Appendix 4 APPENDIX 4. TAKEOFF PERFORMANCE BASED METHOD EXAMPLE, continued
(2) In the weight range of 250,000 pounds to 350,000 pounds, the applicant sees that a change in weight of 10,000 pounds results in a 2.5 knot change in V2 and that this relationship holds across the mid-weight band.
(3) In the weight range of 350,000 to 430,000 pounds, the applicant sees that a change in weight of 10,000 pounds results in a 2 knot change in V2 and that this relationship holds across the high-weight band.
c. The OBWBS accuracies that result in at most a ± 1.5 -knot change in V2 in each band are therefore:
• ± 1.5 knot change × (10,000 pounds/ 2.75 knot change) = ± 5,454 pounds in the low- weight band, or ± 5400 pounds with rounding. This weight offset corresponds to an OBWBS weight accuracy of 2.7% at 200,000 pounds to 2.16% accuracy at 250,000 pounds over the low-weight band.
• ± 1.5 knot change × (10,000 pounds/ 2.5 knot change) = ± 6,000 pounds in the mid-weight band. This weight offset corresponds to an OBWBS weight accuracy of 2.4% above 250,000 pounds to 1.71% accuracy at 350,000 pounds over the mid-weight band.
• ± 1.5 knot change × (10,000 pounds/ 2 knot change) = ± 7,500 pounds in the high- weight band. This weight offset corresponds to an OBWBS weight accuracy of 2.14% above 350,000 pounds to 1.74 % accuracy at 430,000 pounds over the high-weight band.
d. Once again, the applicant can fit a curve across these bands in order to smooth out the discontinuities or jumps in weights at the band edges.
4-4. THE EFFECT OF WEIGHT CHANGE ON TAKEOFF/ACCELERATE-STOP DISTANCE.
a. For an uncorrected (i.e., no runway slope, no wind) takeoff at flaps 5, the applicant determines from AFM data that at the most extreme all-engines-operating takeoff distance situation, a change in 5000 pounds of weight in the high-weight band means a 500 foot difference in takeoff distance, and for less extreme conditions, a change of 5,000 pounds in weight means a change of up to 400 feet in the all-engines-operating takeoff distance across the low-weight to mid-weight bands.
b. The OBWBS accuracies that result in at most a 100-foot increase in the all-engine takeoff distance are therefore on the order of:
• ± 100 foot change × (5,000 pounds / 400 foot change) = ± 1,250 pounds or ± 1,300 pounds after rounding. This weight offset corresponds to an OBWBS weight accuracy of 0.52 % above 250,000 pounds to 0.37% accuracy at 350,000 pounds over the low to mid-weight band.
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Appendix 4 APPENDIX 4. TAKEOFF PERFORMANCE BASED METHOD EXAMPLE, continued
• ± 100 foot change × (5,000 pounds / 500 foot change) = ± 1,000 pounds in the most extreme takeoff distance situation. This weight offset corresponds to an OBWBS weight accuracy of 0.29% above 350,000 pounds to 0.23% accuracy at 430,000 pounds over the highweight band.
4-5. OBWBS OPERATIONAL ACCURACY AND OBWBS-MEASURED WEIGHT CURTAILMENT.
a. OBWBS operational accuracies that result in at most a ± 1.5-knot error or change in V1 or V2, or a 100 foot increase in takeoff or accelerate-stop distance, whichever is greater, are accepted without curtailments or procedural adjustments for OBWBS accuracy.
b. The applicant notes that the weight changes in paragraph 4-4 of this appendix that result in more than a 100 foot change in takeoff/accelerate-stop distance all result in less than a ± 1.5-knot change in V1 or V2 (see paragraphs 4-2 and 4-3 of this appendix, respectively).
Therefore the weight change that results in a 100 foot change to the takeoff/accelerate-stop distances does not set the maximum operational accuracy for OBWBS use without curtailment.
c. The applicant notes that the weight changes in paragraph 4-3 of this appendix that result in a 1.5-knot change in V2 will change V1 by more than 1.5 knots (see paragraph 4-2 of this appendix). Therefore, the weight cha nge that results in a 1.5-knot change in V2 does not set the maximum operational accuracy for OBWBS use without curtailment.
d. The applicant notes that the weight changes in paragraph 4-2 of this appendix that result in a 1.5-knot change in V1 will not change V2 by more than 1.5 knots (see paragraph 4-3 of this appendix). Therefore, the weight cha nge that results in a 1.5-knot change in V1 does set the maximum operational accuracy for OBWBS use without curtailment.
e. Therefore, the applicant concludes that the reported weights from the OBWBS can be used without curtailment for OBWBS operational accuracy as long as the OBWBS-reported weight is within:
• ± 4,300 pounds of the actual airplane weight in the low-weight band.
• ± 5,000 pounds of the actual airplane weight in the mid-weight band.
• ± 6,000 pounds of the actual airplane weight in the high-weight band.
f. In general, the required OBWBS weight accuracy can be expressed in terms of the ratio of these weight uncertainties per band to the actual airplane weight in that band.
g. For example, at an actual weight of 200,000 pounds the OBWBS operational accuracy needs to be ± 2.15 % to use the reported weight without operational curtailment, and for an actual weight of 430,000 pounds the OBWBS operational accuracy needs to be ± 1.4 % to use the reported weight without operational curtailment for OBWBS accuracy.
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Appendix 4 APPENDIX 4. TAKEOFF PERFORMANCE BASED METHOD EXAMPLE, continued
h. Now, per the guidance in paragraph 2-2.d(3) of this AC, the applicant determines the OBWBS system accuracy by obtaining weight and CG measurements from the aircraft while it sits on precision aircraft scales within a controlled environment such as hanger.
i. Suppose for example the OBWBS-reported weight during the system accuracy testing is within:
• ± 1,000 pounds of the actual airplane weight in the low-weight band.
• ± 2,000 pounds of the actual airplane weight in the mid-weight band.
• ± 2,500 pounds of the actual airplane weight in the high-weight band.
j. Then the applicant knows that operational conditions such as configuration changes, wind gusts and winds, temperature changes, passenger movement, etc., can result in up to the following weight errors before the need to curtail the weight and CG envelope for the operational accuracy of the OBWBS:
• ± 3,300 pounds of additional uncertainty about the actual airplane weight in the low-weight band,
• ± 3,000 pounds of additional uncertainty about the actual airplane weight in the mid-weight band, and
• ± 3,500 pounds of additional uncertainty about the actual airplane weight in the high-weight band.
k. Alternatively, if the measured OBWBS system accuracies in these weight bands exceed the weight accuracies resulting in no more than 1.5-knot change in V1, the OBWBS cannot be used without curtailment for OBWBS accuracy at any time.
l. This example illustrates the importance of the OBWBS system accuracy. The better the system accuracy, in general, the larger the operational environment within which the applicant may use the OBWBS system weight measurements without curtailment for OBWBS accuracy.
4-6. CONCLUSIONS.
a. This example shows how an applicant can map out an analysis approach to systematically consider the effect of weight changes on V1, V2 and takeoff/accelerate-stop distances. This analysis determines the operational accuracies that result in at most a ± 1.5 -knot error or change in V1 or V2, or a 100 foot increase in takeoff or accelerate-stop distance, Page A4-5
Appendix 4 APPENDIX 4. TAKEOFF PERFORMANCE BASED METHOD EXAMPLE, continued whichever is greater, which can be accepted without curtailments or procedural adjustments for OBWBS accuracy. OBWBS operational accuracies that result in greater than ± 1.5 knot error or change in V1 or V2, or more than a 100 feet increase in takeoff or accelerate-stop distance, whichever is greater, require appropriate curtailment for OBWBS accuracy.
b. The analysis method shown in this example can be readily modified to consider the effects of pressure altitude, outside air temperature, winds, and runway slope, as appropriate, when determining the relationship of change in weight to change in takeoff/accelerate-stop distance.
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