avmf 2150 lesson nine

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? fig. 61

Compute and sum the moments left and right of the fulcrum. Set them equal to one another and solve for the desired variable: left=right 50 lb.(50 in.) + Y(25 in.)=100 lb.(100 in.) 2,500 + 25Y=10,000 25Y=7,500 Y=300 lb.

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? fig. 32, 33

The effect of a 35-gal. fuel burn on weight balance is required. Burning 35 gal. of fuel will reduce weight by 210 lb. and moment by 158. At 2,680 lb. (2,890 - 210), the 2,294 MOM/100 (2,452 - 158) is above the maximum moment of 2,287; i.e., CG is aft of limits. This is why weight and balance should always be computed for the beginning and end of each flight.

Which items are included in the empty weight of an aircraft?

The empty weight of an airplane includes airframe, engines, and all items of operating equipment that have fixed locations and are permanently installed. It includes optional and special equipment, fixed ballast, hydraulic fluid, unusable fuel, and undrainable oil.

Which action can adjust the airplane's weight to maximum gross weight and the CG within limits for takeoff? fig. 32, 33 Front seat occupants = 425 lb Rear seat occupants = 300 lb Fuel, main tanks = 44 gal

First, determine the total weight to see how much must be reduced. As shown below, this original weight is 3,004 pounds. Fig. 33 shows the maximum weight as 2,950 pounds. Thus, you must adjust the total weight by removing 54 lb. (3,004 - 2,950). Since fuel weighs 6 lb./gal., you must drain at least 9 gallons. To check for CG, recompute the total moment using a new fuel moment of 158 (from the chart) for 210 pounds. The plane now weighs 2,950 lb. with a total moment of 2,437, which falls within the moment limits on Fig. 33. Original Adjusted Moment/100 Weight Weight lb.-in. Empty weight with oil 2,015 2,015 1,554 Front seat 425 425 362 Rear seat 300 300 363 Fuel 264 210 158 3,004 2,950 2,437

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

Both the total weight and the total moment must be calculated. As in most weight and balance problems, you should begin by setting up a schedule as below. Note that the empty weight in Fig. 32 is given as 2,015 with a moment/100 in. of 1,554 (note the change to moment/100 on this chart) and that empty weight includes the oil. The next step is to compute the moment/100 for each item. The front seat occupants' moment/100 is 289 (340 × 85 ÷ 100). The rear seat occupants' moment/100 is 357 (295 × 121 ÷ 100). The fuel (main tanks) weight of 264 lb. and moment/100 of 198 is read directly from the table. The baggage moment/100 is 78 (56 × 140 ÷ 100). The last step is to go to the "Moment limits vs. weight" chart (Fig. 33) and note that the maximum weight allowed is 2,950, which means that the plane is 20 lb. over. At a moment/100 of 2,476, the plane is within the CG limits because the moments/100 may be from 2,422 to 2,499 at 2,950 pounds. Weight Moment/100 lb. lb.-in. Empty weight w/oil 2,015 1,554 Front seat 340 289 Rear seat 295 357 Fuel (44 gal. × 6 lb/gal) 264 198 Baggage 56 78 2,970 2,476

Determine the condition of the airplane: fig. 67 Pilot and copilot = 375 lb Passengers -- aft position = 245 lb Baggage = 65 lb Fuel = 70 gal

Both the total weight and the total moment must be calculated. As in most weight and balance problems, you should begin by setting up a schedule as below. Note that the empty weight in Fig. 67 is given as 2,110 with a moment/100 in. of 1,652 (note the use of moment/100 on this chart), and that empty weight includes the oil. The next step is to compute the moment/100 for each item. The pilot and copilot moment/100 is 318.75 lb.-in. (375 lb. × 85 in. ÷ 100). The passengers (aft position) moment/100 is 333.2 lb.-in. (245 lb. × 136 in. ÷ 100). The baggage moment/100 is 97.5 lb.-in.(65 lb. × 150 in. ÷ 100). The 70-gal. fuel weight is 420 lb., and the moment/100 is 315 lb.-in. (read directly from the table). Weight Moment/100 Empty weight w/oil 2,110 1,652.00 Pilot and copilot 375 318.75 Passengers (aft position) 245 333.20 Baggage 65 97.50 Fuel (70 gal.) 420 315.00 3,215 2,716.45 Note that the gross weight of 3,215 lb. is within the 3,400 lb. maximum allowable by 185 lb., and that the moment/100 of 2,716.45 is within the moment envelope at the intersection with 3,215 lb.

Determine the condition of the airplane: Pilot and copilot = 400 lb Passengers -- aft position = 240 lb Baggage = 20 lb Fuel = 75 gal

Both the total weight and the total moment must be calculated. As in most weight and balance problems, you should begin by setting up a schedule as below. Note that the empty weight in Fig. 67 is given as 2,110 with a moment/100 in. of 1,652 (note the use of moment/100 on this chart), and that empty weight includes the oil. The next step is to compute the moment/100 for each item. The pilot and copilot moment/100 is 340 lb.-in. (400 lb. × 85 in. ÷ 100). The passengers (aft position) moment/100 is 326.4 lb.-in. (240 lb. × 136 in. ÷ 100). The baggage moment/100 is 30 lb.-in. (read directly from the table). The 75-gal. fuel weight is 450 lb., and the moment/100 is 338 lb.-in. (read directly from the table). Weight Moment/100 Empty weight w/oil 2,110 1,652.00 Pilot and copilot 400 340.00 Passengers (aft position) 240 326.40 Baggage 20 30.00 Fuel (75 gal.) 450 338.00 3,220 2,686.40 Note that the gross weight of 3,220 lb. is within the 3,400 lb. maximum allowable by 180 lb., and that this moment/100 of 2,686.4 lb.-in. is within the moment envelope at the intersection with 3,220 lb.

fig. 67 Determine the condition of the airplane: Pilot and copilot = 316 lb Passengers Fwd position = 130 lb Aft position = 147 lb Baggage = 50 lb Fuel = 75 gal

Both the total weight and the total moment must be calculated. As in most weight and balance problems, you should begin by setting up a schedule as below. Note that the empty weight in Fig. 67 is given as 2,110 with a moment/100 in. of 1,652 (note the use of moment/100 on this chart), and that empty weight includes the oil. Be aware that some table values do not result in an accurate mathematical answer. You should use the table as a guide, but do not neglect to check your math. The next step is to compute the moment/100 for each item. The pilot and copilot together weigh 316 lb., and their moment/100 is 268.6 lb.-in. (316 lb. × 85 in. ÷ 100). The passengers (forward position) moment/100 is 144.3 lb.-in. (130 lb. × 111 in. ÷ 100). The passengers (aft position) moment/100 is 199.92 lb.-in. (147 lb. × 136 in. ÷ 100). The baggage moment/100 is 75 lb.-in. (read directly from the table). The 75-gal. fuel weight is 450 lb., and the moment/100 is 338 lb.-in. (read directly from the table). Weight Moment/100 Empty weight w/oil 2,110 1,652.00 Pilot and copilot 316 268.60 Passengers Fwd position 130 144.30 Aft position 147 199.92 Baggage 50 75.00 Fuel (75 gal.) 450 338.00 3,203 2,677.82 Note that the gross weight of 3,203 is within the 3,400-lb. maximum allowable by 197 lb., which is within the CG envelope. CG = 2,677.82 3,203 × 100 = 83.6 in. aft of datum

Determine if the airplane weight and balance is within limits. fig. 32, 33 Front seat occupants = 415 lb Rear seat occupants = 110 lb Fuel, main tanks = 44 gal Fuel, aux. tanks = 19 gal Baggage = 32 lb

Both the weight and the total moment must be calculated. Begin by setting up the schedule shown below. The fuel must be separated into main and auxiliary tanks, but weights and moments for both tanks are provided in Fig. 32. Since 415 lb. is not shown on the front seat table, simply multiply the weight by the arm shown at the top of the table (415 lb. × 85 in. = 35,275 lb.-in.) and divide by 100 for moment/100 of 353 (35,275 ÷ 100 = 352.75). The rear seat moment must also be multiplied (110 lb. × 121 in. = 13,310 pound-inches). Divide by 100 to get 133.1, or 133 lb.-in. ÷ 100. The last step is to go to the "Moment limits vs. weight" chart (Fig. 33). The maximum weight allowed is 2,950, which means that the airplane weight is within the limits. However, the CG is out of limits because the minimum moment/100 for a weight of 2,950 lb. is 2,422. Moment/100 Weight lb.-in. Empty weight w/oil 2,015 1,554 Front seat 415 353 Rear seat 110 133 Fuel, main 264 198 Fuel, aux. 114 107 Baggage 32 45 2,950 2,390

Calculate the moment of the airplane and determine which category is applicable. fig. 34 WEIGHT (LB) MOM/1000 Empty weight 1,350 51.5 Pilot and front passenger 310 --- Rear passengers 96 --- Fuel, 38 gal. --- --- Oil, 8 qt. --- -0.2

First, total the weight and get 1,999 lb. Note that the 38 gal. of fuel weighs 228 lb. (38 gal. × 6 lb./gallon). Find the moments for the pilot and front seat passenger, rear passengers, and fuel by using the loading graph in Fig. 34. Find the oil weight and moment by consulting Note 2 on Fig. 34. It is 15 lb. and -0.2 moments. Note that the reference point for 38 gal. of fuel is not depicted correctly. Use the fuel weight of 228 lb. for the calculation. Total the moments as shown in the schedule below. Now refer to the center of gravity moment envelope. Find the gross weight of 1,999 lb. on the vertical scale, and move horizontally across the chart until intersecting the vertical line that represents the 80.8 moment. Note that a moment of 80.8 lb.-in. falls into the utility category envelope. Weight Moment/1000 lb. lb.-in. Empty weight 1,350 51.5 Pilot and front passenger 310 11.6 Rear passengers 96 6.9 Fuel (38 gal. × 6 lb./gal.) 228 11.0 Oil 15 -0.2 1,999 80.8

An aircraft is loaded 110 pounds over maximum certificated gross weight. If fuel (gasoline) is drained to bring the aircraft weight within limits, how much fuel should be drained?

Fuel weighs 6 lb./gallon. If an airplane is 110 lb. over maximum gross weight, 18.4 gal. (110 lb. ÷ 6) must be drained to bring the airplane weight within limits.

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?

Since fuel weighs 6 lb./gal., draining 15 gal. (90 lb. ÷ 6) will reduce the weight of an airplane that is 90 lb. over maximum gross weight to the acceptable amount.

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

The maximum allowable weight on the "Moment limits vs. weight" chart (Fig. 33) is 2,950 pounds. The total of the given weights is 2,905 lb. (including the empty weight of the airplane at 2,015 lb. and the fuel at 6 lb./gal.), so baggage cannot weigh more than 45 pounds. It is still necessary to compute total moments to verify that the position of these weights does not move the CG out of CG limits. The total moment of 2,459 lies safely between the moment limits of 2,422 and 2,499 on Fig. 33, at the maximum weight, so this airplane can carry as much as 45 lb. of baggage when loaded in this manner. Moment/100 Weight lb.-in. Empty weight w/oil 2,015 1,554 Front seat 387 329 Rear seat 293 355 Fuel, main (35 gal.) 210 158 Baggage 45 63 2,950 2,459

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

The moments for the pilot, front passenger, fuel, and oil must be found on the loading graph in Fig. 34. Total all the moments and the weight as shown in the schedule below. Now refer to the center of gravity moment envelope graph. Find the gross weight of 2,033 on the vertical scale, and move horizontally across the graph until intersecting the vertical line that represents the 79.2 moment. A moment of 79.2 lb.-in. falls into the normal category envelope. Weight Moment/1000 lb. lb.-in. Empty weight 1,350 51.5 Pilot and front seat passenger 380 14.2 Fuel (capacity) 288 13.7 Oil 15 -0.2 2,033 79.2

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? fig. 32, 33

The requirement is the effect of a change in loading. Look at Fig. 32 for occupants. Losing the 180-lb. passenger from the front seat reduces the MOM/100 by 153. Moving the 204-lb. passenger from the rear seat to the front reduces the MOM/100 by about 74 (247 - 173). The total moment reduction is thus about 227 (153 + 74). As calculated below, the CG moves forward from 84.01 to 81.00 inches. Old CG = 226,000 lb.-in./2690 lb = 84.01 in. New CG = 203,300 lb.-in./2,510 lb = 81.00 in.

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

To compute the CG, you must first multiply each weight by the arm to get the moment. Note that the fuel is given as 30 gallons. To get the weight, multiply the 30 by 6 lb. per gal. (30 × 6) = 180 pounds. Weight Arm Moment (lb.) (in.) (lb.-in.) Empty weight 1,495.0 101.4 151,593.0 Pilot and passengers 380.0 64.0 24,320.0 Fuel (30 × 6) 180.0 96.0 17,280.0 2,055.0 193,193.0 Now add the weights and moments. To get CG, you divide total moment by total weight (193,193 ÷ 2,055.0) = a CG of 94.01 inches.

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/1000 Empty weight 1,350 51.5 Pilot and front passenger 250 --- Rear passengers 400 --- Baggage --- --- Fuel, 30 gal. --- --- Oil, 8 qt. --- -0.2 fig. 34

To compute the amount of weight left for baggage, compute each individual moment by using the loading graph and add them up. First, compute the moment for the pilot and front seat passenger with a weight of 250 pounds. Refer to the loading graph and the vertical scale at the left side and find the value of 250. From this position, move to the right horizontally across the graph until you intersect the diagonal line that represents pilot and front passenger. From this point, move vertically down to the bottom scale, which indicates a moment of about 9.2. To compute rear passenger moment, measure up the vertical scale of the loading graph to a value of 400, horizontally across to intersect the rear passenger diagonal line, and down vertically to the moment scale, which indicates approximately 29.0. To compute the moment of the fuel, you must recall that fuel weighs 6 lb. per gallon. The question gives 30 gal., for a total fuel weight of 180 pounds. Now move up the weight scale on the loading graph to 180, then horizontally across to intersect the diagonal line that represents fuel, then vertically down to the moment scale, which indicates approximately 8.7. To get the weight of the oil, see Note 2 at the bottom of the loading graph section of Fig. 34. It gives 15 lb. as the weight with a moment of -0.2. Now total the weights (2,195 lb. including 15 lb. of engine oil). Also total the moments (98.2 including engine oil with a negative 0.2 moment). With this information, refer to the center of gravity moment envelope chart. Note that the maximum weight in the envelope is 2,300 pounds. The amount of 2,300 lb. - 2,195 lb. already totaled leaves a maximum possible 105 lb. for baggage. However, you must be sure 105 lb. of baggage does not exceed the 109 moments allowed at the top of the envelope. On the loading graph, 105 lb. of baggage indicates approximately 10 moments. Thus, a total of 108.2 moments (98.2 + 10) is within the 109 moments allowed on the envelope for 2,300 lb. of weight. Therefore, baggage of 105 lb. can be loaded. Moment/1000 Weight lb.-in. Empty weight 1,350 51.5 Pilot and front seat passenger 250 9.2 Rear passengers 400 29.0 Baggage ? ? Fuel (30 gal. × 6 lb./gal.) 180 8.7 Oil 15 -0.2 2,195 98.2 (without baggage)

fig. 34 Determine the moment with the following data: WEIGHT (LB) MOM/1000 Empty weight 1,350 51.5 Pilot and front passenger 340 --- Fuel (std tanks) Capacity --- Oil, 8 qt. --- ---

To find the CG moment/1000, find the moments for each item and total the moments as shown in the schedule below. For the fuel, the loading graph shows the maximum as 38 gal. for standard tanks (38 gal. × 6 lb. = 228 pounds). (Find the oil weight and moment by consulting Note 2 on Fig. 34; it is 15 lb. and -0.2 moments.) These total 75.4, so this answer is correct. Weight Moment/1000 lb. lb.-in. Empty weight 1,350 51.5 Pilot and front seat passenger 340 12.8 Fuel 228 11.3 Oil 15 -0.2 1,933 75.4

How should the 500-pound weight be shifted to balance the plank on the fulcrum? fig. 60

To find the desired location of the 500-lb. weight, compute and sum the moments left and right of the fulcrum. Set them equal to one another and solve for the desired variable: left = right 500 lb.(X) = 250 lb.(20 in.) + 200 lb.(15 in.) 500X = 8,000 X = 16 in. The 500-lb. weight must be 16 in. from the fulcrum to balance the plank. The weight should be shifted 1 in. to the left.

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

To find the maximum amount of fuel this airplane can carry, add the empty weight (1,350), pilot and front passenger weight (340), rear passengers (310), baggage (45), and oil (15), for a total of 2,060 pounds. (Find the oil weight and moment by consulting Note 2 on Fig. 34. It is 15 lb. and -0.2 moments.) Gross weight maximum on the center of gravity moment envelope chart is 2,300. Thus, 240 lb. of weight (2,300 - 2,060) is available for fuel. Since each gallon of fuel weighs 6 lb., this airplane can carry 40 gallons of fuel (240 ÷ 6 lb. per gallon) if its center of gravity moments do not exceed the limit. Note that long-range tanks were not mentioned; assume they exist. Compute the moments for each item. The empty weight moment is given as 51.5. Calculate the moment for the pilot and front passenger as 12.8, the rear passengers as 22.5, the fuel as 11.5, the baggage as 4.0, and the oil as -0.2. These total to 102.1, which is within the envelope, so 40 gallons of fuel may be carried. Moment/1000 Weight lb.-in. Empty weight 1,350 51.5 Pilot and front seat passenger 340 12.8 Rear passengers 310 22.5 Baggage 45 4.0 Fuel (40 gal. × 6 lb./gal.) 240 11.5 Oil 15 -0.2 2,300 102.1

Calculate the weight and balance and determine if the CG and the weight of the airplane are within limits. fig. 32, 33 Front seat occupants = 350 lb Rear seat occupants = 325 lb Baggage = 27 lb Fuel = 35 gal

Total weight, total moment, and CG must all be calculated. As in most weight and balance problems, you should begin by setting up the schedule as shown below. Next, go to the "Moment limits vs. weight" chart (Fig. 33), and note that the maximum weight allowed is 2,950, which means that this airplane is 23 lb. under maximum weight. At a total moment of 2,441, it is also within the CG limits (2,399 to 2,483) at that weight. Finally, compute the CG. Recall that Fig. 32 gives moment per 100 inches. The total moment is therefore 244,100 (2,441 × 100). The CG is 83.4 (244,100 ÷ 2,927). Moment/100 Weight lb.-in. Empty weight w/oil 2,015 1,554 Front seat 350 298 Rear seat 325 393 Fuel, main (35 gal.) 210 158 Baggage 27 38 2,927 2,441

With the airplane loaded as follows, what action can be taken to balance the airplane? fig. 32, 33 Front seat occupants = 411 lb Rear seat occupants = 100 lb Main wing tanks = 44 gal

You need to calculate the weight and moment of the loaded airplane. The weight of the empty plane, including oil, is 2,015 lb., and it has a moment of 1,554. The 411 lb. in the front seats has a total moment of 349.35 [411 × 85 (ARM) = 34,935 ÷ 100 = 349.35]. The rear seat occupants have a weight of 100 lb. and a moment of 121.0 [100 × 121 (ARM) = 12,100 ÷ 100 = 121.0]. The fuel weight is given on the chart as 264 lb. with a moment of 198. Weight Moment/100 lb. lb.-in. Empty weight 2,015 1,554.00 Front seat 411 349.35 Rear seat 100 121.00 Fuel 264 198.00 Loaded airplane 2,790 2,222.35 On the Fig. 33 chart, the acceptable moment/100 range for 2,790 lb. is 2,243 to 2,374. Thus, the CG of 2,222.35 is forward of the acceptable moment/100 range. Weight Moment/100 lb. lb.-in. Loaded airplane 2,790 2,222.35 Baggage 100 140.00 New loaded airplane 2,890 2,362.35 At 2,890 lb. (2,790 + 100) and a moment/100 of 2,362.35 (2,222.35 + 140), the new loaded airplane is within the acceptable moment/100 range of 2,354 to 2,452.