This category discusses general guidelines and procedures for weighing helicopters and large fixed-wing aircraft exceeding a takeoff weight of 12,500 pounds. Several examples of center of gravity (CG) determination for various operational aspects of these aircraft are also included. Persons seeking approval for a weight and balance control program for aircraft operated under Title 14 of the Code of Federal Regulations (14 CFR) part 91, subpart K, 121, 125, or 135 should consult with the Flight Standards District Office (FSDO) or Certificate Management Office (CMO) that has jurisdiction in their area. Additional information on weight and balance for large aircraft can be found in Federal Aviation Administration (FAA) Advisory Circular (AC) 120-27, Aircraft Weight and Balance Control, FAA Type Certificate Data Sheets (TCDS), and the aircraft flight and maintenance manuals for specific aircraft.
Helicopter Weight and Balance Control
Weight and balance considerations of a helicopter are similar to those of an airplane, except they are far more critical, and the center of gravity (CG) range is much more limited. [Figures 8-1 and 8-2] The engineers who design a helicopter determine the amount of cyclic control authority that is available, and establish both the longitudinal and lateral CG envelopes that allow the pilot to load the helicopter so there is sufficient cyclic control for all flight conditions If the CG is ahead of the forward limit, the helicopter tilts and the rotor disk has a forward pull. To counteract this and maintain a stationary position, rearward cyclic stick displacement would be required. If the CG is too far forward, there may not be enough available cyclic authority to allow the helicopter to flare during landing, and it consequently requires an excessive landing distance.
Figure 8-1. Weight and balance data needed to determine proper loading of a helicopter.
Figure 8-2. Typical helicopter datum, flight stations, and butt line locations.
If the CG is aft of the allowable limits, the helicopter flies with a tail-low attitude and may need more forward cyclic stick displacement than is available to maintain a hover in a no-wind condition. There might not be enough cyclic travel to prevent the tail boom from striking the ground. If gusty winds should cause the helicopter to pitch up during high speed flight, there might not be enough forward cyclic control to safely lower the nose.
Helicopters are approved for a specific maximum gross weight, but it is not safe to operate them at this weight under some conditions. A high density altitude decreases the safe maximum weight as it affects the hovering, takeoff, climb, autorotation, and landing performance.
The fuel tanks on some helicopters are behind the CG, causing it to shift forward as fuel is used. Under some flight conditions, the balance may shift enough that there is not sufficient cyclic authority to flare for landing. For these helicopters, the loaded CG should be computed for both takeoff and landing weights.
Lateral balance of an airplane is usually of little concern and is not normally calculated. Some helicopters, especially those equipped for hoist operations, are sensitive to the lateral position of the CG and their Pilot’s Operating Handbook/Rotorcraft Flight Manual (POH/RFM) include both longitudinal and lateral CG envelopes, as well as information on the maximum permissible hoist load. Figure 8-3 is an example of such CG envelopes.
Figure 8-3. Typical helicopter CG envelopes.
Determining the Loaded CG of a Helicopter
The empty weight and empty weight center of gravity (EWCG) of a helicopter are determined in the same way as for an airplane. See the post on Single-Engine Aircraft Weight and Balance Computations. The weights recorded on the scales supporting the helicopter are added and their distances from the datum are used to compute the moments at each weighing point. The total moment is divided by the total weight to determine the location of the CG in inches from the datum. The datum of some helicopters is located at the center of the rotor mast, but since this causes some arms to be positive (behind the datum) and others negative (ahead of the datum), most modern helicopters have the datum located ahead of the aircraft, as do most modern airplanes. When the datum is ahead of the aircraft, all longitudinal arms are positive.
The lateral CG is determined in the same way as the longitudinal CG, except the distances between the scales and butt line zero (BL 0) are used as the arms. Arms to the right of BL 0 are positive and those to the left are negative. The butt line zero (or sometimes referred to as the buttock) is a line through the symmetrical center of an aircraft from nose to tail. It serves as the datum for measuring the arms used to find the lateral CG. Lateral moments that cause the aircraft to roll clockwise are positive (+), and those that cause it to roll counterclockwise are negative (–).
To determine whether or not a helicopter is within both longitudinal and lateral weight and balance limits, construct a table like the one in Figure 8-4, with the following data specific to the aircraft.
| Empty weight | 1,545 lb |
| EWCG | 101.4 inches aft of the datum |
| Lateral balance | arm. 0.2 inches right of BL 0 |
| Maximum allowable gross weight | 2,250 lb |
| Pilot | 200 lb @ 64 inches aft of datum and 13.5 inches right of BL 0 |
| Passenger | 170 lb @ 64 inches aft of datum and –13.5 in left of BL 0 |
| Fuel (48 gal) | 288 lb @ 96 inches aft of datum and –8.4 inches left of BL 0 |
Check the helicopter CG envelopes in Figure 8-3 to determine whether or not the CG is within limits both longitudinally and laterally.
In the longitudinal CG envelope, draw a line vertically upward from the CG of 94.4 inches aft of datum and a horizontal line from the weight of 2,203 pounds gross weight. These lines cross within the approved area.
In the lateral offset moment envelope, draw a line vertically upward from the –1,705 lb-in point (on the left side of the horizontal axis) and a line horizontally from 2,203 pounds on the gross weight index. These lines cross within the envelope, showing the lateral balance is also within limits.
Effects of Offloading Passengers and Using Fuel
Consider the helicopter in Figure 8-4. The first leg of the flight consumes 26 gallons of fuel, and at the end of this leg, the passenger deplanes. Is the helicopter still within allowable CG limits for takeoff? To find out, make a new chart like the one in Figure 8-5 to show the new loading conditions of the helicopter at the beginning of the second leg of the flight.
Under these conditions, according to the helicopter CG envelopes in Figure 8-3, both the longitudinal CG and the lateral offset moment fall outside of the approved area of the envelope. The aircraft longitudinal CG is too far aft and the potential for excessive tail-low attitudes is very high. Under these conditions, it is possible that there will not be enough forward cyclic authority to maintain level flight The helicopter’s lateral offset moment is too far right and may lead to control issues, as well as an increased hazard of dynamic rollover. One possible option to bring the aircraft loading conditions within the approved envelope is to load either ballast or a passenger, as computed in Figure 8-6 and plotted in Figure 8-3.
Commuter Category and Large Aircraft
Establishing the Initial Weight of an Aircraft
Prior to being placed into service, each aircraft is weighed and the empty weight and CG location established. New aircraft are normally weighed at the factory and are eligible to be placed into operation without reweighing if the weight and balance records were adjusted for alterations and modifications to the aircraft, such as interior reconfigurations.
An aircraft transferred from one operator that has an approved weight and balance program to another operator with an approved program does not need to be weighed prior to use by the receiving operator unless more than 36 calendar months have elapsed since the last individual or fleet weighing, or unless some other modification to the aircraft warrants that the aircraft be weighed. Aircraft transferred, purchased, or leased from an operator without an approved weight and balance program, and that have not been modified or have been minimally modified,can be placed into service without being reweighed if the last weighing was accomplished by an acceptable method (for example, manufacturer’s instructions or AC 43.13-2, Acceptable Methods, Techniques, and Practices—Aircraft Alterations) within the last 12 calendar months and a weight and balance change record was maintained by the operator. It is potentially unsafe to fail to reweigh an aircraft after it has been modified.
When weighing large aircraft, compliance with the relevant manuals, operations specifications, or management specification is required to ensure that weight and balance requirements specified in the Aircraft Flight Manual (AFM) are met in accordance with approved limits. This provides information to the flight crew that allows the maximum payload to be carried safely.
The aircraft should be weighed in still air or an enclosed building after the aircraft has been cleaned. Ensure that the aircraft is in a configuration for weighing with regard to flight controls, unusable fuel, ballast, oil and other operating fluids,and equipment as required by the controlling weight and balance procedure.
Large aircraft are not usually raised off the floor on jacks for weighing; they are weighed on ramp-type scales. The scales must be properly calibrated, zeroed, and used in accordance with the manufacturer’s instructions. Each scale should be periodically checked for accuracy as recommended in the manufacturer’s calibration schedule, either by the manufacturer or by a recognized facility, such as a civil department of weights and measures. If no manufacturer’s schedule is available, the period between calibrations should not exceed 12 months.
Determining the Empty Weight and Empty Weight CG (EWCG)
When the aircraft is properly prepared for weighing, roll it onto the scales, and level it. The weights are measured at three weighing points: the two main wheel points and the nose wheel point. The empty weight and empty weight CG (EWCG) are determined by using the following steps with the results recorded in the weight and balance record for use in all future weight and balance computations.
- Determine the moment index of each of the main-wheel points by multiplying the net weight (scale reading minus tare weight), in pounds, at these points by the distance from the datum, in inches. Divide these numbers by the appropriate reduction factor.
- Determine the moment index of the nose wheel weighing point by multiplying its net weight, in pounds, by its distance from the datum, in inches. Divide this by the reduction factor.
- Determine the total weight by adding the net weight of the three weighing points and the total moment index by adding the moment indexes of each point.
- Divide the total moment index by the total weight and multiply the result by the reduction factor. This gives the CG in inches from the datum.
- Determine the distance of the CG behind the leading edge of the mean aerodynamic chord (LEMAC) by subtracting the distance between the datum and LEMAC from the distance between the datum and the CG. [Figure 9-1]
Figure 9-1. Determining the distance of CG.
- Determine the EWCG in percentage of MAC (percent MAC) by using the formula in Figure 9-2.
Figure 9-2. Determining the EWCG in percent MAC.
Documenting Changes to an Aircraft’s Weight and Balance
The weight and balance system should include methods by which a complete, current, and continuous record of the weight and CG of each aircraft is maintained, such as a log, ledger, or other equivalent electronic means. Alterations and changes affecting the weight and/or balance of the aircraft should be recorded in this log. Changes in the weight or location of weight in or on the aircraft should be recorded whenever the weight change is at or exceeds the weights listed in Figure 9-3.
Determining the Loaded CG of the Airplane in Percent MAC
A loading schedule is used to document compliance with the certificated weight and balance limitations contained in the manufacturer’s AFM and weight and balance manual. The basic operating weight (BOW) and the operating index are entered into a loading schedule like the one in Figure 9-4, and the variables for a specific flight are entered as appropriate to determine the loaded weight and CG.
Figure 9-4. Loading schedule.
Use the data in this example:
| Basic operating weight | 105,500 lb |
| Basic operating index (total moment/1,000) | 98,837.0 |
| MAC | 180.9 in |
| LEMAC | 860.5 |
Figure 9-5 illustrates passenger, cargo, and fuel loading tables. Using these tables, determine the moment indexes for the passengers (PAX), cargo, and fuel.
| Passengers (nominal weight—170 pounds each) | |
| Forward compartment | 18 |
| Aft compartment | 95 |
Cargo
| Forward hold | 1,500 lb |
| Aft hold | 2,500 lb |
Fuel
| Tanks 1 and 3 | 10,500 lb each |
| Tank 2 | 28,000 lb |
The formula in Figure 9-6 can be used to determine the location of the CG in inches aft of the datum.
Figure 9-6. Determining the location of the CG in inches aft of the datum.
Determine the distance from the CG to the LEMAC by subtracting the distance between the datum and LEMAC from the distance between the datum and the CG. [Figure 9-7]
Figure 9-7. Determining the distance from the CG to the LEMAC.
The location of the CG in percent MAC must be known in order to set the stabilizer trim takeoff. [Figure 9-8]
Figure 9-8. Determining the location of the CG in percent MAC.
Operational Empty Weight (OEW)
Operational empty weight (OEW) is the basic empty weight or flet empty weight plus operational items. The operator has two choices for maintaining OEW. The loading schedule may be utilized to compute the operational weight and balance of an individual aircraft, or the operator may choose to establish fleet empty weights for a fleet or group of aircraft.
Reestablishing the OEW
The OEW and CG position of each aircraft should be reestablished at the reweighing. In addition, it should be reestablished through calculation whenever the cumulative change to the weight and balance log is more than plus or minus one-half of 1 percent (0.5 percent) of the maximum landing weight, or whenever the cumulative change in the CG position exceeds one-half of 1 percent (0.5 percent) of the MAC. In the case of rotorcraft and aircraft that do not have a MAC-based CG envelope (e.g., canard equipped airplane), whenever the cumulative change in the CG position exceeds one-half of 1 percent (0.5 percent) of the total CG range, the weight and balance should be reestablished.
When reestablishing the aircraft OEW between reweighing periods, the weight changes may be computed provided the weight and CG location of the modifications are known; otherwise, the aircraft must be reweighed.
Fleet Operating Empty Weights (FOEW)
An operator may choose to use one weight for a fleet or group of aircraft if the weight and CG of each aircraft is within the limits stated above for establishment of OEW. When the cumulative changes to an aircraft weight and balance log exceed the weight or CG limits for the established fleet weight, the empty weight for that aircraft should be reestablished. This may be done by moving the aircraft to another group, or reestablishing new fleet operating empty weights (FOEWs).
Onboard Aircraft Weighing System
Some large transport airplanes have an onboard aircraft weighing system (OBAWS) that, when the aircraft is on the ground, gives the flight crew a continuous indication of the aircraft total weight and the location of the CG in percent MAC. Procedures are required to ensure the onboard weight and balance system equipment is periodically calibrated in accordance with the manufacturer’s instructions.
An operator may use an onboard weight and balance system to measure an aircraft’s weight and balance as a primary means to dispatch an aircraft, provided the FAA has certified the system and approved the system for use in an operator’s weight and balance control program. As part of the approval process, the onboard weight and balance system must maintain its certificated accuracy. The accuracy demonstration test is provided in the maintenance manual portion of the Supplemental Type Certificate (STC) or type certificate of the onboard weight and balance system.
The system consists of strain-sensing transducers in each main wheel and nosewheel axle, a weight and balance computer, and indicators that show the gross weight, the CG location in percent MAC, and an indicator of the ground attitude of the aircraft.
The strain sensors measure the amount each axle deflects and sends this data into the computer, where signals from all of the transducers and the ground attitude sensor are integrated. The results are displayed on the indicators for the flight crew. Using an onboard weight and balance system does not relieve an operator from the requirement to complete and maintain a load manifest.
Determining the Correct Stabilizer Trim Setting
It is important before takeoff to set the stabilizer trim for the existing CG location. There are two ways the stabilizer trim setting systems may be calibrated: in percent MAC and in units airplane nose up (ANU).
If the stabilizer trim is calibrated in percent MAC, determine the CG location in percent MAC as has just been described, then set the stabilizer trim on the percentage figure thus determined. Some aircraft give the stabilizer trim setting in units of ANU that correspond with the location of the CG in percent MAC. When preparing for takeoff in an aircraft equipped with this system, first determine the CG in percent MAC in the way described above, then refer to the stabilizer trim setting chart on the takeoff performance page of the pertinent AFM. Figure 9-9 is an excerpt from the AFM chart on the takeoff performance of a Boeing 737.
Figure 9-9. Stabilizer trim setting in ANU units.
Consider an airplane with these specifications
| CG location | station 635.7 |
| LEMAC | station 625 |
| MAC | 134.0 in |
- Determine the distance from the CG to the LEMAC by using the formula in Figure 9-10.
Figure 9-10. Determining the distance from CG to the LEMAC.
- Determine the location of the CG in percent MAC by using the formula found in Figure 9-11.
Figure 9-11. Determining the location of CG in percent MAC.
Refer to Figure 9-9 for all flap settings and a CG located at 8 percent MAC; the stabilizer setting is 73⁄4 units ANU.
Determining CG Changes Caused by Modifying the Cargo (Part One)
Since large aircraft can carry substantial cargo, adding, subtracting, or moving any of the cargo from one hold to another can cause large shifts in the CG.
Effects of Loading or Offloading Cargo
Both the weight and CG of an aircraft are changed when cargo is loaded or offloaded.In the following example, the new weight and CG are calculated after 2,500 pounds of cargo is offloaded from the forward cargo hold.
Aircraft specifications are
| Loaded weight | 90,000 lb |
| Loaded CG | 22.5 percent MAC |
| Weight change | 2,500 lb |
| Forward cargo hold centroid | station 352.1 |
| MAC | 141.5 in |
| LEMAC | station 549.13 |
- Determine the CG location in inches from the datum before the cargo is removed. Do this by first determining the distance of the CG aft of the LEMAC. [Figure 9-12]
Figure 9-12. Determining the location of CG in inches before cargo is removed.
- Determine the distance between the CG and the datum by adding the CG in inches aft of LEMAC to the distance from the datum to LEMAC. [Figure 9-13]
Figure 9-13. Determining the distance between CG and the datum.
- Determine the moment/1,000 for the original weight. [Figure 9-14]
Figure 9-14. Determining the moment/1,000 for the original weight.
- Determine the new weight and new CG by first determining the moment/1,000 of the removed weight. Multiply the weight removed (2,500 pounds) by the centroid of the forward cargo hold (352.1 inches), and then divide the result by 1,000. [Figure 9-15]
Figure 9-15. Determining the moment/1,000 of the removed weight.
- Subtract the removed weight from the original weight and subtract the moment/1,000 of the removed weight from the original moment/1,000. [Figure 9-16]
- Determine the location of the new CG by dividing the total moment/1,000 by the total weight and multiplying this by the reduction factor of 1,000. [Figure 9-17]
Figure 9-17. Determining the location of new CG.
- Convert the new CG location to percent MAC. First, determine the distance between the CG location and LEMAC. [Figure 9-18]
Figure 9-18. Determining the distance between the CG and LEMAC.
- Then, determine the new CG in percent MAC. [Figure 9-19]
Figure 9-19. Determining the new CG in percent MAC.
Loading 3,000 pounds of cargo into the forward cargo hold moves the CG forward 5.51 inches, from 27.12 percent MAC to 21.59 percent MAC.
Effects of Shifting Cargo From One Hold to Another
When cargo is shifted from one cargo hold to another, the CG changes, but the total weight of the aircraft remains the same. For example, use the following data:
| Loaded weight | 90,000 lb |
| Loaded CG | station 580.97 (22.5 percent MAC) |
| Forward cargo hold centroid | station 352 |
| Aft cargo hold centroid | station 724.9 |
| MAC | 141.5 in |
| LEMAC | station 549 |
To determine the change in CG (∆CG) caused by shifting 2,500 pounds of cargo from the forward cargo hold to the aft cargo hold, use the formula in Figure 9-20.
Figure 9-20. Calculating the change in CG, using index arms.
Since the weight was shifted aft, the CG moved aft and the CG change is positive. If the shift were forward, the CG change would be negative.
Before the cargo was shifted, the CG was located at station 580.97, which is 22.5 percent of MAC. The CG moved aft 10.36 inches, so the new CG is found using the formula from Figure 9-21.
Figure 9-21. Determining the new CG after shifting cargo weight.
Convert the location of the CG in inches aft of the datum to percent MAC by using the formula in Figure 9-22.
Figure 9-22. Converting the location of CG to percent MAC.
The new CG in percent MAC caused by shifting the cargo is the sum of the old CG plus the change in CG. [Figure 9-23]
Figure 9-23. Determining the new CG in percent MAC.
Some AFMs locate the CG relative to an index point rather than the datum or the MAC. An index point is a location specifiedby the aircraft manufacturer from which arms used in weight and balance computations are measured. Arms measured from the index point are called index arms, and objects ahead of the index point have negative index arms, while those behind the index point have positive index arms.
Use the same data as in the previous example, except for these changes:
| Loaded CG | index arm of 0.97, which is 22.5 percent of MAC |
| Index point | fuselage station 580.0 |
| Forward cargo hold centroid | –227.9 index arm |
| Aft cargo hold centroid | +144.9 index arm |
| MAC | 141.5 in |
| LEMAC | –30.87 index arm |
The weight was shifted 372.8 inches (–227.9 + Δ = +144.9, Δ =372.8).
The change in CG can be calculated by using this formula found in Figure 9-24.
Figure 9-24. Determining the change in CG caused by shifting 2,500 pounds of cargo.
Since the weight was shifted aft, the CG moved aft, and the CG change is positive. If the shift were forward, the CG change would be negative. Before the cargo was shifted, the CG was located at 0.97 index arm, which is 22.5 percent MAC. The CG moved aft 10.36 inches, and the new CG is shown using the formula in Figure 9-25.
Figure 9-25. Determining the new CG, moved aft 10.36 inches.
The change in the CG in percent MAC is determined by using the formula in Figure 9-26.
Figure 9-26. The change in the CG in percent MAC.
The new CG in percent MAC is the sum of the old CG plus the change in CG. [Figure 9-27]
Figure 9-27. The new CG in percent MAC.
Notice that the new CG is in the same location whether the distances are measured from the datum or from the index point.
Determining Cargo Pallet Loads and Floor Loading Limits
Each cargo hold has a structural floor loading limit based on the weight of the load and the area over which this weight is distributed. To determine the maximum weight of a loaded cargo pallet that can be carried in a cargo hold, divide its total weight, which includes the weight of the empty pallet and its tie down devices, by its area in square feet. This load per square foot must be equal to or less than the floor load limit.
In this example, determine the maximum load that can be placed on this pallet without exceeding the floor loading limit.
| Pallet dimensions | 36 by 48 in |
| Empty pallet weight | 47 lb |
| Tie down devices | 33 lb |
| Floor load limit | 169 lb per square foot |
The pallet has an area of 36 inches (3 feet) by 48 inches (4 feet), which equals 12 square feet, and the floor has a load limit of 169 pounds per square foot. Therefore, the total weight of the loaded pallet can be 169 × 12 = 2,028 pounds. Subtracting the weight of the pallet and the tie down devices gives an allowable load of 1,948 pounds (2,028 – [47 + 33]).
Determine the floor loading limit that is needed to carry a loaded cargo pallet having the following dimensions and weights:
| Pallet dimensions | 48.5 by 33.5 in |
| Pallet weight | 44 lb |
| Tiedown devices | 27 lb |
| Cargo weight | 786.5 lb |
Figure 9-28. Determining pallet area in square feet.
First, determine the number of square feet of pallet area as shown in Figure 9-28. Then, determine the total weight of the loaded pallet:
| Pallet | 44.0 lb |
| Tiedown devices | 27.0 lb |
| Cargo | 786.5 lb |
| Total | 857.5 lb |
Determine the load imposed on the floor by the loaded pallet. [Figure 9-29] The floor must have a minimum loading limit of 76 pounds per square foot.
Figure 9-29. Determining the load imposed on the floor by the loaded pallet.
Carried
The primary function of a transport or cargo aircraft is to carry payload, which is the portion of the useful load, passengers, or cargo that produces revenue. To determine the maximum amount of payload that can be carried, both the maximum limits for the aircraft and the trip limits imposed by the particular trip must be considered. In each of the following steps, the trip limit must be less than the maximum limit. If it is not, the maximum limit must be used.
These are the specifications for the aircraft in this example
| Basic operating weight (BOW) | 100,500 lb |
| Maximum zero fuel weight | 138,000 lb |
| Maximum landing weight | 142,000 lb |
| Maximum takeoff weight | 184,200 lb |
| Fuel tank load | 54,000 lb |
| Estimated fuel burn en route | 40,000 lb |
- Compute the maximum takeoff weight for this trip. This is the maximum landing weight plus the trip fuel. [Figure 9-30]
Figure 9-30. Finding the maximum takeoff weight.
- The trip limit is lower than the maximum takeoff weight, so it is used to determine the zero fuel weight. [Figure 9-31]
Figure 9-31. Determining zero fuel weight with lower trip limits.
- The trip limit is again lower than the maximum takeoff weight, so use it to compute the maximum payload for this trip. [Figure 9-32]
Figure 9-32. Finding maximum payload with lower trip limits.
Under these conditions, 27,500 pounds of payload may be carried.
Determining the Landing Weight
It is important to know the landing weight of the aircraft in order to set up the landing parameters and to be certain the aircraft is able to land safely at the intended destination.
In this example of a four-engine turboprop airplane, determine the airplane weight at the end of 4.0 hours of cruise under these conditions:
| Takeoff weight | 140,000 lb |
| Pressure altitude during cruise | 16,000 ft |
| Ambient temperature during cruise | –32 °C |
| Fuel burned during descent and landing | 1,350 lb |
Figure 9-33. Standard atmosphere table.
Refer to the U.S. Standard Atmosphere Table in Figure 9-33 and the gross weight table in Figure 9-34 when completing the following steps:
- Use the U.S. Standard Atmosphere Table to determine the standard temperature for 16,000 feet (–16.7 °C).
- The ambient temperature is –32 °C, which is a deviation from standard of 15.3 °C. (–32° – (–16.7°) = –15.3°). It is below standard.
- In the gross weight table, follow the vertical line representing 140,000 pounds gross weight upward until it intersects the diagonal line for 16,000 feet pressure altitude.
- From this intersection, draw a horizontal line to the left to the temperature deviation index (0 °C deviation).
- Draw a diagonal line parallel to the dashed lines for Below Standard from the intersection of the horizontal line and the Temperature Deviation Index.
- Draw a vertical line upward from the 15.3 °C Temperature Deviation From Standard.
- Draw a horizontal line to the left from the intersection of the Below Standard diagonal and the 15.3 °C temperature deviation vertical line. This line crosses the fuel flow–100 pounds per hour per engine index at 11.35 and indicates that each of the four engines burns 1,135 (100 × 11.35) pounds of fuel per hour. The total fuel burn for the 4-hour cruise is shown in Figure 9-35.
Figure 9-35. Determining the total fuel burn for a 4-hour cruise.
The airplane gross weight was 140,000 pounds at takeoff with 18,160 pounds of fuel burned during cruise and 1,350 pounds burned during the approach and landing phase. This leaves a landing weight of 140,000 – (18,160 + 1,350) = 120,490 pounds.
Determining Fuel Dump Time in Minutes
Most large aircraft are approved for a greater weight for takeoff than for landing. To make it possible for them to return to landing soon after takeoff, a fuel jettison system is sometimes installed. It is important in an emergency situation that the flightcrew be able to dump enough fuel to lower the weight to its allowed landing weight. This is done by timing the dumping process.
In this example, the aircraft has two engines operating and these specifications apply
| Cruise weight | 171,000 lb |
| Maximum landing weight | 142,500 lb |
| Time from start of dump to landing | 19 minutes |
Average fuel flow during
| Dumping and descent | 3,170 lb/hr/eng |
| Fuel dump rate | 2,300 lb/minute |
To calculate the fuel dump time in minutes:
- Determine the amount of weight the aircraft must lose to reach the maximum allowable landing weight. [Figure 9-36]
Figure 9-36. Determining the amount of weight the aircraft must lose to reach the maximum allowable landing weight.
- Determine the amount of fuel burned from the beginning of the dump to touchdown. [Figure 9-37] For both engines, this is 52.83 × 2 = 105.66 lb/minute. The engines burn 105.66 lbs of fuel per min for 19 minutes (the duration of the dump), which calculates to 2007.54 pounds of fuel burned between the beginning of the dump and touchdown.
Figure 9-37. Determining the amount of fuel burned from the beginning of the dump to touchdown.
- Determine the amount of fuel needed to dump by subtracting the amount of fuel burned during the dump from the required weight reduction. [Figure 9-38]
Figure 9-38. Determining the amount of fuel needed to dump.
- Determine the time needed to dump this amount of fuel by dividing the number of pounds of fuel to dump by the dump rate. [Figure 9-39]
Figure 9-39. Determine the time needed to dump fuel.
Weight and Balance of Commuter Category Airplanes
The Beech 1900 is a typical commuter category airplane that can be configuredto carry passengers or cargo. Figure 9-40 shows the loading data of this type of airplane in the passenger configuration.
As this airplane is prepared for flight,a manifest is prepared.[Figure 9-41]
- The crew weight and the weight of each passenger is entered into the manifest. The moment/100 for each occupant is determined by multiplying the weight by the arm and dividing by 100. This data is available in the AFM and is shown in the Weight and Moments— Occupants table. [Figure 9-42]
Figure 9-42. Weight and moments—occupants.
- The weight of the baggage in each compartment used is entered with its moment/100. This is determined in the Weights and Moments—Baggage table. [Figure 9-43]
Figure 9-43. Weight and moments—baggage.
- Determine the weight of the fuel. Jet A fuel has a nominal specific gravity at +15 °C of 0.812 and weighs 6.8 pounds per gallon, but at +25 °C, according to the Density Variation of Aviation Fuel Chart [Figure 9-44], it weighs 6.75 lb/gal. Using this chart, determine the weights and moment/100 for 390 gallons of Jet A fuel by interpolating between those for 6.7 lb/gal and 6.8 lb/gal. The 390 gallons of fuel at this temperature weighs 2,633 pounds, and its moment index is 7,866 lb-in/100.
Figure 9-44. Density variation of aviation fuel.
- Add all of the weights and all of the moment indexes. Divide the total moment index by the total weight, and multiply this by the reduction factor of 100. The total weight is 14,729 pounds; the total moment index is 43,139 lb-in/100. The CG is located at fuselage station 292.9. [Figure 9-45]
Figure 9-45. Weights and moments—usable fuel.
- Check to determine that the CG is within limits for this weight. Refer to the Weight and Balance Diagram. [Figure 9-46] Draw a horizontal line across the envelope at 14,729 pounds of weight and a vertical line from the CG of 292.9 inches aft of the datum. These lines cross inside the envelope, verifying the CG is within limits for this weight.
- Figure 9-46. Weight and balance diagram.
Determining CG Changes Caused by Modifying the Cargo (Part Two)
Determining the Maximum Amount of Payload That Can Be Carried
The primary function of a transport or cargo aircraft is to carry payload, which is the portion of the useful load, passengers, or cargo that produces revenue. To determine the maximum amount of payload that can be carried, both the maximum limits for the aircraft and the trip limits imposed by the particular trip must be considered. In each of the following steps, the trip limit must be less than the maximum limit. If it is not, the maximum limit must be used.
These are the specifications for the aircraft in this example
| Basic operating weight (BOW) | 100,500 lb |
| Maximum zero fuel weight | 138,000 lb |
| Maximum landing weight | 142,000 lb |
| Maximum takeoff weight | 184,200 lb |
| Fuel tank load | 54,000 lb |
| Estimated fuel burn en route | 40,000 lb |
- Compute the maximum takeoff weight for this trip. This is the maximum landing weight plus the trip fuel. [Figure 9-30]
Figure 9-30. Finding the maximum takeoff weight.
- The trip limit is lower than the maximum takeoff weight, so it is used to determine the zero fuel weight. [Figure 9-31]
Figure 9-31. Determining zero fuel weight with lower trip limits.
- The trip limit is again lower than the maximum takeoff weight, so use it to compute the maximum payload for this trip. [Figure 9-32]
Figure 9-32. Finding maximum payload with lower trip limits.
Under these conditions, 27,500 pounds of payload may be carried.
Determining the Landing Weight
It is important to know the landing weight of the aircraft in order to set up the landing parameters and to be certain the aircraft is able to land safely at the intended destination.
In this example of a four-engine turboprop airplane, determine the airplane weight at the end of 4.0 hours of cruise under these conditions:
| Takeoff weight | 140,000 lb |
| Pressure altitude during cruise | 16,000 ft |
| Ambient temperature during cruise | –32 °C |
| Fuel burned during descent and landing | 1,350 lb |
Figure 9-33. Standard atmosphere table.
Refer to the U.S. Standard Atmosphere Table in Figure 9-33 and the gross weight table in Figure 9-34 when completing the following steps:
- Use the U.S. Standard Atmosphere Table to determine the standard temperature for 16,000 feet (–16.7 °C).
- The ambient temperature is –32 °C, which is a deviation from standard of 15.3 °C. (–32° – (–16.7°) = –15.3°). It is below standard.
- In the gross weight table, follow the vertical line representing 140,000 pounds gross weight upward until it intersects the diagonal line for 16,000 feet pressure altitude.
- From this intersection, draw a horizontal line to the left to the temperature deviation index (0 °C deviation).
- Draw a diagonal line parallel to the dashed lines for Below Standard from the intersection of the horizontal line and the Temperature Deviation Index.
- Draw a vertical line upward from the 15.3 °C Temperature Deviation From Standard.
- Draw a horizontal line to the left from the intersection of the Below Standard diagonal and the 15.3 °C temperature deviation vertical line. This line crosses the fuel flow–100 pounds per hour per engine index at 11.35 and indicates that each of the four engines burns 1,135 (100 × 11.35) pounds of fuel per hour. The total fuel burn for the 4-hour cruise is shown in Figure 9-35.
Figure 9-35. Determining the total fuel burn for a 4-hour cruise.
The airplane gross weight was 140,000 pounds at takeoff with 18,160 pounds of fuel burned during cruise and 1,350 pounds burned during the approach and landing phase. This leaves a landing weight of 140,000 – (18,160 + 1,350) = 120,490 pounds.
Determining Fuel Dump Time in Minutes
Most large aircraft are approved for a greater weight for takeoff than for landing. To make it possible for them to return to landing soon after takeoff, a fuel jettison system is sometimes installed. It is important in an emergency situation that the flightcrew be able to dump enough fuel to lower the weight to its allowed landing weight. This is done by timing the dumping process.
In this example, the aircraft has two engines operating and these specifications apply
| Cruise weight | 171,000 lb |
| Maximum landing weight | 142,500 lb |
| Time from start of dump to landing | 19 minutes |
Average fuel flow during
| Dumping and descent | 3,170 lb/hr/eng |
| Fuel dump rate | 2,300 lb/minute |
To calculate the fuel dump time in minutes:
- Determine the amount of weight the aircraft must lose to reach the maximum allowable landing weight. [Figure 9-36]
Figure 9-36. Determining the amount of weight the aircraft must lose to reach the maximum allowable landing weight.
- Determine the amount of fuel burned from the beginning of the dump to touchdown. [Figure 9-37] For both engines, this is 52.83 × 2 = 105.66 lb/minute. The engines burn 105.66 lbs of fuel per min for 19 minutes (the duration of the dump), which calculates to 2007.54 pounds of fuel burned between the beginning of the dump and touchdown.
Figure 9-37. Determining the amount of fuel burned from the beginning of the dump to touchdown.
- Determine the amount of fuel needed to dump by subtracting the amount of fuel burned during the dump from the required weight reduction. [Figure 9-38]
Figure 9-38. Determining the amount of fuel needed to dump.
- Determine the time needed to dump this amount of fuel by dividing the number of pounds of fuel to dump by the dump rate. [Figure 9-39]
Figure 9-39. Determine the time needed to dump fuel.
Weight and Balance of Commuter Category Airplanes
The Beech 1900 is a typical commuter category airplane that can be configuredto carry passengers or cargo. Figure 9-40 shows the loading data of this type of airplane in the passenger configuration.
As this airplane is prepared for flight,a manifest is prepared.[Figure 9-41]
- The crew weight and the weight of each passenger is entered into the manifest. The moment/100 for each occupant is determined by multiplying the weight by the arm and dividing by 100. This data is available in the AFM and is shown in the Weight and Moments— Occupants table. [Figure 9-42]
Figure 9-42. Weight and moments—occupants.
- The weight of the baggage in each compartment used is entered with its moment/100. This is determined in the Weights and Moments—Baggage table. [Figure 9-43]
Figure 9-43. Weight and moments—baggage.
- Determine the weight of the fuel. Jet A fuel has a nominal specific gravity at +15 °C of 0.812 and weighs 6.8 pounds per gallon, but at +25 °C, according to the Density Variation of Aviation Fuel Chart [Figure 9-44], it weighs 6.75 lb/gal. Using this chart, determine the weights and moment/100 for 390 gallons of Jet A fuel by interpolating between those for 6.7 lb/gal and 6.8 lb/gal. The 390 gallons of fuel at this temperature weighs 2,633 pounds, and its moment index is 7,866 lb-in/100.
- Add all of the weights and all of the moment indexes. Divide the total moment index by the total weight, and multiply this by the reduction factor of 100. The total weight is 14,729 pounds; the total moment index is 43,139 lb-in/100. The CG is located at fuselage station 292.9. [Figure 9-45]
- Check to determine that the CG is within limits for this weight. Refer to the Weight and Balance Diagram. [Figure 9-46] Draw a horizontal line across the envelope at 14,729 pounds of weight and a vertical line from the CG of 292.9 inches aft of the datum. These lines cross inside the envelope, verifying the CG is within limits for this weight.
- Figure 9-46. Weight and balance diagram.
Determining CG Changes Caused by Modifying the Cargo (Part Three)
Determining the Changes in CG When Passengers Are Shifted
Using the loaded weight and CG of the Beech 1900, calculate the change in CG when the passengers in rows 1 and 2 are moved to rows 8 and 9. [Figure 9-47] Note that there is no weight change, but the moment index has been increased by 1,155 pound-inches/100 to 44,294. The new CG is at fuselage station 300.7. [Figure 9-48]
Figure 9-48. Determining the new CG at fuselage station.
This type of problem is usually solved by using the following two formulas. The total amount of weight shifted is 550 pounds (300 + 250) and both rows of passengers have moved aft by 210 inches (410 – 200 and 440 – 230). The CG has been shifted aft by 7.8 inches, and the new CG is at station 300.7. [Figure 9-49]
Figure 9-49. Determining the new CG at station after CG has shifted aft.
In a large cabin aircraft with high-density seating such as the B737-800, the operator must account for the seating of passengers in the cabin [Figure 9-50]. If assigned seating is used to determine passenger location, the operator must implement procedures to ensure the assignment of passenger seating is incorporated into the loading procedure. It is recommended that the operator take into account the possibility that some passengers may not sit in their assigned seats.
If the actual seating location of each passenger is not known, the operator may assume that all passengers are seated uniformly throughout the cabin or a specified subsection of the cabin. Reasonable assumptions can be made about the manner in which people distribute themselves throughout the cabin. For example, window seats are occupied first followed by aisle seats, followed by the remaining seats (window-aisle-remaining seating). Both forward and rear loading conditions should be considered. The passengers may fill up the window, aisle, and remaining seats from the front of the aircraft to the back, or the back to the front.
If necessary, the operator may divide the passenger cabin into subsections or zones and manage the loading of each zone individually. It can be assumed that passengers will be sitting uniformly throughout each zone.
Another consideration is the in flight movement of passengers, crew, and equipment. It is assumed that all passengers, crew, and equipment are secured when the aircraft is in the takeoff or landing configuration.Standard operating procedures should be taken into account. Examples of items that can move during flight are:
- Flight deck crew members moving to the lavatory.
- Flight attendants moving throughout the cabin.
- Service carts moving throughout the cabin.
- Passengers moving throughout the cabin.
- Passengers moving to the lavatory.
Determining Changes in Weight and CG When the Aircraft Is Operated in Its Cargo Configuration
To determine changes in weight and CG when the aircraft is operated in its cargo configuration,the Beech 1900 is used as an example. Figure 9-51 illustrates the airplane configuration.Notice that the arm of each cargo section is the centroid of that section.
Figure 9-51. Loading data for cargo configuration.
The flight manifest of the Beech 1900 in the cargo configuration is illustrated in Figure 9-52. The BOW includes the pilots and their baggage and there is no separate item for them.
At the standard temperature of 15 °C, the fuel weighs 6.8 pounds per gallon. Refer to Figure 9-45 to determine the weight and moment index of 370 gallons of Jet A fuel. The CG under these loading conditions is located at station 296.2.
Determining the CG Shift When Cargo Is Moved From One Section to Another
To calculate the CG when cargo is shifted from one section to another, use the formula found in Figure 9-53. If the cargo is moved forward, the CG is subtracted from the original CG. If the cargo is shifted aft, add the CG to the original.
Figure 9-53. Shifting cargo from one section to another.
Determining the CG Shift When Cargo Is Added or Removed
To calculate the CG when cargo is added or removed, add or subtract the weight and moment index of the affected cargo to the original loading chart. Determine the new CG by dividing the new moment index by the new total weight, and multiply this by the reduction factor. [Figure 9-54]
Figure 9-54. Determining the new CG by dividing the new moment index by the new total weight, multiplied by the reduction factor.
Determining Which Limits Are Exceeded
When preparing an aircraft for flight,consider all parameters and check to determine that no limits have been exceeded. Consider the parameters below, and determine which limit, if any, has been exceeded.
- The aircraft in this example has a basic empty weight of 9,005 pounds and a moment index of 25,934 pound inches/100.
- The crew weight is 340 pounds and its moment/100 is 439.
- The passengers and baggage have a weight of 3,950 pounds and a moment/100 of 13,221.
- The fuel is computed at 6.8 lb/gal. The ramp load is 340 gallons or 2,312 pounds. Fuel used for start and taxi is 20 gallons, or 136 pounds. Fuel remaining at landing is 100 gallons, or 680 pounds.
- Maximum takeoff weight is 16,600 pounds.
- Maximum zero fuel weight is 14,000 pounds.
- Maximum landing weight is 16,000 pounds.
Take these steps to determine which limit, if any, is exceeded:
- Determine the zero fuel weight, which is the weight of the aircraft with all of the useful load except the fuel on board. [Figure 9-55] The zero fuel weight of 13,295 pounds is less than the maximum of 14,000 pounds, so this parameter is acceptable.
Figure 9-55. Determining the zero fuel weight.
- Determine the takeoff weight and CG. The takeoff weight is the zero fuel weight plus the weight of the ramp load of fuel, minus the weight of the fuel used for start and taxi. The takeoff CG is the moment/100 divided by the weight, and then the result multiplied by 100. The takeoff weight of 15,471 pounds is below the maximum takeoff weight of 16,600 pounds, and a check of the weight and balance diagram shows that the CG at station 298.0 is also within limits. [Figure 9-56]
Figure 9-56. Determining the takeoff weight and CG.
- Determine the landing weight and CG. This is the zero fuel weight plus the weight of fuel at landing. [Figure 9-57] The landing weight of 13,975 pounds is less than the maximum landing weight of 14,000 to 16,000 pounds. According to the weight and balance diagram, the landing CG at station 297.5 is also within limits.
Figure 9-57. Determining the landing weight and CG.
