i. Center of Gravity. The CG is a point about which the nose heavy and tail heavy moments are exactly equal in magnitude. If the aircraft is suspended from the CG, it will not have a tendency to pitch in either direction (nose up or down). The weight of the aircraft (or any object) may be assumed to be concentrated at its CG (see Figure 10-3.)
j. Empty Weight Center of Gravity. The empty weight center of gravity (EWCG) is the CG of an aircraft in its empty weight condition, and is an essential part of the W&B record Formulas for determining the CG for tail and nosewheel type aircraft are given in Figure 10-4.
Typical examples of computing the empty weight and EWCG for aircraft are shown in Figures 10-5 and 10-6.
FIGURE 10-4. EMPTY WEIGHT CENTER OF GRAVITY FORMULAS
- DATUM - DATUM
• D D- C.G -L
NOSE WHEEL TYPE AIRCRAFT
DATUM LOCATED FORWARD OF THE
MAIN WHEELS
TAIL WHEEL TYPE AIRCRAFT
DATUM LOCATED FORWARD OF THE
MAIN WHEELS C.G. = D. (FXL) C.G. = D + RX_ -DATUM - DATUM :.G C.G.
NOSE WHEEL TYPE AIRCRAFT
DATUM LOCATED AFT OF THE
MAIN WHEELS C.G.= - (D+ F XL)
TAIL WHEEL TYPE AIRCRAFT
DATUM LOCATED AFT OF THE
MAIN WHEELS C.G.= -D+ (RXL) C.G. = Distance from datum to center of gravity of the aircraft.
W = The weight of the aircraft at the time of weighing.
D = The horizontal distance measured from the datum to the main wheel weighing point.
L = The horizontal distance measured from the main wheel weighing point to the nose or tail weighing point.
F = The weight at the nose weighing point.
R = The weight at the tail weighing point.
Par 10-2 Page 10-4
FIGURE 10-5. EMPTY WEIGHT AND EMPTY WEIGHT CENTER OF GRAVITY
TAILWHEEL TYPE AIRCRAFT
DATUM (LEADING EDGE OF
WING ROOT SECTION)
COMPUTED-
• C.G.
-TARE 27 LBS.
WEIGHING POINT (© MAIN WHEEL)[ -LEFT SCALE 565 LBS. -RIGHT SCALE 564 LBS/ /67 LBS. SCALE READING
D, MEASURED - WEIGHING POINT -L, MEASURED ( C TAIL WHEEL) TO FIND: EMPTY WEIGHT AND EMPTY WEIGHT CENTER OF GRAVITY Datum is the leading edge of the wing (from aircraft specification) (D) Actual measured horizontal distance from the main wheel weighing point (C main wheel) to the Datum --- -- 3" (L) Actual measured horizontal distance from the rear wheel weighing point (Q rear wheel) to the main wheel weighing point - --222" SOLVING: EMPTY WEIGHT Weighing Scale Net Point Reading # Tare # Weight # Right 564 564 Left 565 565 Rear 67 27 40 Empty Weight (W) 1169 SOLVING: EMPTY WEIGHT CENTER OF GRAVITY Formula: C.G. = D + - RL = 3" + 40x222 = 3" + 7.6" = 10.6" Reference for formula, Figure 10-4.
This case is shown properly entered on a sample weight and balance report form, Figure 10-17 Par 10-2 Page 10-5
FIGURE 10-6. EMPTY WEIGHT AND EMPTY WEIGHT CENTER OF GRAVITY
NOSEWHEEL TYPE AIRCRAFT
DATUM (LEADING EDGE OF
WING ROOT SECTION)
COMPUTED 0 C.G.
COMPUTED LEFT SCALE 620 LBS., TARE 5 LBS.
RIGHT SCALE 609 LBS., TARE 5 LBS.
WEIGHING POINT D, MEASURED (CL NOSEWHEEL) WEIGHING POINT
L, MEASURED (CIMAIN WHEEL) TO FIND: EMPTY WEIGHT AND EMPTY WEIGHT CENTER OF GRAVITY Datum is the leading edge of the wing (from aircraft specification) (D) Actual measured horizontal distance from the main wheel weighing point (C main wheel) to the Datum
- 34.0" (L) Actual measured horizontal distance from the front wheel weighing point (C front wheel) to the main wheel weighing point
67.8" SOLVING: EMPTY WEIGHT Weighing Scale Net Point Reading Tare Weight Right 609 5 604 Left 620 5 615 Front 464 10 454 Empty Weight (W) 1673 SOLVING: EMPTY WEIGHT CENTER OF GRAVITY Formula: C.G. = D - W F xL = 34" - 451 × 67.8 = 34" - 18.4" = 15.6" Reference for formula, Figure 10-4.
Par 10-2 Page 10-6
Par 10-2 Page 10-7
k. Empty Weight Center of Gravity Range. The EWCG range is determined so that the EWCG limits will not be exceeded under standard specifications loading arrangements.
Calculations, as outlined in paragraph 10-18, should be completed when it is possible to load an aircraft in a manner not covered in the Aircraft Specifications or TCDS (extra tanks, extra seats, etc.). The EWCG range, when applicable, is listed in the Aircraft Specifications or TCDS.
Calculation of EWCG is shown in Figures 10-5 and 10-6.
l. Operating Center of Gravity Range. The operating CG range is the distance between the forward and rearward CG limits indicated in the pertinent Aircraft Specifications or TCDS.
These limits are determined for the most forward and most rearward loaded CG positions at which the aircraft meets the requirements of Title 14 of the Code of Federal Regulations (14 CFR). The limits are indicated in the specifications in either percent of MAC or inches from the datum. The CG of the loaded aircraft must be within these limits at all times as illustrated in Figure 10-7.
FIGURE 10-7. OPERATING CENTER OF GRAVITY RANGE
m. Mea n Aerodynamic Chord (MAC). The MAC is established by the manufacturer who defines its leading edge and its trailing edge in terms of inches from the datum. The CG location and various limits are then expressed in percentages of the chord. The location and dimensions of the MAC can be found in the Aircraft Specifications, the TCDS, the AFM, or the aircraft W&B report.
n. Weighing Point. If the CG location is determined by weighing, it is necessary to obtain horizontal measurements between the points on the scale at which the aircraft’s weight is concentrated. If weighed using scales under the landing gear tires, a vertical line passing through the center line of the axle will locate the point on the scale at which the weight is concentrated.
Par 10-2 Page 10-8 This point is called the “weighing point.” Other structural locations capable of supporting the aircraft, such as jack pads on the main spar, may also be used if the aircraft weight is resting on the jack pads. Indicate these points clearly in the W&B report when used instead of the landing gear. Typical locations of the weighing points are shown in Figure 10-8.
FIGURE 10-8. WEIGHING POINT CENTER LINE
o.
Zero Fuel Weight. The maximum permissible weight of a loaded aircraft (passengers, crew, cargo, etc.) less its fuel is zero fuel weight. All weights in excess of maximum zero fuel weight must consist of usable fuel.
Par 10-2 Page 10-9
p. Minimum Fuel. The minimum fuel for balance purposes is 1/12 gallon per maximum except take off horsepower (METO). Minimum fuel is the maximum amount of fuel which can be used in W&B computations when low fuel might adversely affect the most critical balance conditions. To determine the weight of fuel in pounds divide the METO horsepower by two.
q. Full Oil. The full oil is the quantity of oil shown in the Aircraft Specifications or TCDS as oil capacity. Use full oil as the quantity of oil when making the loaded W&B computations.
r. Tare. The weight of chocks, blocks, stands, etc., used when weighing aircraft is called tare and is included in the scale readings. Tare is deducted from the scale reading at each respective weighing point when tare is involved, to obtain the actual aircraft weight.
10-3.–10-13. [RESERVED.]
Par 10-14 Page 10-10 SECTION 2. WEIGHING PROCEDURES
10-14. GENERAL. Weighing procedures may vary with the aircraft and the type of weighing equipment employed. The weighing procedures contained in the manufacturer’s maintenance manual should be followed for each particular aircraft.
10-15. PROCEDURES. Accepted procedures when weighing an aircraft are:
a. Remove excessive dirt, grease, moisture, etc., from the aircraft before weighing.
b. Weigh the aircraft inside a closed building to prevent error in scale reading due to wind.
c. Determine the EWCG by placing the aircraft in a level flight attitude.
d. Have all items of equipment that are included in the certificated empty weight report installed in the aircraft when weighing. These items of equipment are a part of the current W&B report.
e. The scales should have a current calibration before weighing begins. Zero and use the scales in accordance with the scale manufacturer’s instructions. Platform scales and suitable support for the aircraft, if necessary, are usually placed under the wheels of a landplane, the keel of a seaplane float, or the skis of a skiplane. Other structural locations capable of supporting the aircraft, such as jack pads, may be used. Clearly indicate these points and the alternate equipment used in the W&B report.
f. Drain the fuel system until the quantity indicator reads zero or until the tanks are empty with the aircraft in level flight attitude, unless otherwise noted in the TCDS or Aircraft Specifications. The amount of fuel remaining in the tank, lines, and engine is termed residual fuel and is to be included in the empty weight. In special cases, the aircraft may be weighed with full fuel in tanks provided a definite means of determining the exact weight of the fuel is available.
g. The oil system should be filled to the quantity noted in the TCDS or Aircraft Specifications.
NOTE: On Civil Aeronautics Regulations (CAR 3) Certified Aircraft, the weight of the oil was subtracted mathematically to get the empty weight. In 14 CFR part 23 aircraft, the weight of the oil is included in the empty weight.
When weighed with full oil, actual empty weight equals the actual recorded weight less the weight of the oil in the oil tank (oil weight = oil capacity in gallons x 7.5 lb.). Indicate on all W&B reports whether weights include full oil or oil drained. (See Figure 10-9.)
FIGURE 10-9. EMPTY WEIGHT AND EMPTY WEIGHT CENTER OF GRAVITY
WHEN AIRCRAFT IS WEIGHED WITH OIL DATUM
• EMPTY WEIGHT C.G.
AT - 49" OIL TANK 9 QTS_ WEIGHT OF AIRCRAFT WITH OIL IS 1186 LBS. C.G. AS WEIGHED WITH OIL IS +9.7"
EMPTY WEIGHT AND EMPTY WEIGHT CENTER OF GRAVITY (When aircraft is weighed with oil) GIVEN:
Aircraft as weighed with full oil - 1186 Ibs.
Center of gravity " - 9.7" Full oil capacity 9 qts. -- 17 1bs.
SOLVING:
Weight # X Arm" = Moment "# Aircraft as weighed + 1186 + 9.7 + 11504 Less oil 17 - 49.0 + 833 Total + 1169(A) + 12337(B) Empty Weight (A) = 1169 pounds Empty Weight Center of Gravity B = 12337 = + 10.6" 1169
h. Do not set brakes while taking scale reading.
I. Note any tare reading when the aircraft is removed from the scales.
• 10-16. REPAIRS AND ALTERATIONS. These are the major sources of weight changes, and it is the responsibility of the aircraft mechanic making any repairs or alteration to know the weight and location of these changes, and to compute the new CG and record the new empty weight and EWCG data in the AFM.
• 10-17. ANNUAL OR 100-HOUR INSPECTION. After conducting an annual or 100-hour inspection, the aircraft mechanic must ensure the W&B data in the aircraft records is current and accurate.
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Par 10-18 Page 10-12
10-18. W&B COMPUTATIONS. It is often necessary after completing an extensive alteration to establish by computation that the authorized weight and CG limits as shown in the TCDS and Aircraft Specifications are not exceeded. Subparagraph b(2) explains the significance of algebraic signs used in balance computations.
a. The TCDS or Aircraft Specifications contain the following information relating to the subject:
(1) CG range.
(2) EWCG range when applicable.
(3) Leveling means.
(4) Datum.
(5) Maximum weights.
(6) Number of seats and arm.
(7) Maximum baggage and arm.
(8) Fuel capacity and arm.
(9) Oil capacity and arm.
(10) Equipment items and arm.
b. The TCDS do not list the basic required equipment prescribed by the applicable airworthiness regulations for certification. Refer to the manufacturer’s equipment list for such information.
(1) Unit weight for W&B purposes.
Gasoline 6 lb. per U.S. gal.
Turbine Fuel 6.7 lb. per U.S. gal.
Lubricating oil 7.5 lb. per U.S. gal.
Crew and passengers 170 lb. per person.
(2) It is important to retain the proper algebraic sign (+ or -) through all balance computations. For the sake of uniformity in these computations, visualize the aircraft with the nose to the left. In this position, any arm to the left (forward) of the datum is “minus” and any arm to the right (rearward) of the datum is “plus.” Any item of weight added to the aircraft either side of the datum is plus weight, any weight item removed is a minus weight. When multiplying weights by arms, the answer is plus if the signs are the same, and minus if the signs are different.
The following combinations are possible:
Par 10-18 Page 10-13 Items added forward of the datum:
( + ) weight x (-) arm = (-) moment.
Items added to the rear of the datum:
( + ) weight x ( + ) arm = ( + ) moment.
Items removed forward of the datum:
(-) weight x (-) arm = ( + ) moment.
Items removed rear of the datum:
(-) weight x ( + ) arm = (-) moment.
(3) The total weight of the airplane is equal to the weight of the empty aircraft plus the weight of the items added minus the weight of the items removed.
(4) The total moment of the aircraft is the algebraic sum of the empty weight moment of the aircraft and all of the individual moments of the items added and/or removed.
10-19. W&B EXTREME CONDITIONS. The W&B extreme conditions represent the maximum forward and rearward CG position for the aircraft. Include the W&B data information showing that the CG of the aircraft (usually in the fully loaded condition) falls between the extreme conditions.
a. Forward W&B Check. When a forward W&B check is made, establish that neither the maximum weight nor the forward CG limit listed in the TCDS and Aircraft Specifications are exceeded. To make this check, the following information is needed:
(1) The weights, arms, and moment of the empty aircraft.
(2) The maximum weights, arms, and moments of the items of useful load that are located ahead of the forward CG limit.
(3) The minimum weights, arms, and moments of the items of useful load that are located aft of the forward CG limit. A typical example of the computation necessary to make this check, using this data, is shown in Figure 10-10.
b. Rearward W&B Check. When a rearward W&B check is made, establish that neither the maximum weight nor the rearward CG limit listed in the TCDS and Aircraft Specifications are exceeded. To make this check, the following information is needed:
(1) The weight, arms, and moments of the empty aircraft.
(2) The maximum weights, arms, and moments of the items of useful load that are located aft of the rearward CG limit.
(3) The minimum weights, arms, and moments of the items of useful load that are located ahead of the rearward CG limit. A typical example of the computation necessary to make this check, using this data, is shown in Figure 10-11.
FIGURE 10-10. EXAMPLE OF CHECK OF MOST FORWARD WEIGHT AND
BALANCE EXTREME
- DATUM
- NO BAGGAGE
NO PASSENGERS
FULL OIL -MINIMUM FUEL -PILOT ONLY FORWARD C.G. LIMIT TO CHECK: MOST FORWARD WEIGHT AND BALANCE EXTREME.
GIVEN:
Actual empty weight of the aircraft - 1169# Empty weight center of gravity- -+ 10.6" *Maximum weight- --2100# *Forward C.G.. limit - + 8.5" *Oil capacity. 9 qts. - - 17# at -49" *Pilot in farthest forward seat equipped with controls (unless otherwise placarded) -- - 170# at +16" *Since the fuel tank is located to the rear of the forward C.G. limit, munimum fuel should be included.
METO HP = 165 = 13.75 gal. x 64. -- 83# at +22" 12 12 * Information should be obtained from the aircraft specification.
Note: Any items or passengers must be used if they are located ahead of the forward C.G. limit.
Full fuel must be used if the tank is located ahead of the forward C.G. limit.
CHECK OF FORWARD WEIGHT AND BALANCE EXTREME Weight (#) x Arm (*) = Moment (*#) Aircraft empty + 1169 + 10.6 + 12391 + 17 - 49 833 Pilot + 170 + 16 + 2720 Fuel + 83 + 22 + 1826 Total + 1439 (TW) + 16104 (TM) Divide the TM (total moment) by the TW (total weight) to obtain the forward weight and balance extreme.
IM = 16104 = + 11.2" TW 1439 Since the forward C.G. limit and the maximum weight are not exceeded, the forward weight and balance extreme condition is satisfactory.
Par 10-19 Page 10-14
FIGURE 10-11. EXAMPLE OF CHECK OF MOST REARWARD WEIGHT AND
BALANCE EXTREME -DATUM
- MAXIMUM BAGGAGE
- MAXIMUM PASSENGERS FULL OIL→ MAXIMUM FUEL PILOT ONLY REARWARD C.G. LIMIT TO CHECK: MOST REARWARD WEIGHT AND BALANCE EXTREME.
GIVEN:
Actual empty weight of the aircraft • 1169# Empty weight center of gravity- • 10.6" *Maximum weight -- 2100# *Rearward C.G.. limit- • 21.97 *Oil capacity. 9 qts. - - 17# at -49" *Baggage, placarded do not exceed 100 1bs - • 100# at +75.5" *Two passengers in rear seat, 170# x 2 - 340# at +48" *Pilot in most rearward seat equipped with controls (unless otherwise placarded) - 170# at +16" *Since the fuel tank is located aft of the rearward C.G. limit full fuel must be used 240# at +22" * Information should be obtained from the aircraft specification.
Note: If fuel tanks are located ahead of the rearward C.G. limit minimum fuel should be used.
CHECK OF REARWARD WEIGHT AND BALANCE EXTREME Weight (#) x Arm (*) = Moment (*#) Aircraft empty + 1169 + 10.6 + 12391 Oil 17 - 49 833 Pilot (1) + 170 + 16 + 2720 Passenger (2) + 340 + 48 16320 Fuel (40 gals.) + 240 + 22 + 5280 Baggage + 100 + 75.5 + 7550 Total + 2036 (IW) + 43428 (TM) Divide the TM (total moment) by the TW (total weight) to obtain the rearward weight and balance extreme.
IM = 43428 = + 21.3" TW 2036 Since the rearward C.G. limit and the maximum weight are not exceeded, the rearward weight and balance extreme condition is satisfactory.
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