Par 10-14 Page 10-468
EMPTY WEIGHT AND EMPTY WEIGHT CENTER OF GRAVITY (when aircraft is weighed with oil)
GIVEN:
Aircraft as weighed with full oil ------------------------------------------------------------1186 lbs.
Center of gravity ------------------------------------------------------------------------------9.7” Full oil capacity 9 qts.------------------------------------------------------------------------17 lbs.
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” A 1169
FIGURE 10-9. Empty weight and empty weight center of gravity when aircraft is weighed with oil.
The TCDS or Aircraft Specifications contain the following information relating to the subject:
• Center of gravity range.
• Empty weight c.g. range when applicable.
• Leveling means.
• Datum.
• Maximum weights.
• Number of seats and arm.
• Maximum baggage and arm.
• Fuel capacity and arm.
• Oil capacity and arm.
• Equipment items and arm.
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.
Par 10-16 Page 10-469 Unit weight for weight and balance purposes.
Gasoline ----------- 6 pounds per U.S. gal.
Turbine Fuel ------ 6.7 pounds per U.S. gal.
Lubricating oil ---- 7.5 pounds per U.S. gal.
Crew and passengers ----- 170 pounds per person.
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:
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.
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.
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.
WEIGHT AND BALANCE EXTREME CONDITIONS. The weight and balance extreme conditions represent the maximum forward and rearward c.g. position for the aircraft. Include the weight and balance data information showing that the c.g. of the aircraft (usually in the fully loaded condition) falls between the extreme conditions.
Forward Weight and Balance Check. When a forward weight and balance check is made, establish that neither the maximum weight nor the forward c.g.
limit listed in the TCDS and Aircraft Specifications are exceeded. To make th is check, the following information is needed:
The weights, arms, and moment of the empty aircraft.
The maximum weights, arms, and moments of the items of useful load that are located ahead of the forward c.g. limit.
The minimum weights, arms, and moments of the items of useful load that are located aft of the forward c.g. limit. A typical example of the computation necessary to make this check, using this data, is shown in figure 10-10.
Rearward Weight and Balance Check. When a rearward weight and balance check is made, establish that neither the maximum wei ght nor the rearward c.g.
limit listed in the TCDS and Aircraft Specifications are exceeded. To make th is check, the following information is needed:
The weight, arms, and moments of the empty aircraft.
The maximum weights, arms, and moments of the items of useful load that are located aft of the rearward c.g. limit.
Par 10-16 Page 10-470
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, minimum fuel should be included.
METO HP = 165 = 13.75 gal. x 6# ----------------------------------------------------------------------- 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 Oil + 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.
TM = 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.
FIGURE 10-10. Example of check of most forward weight and balance extreme.
Par 10-17 Page 10-471 The minimum weights, arms, and moments of the items of useful load that are located ahead of the rearward c.g. limit. A typical example of the computation necessary to make this check, using this data, is shown in figure 10-11.
LOADING CONDITIONS AND/OR PLACARDS. If the following items have not been covered in the weight and balance extreme condition checks and are not covered by suitable placards in the aircraft, a dditional computations are necessary. These computations should indicate the permissible distribution of fuel, passengers, and baggage that may be carried in the aircraft at any one time without exceeding either the maximum weight or
c.g. range. The conditions to check are:
With full fuel, determine the number of passengers and baggage permissible.
With maximum passengers, determine the fuel and baggage permissible.
With maximum baggage, determine the fuel and the number and location of passengers.
Examples of the computations for the above items are given in figures 10-12, 10-13, and 10-14 respectively.
The above cases are mainly applicable to the lighter type personal aircraft. In the case of the larger type transport aircraft, a variety of loading conditions is possible and it is necessary to have a loading schedule.
EQUIPMENT LIST. A list of the equipment included in the certificated empty weight may be found in either the approved aircraft flight manual or the weight and balance report. Enter into the weight and balance report all required, optional, and special equipment installed in the aircraft at time of weighing and/or subsequent equipment changes.
Required equipment items are listed in the pertinent Aircraft Specifications.
Optional equipment items are listed in the pertinent Aircraft Specifications and may be installed in the aircraft at the option of the owner.
Special equipment is any item not corresponding exactly to the descriptive information in the Aircraft Specifications. This includes items such as emergency locator transmitter (ELT), tail or logo lights, instruments, ashtrays, radios, navigation lights, and carpets.
Required and optional equipment may be shown on the equipment list with reference to the pertinent item number listed in the applicable specifications only when they are identical to that number item with reference to description, weight, and arm given in the specifications.
Show all special equipment items with reference to the item by name, make, model, weight, and arm. When the arm for such an item is not available, determine by actual measurement.
EQUIPMENT CHANGE. The person making an equipment change is obligated to make an entry on the equipment list indicating items added, removed, or relocated with the date accomplished, and identify himself by name and certificate number in the aircraft records.
Examples of items so affected are the installation of extra fuel tanks, seats, and baggage compartments. Figure 10-15 illustrates the effect on balance when equipment items are added within the acceptable c.g. limits and fore and aft of the established c.g. limits.
Par 10-17 Page 10-472
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 -------------------------------------------------------------------------------------- 21.9” *Oil capacity, 9 qts.----------------------------------------------------------------------------------------- 17# at -49” *Baggage, placarded do not exceed 100 lbs------------------------------------------------------------- 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 (TW) + 43428 (TM) Divide the TM (total moment) by the TW (total weight) to obtain the rearward weight and balance extreme.
TM = 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.
FIGURE 10-11. Example of check of most rearward weight and balance extreme.
Par 10-20 Page 10-473
EXAMPLE OF THE DETERMINATION OF THE NUMBER OF PASSENGERS AND BAGGAGE
PERMISSIBLE WITH FULL FUEL
GIVEN:
Actual empty weight of the aircraft----------------------------------------------------------------------- 1169# Empty weight center of gravity --------------------------------------------------------------------------- 10.6” Maximum weight ------------------------------------------------------------------------------------------- 2100# Datum is leading edge of the wing Forward center of gravity limit---------------------------------------------------------------------------- 8.5” Rearward center of gravity limit -------------------------------------------------------------------------- 21.9” Oil capacity, 9 qts.; show full capacity------------------------------------------------------------------- 17# at -49” Baggage, maximum----------------------------------------------------------------------------------------- 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” Full fuel, 40 gals. x 6#-------------------------------------------------------------------------------------- 240# at +22”
Weight (#) x Arm (“) = Moment (“#) Aircraft empty + 1169 + 10.6 + 12391 Oil + 17 - 49 - 833 Full Fuel + 240 + 22 + 5280 Passengers 2 rear + 340* + 48 +16320 Pilot + 170 + 16 + 2720 Baggage + 100 + 75.5 + 7550 Total + 2036 (TW) + 43428 (TM)
Divide the TM (total moment) by the TW (total weight) to obtain the loaded center of gravity.
TM = 43428 = + 21.3” TW 2036
The above computations show that w ith full fuel, 100 pounds of baggage and two passengers in the rear seat may be carried in this aircraft without exceeding either the maximum weight or the approved C. G. range.
This condition may be entered in the loading schedule as follows:
GALLONS OF FUEL NUMBER OF PASSENGERS POUNDS OF BAGGAGE Full 2 Rear 100
* Only two passengers are listed to prevent the maximum weight of 2100 lbs. from being exceeded.
FIGURE 10-12. Loading conditions: determination of the number of passengers and baggage permissible with full fuel.
Par 10-20 Page 10-474
EXAMPLE OF THE DETERMINATION OF TH E POUNDS OF FUEL AND BAGGAGE PERMISSIBLE
WITH MAXIMUM PASSENGERS
Weight (#) x Arm (“) = Moment (“#) Aircraft empty + 1169 + 10.6 + 12391 Oil + 17 - 49 - 833 Pilot + 170 + 16 + 2720 Passenger (1) front + 170 + 16 + 2720 Passenger (2) rear + 340 + 48 +16320 Fuel (39 gals.) + 234 + 22 + 5148 Baggage ---- ---- ---- Total + 2100 + 38466
Divide the TM (total moment) by the TW (total weight) to obtain the loaded center of gravity.
TM = 38466 = + 18.6” TW 2100
The above computations show that w ith the maximum number of passengers, 39 gallons of fuel and zero pounds of baggage ma y be carried in this aircraft without exceeding either the maximum weight or the approved C. G. range.
This condition may be entered in the loading schedule as follows:
GALLONS OF FUEL NUMBER OF PASSENGERS POUNDS OF BAGGAGE *Full *2 Rear * 100 39 1(F) 2(R) None
* Conditions as entered from Figure 10-12 (F) Front seat (R) Rear seat
FIGURE 10-13. Loading conditions: determination of the fuel and baggage permissible with maximum passengers.
Par 10-20 Page 10-475
EXAMPLE OF THE DETERMINATION OF THE FUEL AND THE NUMBER AND LOCATION OF
PASSENGERS PERMISSIBLE WITH MAXIMUM BAGGAGE
Weight (#) x Arm (“) = Moment (“#) Aircraft empty + 1169 + 10.6 + 12391 Oil + 17 - 49 - 833 Pilot + 170 + 16 + 2720 Passenger (1) rear + 170 + 48 + 8160 Passenger (1) front + 170 + 16 + 2720 Fuel (40 gals.) + 240 + 22 + 5280 Baggage + 100 + 75.5 + 7550 Total + 2036 + 37988
Divide the TM (total moment) by the TW (total weight) to obtain the loaded center of gravity.
TM = 37988 = + 18.7 TW 20366
The above computations show that with maximum baggage, full fuel and 2 passengers (1 in the front seat and 1 in the rear seat) may be carried in this aircraft without exceeding either the maximum weight or the approved C. G. range.
This condition may be entered in the loading schedule as follows:
GALLONS OF FUEL NUMBER OF PASSENGERS POUNDS OF BAGGAGE *Full *2 Rear * 100 ** 39 *1(F) 2(R) **None Full 1(F) 1(R) Full
* Conditions as entered from Figure 10-12 ** Conditions as entered from Figure 10-13 (F) Front seat (R) Rear seat
FIGURE 10-14. Loading conditions: determination of the fuel and the number and location of passengers permissible with maximum baggage.
WEIGHTS FORWARD C.G. LIMIT - REARWARD C.G. LIMIT Weights added anywhere between the C.G. limits will not upset the balance of the aircraft.
-WEIGHT FORWARD C.G. LIMIT -REARWARD C.G. LIMIT Any weights added ahead of the forward C.G. limit would tend to upset the balance around the forward balance limit.
WEIGHT FORWARD C.G. LIMIT •REARWARD C.G. LIMIT Any weights added ait of the rearward C.G. limit would tend to upset the balance around the rearward balance limit.
FIGURE 10-15. Effects of the addition of equipment items on balance.
Moment computations for typical equipment changes are given in figure 10-16 and are also included in the sample weight and balance sheet in figure 10-18.
SAMPLE WEIGHT AND BALANCE REPORT.
Suggested methods of tabulating the various data and computations for determining the c.g., both in the empty weight condition and the fully loaded condition, are given in figures 10-17 and 10-18, respectively, and represent a suggested means of recording this information. The data presented in figure 10-17 have previously been computed in figures 10-10 and 10-11 for the extreme load conditions and figure 10-16 for equipment change, and represents suggested means of recording this information.
INSTALLATION OF BALLAST. Ballast is sometimes permanently installed for c.g.
balance purposes as a result of installation or removal of equipment items and is not used to correct a nose-up or nose-down tendency of an aircraft. It is usually located as far aft or as far forward as possible in order to bring the Par 10-20 Page 10-476
9/8/98
c.g. position within acceptable limits with a minimum of weight increase. Permanent ballast is often lead plate wrapped around and bolted to the fuselage primary structure (e.i., tail-post, longerons, members). Permanent ballast invariably constitutes a concentrated load; therefore, the strength of the local structure and the attachment of the ballast thereto should be investigated for the design loading conditions pertinent to that particular aircraft. Placard permanent ballast with Permanent ballast - do not remove. It is AC 43.13-1B desirable to install permanent ballast by pouring melted lead into the tail-post or longerons due to difficulties that may be encountered in subsequent welding repair operations. It should be noted that the installation of permanent ballast results in an increase of aircraft empty weight. See figure 10-19 for ballast computation. The local strength of the compartment in which the ballast is carried and the effect of the ballast on aircraft weight and balance should be investigated when disposable ballast is carried.
Forward Rearward
- Moments (counterclockwise) + Moments (clockwise) Wheel pants added (+6# at -1") Battery added (+29# at +13") Battery removed (-24# at -29") Landing light removed (-1# at +4") DATUM Weight (#) x Arm (") = Moment ("#) ADDED Item 204 wheel pants + 6 - 1 - 6 Item 302b Battery + 29 + 13 +377
REMOVED Item 302a Battery - 24 -29 +696 Item 303 Landing light - 1 + 4 - 4 This condition is shown properly entered on a sample weight and balance report on Figure 10-18 under Equipment Change.
FIGURE 10-16. Example of moment and weight changes resulting from equipment changes.
MAKE MA-700_MODEL A _SERIAL # 0000_REGISTRATION # N1234 DATUM IS leading edge of wing
COMPUTE AS FOLLOWS IF AIRCRAFT WEIGHED Par 10-22 Page 10-477
Par 10-22 Page 10-478
1. Leveling means: level top longeron between front and rear seats.
2. Main wheel weighing point is located ( “FORWARD) (+ 3 “ AFT) of datum.
3. Actual measured distance from the main weight point centerline to the tail (or nose) point centerline 222 “.
4. Oil over and above “ZERO” tank reading = (a. ---- Gals.) (b. ---- Lbs.) (c. ---- In.)
ACTUAL EMPTY WEIGHT
Weight Point Scale Reading - Tare = Net Weight
5. Right 564 0 564
6. Left 565 0 565
7. Tail 67 27 40
8. Nose ---- ---- -----
9. Total Net Weight X X 1169
CENTER OF GRAVITY AS WEIGHED
10. C.G. relative to main wheel weighing point:
(a) Tail wheel airc. (Item 3, 222) x (Item 7, 40 ) = + 7.6 = C.G.
(Item 9, 1169)
(b) Nose wheel airc. (Item 3 ----) x (Item 8 ---- ) = = C.G.
(Item 9 ---- )
11. C.G. relative to datum:
(a) Tail wheel airc. (Item 10a, + 7.6) added to (Item 2, + 3) = +10.6” = C.G.
(b) Nose wheel airc. (Item 10b, ) added to (Item 2, ) = = C.G.
COMPUTE IF AIRCRAFT WEIGHED WITH OIL (Item 4) Weight x Arm = Moment Aircraft Less Oil
(9) (4b)
(11) (4c)
Empty Totals (a) X (b)
(b) ------------------- = (c) ------------------“ = Empty weight C.G.
12. (a)
REPAIR AGENCY DATE Name Number
FIGURE 10-17. Sample weight and balance report to determine empty weight center of gravity.
Par 10-22 Page 10-479
EQUIPMENT LIST *Required or Optional Item Numbers as Shown in Aircraft Specification 1 2 101 102 103 104 105 106 201 202 203 301 302(a) 303 401(a) 402 ---- ---- ---- ---- ---- Special Equipment Item Make Model Weight Arm 3 Flares 1-1/2 Min. XYZ 03 25# 105”
Enter above those items included in the empty weight.
WEIGHT AND BALANCE EXTREME CONDITIONS Approved fwd limit 8.5” Approved max. weight 2100# Approved aft limit 21.9” Item FORWARD CHECK REARWARD CHECK Weight X Arm = Moment Weight X Arm = Moment Airo. Empty + 1169 (9 or 12a) + 10.6 (11 or 12c) + 12391 + 1169 (9 or 12a) + 10.6 (11 or 12c) + 12391 Oil + 17 - 49 - 833 + 17 - 49 - 833 Pilot + 170 + 16 + 2720 + 170 + 16 + 2720 Fuel + 83 + 22 + 1826 + 240 + 22 + 5280 Passenger (s) + 340 + 48 + 16320 Baggage + 100 + 75.5 + 7550 TOTAL + 1439 = TW x + 16104 = TM + 2036 = TW x +43428=TM TM = 16104 = +11.2” = TM = 43428 = +21.3” = TW 1439 TW 2036 Most Forward C.G. location Most Rearward C.G. location
LOADING SCHEDULE Gallons of Fuel Number of Passengers Pounds of Baggage
40 2(R) 100
The above includes pilot and capacity oil.
EQUIPMENT CHANGE Computing New C.G.
Item, Make, and Model* Weight X Arm Moment Airc. Empty + 1169 (9 or 12a) + 10.6 (11 or 12c) + 12391 204 added + 6 - 1 - 6 302(b) added + 29 + 13 + 377 302(a) removed - 24 + 29 + 696 303 removed - 1 + 4 - 4 NET TOTALS - 1179 = NW x + 13454 = NM NM = 13454 = +11.4” = New C.G.
NW 1179 *ITEM NUMBERS WHEN LISTED IN PERTIN ENT AIRCRAFT SPECIFICATION MAY BE USED IN LIEU OF “ITEM, MAKE, AND MODEL”.
PREPARED BY________________________________ DATE________________________
FIGURE 10-18. Sample weight and balance report including an equipment change for aircraft fully loaded.