Appendix C C-5 Table C-8. Moments Resulting From the Window-Aisle-Remaining Assumption for Zone 2 Passenger No.
Assumed Row Assumed Weight Assumed Arm Moment Cumulative Moment 7 4 189 lb 289 in 54,621 in-lb 54,621 in-lb 8 4 189 lb 289 in 54,621 in-lb 109,242 in-lb 9 5 189 lb 318 in 60,102 in-lb 169,344 in-lb 10 5 189 lb 318 in 60,102 in-lb 229,446 in-lb 11 6 189 lb 347 in 65,583 in-lb 295,029 in-lb 12 6 189 lb 347 in 65,583 in-lb 360,612 in-lb Table C-9. Comparison of Moments for Zone 2 Passenger No.
Cumulative Moment from the Zone Centroid Assumption Cumulative Moment From the Window-Aisle-Remaining Assumption Difference 7 60,102 in-lb 54,621 in-lb -5,481 in-lb 8 120,204 in-lb 109,242 in-lb -10,962 in-lb 9 180,306 in-lb 169,344 in-lb -10,962 in-lb 10 240,408 in-lb 229,446 in-lb -10,962 in-lb 11 300,510 in-lb 295,029 in-lb -5,481 in-lb 12 360,612 in-lb 360,612 in-lb 0 in-lb Figure C-3. Sample Passenger Seating Moment (Zone 2)
Appendix C C-6 C.3.3.3 Curtailment Calculation for Zone 3.
Table C-10. Moments Resulting From the Zone Centroid Assumption for Zone 3 Passenger No.
Assumed Weight Assumed Arm Moment Cumulative Moment 13 189 lb 411 in 77,679 in-lb 77,679 in-lb 14 189 lb 411 in 77,679 in-lb 155,358 in-lb 15 189 lb 411 in 77,679 in-lb 233,037 in-lb 16 189 lb 411 in 77,679 in-lb 310,716 in-lb 17 189 lb 411 in 77,679 in-lb 388,395 in-lb 18 189 lb 411 in 77,679 in-lb 466,074 in-lb 19 189 lb 411 in 77,679 in-lb 543,753 in-lb Table C-11. Moments Resulting From the Window-Aisle-Remaining Assumption for Zone 3 Passenger No.
Assumed Row Assumed Weight Assumed Arm Moment Cumulative Moment 13 7 189 lb 377 in 71,253 in-lb 71,253 in-lb 14 7 189 lb 377 in 71,253 in-lb 142,506 in-lb 15 8 189 lb 407 in 76,923 in-lb 219,429 in-lb 16 8 189 lb 407 in 76,923 in-lb 296,352 in-lb 17 9 189 lb 436 in 82,404 in-lb 378,756 in-lb 18 9 189 lb 436 in 82,404 in-lb 461,160 in-lb 19 9 189 lb 436 in 82,404 in-lb 543,564 in-lb Table C-12. Comparison of Moments for Zone 3 Passenger No.
Cumulative Moment from the Zone Centroid Assumption Cumulative Moment From the Window-Aisle-Remaining Assumption Difference 13 77,679 in-lb 71,253 in-lb -6,426 in-lb 14 155,358 in-lb 142,506 in-lb -12,852 in-lb 15 233,037 in-lb 219,429 in-lb -13,608 in-lb 16 310,716 in-lb 296,352 in-lb -14,364 in-lb 17 388,395 in-lb 378,756 in-lb -9,639 in-lb 18 466,074 in-lb 461,160 in-lb -4,914 in-lb 19 543,753 in-lb 543,564 in-lb -189 in-lb
Appendix C C-7 Figure C-4. Sample Passenger Seating Moment (Zone 3) C.3.3.4 Determining the Most Adverse Loading. It is important that an operator examine the above results (from Tables C-4 through C-12) for each zone and determine which loading scenario results in the greatest difference in moments. For zones 1 and 2, having two, three, or four passengers in the zone results in the largest difference between the moments. For zone 3, having four passengers in the zone results in the largest difference. In this case, the operator should curtail the manufacturer’s loading envelope forward and aft by the sum of these moments, 36,666 inch-pounds, to account for the potential variation in passenger seating. In this example, the 36,666 inch-pounds is the sum of 11,340 from Table C-6; 10,962 from Table C-9; and 14,364 from Table C-12.
C.3.3.5 Using Actual Seating Location. Alternatively, an operator may reasonably avoid the above curtailment calculations by determining the actual seating location of each passenger in the cabin. By eliminating potential variation in passenger seating, an operator would not need to make assumptions about passenger seating and would not need to curtail the loading envelope accordingly. An operator choosing to use actual seating location should have procedures in place to ensure that passengers sit in their assigned location.
Appendix C C-8 C.4 Other Curtailments to the Manufacturer’s Loading Envelope.
C.4.1 Variation in Passenger Weight. Because the operator in this example elects to use standard average weights on a small cabin aircraft, an additional curtailment for potential variation in passenger weight is required. The operator should curtail the manufacturer’s loading envelope as described in Appendix D, Additional Curtailment to CG Envelopes for Passenger Weight Variations in Small Cabin Aircraft.
C.4.2 Variation in Fuel Density. For this example, because the loading of fuel does not significantly change the CG of the aircraft, the operator would not need to provide a curtailment for variation in fuel density.
C.4.3 Fuel Movement in Flight. For this sample aircraft, the manufacturer has considered the movement of fuel in flight. Therefore, the operator does not need to include additional curtailments in the operational loading envelope.
C.4.4 Fluids. The sample aircraft does not have a lavatory or catering.
C.4.5 Bags and Freight. The sample aircraft has an aft bag compartment split into two sections.
If the operator has procedures in place to restrict the movement of bags between the two sections, no additional curtailment to the envelope is required.
C.4.6 In-Flight Movement of Passengers and Crewmembers. Because there are no F/As and the aircraft is not equipped with a lavatory, it is reasonable to assume that passengers or crewmembers will not move about the cabin in flight.
C.4.7 Movement of Flaps and Landing Gear. The manufacturer of the sample aircraft has considered the movement of flaps and landing gear in the development of its loading envelope. The operator does not need to include any additional curtailments in its operational loading envelope for the movement of those items.
C.4.8 Fuel Consumption. The fuel vector for the sample aircraft provides a small aft movement that requires a -8,900 inch-pounds curtailment to the aft zero fuel weight limits to ensure the aircraft does not exceed the aft limit as fuel is burned. This equates to a -0.8 inch curtailment at an estimated Basic Empty Weight (BEW) of 11,000 pounds with a linear transition to a -0.6 inch curtailment at maximum zero fuel weight (MZFW) of 16,155 pounds. In this example, the 8,900 inch-pounds is the fuel burn deviation that would bring the aircraft outside the aft CG limit during the course of flight.
C.5 Operational Loading Envelope Diagrams.
C.5.1 Figure C-5, Operational Loading Envelope With a Curtailment for Variations in Passenger Seating, shows the operator’s curtailments to the manufacturer’s loading envelope, based on the assumptions made about variations in passenger seating and weight, as well as fuel consumption.
Appendix C C-9 Figure C-5. Operational Loading Envelope With a Curtailment for Variations in Passenger Seating
9,000 10,000 11,000 12,000 13,000 14,000 15,000 16,000 17,000 18,000 272 276 280 284 288 292 296 300 304 Fuselage Station (Inches Aft of Datum) Weight (LBS) Max Ramp Weight Max Landing Weight Max Zero Fuel Weight Curtailment for Variations to Passenger Weight Curtailment for Fuel Burn Off Curtailment for Variations to Passenger Seating C .5.2 To expand the operational loading envelope, an operator could choose to use the actual seating location of passengers in the cabin and reduce the curtailment for variations in passenger seating. Figure C-6, Operational Loading Envelope Using Actual Seating Location of Passengers, below shows the expansion of the operational loading envelope.
Figure C-6. Operational Loading Envelope Using Actual Seating Location of Passengers 9,000 10,000 11,000 12,000 13,000 14,000 15,000 16,000 17,000 18,000 272 276 280 284 288 292 296 300 304 Fuselage Station (Inches Aft of Datum) Weight (LBS) Max Ramp Weight Max Landing Weight Max Zero Fuel Weight Curtailment for Variations to Passenger Weight Curtailment for Fuel Burn Off
Appendix D D-1 APPENDIX D. ADDITIONAL CURTAILMENT TO CG ENVELOPES FOR
PASSENGER WEIGHT VARIATIONS IN SMALL CABIN AIRCRAFT D.1 The use of average weights for small cabin aircraft requires consideration of an additional curtailment to the center of gravity (CG) envelope for passenger weight variations and male/female passenger ratio. This curtailment is in addition to the standard curtailments discussed in Chapter 2, Aircraft Weights and Loading Schedules, with examples in Appendix C, Sample Operational Loading Envelope.
D.1.1 Passenger weight variation is determined by multiplying the standard deviation (from the source of the average passenger weight used) by the row factor from Table D-1, Row Factor. The following table is a statistical measure that ensures a 95-percent confidence level of passenger weight variation, using the window-aisle-remaining seating method.
Table D-1. Row Factor No. of Rows 2-Abreast 3-Abreast 4-Abreast 2 2.96 2.73 2.63 3 2.41 2.31 2.26 4 2.15 2.09 2.06 5 2.00 1.95 1.93 6 1.89 1.86 1.84 7 1.81 1.79 1.77 8 1.75 1.73 1.69 9 1.70 1.68 1.65 10 1.66 1.65 1.62 11 1.63 1.59 1.59 12 1.60 1.57 1.57 13 1.57 1.54 1.54 14 1.55 1.52 1.52 15 1.53 1.51 1.51 16 1.49 1.49 1.49 17 1.48 1.48 1.48 18 1.46 1.46 1.46 D.1.2 Protect against the possibility of an all-male flight by subtracting the difference between the male and average passenger weight.
D.1.3 The sum of these two provides an additional weight to be used for CG curtailment, similar to the way in which passenger seating variation is calculated.
Appendix D D.2 Calculation of the curtailment passenger weight variation is decided by multiplying the standard deviation by the correction factor and adding the difference between the average male and average passenger weight. For example, assuming a 47-pound standard deviation, the difference between the average all-male and average passenger weight is 10 pounds (from 1999-2000 National Health and Nutrition Examination Survey (NHANES) data), and an aircraft with nine rows in a two-abreast configuration.
The additional weight to be curtailed is determined as follows:
Weight for Additional Curtailment = (47 × 1.70) + (10) = 90 lb.
D.2.1 For the example, the additional curtailment should be accomplished by assuming passenger loading at 90 pounds using the program method for passenger seating variation
(e.g., window-aisle-remaining). Using the window-aisle-remaining method, the additional curtailment in the example is determined to be 59,031 inch-pounds forward and aft.
Table D-2, Sample Curtailment Due to Variations in Passenger Weight and Male/Female Ratio Using Window-Aisle Method, displays the calculations used in this example.
Table D-2. Sample Curtailment Due to Variations in Passenger Weight and Male/Female Ratio Using Window-Aisle Method Passenger Weight: 90 Coach Class (Y) Cabin Centroid: 323.8 Forward Seating Aft Seating Seat Seat Total Total Moment Seat Seat Total Total Moment Row Centroid Moment Weight Moment Deviation Row Centroid Moment Weight Moment Deviation 1 198.0 17,820 90 17,820 -11,321 9 436.0 39,240 90 39,240 10.099
198.0 17,820 180 35,640 -22,642 9 436.0 39.240 180 78.480 20,198 2 228.0 20,520 270 56,160 -31,263 9 436.0 39,240 270 117,720 30.297 2 228.0 20,520 360 76.680 -39,884 407.0 36,630 360 154,350 37,786
258.0 23,220 450 99,900 45,805 407.0 36,630 450 190,980 45,275
258.0 23,220 540 123,120 -51,726 377.0 33,930 540 224,910 50,064 4 289.0 26.010 630 149,130 -54,857 377.0 33,930 630 258,840 54,853 4 289.0 26,010 720 175,140 -57,988 347.0 31,230 720 290.070 56,942 5 318.0 28.620 810 203,760 -58.509 6 347.0 31,230 810 321,300 59.031 5 318.0 28.620 900 232,380 -59,031 5 318.0 28.620 900 349,920 58,509 6 347.0 31,230 990 263,610 -56,942 5 318.0 28.620 990 378,540 57,988 6 347.0 31,230 1,080 294,840 -54,853 4 289.0 26.010 1,080 404,550 54,857
377.0 33,930 1,170 328,770 -50,064 289.0 26.010 1,170 430,560 51,726 7 377.0 33,930 1,260 362,700 45,275 3 258.0 23,220 1,260 453,780 45,805
407.0 36.630 1,350 399,330 -37,786 3 258.0 23,220 1,350 477,000 39,884
407.0 36.630 1,440 435,960 -30,297 2 228.0 20,520 1,440 497,520 31,263
436.0 39,240 1,530 475,200 -20,198 2 228.0 20,520 1,530 518,040 22,642 9 436.0 39,240 1,620 514,440 -10,099 1 198.0 17,820 1,620 535,860 11,321 9 436.0 39,240 1,710 553,680 1 198.0 17,820 1,710 553,680 D-2
Appendix D D-3 D.2.2 The following definitions describe the parameters used in the samples in Tables D-2 and D-3, Sample Curtailment Due to Variations in Passenger Weight and Male/Female Ratio Using Row Count Method:
• Seat Centroid: Location of passenger weight at seat.
• Seat Moment: Additional passenger weight × seat centroid.
• Total Weight: Sum of additional passenger weights (running total).
• Total Moment: Sum of additional passenger moments.
• Moment Deviation: Difference between total moment and moment generated by assuming additional passenger weight is located at the cabin centroid (323.8 in).
D.3 If the operator chooses to use the passenger cabin zone concept (as described in Appendix C) and apply this concept to account for variation in passenger weight, then the row factor in Table D-1 corresponding to the number of rows in each zone should be used.
D.3.1 Considering three cabin zones with each zone containing three rows in a two-abreast configuration, the required row factor (see Table D-1) is 2.41. The row factor is multiplied by the standard deviation and the difference between average all male and average passenger weights is added to provide the additional weight consideration. In our example, the standard deviation is calculated from the NHANES data as 47 pounds, and the difference between average all male and average passenger weights is 10 pounds.
The resulting additional weight for curtailment is 47 × 2.41 + 10 = 123 pounds. This additional weight is applied per the window-aisle-remaining concept for each cabin zone independently and the results are summed to determine the amount of curtailment. In this case, the curtailment is found to be 23,791 inch-pounds forward and aft.
D.3.2 If an operator chooses to use row count, the operator must use the row factor for two rows. In this example, the required row factor is 2.96 (see Table D-1). The row factor is multiplied by the standard deviation and the difference between average all male and average passenger weight is added to provide the additional weight consideration. In our example, the standard deviation is calculated from the NHANES data as 47 pounds, and the difference between average all male and average passenger weights is 10 pounds.
The resulting additional weight for curtailment is 47 × 2.96 + 10 = 149 pounds. This additional weight is applied as if a two-row passenger zone concept is used for passenger seating. The resulting curtailment is determined to be 17,880 inch-pounds forward and aft (see Table D-3).
Appendix D D-4 Table D-3. Sample Curtailment Due to Variations in Passenger Weight and Male/Female Ratio Using Row Count Method Coach Class (Y) Cabin Centroid (Rows 1-2): 213.0 Coach Class (Y) Cabin Centroid (Rows 3-4): 273.5 Coach Class (Y) Cabin Centroid (Rows 5-6): 332.5 Coach Class (Y) Cabin Centroid (Rows 7-8): 392.0 Passenger Weight: 149 Coach Class (Y) Cabin Centroid (Row 9): 436.0 Forward Seating Aft Seating Seat Seat Total Total Moment Seat Seat Total Total Moment Row Centroid Moment Weight Moment Deviation Row Centroid Moment Weight Moment Deviation 1 198.0 29,502 149 29,502 -2,235 9 436.0 64,964 149 64,964 0 1 198.0 29,502 298 59,004 -4,470 9 436.0 64,964 298 129,928 0 2 228.0 33,972 447 92,976 -2,235 9 436.0 64,964 447 194,892 0 2 228.0 33,972 596 126,948 0 8 407.0 60,643 149 60,643 2,235 3 258.0 38,442 149 38,442 -2,310 8 407.0 60,643 298 121,286 4,470 3 258.0 38,442 298 76,884 -4,619 7 377.0 56,173 447 177,459 2,235 4 289.0 43,061 447 119,945 -2,310 7 377.0 56,173 596 233,632 0 4 289.0 43,061 596 163,006 0 6 347.0 51,703 149 51,703 2,161 5 318.0 47,382 149 47,382 -2,161 6 347.0 51,703 298 103,406 4,321 5 318.0 47,382 298 94,764 -4,321 5 318.0 47,382 447 150,788 2,161 6 347.0 51,703 447 146,467 -2,161 5 318.0 47,382 596 198,170 0 6 347.0 51,703 596 198,170 0 4 289.0 43,061 149 43,061 2,310 7 377.0 56,173 149 56,173 -2,235 4 289.0 43,061 298 86,122 4,619 7 377.0 56,173 298 112,346 -4,470 3 258.0 38,442 447 124,564 2,310 8 407.0 60,643 447 172,989 -2,235 3 258.0 38,442 596 163,006 0 8 407.0 60,643 596 233,632 0 2 228.0 33,972 149 33,972 2,235 9 436.0 64,964 149 64,964 0 2 228.0 33,972 298 67,944 4,470 9 436.0 64,964 298 129,928 0 1 198.0 29,502 447 97,446 2,235 9 436.0 64,964 447 194,892 0 1 198.0 29,502 596 126,948 0 Sum of Minimum Moment Deviations -17,880 Sum of Maximum Moment Deviations 17,880
Appendix E E-1 APPENDIX E. OPTIONS TO IMPROVE ACCURACY A number of options are available that enable operators to deviate from standard assumed weights and may provide relief from constraints required when assumed averages are used.
These options include:
E.1 Surveys. Operators might conduct surveys for passenger weights, male/female ratios, and fuel densities. Operators might undertake surveys for entire operator route systems or by specific market or region. Survey practices and data reduction must conform to the requirements defined in this advisory circular (AC). Use of surveys may allow an operator to use passenger and baggage weights that accurately represent the operator’s business model. In addition, a survey may suggest that the assumed male/female ratio is incorrect and appropriate adjustments should be made. For example, let us assume the following results from an approved passenger and baggage survey.
Male passenger weight (M) = 183.3 pounds Female passenger weight (F) = 135.8 pounds Difference between male and average passenger weights = 24.0 pounds Standard deviation of total sample (Sigma) = 47.6 pounds Male/female ratio (Pax Ratio) = 50.6 percent Checked baggage weight = 29.2 pounds Baggage checked planeside = 21.3 pounds Carry-on and personal items weight (CO Wt) = 10.4 pounds Carry-on and personal items per passenger ratio (CO Ratio) = 0.82 pounds Survey conducted in summer months The resulting assumed passenger weight for loading is expressed as:
Passenger Weight = (M × Pax Ratio) + (F × (1 - Pax Ratio)) + (CO Wt × CO Ratio) And is determined as:
Summer Passenger Weight = (183.3 × 0.506) + (135.8 × (1 - 0.506)) +
(10.4 × 0.82) = 169 lb Winter Passenger Weight = 169 + 5 = 174 lb Survey results would also be used to determine the additional curtailment for variations to passenger weight. Assuming a 19-seat aircraft in 2-abreast configuration in our example, the additional weight to be curtailed would be:
Additional Weight for Curtailment = (47 × 1.70) + 24 = 104 lb Also in our example, the assumed surveyed checked baggage weight is 30 pounds. Planeside loaded bags would be assumed to weigh 20 pounds.
Appendix E E-2 E.2 Actual Weights. It is permissible to use actual weights in lieu of standard average, survey-derived average weights (if applicable). Parameters that may use actual weights include passenger weights, checked baggage weights, carry-on bag weights, crew weights, and fuel density/weight.
E.3 Passenger Cabin Zones and Row Count. Passenger cabins may be split up into zones, provided an acceptable procedure for determination of passenger seating is included
(e.g., use of seat assignments or the crew counts each seated passengers by zone). If zones are used, it may be reasonable for the operator to reduce the center of gravity (CG) passenger seating curtailment by accommodating variations within each individual zone separately and totaling the results. Passenger row count allows the operator to reduce the seating variation by accounting for the row in which the passenger is actually seated. An example of use of passenger zones follows.
Note: Assume an aircraft interior as displayed Figure E-1, Sample Aircraft Interior Seating Diagram.
Figure E-1. Sample Aircraft Interior Seating Diagram E .3.1 Assume that for Weight and Balance (W&B) purposes, it is desirable to break up the cabin into passenger zones. Appendix C, Sample Operational Loading Envelope, provides a sample calculation of curtailing for passenger seating variations using a hypothetical normal category 19-seat aircraft with 3 passenger zones. A more accurate W&B calculation requiring less curtailment may be provided by increasing the number of passenger zones. For example, an increase to five passenger zones would result in the following:
E.3.1.1 The passenger zones will be determined as zone 1 (rows 1−2), zone 2 (rows 3−4), zone 3 (rows 5−6), zone 4 (rows 7−8), and zone 5 (row 9). Use of the window-aisle-remaining method will be used in each zone to provide a total curtailment to the CG envelope. (For this sample aircraft, window-aisle-remaining method simply becomes forward and aft end
Appendix E E-3 loading). For each zone, a zone centroid must be calculated by counting the total number of seats and averaging their location:
• Zone 1 centroid = (2 x 198.0 + 2 x 228.0) / (2 + 2) = 213.0 in
• Zone 2 centroid = (2 x 258.0 + 2 x 289.0) / (2 + 2) = 273.5 in
• Zone 3 centroid = (2 x 318.0 + 2 x 347.0) / (2 + 2) = 332.5 in
• Zone 4 centroid = (2 x 347.0 + 2 x 377.0) / (2 + 2) = 392.0 in
• Zone 5 centroid = (3 x 436.0) / (3) = 436.0 in E.3.2 Assuming the standard winter passenger weight of 189 pounds (as determined in Appendix C) is used in the curtailment, the calculation of the total moment is required for comparison to the zone moment, assuming each passenger is seated at the centroid of each passenger zone. The total moment is found by summing the individual moments calculated at each occupied seat in the window-aisle-remaining progression.
Forward Curtailment CalculationsZone 1 Pax Row Arm Total Moment Zone Centroid Zone Moment Delta Moment 1 1 198.0 37,422 213.0 40,257 -2,835 2 1 198.0 74,844 213.0 80,514 -5,670 3 2 228.0 117,936 213.0 120,771 -2,835 4 2 228.0 161,028 213.0 161,028 0 Forward Curtailment CalculationsZone 2 Pax Row Arm Total Moment Zone Centroid Zone Moment Delta Moment 1 3 258.0 48,762 273.5 51,692 -2,930 2 3 258.0 97,524 273.5 103,383 -5,859 3 4 289.0 152,145 273.5 155,075 -2,930 4 4 289.0 206,766 273.5 206,766 0 Forward Curtailment CalculationsZone 3 Pax Row Arm Total Moment Zone Centroid Zone Moment Delta Moment 1 5 318.0 60,102 332.5 62,843 -2,741 2 5 318.0 120,204 332.5 125,685 -5,481 3 6 347.0 185,787 332.5 188,528 -2,741 4 6 347.0 251,370 332.5 251,370 0 Forward Curtailment CalculationsZone 4 Pax Row Arm Total Moment Zone Centroid Zone Moment Delta Moment 1 7 377.0 71,253 392.0 74,088 -2,835 2 7 377.0 142,506 392.0 148,176 -5,670 3 8 407.0 219,429 392.0 222,264 -2,835 4 8 407.0 296,352 392.0 296,352 0 Forward Curtailment CalculationsZone 5 Pax Row Arm Total Moment Zone Centroid Zone Moment Delta Moment 1 9 436.0 82,404 436.0 82,404 0 2 9 436.0 164,808 436.0 164,808 0 3 9 436.0 247,212 436.0 247,212 0