6.3 Ballast Calculations, Equipment Changes & Percent MAC

6.3 Ballast Calculations, Equipment Changes & Percent MAC

[!NOTE] Engineering Rigor in Modifications: Whenever an aircraft undergoes structural alteration, equipment replacement, or avionics modernization, the IA must verify the mathematical validity of the revised empty weight and center of gravity. When equipment alterations push the aircraft beyond approved operational limits, corrective engineering—including the precise calculation, fabrication, and structural installation of permanent ballast—is legally required under 14 CFR Part 43. On transport and high-performance aircraft, the IA must also be fluent in converting between linear datum stations and percentage of Mean Aerodynamic Chord (%MAC).

Modifications to certificated aircraft occur continuously throughout their operational lifespans. As an Inspection Authorization (IA) holder, every time you review an alteration or approve an aircraft for return to service on FAA Form 337, you must ensure that the equipment list, empty weight, and center of gravity have been updated in accordance with 14 CFR § 43.13 and AC 43.13-1B Chapter 10. This section details the mathematical principles governing equipment changes, ballast calculations, structural crashworthiness standards, and Mean Aerodynamic Chord (%MAC) conversions.

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Equipment Alterations: Addition, Removal, and Relocation Mathematics

When equipment changes occur, physical reweighing is not always required. If the exact weight and arm of the affected equipment are known, the IA may mathematically compute the revised empty weight and revised Empty Weight Center of Gravity (EWCG) using the moment bookkeeping method:

$\text{New Empty Weight} = \text{Old Empty Weight} \pm \text{Added/Removed Weights}$ $\text{New Total Moment} = \text{Old Empty Moment} \pm \text{Added/Removed Moments}$ $\text{New EWCG} = \frac{\text{New Total Moment}}{\text{New Empty Weight}}$

Mathematical Sign Conventions Matrix

Careful tracking of algebraic signs is essential when dealing with items located forward or aft of the datum:

[!WARNING] Classic FAA Exam Trap: Removing an item located forward of the reference datum (negative arm) removes negative moment from the aircraft. Subtracting a negative number produces a positive moment addition ($-\text{Weight} \times -\text{Arm} = +\text{Moment}$), which shifts the aircraft's center of gravity rearward!

Relocating Equipment

When existing equipment is moved from one station to another, the aircraft's total weight remains unchanged ($\Delta W = 0$). The moment change is calculated by multiplying the weight by the distance shifted: $\text{Moment Change} = \text{Weight} \times (\text{New Arm} - \text{Old Arm})$ $\text{New Moment} = \text{Old Moment} + \text{Moment Change}$

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Ballast Calculations and Placement Principles

When an alteration, structural repair, or engine replacement shifts the empty weight CG beyond certified limits, ballast must be installed to restore the CG to an airworthy position.

Temporary vs. Permanent Ballast

• Temporary Ballast: Installed to compensate for temporary, non-standard flight configurations (such as solo flights in tandem aircraft, skydiving jumps, or ferry flights). Temporary ballast is carried as part of the useful load, must be easily removable, securely tied down, and clearly placarded with its weight and operational restrictions.
• Permanent Ballast: Permanently bolted to the aircraft primary structure to correct a permanent CG imbalance. Permanent ballast is treated as an integral component of the aircraft empty weight, recorded on FAA Form 337, and listed in the equipment list.

The Permanent Ballast Formula

The required weight of ballast is determined by establishing a balance of moments about the desired CG: $\text{Ballast Weight} \times (\text{Ballast Arm} - \text{Desired CG}) = \text{Aircraft Empty Weight} \times (\text{Desired CG} - \text{Present CG})$

Solving for Ballast Weight yields the governing FAA formula: $\text{Ballast Weight} = \frac{\text{Aircraft Empty Weight} \times \text{Distance between Present CG and Desired CG}}{\text{Distance between Ballast Arm and Desired CG}}$ $\text{Weight}_{\text{ballast}} = \frac{W_{\text{aircraft}} \times |\text{Present CG} - \text{Desired CG}|}{|\text{Arm}_{\text{ballast}} - \text{Desired CG}|}$

[!IMPORTANT] Crucial Denominator Rule: The denominator in the ballast formula is the distance from the ballast installation arm to the desired CG, NOT the distance to the present CG. Using the present CG in the denominator is one of the most common calculation errors on the IAR exam.

Step-by-Step Worked Ballast Problem

An altered aircraft has an empty weight of 2,400 lbs and an EWCG located at Station +62.0 inches. The certified maximum aft CG limit (Desired CG) is Station +60.0 inches. Ballast can be bolted to the engine firewall bulkhead at Station +10.0 inches. How much ballast must be installed?

1. Identify parameters:
   • Aircraft Weight ($W_{\text{aircraft}}$) = $2,400 \text{ lbs}$
   • Present CG = $+62.0 \text{ inches}$
   • Desired CG = $+60.0 \text{ inches}$
   • Ballast Arm ($\text{Arm}_{\text{ballast}}$) = $+10.0 \text{ inches}$
2. Compute distances:
   • Distance from Present CG to Desired CG ($\Delta \text{CG}$) = $62.0 - 60.0 = 2.0 \text{ inches}$
   • Distance from Ballast Arm to Desired CG = $60.0 - 10.0 = 50.0 \text{ inches}$
3. Apply formula: $\text{Ballast Weight} = \frac{2,400 \text{ lbs} \times 2.0 \text{ in}}{50.0 \text{ in}} = \frac{4,800}{50.0} = \mathbf{96.0 \text{ lbs}}$
4. Mathematical Verification:
   • Present Moment: $2,400 \text{ lbs} \times 62.0 \text{ in} = 148,800.0 \text{ in-lb}$
   • Ballast Moment: $96.0 \text{ lbs} \times 10.0 \text{ in} = 960.0 \text{ in-lb}$
   • New Total Weight: $2,400 + 96.0 = 2,496.0 \text{ lbs}$
   • New Total Moment: $148,800.0 + 960.0 = 149,760.0 \text{ in-lb}$
   • $\text{New EWCG} = \frac{149,760.0}{2,496.0} = \mathbf{+60.00 \text{ inches}}$ (Precisely matches the desired limit).

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Structural Crashworthiness & Installation Standards for Permanent Ballast

Because permanent ballast consists of concentrated heavy materials (lead blocks, steel plates, brass), improper installation poses severe structural and occupant hazards during sudden decelerations. The emergency-landing-condition rules — CAR 3.386 for legacy aircraft and 14 CFR § 23.561 for Part 23 aircraft — set the inertia factors that a ballast installation and its attaching structure must withstand:

Emergency-Landing Inertia Factors

Ballast mountings must withstand the ultimate inertia forces prescribed for items of mass by the emergency-landing-condition rule in the aircraft's own certification basis. That basis is printed on the TCDS or Aircraft Specification, and the numbers differ by rule and by amendment level:

• CAR 3 (§ 3.386) and early Part 23 aircraft: the classic legacy set, with 9.0g forward as the governing case for a firewall or forward-bulkhead installation.
• Later Part 23 amendments: higher item-of-mass factors apply — do not carry a 9.0g assumption onto an aircraft certificated under a newer amendment.
• 14 CFR Part 23 Amendment 64 and later: the airworthiness standards were restructured into performance-based rules, and the applicable inertia factors come from the accepted means of compliance for that certification basis.

Because the correct multiplier is basis-dependent, the IA's job is to look it up rather than recall it. Read the certification basis off the data sheet first, then apply that rule's factors.

Engineering application: on a CAR 3 aircraft, the 96.0-lb ballast block calculated above must be secured by structural brackets and aviation-standard fasteners able to restrain at least $96.0 \text{ lbs} \times 9.0\text{g} = \mathbf{864.0 \text{ lbs}}$ forward without failure — a figure that makes plain why ballast may never be hung on skin or on a nonstructural bracket.

Attachment and Marking Mandates

1. Primary Structure: Ballast must be bolted directly to primary structural longerons, engine mount rings, or heavy fuselage bulkheads using AN aircraft bolts, steel self-locking nuts, or safety-wired castellated nuts. It must never be attached solely to sheet metal skin.
2. Identification and Placarding: The ballast mass must be painted bright red and permanently stenciled in high-contrast lettering: PERMANENT BALLAST — DO NOT REMOVE (e.g., in vivid white).
3. Regulatory Documentation: Installing permanent ballast constitutes a major alteration requiring FAA Form 337 execution and an IA return-to-service sign-off.

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Mean Aerodynamic Chord (MAC) Principles and Conversions

On transport category, multi-engine, and high-performance aircraft featuring tapered or swept wings, aerodynamic forces vary continuously along the wing span. On these aircraft, expressing the center of gravity in inches from an arbitrary datum does not convey aerodynamic meaning regarding flight stability or control margins. Therefore, CG is expressed as a percentage of the Mean Aerodynamic Chord (%MAC).

Aerodynamic Definitions

• Mean Aerodynamic Chord (MAC): The chord of an imaginary rectangular airfoil having the same aerodynamic lift, drag, and pitching moment characteristics as the actual complex wing.
• LEMAC: Leading Edge of the Mean Aerodynamic Chord (distance in inches from datum to the leading edge of the MAC).
• TEMAC: Trailing Edge of the Mean Aerodynamic Chord (distance in inches from datum: $\text{TEMAC} = \text{LEMAC} + \text{MAC}$).

Conversion Formulas

1. Converting Inches from Datum to %MAC: $\% \text{MAC} = \left(\frac{\text{CG in inches} - \text{LEMAC}}{\text{MAC}}\right) \times 100$
2. Converting %MAC to Inches from Datum: $\text{CG in inches} = \text{LEMAC} + \left(\frac{\% \text{MAC}}{100} \times \text{MAC}\right)$

Worked %MAC Conversion Examples

Example 1: Inches to %MAC

An aircraft has a reference datum at the nose tip.

• $\text{LEMAC} = \text{Station } +320.0 \text{ inches}$
• $\text{MAC} = 140.0 \text{ inches}$
• Calculated $\text{CG} = \text{Station } +362.0 \text{ inches}$ $\% \text{MAC} = \left(\frac{362.0 - 320.0}{140.0}\right) \times 100 = \left(\frac{42.0}{140.0}\right) \times 100 = \mathbf{30.0\% \text{ MAC}}$

Example 2: %MAC to Inches from Datum

The TCDS for a turboprop transport aircraft specifies that the forward flight CG limit is 18.0% MAC and the aft limit is 32.0% MAC. The wing parameters are $\text{LEMAC} = \text{Station } +500.0 \text{ inches}$ and $\text{MAC} = 180.0 \text{ inches}$.

• Forward limit in inches: $\text{Forward CG} = 500.0 + \left(\frac{18.0}{100} \times 180.0\right) = 500.0 + 32.4 = \mathbf{+532.4 \text{ inches}}$
• Aft limit in inches: $\text{Aft CG} = 500.0 + \left(\frac{32.0}{100} \times 180.0\right) = 500.0 + 57.6 = \mathbf{+557.6 \text{ inches}}$

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Summary of Core Formulas for Equipment, Ballast & %MAC

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High-Yield Exam Traps & Best Practices

• Ballast Formula Denominator: Always use the distance between the ballast location and the desired CG limit, never the distance to the present CG.
• Signs on Removed Forward Items: Removing an item with a negative arm subtracts a negative moment, which produces an increase in total moment, shifting the CG aft.
• LEMAC as the Baseline: %MAC is measured strictly from LEMAC, not from the reference datum.
• Ballast Identification: Permanent ballast must be painted red, labeled "PERMANENT BALLAST — DO NOT REMOVE", and secured against the forward emergency-landing inertia factor of the aircraft's certification basis (9.0g for a CAR 3 airplane; check the data sheet before assuming).