balance. Large aircraft must have fuel loaded in a particular manner determined by the total load, and then the tanks must be selected in a sequence that will keep the load in balance. Swept-wing aircraft have special problems along these lines. Fuel in outboard tanks has a tendency to rotate the aircraft in a tail-heavy direction and fuel in inboard tanks adds to a nose-heavy condition (fig. 7). The use of fuel from swept-wing tanks must be carefully managed to keep c.g. under control.
OUTBOARD FUEL = TAIL HEAVY
INBOARD FUEL = NOSE HEAVY the main cabin. Particular care must be taken to restrain this type load with proper tiedown devices.
MANAGEMENT OF WEIGHT AND
BALANCE CONTROL Weight and balance control is a matter of serious concern to all pilots and to many people on the ground who are involved in the support of flight.
The pilot has control over the loading and fuel management within established limits for the particular aircraft. The pilot has weight and balance information available in the form of aircraft records and operating handbooks. Loading information is also available in the form of placards in baggage compartments and on tank caps. The aircraft owner or operator should make certain that up-to-date information is available in the aircraft FIGURE 7. Effect of fuel in swept-wing aircraft.
SHIFTING OF LOOSE CARGO The shifting of cargo or baggage during flight can result in several hazards, not the least of which is a dangerous balance condition. If the c.g. of an aircraft is already near the forward or aft limit, a significant longitudinal shift of cargo may make control difficult or impossible. This hazard is most likely to occur in aircraft having cargo poorly secured in for the pilot's use.
The owner or operator of the aircraft should insure that maintenance personnel make appropriate entries in the aircraft records when repairs or modifications have been accomplished. Weight changes must be accounted for and proper notations made in weight and balance records. Without such notations, the pilot has no foundation upon which to base calculations and decisions.
The aircraft manufacturer and the FAA (Federal Aviation Administration) have major roles in designing and certificating the aircraft with a safe and workable means of controlling weight and balance.
If the prototype aircraft has weight and balance control problems which are potentially dangerous, design changes are made before the aircraft is type certificated.
Chapter 2
TERMS AND DEFINITIONS Weight x Arm = Moment The student of weight and balance needs to be familiar with terms used in publications related to many aspects of the subject. These terms are fairly well standardized; however, terms related to general aviation aircraft do not always apply to air carrier aircraft. Where there is a difference, the following definitions will indicate to which type of aircraft the term applies.
1. Arm (moment arm) -is the horizontal distance in inches from the reference datum line to the center of gravity of the item. The algebraic sign is plus (+) if measured aft of the datum, and minus. (-) if measured forward of the datum.
2. Center of gravity (c.g.)-is the point about which an aircraft would balance if it were possible to suspend it at that point. It is the mass center of the aircraft, or the theoretical point at which the entire weight of the aircraft is assumed to be concentrated.
It may be expressed in percent of MAC (mean aerodynamic chord) or in inches from The reference datum.
3. Center of gravity limits-are the specified forward and aft or lateral points beyond which the c.g. must not be located during takeoff, flight or landing. These limits are indicated on pertinent FAA aircraft type certificate data sheets, specifications, or weight and balance records, and meet the requirements of Federal Aviation Regulations.
4. Center of gravity range-is the distance between the forward and aft c.g. limits indicated on pertinent aircraft specifications.
5. Datum (reference datum) -is an imaginary vertical plane or line from which all measurements of arm are taken. The datum is established by the manufacturer. Once the datum has been selected, all moment arms and the location of permissible c.g. range must be taken with reference to that point.
6. Delta-is a Greek letter expressed by the symbol A. It is used in weight and balance calculations, as well as in other forms of mathematics, to indicate a change of values.
As an example, 4 c.g. indicates a change (or movement) of the c.g.
7. Fuel load-is the expendable part of the load of the aircraft. It includes only usable fuel, not fuel required to fill the lines or that
C.G. RANGE FWD LIMIT • AFT LIMIT DATUM MINI (+)
ARM ARM DATUM MOMENT = 700 LBS-IN (+ )ARM 70' T IOLBS STA O STA 70 LEMAC DATUM
• C.G (+) ARM MAC STA 0 STA 50 FIGURE 8. Definitions.
which remains trapped in the tank sumps. 10,000 are used to simplify weight and bal-
8. LEMAC-is the leading edge of the mean ance calculation processes.
aerodynamic chord. 13. Standard weights-have been established
9. Moment-is the product of the weight of an pressed in pound-inches (Ib.-in.) or inch- item multiplied by its arm. Moments are ex- to be used in lieu of available actual weights. balance computations. These weights are not for numerous items involved in weight and
10. Moment index (or index) -is a moment pounds. Total moment is the weight of the aircraft multiplied by the distance between the datum and the c.g. of charter flights and other special services involving the carriage of special groups; e.g., Standard passenger weights should not be used in computing the weight and balance athletic groups, small foreign nationals, etc.
divided by a constant such as 100, 1,000, or Some of the standard weights are:
10,000. The purpose of using a moment in- General aviation - crew dex is to simplify weight and balance com- and passenger 170 lh.
putations of large aircraft where heavy items Air carrier - passenger and long arms result in large, unmanageable Air carrier - passenger (summer) 160 1b.
numbers.. (winter) .. 165 Ib.
11. Mean aerodynamic chord (MAC) -is the Air carrier - male trailing edge of the wing. The MAC is specified for the aircraft by determining the average distance from the leading edge to the Air carrier - female Air carrier - all other cabin attendant rabin attendant 130 Ib. 150 lb.
average chord of an imaginary wing which crewmembers 170 Ib.
has the same aerodynamic characteristics as Air carrier - carry-on
12. Reduction factor--is the constant which the actual wing. Gasoline Oil ..: haggage 5 lb. 6 lb./U.S. gal. 7.5 lb./U.S. gal.
when divided into a moment results in an Water 8.35 lb./U.S. gal.
index. Reduction factors of 100, 1,000, or Jet fuel 6.7 1b./ U.S. gal.
14. Station-is a location in the aircraft which is identified by a number designating its distance in inches from the datum. The datum is, therefore, identified as station zero.
The station and arm are usually identical.
An item located at station +50 would have an arm of 50 inches.
15. Useful load-is the weight of the pilot, copilot, passengers, baggage, usable fuel, and drainable oil. It is the empty weight subtracted from the maximum allowable takeoff weight. This term applies to general aviation aircraft only.
16. Weight, basic operating-is the weight of the aircraft, including the crew, ready for flight but without payload and fuel. This term is only applicable to transport aircraft.
17. Weight, empty-consists of the airframe, engines, and all items of operating equipment that have fixed locations and are permanently installed in the aircraft. It includes optional and special equipment, fixed ballast, hydraulic fluid, and undrainable (residual) fuel When oil is used for propele eathering, such oil is included as residual
18. Weight, maximum landing-is the maximum weight at which the aircraft may normally be landed. The maximum landing weight may be limited to a lesser weight when runway length or atmospheric conditions are adverse.
19. Weight, maximum takeoff-is the maximum allowable weight at the start of the takeoff run. Some aircraft are approved for loading to a greater weight (ramp or taxi) only to allow for fuel burnoff during ground operation. The takeoff weight for a particular flight may be limited to a lesser weight when runway length, atmospheric conditions, or other variables are adverse.
20. Weight, maximum allowable zero fuelis the maximum weight authorized for the aircraft not including fuel load. Zero fuel weight for each particular flight is the operating weight plus the payload.
21. Weight, ramp or taxi-is the maximum takeoff gross weight plus fuel to be burned during taxi and runup.
AIRCRAFT WEIGHT NOMENCLATURE (Transport Aircraft) Term Example (pounds) Notes Empty weight 65.000 Includes: Basic structure, hydraulic fuid, air conditioning Auid, and residual fuel and oil.
+ Operating items 5,000 Includes: Crew, crew luggage, oil, water, alcohol, and normal passenger service equipment.
= Basic operating weight 70,000 + Payload 20,000 Includes: Passengers, baggage, and cargo.
= Zero fuel weight 90,000 + Fuel load 31,000 Includes: All usable fuel.
= Ramp or taxi weight 121,000
- Ramp fuel . 1,000 Includes: Fuel used prior to takeoff.
= Takeoff weight 120,000
- Fuel used 20,000 Includes: Fuel burned or dumped.
= Landing weight • 100,000 (General Aviation Aircraft) Empty weight . .2,905 Includes: Airframe, engines, all fixed and permanent operating equipment, and residual fuel and oil.
+ Useful load 1,695 Includes: Pilot, copilot, passengers, baggage, fuel, and oil.
= Takeoff weight .4,600
- Fuel used 460 Includes: Fuel burned.
= Landing weight . 4,140 NoTE.-The weights above are used for illustration only. The actual values will vary for each aircraft and each flight.
Chapter 3
EMPTY WEIGHT CENTER OF GRAVITY Weighing aircraft with accurately calibrated scales is the only sure method of obtaining an accurate empty weight and c.g. location. The use of weight and balance records in accounting for and correcting the aircraft weight and balance location is reliable over certain periods of time. Over extended intervals, however, unknown service weight pickup and other factors will render the basic weight and c.g. data inaccurate. For this reason, periodic aircraft weighings are desirable. Aircraft may also be weighed when major modifications or repairs are made, when the pilot reports unsatisfactory flight characteristics such as nose or tail heaviness, and when recorded weight and balance data are suspected to be in error. The pilot or owner may never actually weigh an aircraft but he should be aware of the general procedure and requirements.
WEIGHING EQUIPMENT The type of equipment which is used to weigh aircraft will vary with the aircraft size. Light air- 10 craft may be weighed on commercial type platform scales. Large aircraft are usually weighed with electronic weighing sets (fig. 9). In any case, the individual scale or the electronic cell should have a capacity rating suitable for the size of the aircraftfor instance, three scales with 5,000 lb.' ratings would be suitable to weigh a 10,000 lb. aircraft while an electronic cell set with cells of 50,000 lb.
capacity would be needed for a 100,000 lb. aircraft.
Only weighing equipment that is maintained and calibrated to acceptable standards should be used to weigh aircraft.
Jacks are ordinarily used for leveling an aircraft.
Care should be taken to use jacks of sufficient capacity and extension for the particular aircraft.
Adapters for jack points or blocks for wheels are necessary to prevent the aircraft from moving or falling when it has been raised off the ground. Accurate spirit levels are used to assure that the aircraft is in a level position. Large aircraft are often checked
FIGURE 9. Electronic weighing kit.
for level by the use of a surveyor's transit. Plumb bobs, straight edges, and chalk lines are some other items of auxiliary equipment used during the weighing process.
WEIGHING PROCEDURE The aircraft should be weighed in accordance with instructions in the manufacturers' manuals or other pertinent technical data. Typical procedures include:
a. The aircraft should be cleaned inside and out.
b. The aircraft equipment should be checked against the equipment list section of the weight and balance record (fig. 21). This list should have been updated to account for all equipment changes made after the list was initially established by the manufacturer. All items which are not included as fixed equipment on the updated list should be removed for the empty weight check.
c. Fuel tanks should be drained in accordance with the manufacturer's instructions. In lieu of specific instructions, the tanks can be drained until the tank quantity gauges read "zero" or empty in level flight attitude. The amount of fuel remaining in the tanks, lines, and engines is termed "residual fuel" and it is to be included in the empty weight. In certain cases, it may not be feasible to drain the fuel tanks; if this is so, fill the tanks to capacity.
The weight of the fuel in the tanks should then be calculated and later subtracted from the total weight to obtain the empty weight.
d. Unless otherwise noted in the aircraft specification, the oil system should be completely drained through the normal drain ports. Under these conditions, the amount of oil remaining in the tanks, lines, and engine is termed "residual oil" and it will be included in the empty weight. When the aircraft is weighed without draining the oil, the tanks should be filled to capacity. The oil weight can then be calculated at a standard weight of 7.5 Ibs./gal.
e. Reservoirs or tanks containing hydraulic fluid.
anti-icing fluid and other liquids which are considered part of the empty weight should be filled to capacity.
f. Generally, all aircraft are weighed in a level position. This means the aircraft is placed in an attitude in which its longitudinal and lateral axes are parallel to a horizontal surface.
Leveling devices such as leveling lugs and jig-located brackets and plates have been accurately installed on the aircraft by the manufacturer to facilitate the leveling procedure.
The methods used to level specific aircraft vary with the type of aircraft and the leveling instructions provided by the manufacturer.
1. Jacks which are used for leveling should never be employed on the aircraft other than at the specified jacking points. If wing and fuselage jacks are used to level the aircraft, it may be necessary to prevent the gear shock struts from extending when the aircraft is raised. The manufacturer's instructions will indicate the appropriate procedures in this case.
2. During the leveling procedure, extreme care should be exercised to avoid side loads which may cause the aircraft to slip off the jacks. When raising the aircraft with two wing or two main landing gear jacks, they should be actuated simultaneously in order to maintain the aircraft in a laterally level attitude. General instructions for various types of aircraft are as follows:
(a) Nose wheel oleo struts or tires may be inflated or deflated to level the aircraft. They may also be used to obtain an approximately level position prior to jacking the aircraft.
(b) A hoist or jack should be employed to level tail-wheel aircraft when the aircraft is too heavy to raise the tail
(c) Normally, the smaller type of rotary.
90°
FIREWALL
L DATUM FIGURE 10. Measurement of reaction points.
wing aircraft incorporating skids rest in approximately level position.
Larger rotary-wing aircraft with oleo struts may be placed in the level position by inflating or deflating the struts.
(d) A float plane may be weighed by placing the floats on four scales with suitable blocks to obtain concentrated reaction points. Care must be taken to prevent damage to the floats from this concentrated loading. Ordinarily, the normal landplane leveling points are used. The floats are not necessarily level. Amphibians can be weighed with the landing gear down and on the scales.
g. Once the aircraft is in the level position, it is necessary to measure and record dimensions.
Three horizontal dimensions need to be measured to determine the horizontal location of the c.g. of the aircraft as weighed. In some cases, these dimensions can be obtained from aircraft records. When the landing gear wheels are used as weighing (reaction) points, the three dimensions to be determined are as fo!- lows (see fig. 10) :
1. The horizontal distance from the reference datum to some known jig point. This dimension, for small aircraft, is usually zero because the reference datum is an easily identified location, such as the firewall or wing leading edge. It is particularly important to determine such a dimension if the datum is located ahead of the nose of the aircraft.
2. The distance from the jig point to a lateral line passing through the main gear reaction points. This measurement should be made along a line which is parallel to the longitudinal axis of the aircraft.
3. The wheel base or distance between the main and forward or aft reaction points.
Measuring these distances can be accomplished by projecting the required points to the hangar floor.
To project the jig point to the hangar floor, a plumb bob may be suspended from the center of the jig point so that the plumb bob is approximately one half inch above the floor. When the swing of the bob dampens, a cross mark is made on the floor directly under the tip of the plumb bob. The main reaction points are projected to the floor in the same manner. After marking the crosses for the two main gear points, a chalked string is stretched between them. The string is then snapped to the floor, leaving a clear straight chalkline between the main reaction points. The nose or tail reaction point is projected to the hangar floor in a similar manner (fig. 10).
After these points are projected to the floor it is a simple matter to measure the required dimensions.
When measuring these distances, it is necessary that the tape be parallel to the centerline of the aircraft.
Measurements made from the main reaction points DATUM 94" FIGURE 11. Weighing aircraft on platform scales.
are taken perpendicular to the chalkline joining these two points. When fuselage and wing jack points are used as reaction points in weighing the aircraft, it is unnecessary to measure dimensions.
These points will remain fixed and their moment arms may be found in the aircraft records. Care must be taken to use the fixed reaction points indicated in the records for the particular aircraft being measured. Because of manufacturing tolerances, and minor model changes. the fixed reaction points are not necessarily identical for all aircraft of a particular type.
Weighing procedures may vary with the aircraft and the type of weighing equipment employed. The weighing procedures contained in the manufacturers' manuals should be followed for each particular aircraft. The following general instructions illustrate a common method and some of the typical precautions (see fig. 11) :
a. Aircraft are weighed in closed hangars to avoid vibrations or lift forces which would otherwise be caused by air flowing over the lifting surfaces. Such vibrations or aerody.
namic forces would result in fluctuating scale realings and increase the possibility of error.
b. The aircraft must be dry before it is weighed.
An aircraft should never be weighed immediately after it has been washed.
c. The aircraft should be weighed in the level attitude. If the main wheels are used as reaction points, the brakes should not be setresultant side loads on the scales or weighing units may cause erroneous readings.
d. The aircraft should be raised simultaneously on all reaction points, especially when using electronic weighing equipment. When the aircraft is supported at the weighing reaction points only, and is in the level position, scale readings may be obtained (fig. 11).
e. Several readings are taken for each reaction point and the average reading is entered on the aircraft weighing form.
f. Before the aircraft is lowered, it is necessary to make certain that all necessary measurements and scale readings have been obtained and recorded. The scales or cells should be rechecked for errors and compared to the calibration errors recorded before the weighing process. Appropriate calibration corrections or re-weighing may then be necessary.
g. When data for comparison is available, an attempt should be made to verify the results obtained from each weighing. Verification may be made by comparing results with a previous weighing of an aircraft of the same
FINDING CENTER OF GRAVITY After the necessary dimensions and weights have been obtained, the empty weight and the empty c.g.
can be calculated. Empty weight is the total of the three scale readings after subtracting the weight of tare items plus or minus calibration errors. This weight is important for subsequent calculation of maximum weight and also is a necessary factor in the determination of c.g.
Center of gravity computations may be accomplished by several methods. Fundamentally, the c.g.
is the point at which all the weights of the aircraft can be considered to be concentrated. The average location of the weights can, therefore, be obtained by dividing the total moments (wt. X arm) by the total weight. The process then involves multiplying each measured weight by its arm-to obtain a moment and adding the moments.
Example 1.
Weight (lb.) Arm (in.) Moment (lb.-in.)
Right wheel ... 564 3 1,692 Left wheel .... 565 3 1,695 Rear wheel ... 40 225 9,000 Total ... 1,169 . ... 12,387 12,387 = 10.6 in. aft of datum 1,169 Extra care must be taken in these types of empty weight calculations if one or more of the arms is located ahead of the datum. In this event, the algebraic sign of the arm and moment will be negative. It should be remembered that a positive number (the weight) times a negative number (the arm) results in a negative number (the moment). Following the multiplication step, additional care must be taken when adding wheel moments to obtain total moments and when dividing total moments by total weight to obtain c.g. In all these mathematical operations, the significance of the algebraic sign must be The c.g. can also be obtained by the use of a special formula:
c.g. =D+ W 13
DATUM _ DATUM D
NOSE WHEEL TYPE AIRCRAFT
DATUM LOCATED FORWARD OF
THE MAIN WHEELS C.G. = D - -L
TAIL WHEEL TYPE AIRCRAFT
DATUM LOCATED FORWARD OF
THE MAIN WHEELS DATUM D _— DATUM C.G.
- L-
NOSE WHEEL TYPE AIRCRAFT TAIL WHEEL TYPE AIRCRAFT
THE MAIN WHEELS DATUM LOCATED AFT OF THE MAIN WHEELS DATUM LOCATED AFT OF C.G.=- (D+ C.G. = Distance from datum to center of gravity of the aircraft.
W = The weight of the aircraft at the time of weighing.
D = The horizontal distance measured from the datum to the main wheel weighing point.
L = The horizontal distance measured from the main wheel weighing point to the nose or tail weighing point.
F = The weight at the nose weighing point.
R = The weight at the tail weighing point.
FIGURE 12. Empty weight c.g. formulas.
This formula and others which are applicable to nose-wheel aircraft and those with the datum located in an aft position are shown in figure 12, together with definitions of the symbols involved. The use of these formulas simplifies the calculations in several ways. In effect, the datum is mathematically moved to the main gear by this process, resulting in relatively small moments which are easy to handle in weight and balance calculations. A major benefit of the use of these formulas is the elimination of multiplication steps that involve negative arms and negative moments.
is the same but the process is somewhat simplified because the step of multiplication of each weight and arm has been eliminated. The solution shown in figure 13 shows how the information is entered in the empty weight c.g. part of a weight and balance report form.
An aeronautical computer (fig. 14) can be used to further simplify the problem when the formula is converted into a proportion form:
Example 2.
A solution to the problem in example 1 by use of the c.g. formula is shown in figure 13. The answer The computer solution (7.6 in.) is then added to the 14
DATUM (LEADING EDGE
OF WING ROOT SECTION)
COMPUTED → C.G.
- TARE 27 LBS LEFT SCALE 565 LBS SCALE READING MAIN WHEEL - RIGHT SCALE 564 LBS 67 LBS
WEIGHING POINT
D,MEASURED
L,MEASURED TO FIND: EMPTY WEIGHT AND EMPTY WEIGHT CENTER OF
GRAVITY GIVEN: Datum is the leading edge of the wing.
D, Measured distance from main wheel to datum = 3" L, Measured distance from main to tail wheel = 222" SOLVING: EMPTY WEIGHT Weighing Scale Net Point Reading Tare Weight Right 564 564 Left 565 565 Rear 67 27 40 Empty Weight (W) 1169 SOLVING: EMPTY WEIGHT CENTER OF GRAVITY C.G. = D+ (R×L) = 3 + (40 × 222/ 1169) = 3 + 7.6 = 10.6" FIGURE 13. Empty weight and empty weight c.g.
TAIL WHEEL WEIGHT DISTANCE FROM MAIN WHEEL TO C.G.
TOTAL WEIGHT DISTANCE BETWEEN MAIN AND TAIL WHEEL
SETUP THESE NUMBERS READ ANSWER ON OUTER SCALE 1169 40 222 = 7.6 7.6
SOICOR ALT ISS NST MIT 3 00Ù COMPUTER.
TEMPERATURE FOR AIRSPEED ANO
DENSITY ALTITUDE 1 40 MOURS I 8- TYPE MO +
RESEMINAL INSI PROPERTY BASRUMMES COL DEAD FIGURE 14. Computer solution-empty weight c.g.
arm of the main wheels (3 in.) to obtain the c.g.
location (10.6 in.) aft of datun.
PERCENT OF MEAN AERODYNAMIC
CHORD (MAC) Expression of the c.g. relative to the*MAC is a common practice. The c.g. position is expressed as a % MAC (percent of the mean aerodynamic chord) and the c.g. limits are expressed in the same manner (fig. 15).
The relative positions of the c.g. and the aerodynamic center or center of lift of the wing have critical effects on the fight characteristics of the aircraft. Consequently, relating the c.g. loration to the chord of the wing is convenient from a design and LEMAC C.G. = 25% MAC 15".
→ C.G.
-MAC = 60" FICURE 15. Percent of mean aerodynamic chord.
16 operations standpoint. Normally, an aircraft will have acceptable flight characteristics if the c.g. is located somewhere near the 25% average chord point. This means the c.g. is located one-fourth of the total distance back from the leading edge of the average wing section. Such a location will place the c.g. forward of the aerodynamic center for most airfoils.
The mean aerodynamic chord is established by the manufacturer. If the wing is not swept and has a constant chord, the straight line distance from leading edge to trailing edge (the chord) would also be the MAC. However, if the wing is swept or tapered, the mean aerodynamic chord is more complicated to define, and the manufacturer's description is the only reliable description for weight and balance purposes. The MAC can be defined as the "chord of an imaginary airfoil which has the same aerodynamic characteristics as the actual airfoil."
In summary, the MAC is established by the manufacturer who defines its leading edge (LEMAC) and its trailing edge in terms of inches from datum.
The c.g. location and various limits are then expressed in percentages of the MAC. The following