Overview

Weight affects the flight performance of an aircraft in many respects. An airplane which is overloaded will be deficient in performance because:

Higher takeoff speed is required.
Longer take-off run.
Reduced rate of climb performance
Shorter range of flight
Reduced cruise speed
Reduced maneuverability
Higher stall speed
Higher landing speed
Longer landing roll

An aircraft in flight is very similar. The pivot point (fulcrum) is the located at the Center of Lift of the wing. The load on the left is the total weight of the aircraft located at the Center of Gravity (CG) with a counter-balancing force on the right provided by the elevators. 

In order to calculate where the center of gravity is located, the manufacturer specifies some point in the aircraft as a reference point (DATUM). In many Cessna 172 type aircraft, the datum is located at the lower firewall of the cabin, just ahead of the rudder pedals. You as a pilot do not need to know where this is located in order to calculate weight and balance, as the manufactirer provided moment arm and/or moment in the weight and balance tables for the aircraft. An aircraft mechanic must know where whis point is, however, if equipment change is made to the aircraft which changes either the aircraft CG or Empty Weight.

An airplane is designed and certified to withstand specified loading on it’s structure. As long as the gross weight and load factor are within limits, the aircraft can be operated safely. Continued operaton of an aircraft in an overloaded condition can cause structural failures. Metal fatigue is hastened, and can lead to stress failures even in normal operating modes.

An aft CG location causes the airplane to require more "nose down" elevator for stall recovery. A forward CG enhances stall recovery as the aircraft will naturally want to "nose down".

MOMENT -- the product of a moment arm and the associated weight. (Weight x Arm)

EMPTY WEIGHT-- the combined weight of the aircraft, and permanently mounted equipment. It includes unusable fuel and hydraulic fluid. Most manufactures include the oil in the empty weight.

Center of Gravity -- the point at which the airplane will be in balance.

CG Limits -- the most forward and most rearward CG points specified by the manufacturer for safe control.

CG Range -- the distance from the most forward and rearward CG points as specified for the given aircraft.

DATUM -- a point in the aircraft from which all moment arms are measured.

FUEL LOAD -- the weight of the useable fuel. It does not include unusable fuel in the tanks and lines.

GROSS WEIGHT-- Total weight of aircraft, fuel, passengers and baggage.

MAX LANDING WEIGHT - Maximum gross weight allowed for landing.

MAX RAMP WEIGHT -- Maximum gross weight prior to taxi and take-off.

MAX TAKEOFF WEIGHT -- the maximum allowable weight at start of takeoff run

USEFUL LOAD -- Gross weight minus the empty aircraft weight.

STANDARD WEIGHTS -- Gasoline 6 lb. per gal; Oil 7.5 lb. per gal. (US Measure)

1. Center of Gravity Calculations
2. Center of Gravity Graphs
3. Center of Gravity Tables
4. Loading Schedules (Placards)

All moments aft of the datum are positive numbers. All moments forward of the datum are negative. In the example, the oil is the only negative moment since it is forward of the DATUM.. Calculate the weight of oil at 7.5 pounds per gallon. Calculate fuel at 6 pounds (US) per gallon.

1. Add up all weights, including empty aircraft
2. Multiply each weight by it’s moment arm in inches to get the moment for that item.
3. Add up all the moments
4. Divide the sum of the moments by the total weight to get the CG

In the example, CG? = 10820/1317.5 = 8.21 in. aft of the datum.

EXAMPLE: Determine the Load and moment from the loading graph above for each of the following load items.

2. Pilot & Passenger - Add weight for Pilot and Passenger. In this example 400lb. Go up the left side (Y axis) of the graph to 400 lb. weight, then horizontal to the “Pilot & Passenger” line. Read vertically down from the intersection to the horizontal (X) axis, and read a Moment/1000 value of 15.0.

3. Baggage - The baggage weight is 120 lb. Go up left side of the upper graph to a load of 120 lb. Continue horizontally to intersect the “baggage” line. Go downward from this intersection and read a Moment/1000 value of 11.5.

4. Fuel -- 38 gallons at 6 pounds per gallon is 228 pounds. Go up the left side of graph to a weight value of 228 lbs., then horizontally to intersect the“fuel line. Go downward to read a Moment/1000 value of 11.0.

5. Oil was not included in the empty weight of this aircraft, therefore it must be entered into the calculation. Two gallons of oil is 15 lb. The moment is -0.2 lb-in.

Go up the left side to a total load of 2127 lbs. Draw a horizontal line. Go along the bottom scale to find the loaded aircraft moment / 100 value of 89.0. Draw a vertical line. The aircraft is properly loaded if the intersection of the horizontal and vertical lines is within the envelope.

Procedure:
Subtract the Weight and Moment of the burned fuel from the initial values to arrive at a new set of values. At 6 pounds per gallon, the burned fuel weight is 300 pounds.

Also, a 200 pound passenger moves from Station 50 to Station 90. (Note: Some problems will state the CG location as "Station". The 50 and 90 are CG location in inches aft of datum respectively).

Find New CG.

Procedure:
1. Subtract burned Fuel
2. Subtract Passenger who moves from the old location.
3. Add passenger who moves to the new location.