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# Private Pilot | Lesson 10 - Aircraft Weight and Balance

## 10.1 Weight and Balance Definitions

Empty weight - Empty weight consists of the airframe, engine, and all items of operating equipment permanently installed in the airplane, including optional special equipment, fixed ballast, hydraulic fluid, unusable fuel, and undrainable (or, in some aircraft, all) oil.

Center of Gravity - The center of gravity (CG) is the point of balance along the airplane's longitudinal axis. By multiplying the weight of each component of the airplane by its arm (distance from an arbitrary reference point, called the reference datum), that component's moment is determined. The CG of the airplane is the sum of all the moments divided by the total weight.

AVGAS, Standard Weight - The standard weight of aviation gasoline (AVGAS) has been established as 6 lbs./gal.

EXAMPLE:

25 gal. of AVGAS is equal to 150 lbs. (25 x 6 = 150)

Ascent Quick Quiz
##### Ascent Quick Quiz - 10.1 Weight and Balance Definitions
Question 1: Which items are included in the empty weight of an aircraft?

Question 2: 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?

Question 3: 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?

## 10.2 Determining Weight and Balance Using Center of Gravity Graphs

In order to ensure that your aircraft is loaded correctly, you will have to determine the center of gravity for each planned flight. You accomplish this task using two graphs; the Loading Graph, and the Center of Gravity Moment Envelope. (On the FAA Knowledge Test, both of these graphs are depicted on figure 35.)

Generally, you would first use the Loading Graph to determine the total loaded aircraft moment with the given configuration variables of fuel, passengers, and cargo for your planned flight. Once you've determined the total loaded aircraft moment, you would then plot that on the Center of Gravity Moment Envelop graph to ensure that you're operating within the safe center of gravity limits for your aircraft.

On most Loading Graphs, the load weight in pounds is listed on the vertical axis. Diagonal lines represent various items such as fuel, baggage, pilot and front seat passengers, and back seat passengers. 1. Determine which diagonal line to use for the item to be measured (fuel, front passengers, rear passengers, baggage).
2. Move up and right along the diagonal line until you intercept the horizontal line for the appropriate load weight amount.
3. From that point drop straight down to the bottom of the chart and note down the load moment listed on the horizontal axis.
4. Repeat steps 1-3 for any remaining load items.
5. Total the weights and moments for all items.

EXAMPLE:

Determine the load (total) moment/1,000 in the following situation:

 Weight (lb.) Moment/1,000 (lb.-in.) Empty weight 1,350 51.5 Pilot & front seat passenger 310 --- solve for this Baggage 100 --- solve for this Usable fuel 228 --- solve for this Oil (8 qt.) 15 --- solve for this

This is found as follows:

1. Compute the moment of the pilot and front seat passenger using the loading graph. Using "Pilot & Front Passenger" diagonal line, move up and right along the diagonal line until you intercept the horizontal line for 310 lbs. Drop straight down, and note the load moment of 11.5.
2. Repeat the steps for baggage using the "Baggage or Passenger on Child's Seat" diagonal line. Move up and right along the diagonal line until you intercept the horizontal line for 120 lbs. Drop straight down, and note the load moment of 9.5.
3. Repeat the steps for baggage using the "Fuel" diagonal line. Move up and right along the diagonal line until you intercept the horizontal line for 228 lbs (the maximum value for standard tanks). Drop straight down, and note the load moment of 11.0.
4. Note 2 below the Loading Graph indicates that a moment of -0.2 should be used for 8 quarts of engine oil.
5. Add all of the positive moments to and obtain a total of 83.5. Then subtract the negative moment for the engine oil to obtain the total loaded aircraft moment of 83.3.

So, you've determined the total load moment /1,00 to be 83.3, as shown in the completed table:

 Weight (lb.) Moment/1,000 (lb.-in.) Empty weight 1,350 51.5 Pilot & front seat passenger 310 15.0 Baggage 100 11.5 Usable fuel 228 11.0 Oil (8 qt.) 15 -0.2 ------- ------- TOTALS: 2,003 weight 83.3 moment

The center of gravity moment envelope chart is a graph showing center of gravity moment limits for various gross weights. The loaded aircraft weight is depicted on the vertical axis, and the loaded aircraft moment is depicted on the horizontal axis. The envelope is the boxed-in area of the graph, and depicts the safe operating limits for the center of gravity, as well as the maximum weight of the aircraft, which is depicted by the top line of the envelope. 1. Using your total loaded aircraft weight (found in the example above), find the appropriate horizontal line, then mark along that line across the graph.
2. Then, using your total loaded aircraft moment (from example above), find the appropriate vertical line, and mark along that line up the graph.
3. Note the point of intersection of the two lines.
1. The point of intersection should fall within the CG envelop (the boxed-in region), and
2. should fall just on, or below, the top line of the envelop (the aircraft's maximum weight allowance).

EXAMPLE:

Using the data above, plot the weight of 2,003 lb. on the horizontal axis, and the moment of 83.3 on the vertical axis. move across the chart to the moment line of 83.3.

The point of intersection will indicate that the aircraft is within the CG envelope (normal category) and below the aircraft's gross weight (2,300 lb.) limit.

Ascent Quick Quiz
##### Ascent Quick Quiz - 10.2 Determining Weight and Balance Using Center of Gravity Graphs
Question 1: The CG is located how far aft of datum?
```GIVEN:                                  WEIGHT (LB)    ARM(IN)  MOMENT(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            ---
```

Question 2: (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/1000Empty weight                   1,350          51.5Pilot and front passenger        250           ---Rear passengers                  400           ---Baggage                          ---           ---Fuel, 30 gal.                    ---           ---Oil, 8 qt.                       ---          -0.2
```

Question 3: (Refer to figure 35.) Calculate the moment of the airplane and determine which category is applicable.

```                            WEIGHT (LB)     MOM/1000Empty weight                   1,350          51.5Pilot and front passenger        310           ---Rear passengers                   96           ---Baggage                          ---           ---Fuel, 38 gal.                    ---           ---Oil, 8 qt.                       ---          -0.2
```

Question 4: (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/1000Empty weight                   1,350          51.5Pilot and front passenger        340           ---Rear passengers                  310           ---Baggage                           45           ---Oil, 8 qt.                       ---           ---
```

Question 5: (Refer to figure 35.) Determine the moment with the following data:

```                            WEIGHT (LB)     MOM/1000Empty weight                   1,350          51.5Pilot and front passenger        340           ---Fuel (std tanks)             Capacity          ---Oil, 8 qt.                       ---           ---
```

Question 6: (Refer to figure 35.) 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.                       ---           ---
```

## 10.3 Determining Weight and Balance Using Center of Gravity Tables

Another method to determine if an aircraft's loaded weight and center of gravity is within limits is to use tables instead of graphs. The Useful Load Weights and Moment Table (figure 33) and the Moment Limits vs Weight Table (figure 34) are used when solving weight and balance problems using tables.  To use these tables, first, determine the total loaded aircraft weight and the loaded aircraft moment/100 from the Useful Load Weights and Moments Table (figure 33).

1. Locate the specified weight for each loading item (passengers, baggage, fuel) and read the moment directly from the table.
• If a weight is between two given table values, you can use the basic formula to determine the moment: Weight × Arm = Moment
3. Total the moments for all loading items, and divide by 100 to get the loaded aircraft moment/100.

Then, use the Moment Limits vs. Weight Table (figure 34) to see if the total loaded aircraft moment is within maximum and minimum limits for the gross weight.

Ascent Quick Quiz
##### Ascent Quick Quiz - 10.3 Determining Weight and Balance Using Center of Gravity Tables
Question 1: (Refer to figure 33 and figure 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

Question 2: (Refer to figure 33 and figure 34.) Calculate the weight and balance and determine if the CG and the weight of the airplane are within limits.
 Front seat occupants . . . . . . . . . . . . . . . . . . . . . . . . 350 lb Rear seat occupants . . . . . . . . . . . . . . . . . . . . . . . . 325 lb Baggage . . . . . . . . . . . . . . . . . . . . . . . . 27 lb Fuel . . . . . . . . . . . . . . . . . . . . . . . . 35 gal

Question 3: (Refer to figure 33 and figure 34.) 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

Question 4: (Refer to figure 33 and figure 34.) Determine if the airplane weight and balance is within limits.
 Front seat occupants . . . . . . . . . . . . . . . . . . . . . . . . 415 lb Rear seat occupants . . . . . . . . . . . . . . . . . . . . . . . . 110 lb Fuel, main tanks . . . . . . . . . . . . . . . . . . . . . . . . 44 gal Fuel, aux. tanks . . . . . . . . . . . . . . . . . . . . . . . . 19 gal Baggage . . . . . . . . . . . . . . . . . . . . . . . . 32 lb

Question 5: (Refer to figure 33 and figure 34.) Which action can adjust the airplane's weight to maximum gross weight and the CG within limits for takeoff?
 Front seat occupants . . . . . . . . . . . . . . . . . . . . . . . . 425 lb Rear seat occupants . . . . . . . . . . . . . . . . . . . . . . . . 300 lb Fuel, main tanks . . . . . . . . . . . . . . . . . . . . . . . . 44 gal

Question 6: (Refer to figure 33 and figure 34.) With the airplane loaded as follows, what action can be taken to balance the airplane?
 Front seat occupants . . . . . . . . . . . . . . . . . . . . . . . . 411 lb Rear seat occupants . . . . . . . . . . . . . . . . . . . . . . . . 100 lb Main wing tanks . . . . . . . . . . . . . . . . . . . . . . . . 44 gal

Question 7: (Refer to figure 33 and figure 34.) 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?

Question 8: (Refer to figure 33 and figure 34.) 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?