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Flight Performance - Level 3

Weight and Balance-Section 2

There are several methods by which weight and balance calculations may be made for any loading situation.

 

A.  FINDING BALANCE BY COMPUTATION METHOD

For this example, an airplane with a basic weight of 1575 lb. and an authorized gross weight of 2600 lb. has been selected. The balance datum line for the airplane, selected by the manufacturer, is the firewall. The recommended C.G. limits are 35.5" to 44.8".

List in table form the airplane (basic weight), pilot, passengers, fuel, oil, baggage, cargo, etc., their respective weights and arms. Calculate the balance moment of each. Total the weights. Total the balance moments. Divide the total balance moment by the total weight to find the moment arm (i.e. the position of the C.G.).

(Note: In this example, the oil is listed as a separate item and the balance datum line is the firewall in order to give an example of a negative moment arm.)

The moment arm for this loading of the airplane is 42.52" (110,270-- 2593). The total weight (2593 lb.) of the loaded airplane is less than the authorized gross weight (2600 lb.). The moment arm falls within the C.G. range (35.5" to 44.8"). The airplane is, therefor, properly loaded.

 

Item

Weight


Lb.

Item Moment Arm

Inches

Balance Moment

Inch-Lb.

Basic Airplane

1575

+36

+56,700

Pilot

165

+37

+6,105

Passenger (front seat)

143

+37

+5,291

Passenger (rear seat)

165

+72

+11,880

Child (rear seat)

77

+72

+5,544

Baggage

90

+98

+8,820

Fuel

360

+45

+16,200

Oil

18

-15

- 270

Total

2593

42.53

110,270

 

The above example examines the situation of an airplane almost at gross weight with the C.G. in a rearward position but within the C.G. range. If this calculation had resulted in a C.G. position that was aft of the C.G. limits, even though the total weight of the airplane was under the authorized gross weight, it would be necessary either to lighten the load or to shift the load by, for example, having the passengers change seats.

A lightly loaded airplane at the end of a flight when the fuel is almost all consumed may experience the situation that the C.G. moves forward beyond the permissible C.G. range. In some airplanes, when flying with only the pilot on board and no passengers or baggage, it is necessary to carry some suitable type of ballast to compensate for a too far forward C.G. Every pilot should, therefore, calculate the moment arm for the lightest possible loading of his airplane to determine if it is acceptable.

 

B.  FINDING BALANCE BY GRAPH METHOD

Most Airplane Flight Manuals include tables and graphs for calculating weight and balance. They are very easy to use and eliminate the time consuming mathematical steps of the computation.

 

C.  WEIGHT AND BALANCE AND FLIGHT PERFORMANCE

The flight characteristics of an airplane at gross weight with the C.G. very near its most aft limits are very different from those of the same airplane lightly loaded.

For lift and weight to be in equilibrium in order to maintain any desired attitude of flight (see Theory of Flight), more lift must be produced to balance the heavy weight. To achieve this, the airplane must be flown at an increased angle of attack. As a result, the wing will stall sooner (i.e. at a higher airspeed) when the airplane is fully loaded than when it is light. Stalling speed in turns (that is, at increased load factors) will also be higher. In fact, everything connected with lift will be affected. Take-off runs will be longer, angle of climb and rate of climb will be reduced and, because of the increased drag generated by the higher angle of attack, fuel consumption will be higher than normal for any given airspeed. Severe g-forces are more likely to cause stress to the airframe supporting a heavy payload.

An aft C.G. makes the airplane less stable, making recovery from maneuvers more difficult. The airplane is more easily upset gusts. However, with an aft C.G., the airplane stalls at a slightly lower airspeed. To counteract the tail heaviness of the aft C.G., the elevator must be trimmed for an up load. The horizontal stabilizer, as a result, produces extra lift and the wings, correspondingly, hold a slightly lower angle of attack.

An airplane with a forward center of gravity, being nose heavy, is more stable but more pressure on the elevator controls will be necessary to raise the nose - a fact to remember on the landing flare. The forward C.G. means a somewhat higher stalling speed another fact to remember during take-offs and landings.

Every pilot should be aware of these general characteristics, shared by most airplanes, when they are loaded to their weight and balance limits. The important thing to remember is that these characteristics are more pronounced as the limits are approached and may become dangerous if they are exceeded. Overloading, as well as the immediate degradation of performance, subjects the airplane to unseen stresses and precipitates component fatigue.


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Updated: March 12, 2004