small static margin between CG and aerodynamic neutral point.

Pitch Control Stick Forces Heavy / Stiff Light / Highly Sensitive Higher vs. lower hinge moments on elevator to deflect stabilizer.

Stall Speed ( V S V_S V S ​ ) Higher Lower Wing must support Gross Weight + Tail Downforce; forward CG increases tail downforce.

Trim Drag High Low Induced drag caused by horizontal stabilizer generating large downward lift.

Cruise Fuel Burn / Range Increased Burn / Reduced Range Decreased Burn / Extended Range Direct penalty of trim drag and higher required wing coefficient of lift ( C L C_L C L ​ ).

Takeoff Ground Roll Longer Roll Shorter Roll Higher rotation speed requirement and greater stabilizer deflection needed.

Landing Flare Control Reduced Elevator Authority Abundant Elevator Authority Ground effect and low speed demand maximum upward elevator deflection.

Stall Recovery Difficulty Easy (Nose drops naturally) Difficult / Risk of Deep Stall CG forward of CP provides natural pitch-down restoring moment.

Governing Certification Limit Controllability Limit Stability Limit Part 25 certification criteria for elevator power vs. dynamic stability.

6. Takeoff Pitch Trim Setting & The Green Band

On transport category jet aircraft, the horizontal stabilizer is not fixed; it is an all-moving, trimmable horizontal stabilizer (THS) driven by a high-torque jackscrew motor. The flight deck trim indicator features a Green Band that designates the allowable takeoff trim range. FLIGHT DECK STABILIZER TRIM INDICATOR

• ┌─────────────────────────────────────┐
• │ NOSE UP │
• │ 10 ─── │
• │ 8 ─── ┌───────────────────────┐ │
• │ 6 ─── │ │ │ <- GREEN BAND

Takeoff trim is selected from the approved aircraft CG/trim relationship; cockpit indications can be trim units, stabilizer angle, or other aircraft-specific units rather than percent MAC.

• │ 2 ─── │ (Calibrated in %MAC)│ │ for dispatch %MAC
• │ 0 ─── └───────────────────────┘ │
• │ -2 ─── │
• │ NOSE DOWN │
• └─────────────────────────────────────┘
• %MAC to Trim Setting Translation

Takeoff trim is selected from the approved aircraft CG/trim relationship; cockpit indications can be trim units, stabilizer angle, or other aircraft-specific units rather than percent MAC.

Forward %MAC (Nose-Heavy): Demands a higher nose-up stabilizer trim setting (e.g., 7.5 units 7.5\text{ units} 7.5 units nose-up) to provide the necessary upward rotation force when the pilot pulls back on the control column at V R V_R V R ​ .

Aft %MAC (Tail-Heavy): Demands a lower or more nose-down stabilizer trim setting (e.g., 3.5 units 3.5\text{ units} 3.5 units nose-up) to prevent the aircraft from rotating prematurely on its own.

The Fatal Danger of Takeoff Mis-Trim

Setting the takeoff stabilizer trim incorrectly based on erroneous dispatch %MAC calculations has caused numerous fatal transport accidents:

Trim Set Too Far Nose-Down: At rotation speed ( V R V_R V R ​ ), the pilot pulls back on the control yoke, but the stabilizer generates insufficient rotation moment. The aircraft remains glued to the runway, consuming thousands of feet of remaining pavement, potentially resulting in a high-speed runway overrun.

Trim Set Too Far Nose-Up: During the takeoff roll, as the aircraft accelerates toward V R V_R V R ​ , the horizontal stabilizer generates excessive aerodynamic rotation force. The aircraft auto-rotates prematurely at low airspeed, potentially causing a severe tailstrike on the runway or pitching up violently into an unrecoverable aerodynamic stall immediately upon liftoff.

• 7. Worked Operational Calculations
• Calculation 1: Converting Station Inches to %MAC

A Boeing 737-800 flight has the following structural specifications:

• LEMAC = 805.0 inches \text{LEMAC} = 805.0\text{ inches} LEMAC = 805.0 inches
• TEMAC = 1 , 055.0 inches \text{TEMAC} = 1,055.0\text{ inches} TEMAC = 1 , 055.0 inches
• Current Calculated Takeoff CG = Station 865.0 inches

Step 1: Calculate MAC Length MAC = TEMAC − LEMAC = 1 , 055.0 − 805.0 = 250.0 inches \text{MAC} = \text{TEMAC} - \text{LEMAC} = 1,055.0 - 805.0 = 250.0\text{ inches} MAC = TEMAC − LEMAC = 1 , 055.0 − 805.0 = 250.0 inches

Step 2: Calculate %MAC % MAC = CG Station − LEMAC MAC × 100 % = 865.0 − 805.0 250.0 × 100 % = 60.0 250.0 × 100 % = 24.0 % MAC \%\text{MAC} = \frac{\text{CG Station} - \text{LEMAC}}{\text{MAC}} \times 100\% = \frac{865.0 - 805.0}{250.0} \times 100\% = \frac{60.0}{250.0} \times 100\% = 24.0\%\text{ MAC} % MAC = MAC CG Station − LEMAC ​ × 100% = 250.0 865.0 − 805.0 ​ × 100% = 250.0 60.0 ​ × 100% = 24.0% MAC

Calculation 2: Converting Target %MAC to Fuselage Station

A dispatcher wants to configure a wide-body transport to an optimal fuel-efficiency target of 28.5 % MAC 28.5\%\text{ MAC} 28.5% MAC for a long-haul transoceanic flight. The aircraft specifications are:

• LEMAC = 940.0 inches \text{LEMAC} = 940.0\text{ inches} LEMAC = 940.0 inches
• MAC = 310.0 inches \text{MAC} = 310.0\text{ inches} MAC = 310.0 inches

Calculation: Target CG Station = LEMAC + ( % MAC 100 × MAC ) = 940.0 + ( 0.285 × 310.0 ) = 940.0 + 88.35 = 1 , 028.35 inches \text{Target CG Station} = \text{LEMAC} + \left( \frac{\%\text{MAC}}{100} \times \text{MAC} \right) = 940.0 + (0.285 \times 310.0) = 940.0 + 88.35 = 1,028.35\text{ inches} Target CG Station = LEMAC + ( 100 % MAC ​ × MAC ) = 940.0 + ( 0.285 × 310.0 ) = 940.0 + 88.35 = 1 , 028.35 inches

The load planning system must distribute cargo and fuel so that the final takeoff center of gravity sits at Station 1,028.4 inches.

• 8. Practical Traps & Operational Scenarios
• Practical Trap: Swept-Wing Fuel Burn CG Migration

In swept-wing aircraft, the wing fuel tanks are swept backward along the leading edge. The outboard fuel tanks are physically located much farther aft along the fuselage than the inboard main tanks or the center tank. As engines burn fuel in flight, the sequencing of fuel consumption (e.g., burning center tank fuel first, followed by main wing tanks) causes the center of gravity to migrate continuously along the longitudinal axis. In some transport jets, burning wing fuel shifts the CG forward initially, then shifts it rapidly aft as the outboard wing tanks drain. Dispatchers must ensure that the aircraft remains inside the certified %MAC envelope at all times: at Takeoff, En Route, and Zero Fuel.

Operational Scenario: Takeoff Stabilizer Trim Setting Discrepancy

A flight crew receives an updated electronic load sheet showing Takeoff CG has moved from 21.0 % MAC 21.0\%\text{ MAC} 21.0% MAC to 29.0 % MAC 29.0\%\text{ MAC} 29.0% MAC due to late-arriving connecting passengers seated in the rear cabin. The crew verifies that the new CG is inside the takeoff envelope, but neglects to spin the stabilizer trim wheel from 6.8 units 6.8\text{ units} 6.8 units down to 4.2 units 4.2\text{ units} 4.2 units . Upon reaching V R V_R V R ​ , the aircraft violently auto-rotates, triggering the stick shaker stall warning at 50 feet AGL. The captain immediately applies firm forward column pressure to arrest the pitch excursion. Maintaining strict procedural discipline to update stabilizer trim whenever %MAC changes is a critical barrier against loss of control.

Official References

Source check: 2026-10-12 . FAA W&B handbooks and current addenda ; AC 120-27F aircraft W&B control ; Transport landing-load assumptions § 25.473 . For operational use, apply current issued authorizations and the assigned aircraft’s approved data.