9.weight-balance-principles. Weight and Balance Principles
Weight and balance is one of the most important pre-flight considerations for the pilot in command. An aircraft loaded outside its approved weight or center of gravity (CG) limits suffers degraded performance, reduced controllability, and — at the extremes — structural failure or loss of control. Compliance is not optional: 14 CFR 91.9 requires operation in accordance with the operating limitations specified in the approved Aircraft Flight Manual (AFM)/Pilot's Operating Handbook (POH), and 14 CFR 91.103 requires the pilot to determine takeoff and landing performance, which depends directly on weight.
Effects of Weight
Excess weight degrades nearly every performance parameter:
- Higher takeoff speed and longer takeoff roll
- Reduced rate and angle of climb
- Lower service ceiling
- Reduced cruise speed and range
- Reduced maneuverability
- Higher stall speed (Vs increases with the square root of the weight ratio)
- Higher approach and landing speed and longer landing roll
- Increased structural stress, especially in turbulence and during landing
At a given load factor, the wing must produce lift equal to weight times load factor. Heavier aircraft therefore stall at higher indicated airspeeds and require more runway to accelerate to liftoff speed and to decelerate after touchdown.
Center of Gravity and Balance
The center of gravity (CG) is the theoretical point at which the entire weight of the aircraft is considered to be concentrated. The CG must fall within the forward and aft limits published in the AFM/POH or the aircraft is unsafe to fly.
A forward CG produces:
- Higher stall speed (the tail must produce more downforce, which the wing must offset with more lift)
- Slower cruise speed (more induced drag from increased wing AOA)
- More stable longitudinal behavior
- Higher elevator forces; in extreme cases, insufficient elevator authority to flare
An aft CG produces:
- Lower stall speed and slightly higher cruise speed
- Reduced longitudinal stability — the aircraft becomes increasingly difficult to recover from stalls and spins
- Lighter, more sensitive elevator forces
- In extreme cases, an unrecoverable stall/spin
Aft CG is generally the more dangerous condition because it erodes the very stability the pilot depends on for stall and spin recovery.
Key Terminology
- Datum — an imaginary vertical reference plane from which all horizontal arms are measured. Specified by the manufacturer.
- Arm — horizontal distance, in inches, from the datum to the center of an item. Aft of the datum is positive; forward is negative.
- Moment — the product of weight and arm (Moment = Weight × Arm), expressed in inch-pounds. Moment is a measure of rotational tendency about the datum.
- Station — a location along the aircraft expressed as a distance from the datum.
- Empty weight — weight of the airframe, engine(s), all permanently installed equipment, unusable fuel, and (typically) full operating fluids including engine oil.
- Useful load — maximum takeoff weight minus empty weight; includes pilot, passengers, baggage, and usable fuel.
- Maximum ramp/taxi weight — maximum allowable for ground operations, including fuel for taxi and runup.
- Maximum takeoff weight (MTOW) — maximum allowed at brake release.
- Maximum landing weight — maximum allowed at touchdown.
- Maximum zero fuel weight — maximum weight without usable fuel; any additional load must be fuel (applies to some aircraft).
The Computation
The CG is found by dividing total moment by total weight:
CG (inches aft of datum) = Total Moment ÷ Total Weight
Procedure:
- List each item: pilot, front passengers, rear passengers, baggage compartment(s), fuel.
- Multiply each weight by its published arm to get a moment.
- Sum weights and sum moments.
- Divide total moment by total weight to get the CG.
- Compare total weight to MTOW and the resulting CG to the published forward and aft limits at that weight (the CG envelope).
Example
A Cessna 172 with empty weight 1,680 lb at moment 64,000 in-lb is loaded with a 170-lb pilot at arm 37 in (6,290 in-lb), a 160-lb passenger at arm 37 in (5,920 in-lb), 40 lb of baggage at arm 95 in (3,800 in-lb), and 40 gal usable fuel (240 lb) at arm 48 in (11,520 in-lb).
- Total weight: 1,680 + 170 + 160 + 40 + 240 = 2,290 lb (under 2,300 MTOW ✓)
- Total moment: 64,000 + 6,290 + 5,920 + 3,800 + 11,520 = 91,530 in-lb
- CG: 91,530 ÷ 2,290 = 39.97 in aft of datum
If the published envelope at 2,290 lb is 35.0–47.3 in, the airplane is within limits.
Weight Shift Formula
When redistributing load to bring CG within limits, use:
Weight to shift ÷ Total weight = Distance CG shifts ÷ Distance between arms
Fuel burn during flight also shifts CG; pilots must verify CG remains within limits at landing weight, not just takeoff weight.
A disciplined weight-and-balance computation before every flight — especially with full seats, baggage, or non-standard loads — is a defining habit of a professional pilot.