Weight and balance

Enough power is not enough

Weight and balance is the science of determining where an aircraft's weight acts and ensuring that it remains within safe limits. An aircraft can have enough power to fly and still be unsafe if its center of gravity (CG) is outside approved limits. For this reason, every aircraft operation, modification and maintenance action must consider its effect on weight and balance.

At its core, weight and balance is an application of a simple physical principle: an aircraft behaves like a lever, and every item on board creates a turning force around a reference point.

The law of the lever

Weight and balance calculations are based on moments and leverage. Imagine a seesaw: a heavier child closer to the center may balance a lighter child farther away. The balancing effect depends not only on weight, but also on distance. Aircraft work exactly the same way.

Datum

The datum is an imaginary vertical reference plane selected by the manufacturer. It serves as the starting point from which all aircraft measurements are made. It does not need to be physically located on the aircraft. The datum may be:

• Ahead of the nose
• At the nose
• At the firewall
• At another manufacturer-defined location

Arm

The arm is the horizontal distance between the datum and an item, such as passenger seats, fuel tanks, cargo compartments, batteries and avionics equipment. The farther an item is from the datum, the greater its leverage effect. Arms may be:

• Positive (aft of the datum)
• Negative (forward of the datum)

Moment

A moment is the turning force produced by a weight acting at a specific distance from the datum. The formula is moment = weight × arm. Notice that the same weight creates a much larger moment when placed farther from the datum. For example:

• 100 lb at an arm of 20 in = 2,000 lb-in
• 100 lb at an arm of 60 in = 6,000 lb-in

The center of gravity (CG)

The center of gravity is the point at which the aircraft would balance if suspended. It represents the location where the aircraft's entire weight is considered to act.

Every weight added to an aircraft affects the CG. Moving a relatively small object a large distance can sometimes shift the CG more than adding a heavier object near the center of the aircraft.

Calculating the center of gravity

The CG location is determined by combining all weights and moments. The result is the CG location expressed as an arm measured from the datum.

• Step 1, determine each weight: include all applicable items, such as the empty aircraft weight, crew, passengers, fuel, cargo, baggage and equipment.
• Step 2, find each arm: use the approved weight and balance data or equipment list to identify the arm for each item.
• Step 3, calculate each moment: multiply weight × arm for every item.
• Step 4, add the totals: calculate the total weight and the total moment.
• Step 5, calculate the CG: CG = total moment ÷ total weight.

A worked example

• Empty aircraft: 2,000 lb at 80 in = 160,000 lb-in
• Pilot: 180 lb at 85 in = 15,300 lb-in
• Passenger: 180 lb at 120 in = 21,600 lb-in
• Baggage: 50 lb at 180 in = 9,000 lb-in

Reading the example

The totals are a weight of 2,410 lb and a moment of 205,900 lb-in. The CG is 205,900 ÷ 2,410 = 85.4 in, so the CG is located 85.4 inches aft of the datum.

Mean aerodynamic chord (MAC)

Transport-category aircraft typically express CG as a percentage of the mean aerodynamic chord (MAC). The MAC is a representative average wing chord used for aerodynamic calculations.

The formula is % MAC = (CG distance aft of the MAC leading edge ÷ MAC length) × 100. Expressing CG as a percentage of MAC allows engineers and pilots to compare loading conditions consistently regardless of aircraft size.

For example, a CG at 25% MAC is farther forward than a CG at 35% MAC. Most aircraft operating manuals specify an approved CG range using MAC percentages.

Why center of gravity matters

The location of the CG has a major effect on aircraft stability, controllability and performance. An aircraft can be:

• Within weight limits but outside CG limits
• Within CG limits but overweight
• Completely airworthy only when both requirements are satisfied

Forward CG

A forward CG increases stability but reduces maneuverability. An excessively forward CG may prevent the aircraft from generating enough elevator authority during takeoff or landing flare. Effects include:

• Heavier elevator control forces
• Reduced pitch responsiveness
• Longer takeoff rolls
• Higher rotation speeds
• Increased stall speed
• Longer landing distances

Aft CG

An aft CG reduces the amount of stabilizing force required from the tail. Benefits include lower drag, improved cruise efficiency and lighter control forces.

However, excessive aft CG is extremely dangerous, and for this reason aft CG limits are treated very seriously. Effects include:

• Reduced longitudinal stability
• Increased sensitivity to control inputs
• More difficult stall recovery
• Risk of deep stall conditions
• Potential loss of controllability

Overweight conditions

An aircraft may have the correct CG yet still exceed its maximum allowable weight. Weight limits protect the aircraft structure as well as its performance capabilities. Overweight operation can result in:

• Longer takeoff distance
• Reduced climb performance
• Lower acceleration
• Increased stall speed
• Increased landing distance
• Higher structural loads

The maintenance technician's role

Maintenance personnel affect weight and balance whenever equipment is added, removed, relocated, repaired or replaced with different components. Even relatively small changes can affect CG calculations. Examples include:

• Installing new avionics
• Relocating batteries
• Adding antennas
• Replacing interior components
• Modifying cargo systems

Equipment lists

Every certificated aircraft maintains an approved equipment list that identifies installed equipment, the weight of each item and the location of each item. Whenever equipment changes, the list must be updated.

Weight and balance records

These records become part of the aircraft's permanent documentation. Following modifications, technicians must update:

• Empty weight
• Empty-weight CG
• Equipment list
• Weight and balance report

Aircraft weighing

Aircraft must occasionally be weighed to establish accurate weight and balance data. During weighing:

• The aircraft is leveled: manufacturers specify a precise leveling attitude to ensure accurate measurements.
• Fluid conditions are controlled: the maintenance manual specifies required conditions such as empty fuel or unusable fuel only, full operating fluids and hydraulic fluid quantities.
• Accurate scales are used: aircraft are weighed using calibrated scales positioned beneath the landing gear.

What weighing produces

The resulting measurements are used to calculate the empty weight, the empty-weight CG and revised moment values.

Common weight and balance mistakes

Small errors can accumulate over time and significantly affect the accuracy of the aircraft's weight and balance records. Errors can occur when:

• Equipment changes are not recorded
• Incorrect arms are used
• Fuel quantities are calculated incorrectly
• Weight estimates replace actual measurements
• Equipment lists are outdated

Key takeaways

• Weight and balance is based on the law of the lever.
• Moment = weight × arm.
• Center of gravity (CG) = total moment ÷ total weight.
• Large aircraft commonly express CG as a percentage of mean aerodynamic chord (MAC).
• A forward CG increases stability but may reduce controllability.
• An aft CG improves efficiency but can create serious stability and recovery problems.
• Overweight aircraft suffer performance and structural penalties.
• Every maintenance action that changes installed equipment must be reflected in the weight and balance records.

The bottom line

Weight and balance is much more than a paperwork exercise. It determines whether an aircraft can rotate properly during takeoff, remain stable in flight, recover from stalls and land safely. Every pound added to an aircraft and every inch it is moved affects the center of gravity. Understanding datum, arm, moment and CG calculations allows technicians and operators to ensure that an aircraft remains both legal and safe throughout its service life.