Flight Science 1: Chapter 11 Quiz

(Refer to Figure 60.) How should the 500-pound weight be shifted to balance the plank on the fulcrum?

1 inch to the left. 1. Find the moments left and right of the fulcrum, and set them equal to one another. left = right 500(X) = 250(20) + 200(15) 500X = 8,000 X = 16 inches 2. The 500-pound weight must be 16 inches from the fulcrum to be in balance. It is currently located at 15 inches, therefore the weight should be shifted 1 inch to the left.

(Refer to Figure 34.) What is the maximum amount of baggage that may be loaded aboard the airplane for the CG to remain within the moment envelope?WEIGHT (LB) MOM/1000Empty weight 1,350 51.5Pilot and front passenger 250 --Rear passengers 400 --Baggage -- --Fuel, 30 gal -- --Oil, 8 qt -- -0.2

105 pounds. Use the following steps: 1. Find total weight and moment index (except baggage) by using the loading graphs in FAA Figure 34. Note that the reduction factor is 1,000 in this problem. The standard weight for gasoline is 6 lbs/U.S. gallon, and for oil, 7.5 lbs/U.S. gallon. Item Weight Moment/1,000 B.E.W. 1,350 lbs 51.5lbs-in Pilot & Pax (a) 250 lbs 9.3 lbs-in Rear Pax (b) 400 lbs 29.3 lbs-in Fuel (30 x 6) (c) 180 lbs 8.7 lbs-in Oil 15 lbs -0.2 lbs-in Total 2,195 lbs 98.6 lbs-in 2. Calculate the maximum allowable weight for baggage: 2,300 - 2,195 = 105 pounds 3. Add baggage and calculate the new totals for weight and moment index. Weight Moment/1,000 2,195 lbs 98.6 lbs-in + 105 lbs 10.0lbs-in 2,300 lbs 108.6 lbs-in 4. Plot the position of the point determined by 2,300 pounds and the moment of 108.6 lbs-in/1,000 on the center of gravity moment envelope graph. The point is in the normal category envelope.

If an aircraft is loaded 90 pounds over maximum certificated gross weight and fuel (gasoline) is drained to bring the aircraft weight within limits, how much fuel should be drained?

15 gallons. 1. Determine the total weight to be removed (90 pounds) and the weight per gallon of gasoline (6 pounds). 2. Calculate the amount of gasoline to be drained using the formula: Gallons = Pounds ÷ Pounds/Gallon or: 90 ÷ 6 = 15 gallons ^

(Refer to Figures 32 and 33.) Determine if the airplane weight and balance is within limits. Front seat occupants 340 lb Rear seat occupants 295 lb Fuel (main wing tanks) 44 gal Baggage 56 lb

20 pounds overweight, CG within limits. When multiplying a weight by its arm you must divide by 100 to get moment index (Moment/100). Moments listed in FAA Figures 32 and 33 are already divided by 100, and are therefore moment indexes. 1. Calculate weight and moment index using the information from the question and from FAA Figures 32 and 33 and the formula: Weight x Arm ÷ 100 = Moment/Index Item Weight Arm Moment/100 Empty weight 2,015 lbs 1,554.0 lbs-in Front seat 340 lbs 85 289.0 lbs-in Rear seat 295 lbs 121 357.0 lbs-in Fuel (44 x 6) 264 lbs 75 198.0 lbs-in Baggage 56 lbs 140 78.4 lbs-in Total 2,970 lbs 2,476.4 lbs-in 2. Consult the Moment Limits vs. Weight Table, FAA Figure 33. The aircraft weight is 2,970 pounds or 20 pounds in excess of the maximum weight on the chart. The moment of 2,476.4 lbs-in would be within limits if the chart went to 2,970 pounds gross weight. ^

(Refer to figure 61.) If 50 pounds of weight is located at point X and 100 pounds at point Z, how much weight must be located at point Y to balance the plank?

300 pounds. Find the moments left and right of the fulcrum, and set them equal to one another. Left = right 50(50) + Y(25) = 100(100) 2,500 + 25Y = 10,000 Y = 300 pounds

(Refer to Figure 34.) What is the maximum amount of fuel that may be aboard the airplane on takeoff if loaded as follows?WEIGHT (LB) MOM/1000Empty weight 1,350 51.5Pilot and front passenger 340 --Rear passengers 310 --Baggage 45 --Oil, 8 qt -- --

40 gallons. 1. Find the total weight and moment index (except fuel) by using the loading graph in FAA Figure 34. Item Weight Moment/1,000 B.E.W. 1,350 lbs 51.5 lbs-in Pilot & Pax (a) 340 lbs 12.6 lbs-in Rear Pax (b) 310 lbs 22.6 lbs-in Baggage (c) 45 lbs 4.2 lbs-in Oil (d) 15 lbs -0.2 lbs-in Total 2,060 lbs 90.7 lbs-in 2. Calculate the additional fuel weight which can be added: 2,300 - 2,060 = 240 lbs 3. Calculate the number of gallons of fuel at 6 lbs/gallon: 240 ÷ 6 = 40 gallons 4. Calculate the added fuel moment index from the graph (40 gal fuel - 11.5 MOM/1,000). 5. Calculate the new total weight and moment index: Weight Moment/1,000 2,060 lbs 90.7 lbs-in + 240 lbs 11.5 lbs-in 2,300 lbs 102.2 lbs-in 6. Plot the position of the point determined by 2,300 pounds and a moment index of 102.2 lbs-in/1,000. The point lies on the normal category envelope.

(Refer to Figures 32 and 33.) What is the maximum amount of baggage that can be carried when the airplane is loaded as follows? Front seat occupants 387 lb Rear seat occupants 293 lb Fuel 35 gal

45 pounds. 1. When multiplying a weight times its arm you must divide by 100 to get moment index. Calculate total weight and total moment index using the information from the question and from FAA Figures 32 and 33 and the formula: Weight x Arm ÷ 100 = Moment/Index Item Weight Arm Moment/100 Empty weight 2,015 lbs 1,554.0 lbs-in Front seat 387 lbs 85 329.0 lbs-in Rear seat 293 lbs 121 354.5 lbs-in Fuel (35 x 6) 210 lbs 75 157.5 lbs-in Total 2,905 lbs 2,395.0 lbs-in 2. The maximum takeoff weight is 2,950 pounds. Calculate what the allowed baggage weight would be: 2,950 - 2,905 = 45 pounds 3. Verify that the CG would remain within the allowable range with this much baggage by calculating the new weight and moment index. Item Weight Arm Moment/100 Original total 2,905 lbs 2,395.0 lbs-in Baggage + 45 lbs 140 + 63.0 lbs-in New Total 2,950 lbs 2,458.0 lbs-in 4. Consult the Moment Limit vs. Weight Table, FAA Figure 33. For a weight of 2,950 pounds, the range of allowable moments is 2,422 to 2,499. The new total moment index of 2,458.0 is acceptable.

(Refer to Figure 34.) Determine the aircraft loaded moment and the aircraft category. WEIGHT (LB) MOM/1000Empty weight 1,350 51.5Pilot and front passenger 380 --Fuel, 48 gal 288 --Oil, 8 qt -- --

79.2, normal category. Use the following steps: 1. Find the total weight and moment index by using the loading graph from FAA Figure 34. Item Weight Moment/1,000 B.E.W. 1,350 lbs 51.5 lbs-in Pilot & Pax (a) 380 lbs 14.0 lbs-in Fuel (b) 288 lbs 13.8 lbs-in Oil (c) 15 lbs -0.2 lbs-in Total 2,033 lbs 79.1 lbs-in 2. Plot the position of the point determined by 2,033 lbs. and a moment of 79.1 lbs-in/1,000. The point is within the normal category envelope.

(Refer to Figures 32 and 33.) Calculate the weight and balance and determine if the CG and the weight of the airplane are within limits.Front seat occupants 350 lbRear seat occupants 325 lbBaggage 27 lbFuel 35 gal

CG 83.4, within limits. Use the following steps: 1. Calculate weight and moment index using the information from the problem and from FAA Figures 32 and 33 and the formula: Weight x Arm ÷ 100 = Moment/Index Item Weight Arm Moment/100 Empty weight 2,015 lbs 1,554.0 lbs-in Front seat 350 lbs 85 297.5 lbs-in Rear seat 325 lbs 121 393.3 lbs-in Baggage 27 lbs 140 37.8 lbs-in Fuel (35 x 6) 210 lbs 75 157.5 lbs-in Total 2,927 lbs 2,440.1 lbs-in 2. Calculate the position of CG using the formula: CG = Total Mom Ind ÷ Total Weight x Reduction Factor or: CG = 2,440.1 ÷ 2,927 x 100 = 83.4 inches aft of datum ^

GIVEN:WEIGHT ARM MOMENT(LB) (IN) (LB-IN)Empty weight 1,495.0 101.4 151,593.0Pilot and passengers 380.0 64.0 --Fuel (30 gal usable-no reserve) -- 96.0 --The CG is located how far aft of datum?

CG 94.01. 1. Compute the total weight and moment using the formula: Weight x Arm = Moment or: Item Weight Arm Moment Empty weight 1,495.0 101.4 151,593.0 Pilot & passenger 380.0 64.0 24,320.0 Fuel (30 x 6) 180.0 96.0 17,280.0 Total 2,055.0 lbs 193,193.0 2. Compute the center of gravity using the formula: CG = Total Moment ÷ Total Weight or: CG = 193,193 ÷ 2,055 = 94.01 inches aft of datum

(Refer to Figures 32 and 33.) Which action can adjust the airplane's weight to maximum gross weight and the CG within limits for takeoff?Front seat occupants 425 lbRear seat occupants 300 lbFuel, main tanks 44 gal

Drain 9 gallons of fuel. Use the following steps: 1. Calculate the original weights and moment index using the information from the problem and FAA Figures 32 and 33, and the formula: Weight x Arm ÷ 100 = Moment/Index Item Weight Arm Moment/100 Empty weight 2,015 lbs 1,554.0 lbs-in Front seat 425 lbs 85 361.3 lbs-in Rear seat 300 lbs 121 363.0 lbs-in Fuel (44 x 6) 264 lbs 75 198.0 lbs-in Total 3,004 lbs 2,476.3 lbs-in 2. If the aircraft has a maximum allowable takeoff weight of 2,950 lbs, compute the weight to be removed to reach an acceptable takeoff weight. 3,004 - 2,950 = 54 pounds 3. Compute the amount of fuel (in gallons) that totals 54 lbs: 54 ÷ 6 = 9 gallons 4. Compute the revised weight and moment index: Item Weight Arm Moment/100 Original totals 3,004 lbs 2,476.3 lbs-in Fuel - 54 lbs 75 - 40.5 lbs-in New Total 2,950 lbs 2,435.8 lbs-in 5. Consult the Moment Limits vs. Weight Chart. At 2,950 lbs takeoff weight, 2435.8 is within the Moment Limits.

(Refer to Figure 67.) What effect does a 30-gallon fuel burn have on the weight and balance if the airplane weighed 2,784 pounds and the MOM/100 was 2,222 at takeoff?

Moment will decrease to 2,087 lbs-in. The original CG is 2,222 / 2,784 = 79.8. Figure 67 includes a table summarizing fuel weights and moments. Burning 30 gallons of fuel will result in a 180-pound reduction, making the new airplane weigh 2604 pounds (2,784 - 180). The moment is reduced by 135, making the new MOM/100 = 2,087 (2,222 - 135). The new CG is 2,087 / 2604 = 80.1. Answer (A) is incorrect because the CG will increase from 79.8 to 80.1. Answer (B) is incorrect because 2,357 is an increase of 135 lbs-in.

(Refer to Figures 32 and 33.) Upon landing, the front passenger (180 pounds) departs the airplane. A rear passenger (204 pounds) moves to the front passenger position. What effect does this have on the CG if the airplane weighed 2,690 pounds and the MOM/100 was 2,260 just prior to the passenger transfer?

The CG moves forward approximately 3 inches. Use the following steps: 1. Consider the effect on the total weight. Item Weight Original weight 2,690 pounds Deplaned passenger -180 pounds New Weight 2,510 pounds 2. Consider the effect on the total moment index using the arms given in FAA Figure 32, and the formula: Weight x Arm ÷ 100 = Moment/Index Item Weight Arm Moment/100 Original weight & Mom Ind 2,690 2,260.0 lbs-in Passenger exiting, front -180 85 -153.0 lbs-in Passenger exiting, rear -204 121 -246.8 lbs-in Passenger into front + 204 85 + 173.4 lbs-in New Total Weight & Moment 2,510 2,033.6 lbs-in 3. Determine both the original and new CG using the formula: CG = Total Mom Ind ÷ Total Weight x Reduction Factor or: a. Original CG = 2,260 ÷ 2,690 x 100 = 84.0 inches aft of datum b. New CG = 2,033.6 ÷ 2,510 x 100 = 81.0 inches aft of datum 4. Calculate the change in CG: 84 - 81 = 3 inches (forward)

(Refer to Figures 32 and 33.) What effect does a 35-gallon fuel burn (main tanks) have on the weight and balance if the airplane weighed 2,890 pounds and the MOM/100 was 2,452 at takeoff?

Weight is reduced by 210 pounds and the CG is aft of limits. Use the following steps: 1. Calculate the change in both weight and moment index caused by a burn of 35 gallons, using the information from FAA Figures 32 and 33. Weight x Arm ÷ 100 = Moment/Index Item Weight Arm Moment Fuel (35 x 6) 210 lbs 75 158 lbs-in 2. Determine the effect of burn on total weight and moment index: Item Weight Arm Moment/100 Original total 2,890 lbs 2,452.0 lbs-in Fuel burn - 210 lbs 75 - 158.0 lbs-in New Total 2,680 lbs 2,294.0 lbs-in 3. Consult the Moment Limits vs. Weight Table (FAA Figure 33). The allowed range of moment indexes for a weight of 2,680 lbs is 2,123 to 2,287 lbs-in/100. Hence the new moment index exceeds the maximum allowed and the CG is aft of limits.

(Refer to Figures 32 and 33.) Determine if the airplane weight and balance is within limits.Front seat occupants 415 lbRear seat occupants 110 lbFuel, main tanks 44 galFuel, aux. tanks 19 galBaggage 32 lb

Weight within limits, CG out of limits. Use the following steps: 1. Calculate weight and moment index using the information from the problem and from FAA Figures 32 and 33, and the formula: Weight x Arm ÷ 100 = Moment/Index Item Weight Arm Moment/100 Empty weight 2,015 lbs 1,554.0 lbs-in Front seat 415 lbs 85 352.8 lbs-in Rear seat 110 lbs 121 133.1 lbs-in Fuel main 44 x 6 264 lbs 75 198.0 lbs-in Fuel aux. 19 x 6 114 lbs 94 107.2 lbs-in Baggage 32 lbs 140 44.8 lbs-in Total 2,950 lbs 2,389.9 lbs-in 2. Calculate the CG using the formula: CG = Total Mom Ind ÷ Total Weight x Reduction Factor or: CG = 2,389.9 ÷ 2,950 x 100 = 81.0 inches aft of datum 3. Consult the Moment Limits vs. Weight Table (FAA Figure 33). A CG of 81 inches is 1.1 inches forward of the forward CG limit for a weight (allowed) of 2,950 pounds (2422/2950 = 82.1; 82.1 - 81 = 1.1 inches forward).