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
Appendix E E-4 The curtailment for passenger seating variation is determined by adding the largest delta moments from each of the passenger zones. In our example, the curtailment to the forward CG limit for passenger seating variation is -22,680 inch-pounds (-5,670 + -5,859 + -5,481 + -5,670 + 0). Similarly, the curtailment to the aft limit of the CG envelope using the window-aisle-remaining method loading from the most aft seat row moving forward (in each zone) would result in an adjustment of +22,680 inch-pounds. These curtailments compare favorably to the curtailments of + 36,666 inch-pounds determined in the sample provided for three passenger zones in Appendix C.
E.4 Actual Male/Female Counts. Loading systems may use separate male and female assumed passenger weights for each operation. If the operator’s W&B program is approved for use of male/female weights, then the operator must count the number of male passengers and female passengers separately. The male and female weights used may be from the development of standard passenger weight or they may be determined through an operator-developed survey. Use of male/female weights may be for entire operations or for a particular route or region.
E.5 Male/Female Ratios. An example of how male/female ratios can be applied to W&B systems follows.
E.5.1 Assuming the operator is using the survey results as described in paragraph E.1 above, the assumed male and female passenger weights, including surveyed average carry-on baggage, are computed as:
Male passenger weight (summer) = 183.3 + 10.4 × 0.82 = 192 lb Male passenger weight (winter) = 192 + 5 = 197 lb Female passenger weight (summer) = 135.8 + 10.4 × 0.82 = 144 lb Female passenger weight (winter) = 144 + 5 = 149 lb E.5.2 The W&B manifest would provide for identification of male/female identification and the passenger weights would be summed accordingly. For instance, 7 male and 11 female passengers would result in a total passenger weight of (7 × 192) + (11 × 144) = 2,928 pounds.
E.6 Adolescent (Child) Weights. In most circumstances, an operator may consider any passenger who is younger than 13 years old and is occupying a seat to weigh less than an adult passenger. The standard average adolescent child weights can be calculated utilizing Table 3-1, Example of Standard Average Passenger Weights, and the latest CDC/NHANES report.
E.7 Automation. Automation may also be used to provide a more accurate W&B program.
Examples of automation include use of seat assignments for the determination of passenger moment and historical seating to determine passenger moment.
Appendix F F-1 APPENDIX F. WEIGHT AND BALANCE CHECKLIST Which operators should use this AC? See paragraph 1.2.
Does the operator use individual aircraft Basic Empty Weights (BEW) or Fleet Operating Empty Weights (FOEW)? See paragraph 2.1.3.
Does the operator have an individual aircraft weighing program or a fleet weighing program?
See paragraph 2.1.4.
Each operator should construct a loading envelope with curtailments. See Chapter 2, paragraphs 2.2 and 2.3.
What is the aircraft cabin size? See paragraph 1.2.2 and Table 1-1, Aircraft Cabin Size.
a. If the aircraft is a large cabin aircraft, then see paragraph 3.1.1.4:
Large Cabin Aircraft
1. For standard average weights, see paragraph 3.2.
2. For survey-derived average weights, see paragraph 3.3.
3. For actual weight programs see paragraph 3.4.
b. If the aircraft is a medium cabin aircraft, then see paragraph 3.1.1.5:
Medium Cabin Aircraft Treated as Large
1. See Large Cabin Aircraft items 1−3 above, and Medium Cabin Aircraft Treated as Small
1. See Small-Cabin Aircraft items 1−2 below.
c. If the aircraft is a small cabin aircraft, then see paragraph 3.1.1.6:
Small Cabin Aircraft
1. If the aircraft meets the performance criteria stated in item 2 under paragraph 3.1.1.6,
a. See paragraph 3.1 for standard average weights and Appendix D, Additional Curtailment to CG Envelopes for Passenger Weight Variations in Small Cabin Aircraft, for additional center of gravity (CG) envelope curtailment, or
b. See paragraph 2.3 for survey-derived average weights and Appendix D for additional CG envelope curtailment.
2. If the aircraft does not meet the performance criteria stated in item 2 under paragraph 3.1.1.6 or the operator elects to use actual weights, then:
a. For actual weight programs see paragraph 3.4.
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