Weight and Balance

WEIGHT=20 AND BALANCE
Overview Weight affects the flight performance = of an=20 aircraft in many respects. An airplane which is overloaded will be = deficient in performance because: Higher takeoff speed is = required. Longer=20 take-off run. Reduced rate of climb performance Shorter = range of=20 flight Reduced cruise speed Reduced = maneuverability Higher stall=20 speed Higher landing speed Longer landing=20 roll
Balance=20 Principles
As shown in the figure below, the aircraft is = somewhat like a=20 childs "teeter-totter" with respect to longitudinal balance. For = the plank=20 to be in balance, *The sum of the moment s on each side of = the pivot=20 point (fulcrum) must be equal.* A *MOMENT* is = simply=20 the weight multiplied by a moment arm (distance) from some = reference=20 point. In this example, the moments are measured from the center = fulcrum=20 point.
As seen, the=20 plank is in balance because the sum of the moments on each side = equals=20 5000 pound inches. If a weight on either side is moved, or a = weight is=20 changed, the plank will no longer be in balance. An aircraft in flight is very = similar. The=20 pivot point (fulcrum) is the located at the *Center of = Lift=20 of the wing. The load on the left is the total weight of the = aircraft=20 located at the Center of Gravity (CG)* with a=20 counter-balancing force on the right provided by the=20 elevators.
Note that if the location of the CG or the weight on = the left=20 changes, the elevator force must also change in order to maintain = the=20 balance. Also note, if the fulcrum (center of wing lift) changes, = the=20 elevator force must be changed to maintain a balanced condition. = Such an=20 event can occur when the angle of attack and/or engine thrust is=20 changed
The=20 Center of Gravity
As = previously=20 stated, the weight of an aircraft and its load is distributed = throughout=20 the aircraft as shown below by the small downward arrows. All of = the small=20 individual weights can be resolved into one single weight acting = at=20 the Center of Gravity and shown as the large arrow.. =

From the analogy=20 of the plank above, we can see that if we change either the weight = of the=20 aircraft, or the center of gravity, this in turn changes the force = (either=20 up or down) that the elevator must produce. =

For each aircraft design, the manufacturer specifies = a maximum=20 weight for operation of the aircraft, and also a maximum forward = and=20 rearward location of the Center of Gravity (CG). This is called = the=20 *CG RANGE. For safe operation, the aircraft must be = operated=20 within these parameters. In order to calculate where the = center of=20 gravity is located, the manufacturer specifies some point in the = aircraft=20 as a reference point (DATUM).* In many Cessna 172 = type=20 aircraft, the datum is located at the lower firewall of the cabin, = just=20 ahead of the rudder pedals. You as a pilot do not need to know = where this=20 is located in order to calculate weight and balance, as the = manufactirer=20 provided moment arm and/or moment in the weight and balance tables = for the=20 aircraft. An aircraft mechanic must know where whis point is, = however, if=20 equipment change is made to the aircraft which changes either the = aircraft=20 CG or Empty Weight. An airplane is designed and certified = to=20 withstand specified loading on it=92s structure. As long as the = gross weight=20 and load factor are within limits, the aircraft can be operated = safely.=20 Continued operaton of an aircraft in an overloaded condition can = cause=20 structural failures. Metal fatigue is hastened, and can lead to = stress=20 failures even in normal operating modes. =
Effect=20 on Wing Loading
The location of the CG affects the total load which = the wings=20 must sustain. If the CG is at or near the Center of Lift of the = wing the=20 elevators do not have to generate much (if any) downward force. If = the CG=20 is aft of the center of lift, the elevators must produce an upward = force.=20 If the aircraft is nose heavy (forward CG) the load on the wing = and=20 elevator surfaces will be greater. An aft CG location causes the = airplane to=20 require more "nose down" elevator for stall recovery. A forward CG = enhances stall recovery as the aircraft will naturally want to = "nose=20 down".
Definitions
*MOMENT ARM* -- a horizontal distance of = an object=20 measured from a defined =93datum=94 point to the CG of the object, = usually=20 measured in inches. A (+) arm means the object is behind the = datum. A (-)=20 arm indicates the object is forward off the datum point. = *MOMENT* -- the product = of a moment=20 arm and the associated weight. (Weight x Arm) EMPTY WEIGHT-- the combined = weight of=20 the aircraft, and permanently mounted equipment. It includes = unusable fuel=20 and hydraulic fluid. Most manufactures include the oil in the = empty=20 weight. Center of Gravity -- the point = at which=20 the airplane will be in balance. CG Limits -- the most forward = and most=20 rearward CG points specified by the manufacturer for safe control. = CG Range -- the distance from = the most=20 forward and rearward CG points as specified for the given = aircraft.=20 DATUM -- a point in the = aircraft from=20 which all moment arms are measured. FUEL LOAD -- the weight of the = useable=20 fuel. It does not include unusable fuel in the tanks and lines.=20 GROSS WEIGHT-- Total weight of = aircraft,=20 fuel, passengers and baggage. MAX LANDING WEIGHT - Maximum = gross=20 weight allowed for landing. MAX RAMP WEIGHT -- Maximum = gross weight=20 prior to taxi and take-off. MAX TAKEOFF WEIGHT -- the = maximum=20 allowable weight at start of takeoff run USEFUL LOAD -- Gross weight = minus the=20 empty aircraft weight. *STANDARD WEIGHTS* -- = Gasoline 6=20 lb. per gal; Oil 7.5 lb. per gal. (US Measure) =
Methods=20 of Determining Weight and Balance
The method of=20 determining weight and balance may vary with aircraft manufacturer = and=20 type of aircraft. These methods are: 1. Center of Gravity = Calculations 2. Center=20 of Gravity Graphs 3. Center of Gravity Tables 4. Loading = Schedules=20 (Placards)
Center=20 of Gravity Calculations
To determine the location CG, add up all the weights = and all=20 the moments. Divide the sum of the moments by the sum of the = weights. This=20 is illustrated in the diagram. All moments aft of the datum are = positive=20 numbers. All moments forward of the datum are negative. In the = example,=20 the oil is the only negative moment since it is forward of the = DATUM..=20 Calculate the weight of oil at 7.5 pounds per gallon. Calculate = fuel at 6=20 pounds (US) per gallon.

The procedure to calculate the CG is as follows:=20 1. Add up all weights, including = empty=20 aircraft 2. Multiply each weight by it=92s moment arm in inches = to get=20 the moment for that item. 3. Add up all the moments 4. = Divide the=20 sum of the moments by the total weight to get the=20 CG
A=20 TYPICAL W/B PROBLEM
ITEM	WEIGHT lbs	MOMENT ARM in. =	MOMENT LB IN
A =3D AIRCRAFT	1000=20	6	6000=20
P =3D Pilot	150=20	11=20	1650 =
B =3D = BAGGAGE	40=20	32	1280
O =3D = OIL	7.5	-4	-30
F =3D FUEL =	120	16	1920
TOTAL =	1317.5	CG?	10820
In the = example, CG? =3D=20 10820/1317.5 =3D 8.21 in. aft of the datum.=20
Loading=20 Graph
Frequently the manufacturer provides a graphical = method for=20 determining weight and balance.

Determine the load moment for each load item using = the=20 appropriate line in the graph. For example, for pilot and front = seat=20 passenger, total the combined load weight. Go up the Load Weight = axis (Y=20 axis) to the pilot & passenger weight. Then go horizontal to = the pilot=20 & passenger line (Red line). Then go down to the X axis to = find the=20 load moment/1000. Do the same for fuel (blue line), rear = passengers (green=20 Line) and baggage (black line). Total up the weight and the Load = Moments.=20 EXAMPLE: Determine the Load and = moment from the=20 loading graph above for each of the following load items.=20
Weight=20 and Balance Using Loading Graphs
	Weight	**Moment
Empty=20 Weight	1,364	51.7
Front=20 Seats	400	15.0
Baggage=20	120	11.5
Fuel (38=20 gal)	228	11.0
Oil (2 gal)=20	15	-0.2
TOTAL	2,127	89.0
Derive the=20 values as follows:
1. Empty Weight and moment are values provided by the = manufacturer. 2. Pilot & Passenger - Add weight = for Pilot=20 and Passenger. In this example 400lb. Go up the left side (Y axis) = of the=20 graph to 400 lb. weight, then horizontal to the =93Pilot & = Passenger=94=20 line. Read vertically down from the intersection to the horizontal = (X)=20 axis, and read a Moment/1000 value of 15.0. 3. Baggage - The baggage weight is = 120 lb. Go=20 up left side of the upper graph to a load of 120 lb. Continue = horizontally=20 to intersect the =93baggage=94 line. Go downward from this = intersection and=20 read a Moment/1000 value of 11.5. 4. Fuel -- 38 gallons at 6 pounds per = gallon is=20 228 pounds. Go up the left side of graph to a weight value of 228 = lbs.,=20 then horizontally to intersect the=93fuel line. Go downward to = read a=20 Moment/1000 value of 11.0. 5. Oil was not included in the empty = weight of=20 this aircraft, therefore it must be entered into the calculation. = Two=20 gallons of oil is 15 lb. The moment is -0.2=20 lb-in.
Loading=20 Envelope
Once the total weight and the total moment/1000 is = found, use=20 the load and CG envelope to ascertain that the aircraft is = properly=20 loaded. Go up the left side to a total load = of 2127=20 lbs. Draw a horizontal line. Go along the bottom scale to find the = loaded=20 aircraft moment / 100 value of 89.0. Draw a vertical line. The = aircraft is=20 properly loaded if the intersection of the horizontal and vertical = lines=20 is within the envelope.

According to=20 this envelope, if the weight is greater than 2300 pounds, the = aircraft is=20 overloaded. If the intersection is outside the envelope laterally, = the=20 loading is out of proper CG range.
Center of Gravity=20 Tables
Some=20 manufacturers provide tables instead of graphs or calculation. = This method=20 is fairly lengthy, and is used infrequently for small aircraft. = Therefore=20 this method will not be covered herein.
Weight Shift and = Change
The approach to=20 solving both Weight Change and Weight Shift is the same. The = simplest=20 method is to REMOVE a changed item, and to ADD the new or shifted = item=20 into the new location.
Weight = Change
*Example 1:* An airplane takes off = with a Gross=20 Weight of 6230 lb., and a CG of 79.0. The CG of the fuel is at = 87.00 aft=20 of datum. What is the *New CG* location after 50 = gallons of=20 fuel is burned? *Procedure:* Subtract = the Weight=20 and Moment of the burned fuel from the initial values to arrive at = a new=20 set of values. At 6 pounds per gallon, the burned fuel weight is = 300=20 pounds.
WEIGHT CHANGE=20 PROBLEM
	WEIGHT	CG	MOMENT
Initial=20 Weight	6230	79.00	492,170
Burned=20 Fuel	-300	87.00	-26,100
New Weight=20	5930	New CG	466,070
NEW CG (after Fuel Burned) =3D 466,070 = / 5930 =3D=20 78.59
Weight=20 Shift
*Example 2:* The gross weight of the = aircraft is=20 3,000 lbs. with a CG of 60 in. Since takeoff, 25 gallons of fuel = has been=20 used. The fuel cell CG is 65 in. aft of Datum (Station = 65). Also, a 200 pound passenger moves = from Station=20 50 to Station 90. (Note: Some problems will state the CG location = as=20 "Station". The 50 and 90 are CG location in inches aft of datum=20 respectively). Find *New CG. = Procedure:* 1. = Subtract burned=20 Fuel 2. Subtract Passenger who moves from the old = location. 3. Add=20 passenger who moves to the new = location.
WEIGHT SHIFT=20 PROBLEM
	Weight	CG Station	Moment
Initial=20 Loading	300	60.00	180,000
Fuel Burned=20	-150	65.00	9,750
Passenger Off=20	-200	50.00	-10,000
Passenger=20 On	+200	90.00	+18,000
New=20 Totals	2850	New CG	178,250
New=20 Cg =3D 178,250 / 2850 =3D Station 62.54 =

Overview