Appendix 4 APPENDIX 4. ADDITIONAL CURTAILMENTS TO CG ENVELOPES TO ACCOUNT
FOR VARIATIONS TO PASSENGER WEIGHTS
a. 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.
(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 4-1. The following table ensures a 95-percent confidence level of passenger weight variation, using the window-aisle-remaining seating method.
TABLE 4-1. 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 1.78 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
(2) Protect against the possibility of an all-male flight by subtracting the difference between the male and average passenger weight.
(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.
b. If the operator chooses to use the passenger cabin zone concept (as described in Appendix 3) and apply this concept to account for variation in passenger weight, then the row factor in Table 4-1 corresponding to the number of rows in each zone should be used. For the purposes of this curtailment, the zone can be no smaller than two rows, if row count is used for passenger seating calculations. Therefore, if an operator chooses to use row count, the operator must use the row factor for two rows.
Appendix 4
c. Calculation of the curtailment passenger weight variation is decided by multiplying the standard deviation by the correction factor and adding the difference between male and female passenger weight. For example, assuming a 47 pound standard deviation, the difference between the average passenger weight and an all-male weight is 10 pounds (from 1999–2000 National Health and Nutrition Examination Survey (NHANES) data), and a sample aircraft with 9 rows in a 2-abreast configuration. The additional weight to be curtailed is determined as:
Weight for Additional Curtailment = (47 × 1.70) + (10) = 90 lbs
d. 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 62,310 inch-pounds forward and aft. Table 4-2 displays the calculations used in this example.
NOTE: The following definitions describe the parameters used in the sample:
• 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)
Appendix 4 TABLE 4-2. SAMPLE CURTAILMENT DUE TO VARIATIONS IN PASSENGER
WEIGHT AND MALE/FEMALE RATIO USING WINDOW-AISLE METHOD Coach Class (Y) Cabin Centroid 323.8 Passenger Weight: 95 Forward Seating Aft Seating Seat Seat Total Total Moment Seat Seat Total Total Moment Centroid Moment Weight Moment Deviation Centroid Moment Weight Moment Deviation
198.0 18,810 95 18,810 -11,950 436.0 41,420 95 41,420 10,660
198.0 18,810 190 37,620 -23,900 436.0 41,420 190 82,840 21,320
228.0 21,660 285 59,280 -33,000 436.0 41,420 285 124,260 31,980
228.0 21,660 380 80,940 -42,100 407.0 38,665 380 162,925 39,885
258.0 24,510 475 105,450 -48,350 407.0 38,665 475 201,590 47,790
258.0 24,510 570 129,960 -54,600 377.0 35,815 570 237,405 52,845
289.0 27,455 665 157,415 -57,905 377.0 35,815 665 273,220 57,900
289.0 27,455 760 184,870 -61,210 347.0 32,965 760 306,185 60,105
318.0 30,210 855 215,080 -61,760 347.0 32,965 855 339,150 62,310
318.0 30,210 950 245,290 -62,310 318.0 30,210 950 369,360 61,760
347.0 32,965 1,045 278,255 -60,105 318.0 30,210 1,045 399,570 61,210
347.0 32,965 1,140 311,220 -57,900 289.0 27,455 1,140 427,025 57,905
377.0 35,815 1,235 347,035 -52,845 289.0 27,455 1,235 454,480 54,600
377.0 35,815 1,330 382,850 -47,790 258.0 24,510 1,330 478,990 48,350
407.0 38,665 1,425 421,515 -39,885 258.0 24,510 1,425 503,500 42,100
407.0 38,665 1,520 460,180 -31,980 228.0 21,660 1,520 525,160 33,000
436.0 41,420 1,615 501,600 -21,320 228.0 21,660 1,615 546,820 23,900
436.0 41,420 1,710 543,020 -10,660 198.0 18,810 1,710 565,630 11,950
436.0 41,420 1,805 584,440 0 198.0 18,810 1,805 584,440 0 -6.2 6.2
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Appendix 5 APPENDIX 5. OPTIONS TO IMPROVE ACCURACY A number of options are available that enable operators to deviate from standard assumed weights and may also provide relief from constraints required when assumed averages are used.
These options include:
(1) Surveys. Surveys may be accomplished for passenger weights (to include carry-on bags), checked baggage weights, male/female ratios and fuel densities. These surveys may be conducted for entire operator route systems, or by specific market or region. Surveys 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 less than the standard specified in this AC. Also, a survey may find that the assumed male/female ratio is incorrect and appropriate adjustments must be made. For example, let’s 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 plane-side = 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 = 0.506 × 183.3 + (1 - 0.506) × 135.8 + 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 = (47.6 × 1.70) + 24 = 104.9 lb
Also in our example, the assumed checked baggage weight is 30 pounds. Plane-side loaded bags would be assumed to weigh 20 pounds. (These weights are the standard average weights provided for a no-carry-on baggage program as described in Chapter 3, Section 2).
Appendix 5
(2) Actual Weights. It is permissible to use actual weights in lieu of standard average, segmented, or 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.
(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 crew counts 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 suggested in this AC by accommodating variations within each individual zone separately and totaling the results. Passenger row count allows the operator to eliminate the seating variation by accounting for where the passenger is actually seated.
An example of use of passenger zones follows.
Assume an aircraft interior as displayed in Figure 5-1.
FIGURE 5-1. SAMPLE AIRCRAFT INTERIOR SEATING DIAGRAM
(Diagram courtesy of Raytheon Aircraft Company)
Assume that for weight and balance purposes, it is desirable to break the cabin up into three passenger zones. The passenger zones will be determined as zone 1 (rows 1−3), zone 2 (rows 4−6), and zone 3 (rows 7−9). 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, windowaisle-remaining method simply becomes forward and aft end loading). For each zone, a zone centroid must be calculated by counting the total number of seats and averaging their location.
Appendix 5
Zone 1 centroid = (2 × 198.0 + 2 × 228.0 + 2 × 258.0) / (2 + 2 + 2) = 228.0 in.
Zone 2 centroid = (2 × 289.0 + 2 × 318.0 + 2 × 347.0) / (2 + 2 + 2) = 318.0 in.
Zone 3 centroid = (2 × 377.0 + 2 × 407.0 + 3 × 436.0) / (2 + 2 + 3) = 410.9 in.
Assuming the standard winter passenger weight of 195 pounds is used for the curtailment, the calculation of total moment is required for comparison to 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 38,610 228.0 44,460 -5,850 2 1 198.0 77,220 228.0 88,920 -11,700 3 2 228.0 121,680 228.0 133,380 -11,700 4 2 228.0 166,140 228.0 177,840 -11,700 5 3 258.0 216,450 228.0 222,300 -5,850 6 3 258.0 266,760 228.0 266,760 0
Forward Curtailment CalculationsZONE 2 Pax Row Arm Total Moment Zone Centroid Zone Moment Delta Moment 1 4 289.0 56,355 318.0 62,010 -5,655 2 4 289.0 112,710 318.0 124,020 -11,310 3 5 318.0 174,720 318.0 186,030 -11,310 4 5 318.0 236,730 318.0 248,040 -11,310 5 6 347.0 304,395 318.0 310,050 -5,655 6 6 347.0 372,060 318.0 372,060 0
Forward Curtailment CalculationsZONE 3 Pax Row Arm Total Moment Zone Centroid Zone Moment Delta Moment 1 7 377.0 73,515 410.9 80,117 -6,602 2 7 377.0 147,030 410.9 160,234 -13,204 3 8 407.0 226,395 410.9 240,351 -13,956 4 8 407.0 305,760 410.9 320,469 -14,709 5 9 436.0 390,780 410.9 400,586 -9,806 6 9 436.0 475,800 410.9 480,703 -4,903 7 9 436.0 560,820 410.9 560,820 0
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 -37,719 inch-pounds (-11,700 + -11,310 + -14,709).
Similarly, curtailment to the aft limit of the CG envelope using window-aisle-remaining method loading from the most aft seat row moving forward (in each zone) would result in an adjustment of 37,719 inch-pounds. Figures 5-2 through 5-4 graphically show the curtailments for each passenger zone through use of forward and aft end loading using our example.
Appendix 5 FIGURE 5-2. SAMPLE PASSENGER SEATING MOMENT
Sample Development of Passenger Seating Curtailment Cabin Zone 1 0 200 400 600 800 1000 1200 1400 275 280 285 290 295 300 Fuselage Station (Inches Aft of Datum) Passenger Weight - pounds Forward Seating Moment Aft Seating Moment Possible Seating Moment Variation within Passenger Cabin Zone
Appendix 5 FIGURE 5-3. SAMPLE PASSENGER SEATING MOMENT
Sample Development of Passenger Seating Curtailment Cabin Zone 2 0 200 400 600 800 1000 1200 1400 275 280 285 290 295 300 Fuselage Station (Inches Aft of Datum) Passenger Weight - pounds Forward Seating Moment Aft Seating Moment Possible Seating Moment Variation within Passenger Cabin Zone
Appendix 5 FIGURE 5-4. SAMPLE PASSENGER SEATING MOMENT
Sample Development of Passenger Seating Curtailment Cabin Zone 3 0 200 400 600 800 1000 1200 1400 1600 275 280 285 290 295 300 Fuselage Station (Inches Aft of Datum) Passenger Weight - pounds Forward Seating Moment Aft Seating Moment Possible Seating Moment Variation within Passenger Cabin Zone
(4) Actual M/F Counts. Loading systems may use separate male and female assumed passenger weights for each operation. If the operator’s weight and balance 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 as described in this AC or they may be determined through an operator-developed survey as also described in this AC. Use of male/female weights may be for entire operations or for a particular route and/or region of flying.
An example of how male/female ratios can be applied to weight and balance systems follows.
Assuming the operator is using the survey results as described in subparagraph (1) above, the assumed male and female passenger weights, including 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 Page 6
Appendix 5
The weight and balance 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.
(5) Adolescent (Child) Weights. In most circumstances, an operator may consider any passenger less than 13 years of age, who is occupying a seat, to weigh less than an adult passenger as described in this AC. The standard adolescent child weights can be found in Table 3-1 of Chapter 3.
(6) Standard Weights with Approved No-Carry-on Baggage Program.
Summer Passenger Weight = 184 lb Winter Passenger Weight = 189 lb Checked Baggage Weight = 30 lb each Baggage Checked Plane-side = 20 lb each
Inclusion in the no-carry-on baggage program does not preclude use of actual or surveyed weights for passengers, carry-on/personal items, checked baggage, or baggage checked planeside.
(7) Automation. Automation may also be used to provide a more accurate weight and balance program. Examples of automation include use of seat assignments for the determination of passenger moment and historical seating to determine passenger moment.
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