Aviation Theory Centre, Basic Aeronautical Knowledge, Question 53

atc-bak-question-53.md

ATC Basic Aeronautical Knowledge

Question 53

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We are given

Aircraft	Value
BEW	695kg
Moment	19788IU
MTOW	1115kg
MTOWutility	925kg
Fuel arm	2950IU
Baggage arm	4210IU
Row 1 arm	2750IU
Row 2 arm	3600IU
Oil arm	1230IU

Flight	Value
Pilot	60kg
Instructor	75kg
PAX	none
Baggage	none

• Aircraft empty weight includes unusable fuel and undrainable oil
• All arms in mm aft of datum
• 1 IU = 100kg/mm
• Avgas Specific Gravity = 0.71kg/L
• Maximum baggage = 122kg

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We are asked

The maximum amount of fuel on board that will allow "utility category" operations immediately after take-off is closest to:

• 62 litres
• 88 litres
• 100 litres
• 123 litres
• 135 litres

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Working out

• Known rule: Weight * Arm = Moment

Initial table of known values

Name	Weightkg	Armmm	Moment100kg/mm
Aircraft	695		19788
Oil	7	1230
Row 1	135	2750
Row 2	0	3600
Bag	0	4210

Calculate gaps using Known Rule

• Aircraft arm_mm: (19788 * 100) / 695 = 2847 (irrelevant)
• Oil moment_100kg/mm: (7 * 1230) / 100 = 86
• Row 1 moment_100kg/mm: (135 * 2750) / 100 = 3713
• Row 2 moment_100kg/mm: (0 * 3600) / 100 = 0
• Bag moment_100kg/mm: (0 * 4210) / 100 = 0

Name	Weightkg	Armmm	Moment100kg/mm
Aircraft	695	2847	19788
Oil	7	1230	86
Row 1	135	2750	3713
Row 2	0	3600	0
Bag	0	4210	0

Calculate Zero Fuel Weight (ZFW)

• ZFW_kg = 695 + 7 + 135 + 0 + 0 = 837
• ZFW moment_100kg/mm = 19788 + 86 + 3713 + 0 + 0 = 23587

Name	Weightkg	Armmm	Moment100kg/mm
Aircraft	695	2847	19788
Oil	7	1230	86
Row 1	135	2750	3713
Row 2	0	3600	0
Bag	0	4210	0
ZFW	837		23587

Add fuel from ZFW to MTOW

• insert maximum fuel up to MTOW
• MTOW_utility is given 925kg
• insert fuel_kg: 925 - 837 = 88
• Fuel arm is given 2950IU
• Apply Known Rule to determine fuel moment_100kg/mm
  • 88 * 2950 / 100 = 2596

Name	Weightkg	Armmm	Moment100kg/mm
Aircraft	695	2847	19788
Oil	7	1230	86
Row 1	135	2750	3713
Row 2	0	3600	0
Bag	0	4210	0
ZFW	837		23587
Fuel	88	2950	2596

Calculate All Up Weight (AUW)

• AUW_kg = 837 + 88 = 925
• AUW moment_100kg/mm = 23587 + 2596 = 26183
• AUW arm_mm = (AUW moment * 100) / AUW
• AUW arm_mm = (26183 * 100) / 925 = 2830

Name	Weightkg	Armmm	Moment100kg/mm
Aircraft	695	2847	19788
Oil	7	1230	86
Row 1	135	2750	3713
Row 2	0	3600	0
Bag	0	4210	0
ZFW	837		23587
Fuel	88	2950	2596
AUW	925	2830	26183

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Determine if we are in weight and balance

Weight

• AUW = 925kg
• MTOW_utility = 925kg
• Is AUW less than or equal to MTOW_utility? Yes
• Is our baggage weight less than or equal to maximum baggage? Yes
• Therefore, we are within weight

Balance

• Using the loading chart, plot the AUW (925kg) against the AUW arm (2830mm)
• Does the point X fall within the Utility Category? Yes
• Therefore, we are within balance

Final determination of answer

• We may carry 88kg of fuel and remain within weight and balance
• Avgas Specific Gravity is given 0.71kg/L
• Calculate the quantity_litres of 88kg of fuel
• 88 / 0.71 = 123.9
• Potential answers_litres [62, 88, 100, 123, 135]

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Therefore, the answer is 123 litres

That is the Answer I got however in the text book answer 53 says D which is 123 liters.
Edit the answer is 123 liters because kg is always the less amount than fuel its 88 Divided .71 = 123

You're right, I'll update. I think I was documenting an error that was made. Thanks!