CHAPTER 14: Weight and Balance

Weight and Balance Importance

Critical factors affecting Safety, Performance, Efficiency of any A/C

Proper Loading Benefits

Ensures A/C performs within its Limits (Structural Aerodynamic),

• handles Predictably

• achieves Optimal Fuel Consumption.

Improper Loading Consequences

Can result in

• Reduced Performance

• Control Difficulties

• Loss of Stability

during critical phases such as T/O or Landing.

Jet Aircraft vs. Small Aircraft W&B

Jets require Precise Calculations based on defined Weight Categories & Reference Points.

Small aircraft W&B is often estimated Visually.

Pilot Operational Responsibility

Pilots remain solely responsible for the overall safety of the flight even if they are not directly involved in the physical loading process.

Standardized Definitions Purpose

prevent miscalculations affecting stability by Ensuring

• Accurate Load Distribution

• compliance with operational limits

Basic Empty Weight (BEW)

Weight of A/C, including all

• Fixed Equipment

• Unusable Fuel

• Full Operating Fluids (engine-oil, hydraulic-fluid, etc.).

Formula:

BEW = Empty A/C + Unusable Fuel + Operating Fluids

Unusable Fuel

Remains after fuel Run-Out test as per regulations

• Divided into two parts:

  • Drainable: removed by Sump Drains

  • Trapped: Cannot be removed

• Not considered usable for flight operations

Usable Fuel

Amount of total fuel available for engine use during flight.

Usable Fuel = Total Fuel - Unusable Fuel

Dry Operating Weight (DOW)

Total weight of A/C ready for operation, Including:

• Crew

• Catering

• Potable Water

• Special Equipment

Excluding:

• Usable fuel

• Traffic-Load

Formula:

DOW = BEW + Crew + Operational Items

Zero Fuel Weight (ZFW)

Weight of A/C + Payload Without Usable Fuel.

It Must never exceed the Max. Zero Fuel Weight

Formula:
ZFW = DOW + Payload (Passengers + Baggage + Cargo)

Payload

Total weight of Revenue load, including;

PAX, cargo or mail.

Formula:

(Payload = ZFW – DOW)

Useful Load

Consists of:

• Payload

• Usable Fuel

• Engine-Injection fluid.

Formula:
Useful Load = MTOW - BEW

Ramp/Taxi Weight

Total weight of A/C @ Ramp, including fuel, passengers, and cargo

Before Engine Start

Formula:
Ramp/Taxi weight = ZFW + Usable Fuel

Takeoff Weight (TOW)

Weight of the equipped, loaded, and fueled A/C @ T/O
TOW = Ramp - Taxi Fuel

Landing Weight (LW)

A/C Weight at TD (Touch-Down)

Formula:
LW = TOW - Trip Fuel Burned

Gross Weight (GW)

Total weight of A/C after All items have been Added.

Maximum Zero Fuel Weight (MZFW)

Maximum Permissible weight of A/C Without→Usable fuel.

Formula:
AZFW ≤ MZFW

Maximum Takeoff Weight (MTOW)

Max. Permissible structural (by design) total A/C weight for T/O Formula:
TOW ≤ MTOW

Maximum Landing Weight (MLW)

Maximum permissible structural (by design) total A/C weight at TD.

Formula:
LW ≤ MLW

Maximum Ramp/Taxi Weight (MTW)

Max. Allowable weight Authorized for Taxi-Operations prior to takeoff; it includes Taxi & Run-Up fuel.

Formula:
Max. Ramp/Taxi weight ≤ MTW

Datum Line

Imaginary Reference Vertical plane line,

Established by Manufacturer,

from which all Horizontal Distances for balance Calculations are Measured.

Body Station Numbers

Reference points along Length of A/C

Measured in Inches or Millimeters

from Datum-line to locate: Components & Weight items.

usually Located near or ahead ofA/Cs nose as shown.

Arm (Moment Arm)

Horizontal distance from Datum-Line to→CG of an item

Moment

Measurement of Tendency to produce Rotation

about a point or axis.

Formula:
Moment = Weight × Arm

Center of Gravity (CG)

Specific point where Total weight of A/C

is evenly Balanced in all Directions.

Empty Weight Center of Gravity (EWCG)

Center of gravity of A/C in its basic empty weight condition.

CG Position Stability

An object has only One CG, Position remains Constant

Unless there is Change in:

• Physical Characteristics

• Load Distribution.

Airplane CG Limits

CG must stay within prescribed limits to maintain A/C

Aerodynamic Stability.

Bar Balance Calculation Example

A 10-pound weight with a 20-inch arm creates a moment of 200 pound-inches, balancing a 20-pound weight with a 10-inch arm (200 pound-inches).

Moment Measurement Unit

Measured in Pound.Inches

Airplane Weight and Balance Consistency

as A/C’s CG shifts with every loading,

Fixed datum line is Established

as an Arbitrary Reference for All Calculations.

Datum Line Placement

Positioned @ or Ahead of Nose in most modern transport aircraft

to ensure all moments are +Positive and prevent negative values.

CG Determination Principle

Calculated by finding the point where: sum of all moments

Relative to Datum is balanced by Total weight.

Formula:
CG = Total Moment ÷ Total Weight

CG Calculation Example Numbers

Weights of 5 lb at 10 in, 10 lb at 15 in, and 15 lb at 40 in result in a CG location of 26.7 in from the datum.

Mean Aerodynamic Chord (MAC)

Chord length of an imaginary airfoil section producing;

Same Aerodynamic Force Characteristics as Actual Wing.

MAC Usage

Define Relative Locations of:

1. Wing’s CP

2. A/C’s CG

Leading Edge Mean Aerodynamic Chord (LEMAC)

Distance in inches from

Datum-Line to Leading Edge

Trailing Edge Mean Aerodynamic Chord (TEMAC)

Distance in inches from

Datum-Line to Trailing Edge

MAC Length (100% MAC)

Difference between LEMAC & TEMAC Positions.

MAC Example Values

LEMAC = 860.2 inches.
TEMAC = 1040.9 inches.
MAC length (100% MAC) = 180.7 inches.

CG Limit Expression

Forward & Aft CG limits are expressed as % Percentages of MAC,

Measured from LEMAC.

%MAC Calculation Formula

%MAC = (Distance from LEMAC ÷ MAC Length) × 100

%MAC Calculation Example 1

If the forward limit is 25.3 inches from LEMAC and MAC is 180.7 inches:
(25.3 ÷ 180.7) = 14% MAC.

%MAC Calculation Example 2

If the forward limit is 45 inches from LEMAC and MAC is 180.7 inches:
(45 ÷ 180.7) = 25% MAC.

Load Index

Figure representing a CG position used for calculations in:

• Manual or Computerized Load

• Trim Sheets.

Dry Operating Index (DOI)

Figure representing a CG position of Dry Operating Weight, unique for each A/C’s:

• Tail Number

• Cabin Configuration.

Load Index Zero Fuel Weight (LIZFW)

Calculated by distributing passenger and cargo load

Load Index Takeoff Weight (LITOW)

Determined by adding

Fuel weight index correction to LIZFW

Manual Load Sheet

Hand-prepared document using

• Standard Charts

• Arm Values;

This method ensures safe loading but it is;

• Time-Consuming

• High likelihood of Human-Error.

Computerized Load Sheet

Generated using Software, instantly Calculates;

ZFW, TOW, LW, and CG with;

• High-Accuracy

• Allows for last-minute load changes (LMC)