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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?
ANSWER: 15 gallons.
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.
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?
ANSWER: CG 94.01.
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 gal. To get the weight multiply
the 30 by 6 lb. per gal. (30 x 6) = 180 lb.
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 x 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 in.
Figure 35
(Refer to figure 35.) 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
ANSWER: 105 pounds.
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 lb.
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 gal. The question gives 30 gal., for a total
fuel weight of 180 lb. 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. 35. It gives 15 lb. as the weight
with a moment of -.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 lb. 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. x 6 lb./gal.) 180 8.7
Oil 15 -0.2
2,195 98.2
(without baggage)
Figure 35
(Refer to figure 35.) Calculate the moment of the airplane and
determine which category is applicable.
WEIGHT (LB) MOM/1000
Empty weight 1,350 51.5
Pilot and front passenger 310 ---
Rear passengers 96 ---
Baggage --- ---
Fuel, 38 gal. --- ---
Oil, 8 qt. --- -0.2
ANSWER: 80.8, utility category.
First, total the weight and get 1,999 lb.
Note that the 38 gal. of fuel weighs 228 lb. (38 gal. x 6 lb./gal.).
Find the moments for the pilot and front seat passengers,
rear passengers, and fuel by using the loading graph in Fig.
35. Find the oil weight and moment by consulting Note (2)
on Fig. 35. It is 15 lb. and -0.2 moments. 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 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.
Moment/1000
Weight lb.-in.
Empty weight 1,350 51.5
Pilot and front seat passenger 310 11.5
Rear passengers 96 7.0
Fuel (38 gal. x 6 lb./gal.) 228 11.0
Oil 15 -0.2
1,999 80.8
Figure 35
(Refer to figure 35.) What is the maximum amount of fuel that may
be aboard the airplane on takeoff if loaded as follows?
WEIGHT (LB) MOM/1000
Empty weight 1,350 51.5
Pilot and front passenger 340 ---
Rear passengers 310 ---
Baggage 45 ---
Oil, 8 qt. --- ---
ANSWER: 40 gallons.
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 lb. (Find the oil
weight and moment by consulting Note (2) on Fig. 35. 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 gal. of fuel
(240/6 lb. per gal.) 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 12.5, 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 101.8, which is within the envelope, so 40 gal. of fuel
may be carried.
Moment/1000
Weight lb.-in.
Empty weight 1,350 51.5
Pilot and front seat passenger 340 12.5
Rear passengers 310 22.5
Baggage 45 4.0
Fuel (40 gal. x 6 lb./gal.) 240 11.5
Oil 15 -0.2
2,300 101.8
Figure 35
(Refer to figure 35.) 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. --- ---
ANSWER: 74.9 pound-inches.
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. x 6 lb. =
228 lb.). (Find the oil weight and moment by consulting Note
(2) on Fig. 35; it is 15 lb. and -0.2. moments.) These total 74.9,
so this answer is correct.
Moment/1000
Weight lb.-in.
Empty weight 1,350 51.5
Pilot and front seat passenger 340 12.6
Fuel 228 11.0
Oil 15 -0.2
1,933 74.9
Figure 35
(Refer to figure 35.) Determine the aircraft loaded moment and the
aircraft category.
WEIGHT (LB) MOM/1000
Empty weight 1,350 51.5
Pilot and front passenger 380 ---
Fuel, 48 gal 288 ---
Oil, 8 qt. --- ---
ANSWER: 79.2, normal category.
The moments for the pilot, front
passenger, fuel, and oil must be found on the loading graph
in Fig. 35. 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.
Moment/1000
Weight 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
Figure 33 Figure 34
(Refer to figures 33 and 34.) 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
ANSWER: 20 pounds overweight, CG within limits.
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. 33 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 x 85 ÷ 100).
The rear seat occupants' moment/100 is 357 (295 x 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 x 140 ÷ 100).
The last step is to go to the Moment Limits versus Weight
chart (Fig. 34), 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 lb.
Moment/1000
Weight lb.-in.
Empty weight w/oil 2,015 1,554
Front seat 340 289
Rear seat 295 357
Fuel (44 gal. x 6 lb/gal) 264 198
Oil 56 78
2,970 2,476
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