1.03.03 MASS AND BALANCE1 . 0 3 F L I G H T P E R F O R M A N C E

Design Limit Load (DLL) - is the maximum load that can be applied

to the structure repeatedly during normal operations without

inducing excessive fatigue.

Design Ultimate Load (DUL) = DLL + a factor of safety of 50%. It is

the minimum load the structure must be able to absorb in an

emergency (heavier than normal landing or flight in exceptional

gusty wind conditions) without collapsing. In case of excess of the

DUL the structure is likely to suffer some permanent damage and

may even collapse altogether.

LOAD LIMITS LIMITATIONS

OVERLOADING LIMITATIONS

With an increase in weight performance is reduced:

• Take off and landing distances will increase

• V1 decision speed, VR rotation speed, V2 screen height, and the stopping

distance will all increase

• The climb gradient, rate of climb and ceiling height will all reduce

• The rate of descent will increase

• The stalling speed will increase and maximum speed will reduce

• The safety margins and the effective speed range between low and high

speed buffet will reduce

• Drag and fuel consumption will increase

• Range and endurance will reduce

CENTER OF GRAVITY LIMITS LIMITATIONS

• The Centre of Gravity limits is a range of movement of CG between a maximum forward position and a

maximum aft position which are set by the aircraft manufacturer and cannot be exceeded.

• The CG must be on one of the limits or within the limit range at all times.

• The limits are given in the Flight manual and are defined relative to the datum.

• They may also be given as a percentage of the mean chord of the wing. The mean chord was known as

the Standard mean Chord but is now known as the Mean Aerodynamic Chord or more simply, the MAC.

OUT OF FORWARD CG LIMIT LIMITATIONS

• Drag increases, consequently, fuel consumption,

range and endurance decrease

• The longitudinal stability is increased

• The increase in tail down force is equivalent to an

increase in weight; consequently the stall speed will

increase

• The ability to pitch the nose up or down will

decrease because of the increased stability

• Take-off speeds V1 , VR , VMU will increase

CG

Lift (on wings)

Lift (on stabilizer)

CG limits

weight

VMU - Min lift off speed

CG OUT THE AFT LIMIT LIMITATIONS

A CG outside the aft limit:

• Longitudinal stability is reduced and, if the CG is too

far aft, the aircraft will become very unstable. Stick

forces in pitch will be light, leading to the possibility

of over stressing the aircraft by applying excessive

‘g’

• Recovering from a spin may be more difficult as a

flat spin is more likely to develop.

• Range and endurance will probably decrease due to

the extra drag caused by the extreme maneuvers

• Glide angle may be more difficult to sustain

because of the tendency for the aircraft to pitch up.

CG

Lift (on wings)

Lift (on stabilizer)

CG limits

weight

DATUM BALANCE ARM AND MOMENT

A point along the longitudinal axis (center line) of the

aeroplane (or it extension) designated by the manufacturer as

the zero or reference point from which all balance arms begin.

By taking moments about the balance arm the CG position of

the aircraft can be determine. For the purposes of this phase

of study the lateral displacement of the CG from the

longitudinal axis is assumed to be zero.

BALANCE ARM BALANCE ARM AND MOMENT

The distance from the aircraft’s Datum to the CG position or

centroid of a body of mass.

For example, the centroid of a square or rectangle is the exact

center of the square or rectangle and, in such cases, the

balance arm is the distance from the datum to the exact

center of the square or rectangle. Unfortunately, cargo bays

are seldom exact squares or rectangles and so the centroid

(the point the total weight acts through) is given by the

manufacturer.

For the purposes of calculations, all balance arms ahead of (in

front of) the datum are given a negative (-) prefix and those

behind (aft of) the datum are given a positive (+) prefix.

LOADING INDEX BALANCE ARM AND MOMENT

Force (or Mass) x Arm = Moment

For example, moment is: 2415 lbs x 77.7 in = 187645.5 lbs in

A Loading Index is simply a moment divided by a constant and

has the effect of reducing the magnitude of the moment to

one that is much easier to operate.

For this example constant = 100

Loading index: moment/100 = 1876.46

UNITS CONVERSIONS UNITS OF VOLUME AND MASS

Mass Conversions

• Pounds (lb) to Kilograms (kg): lb x 0.454

• Kilograms (kg) to Pounds (lb): kg x 2.205

Volumes (Liquid)

• Imperial Gallons to Liters (l): Imp. Gall x 4.546

• US Gallons to Liters (l): US Gall x 3.785

Lengths

• Feet (ft) to Meters (m): ft x 0.305

• Inches (in) to Meters (m): In x 0.0254

QUANTITY/MASS CONVERSION CHART

UNITS OF VOLUME AND MASS

In order to convert quantity (gallons or liters) into mass (lbs

or kilograms) and visa versa, the density or the specific

gravity (sg) of the fuel must be known.

Density is defined as mass per unit volume and relative

density or specific gravity (sg).

However, if, for some unforeseen reason, the actual fuel

density is not known, a standard fuel density, as specified

by the operator in the Operations Manual, must be used

CALCULATION OF FUEL MASS CG CALCULATION

Economic or other reasons

Absolute emergency use only

(Usually 3% to 5% of the trip fuel) Sufficient to allow for a

diversion from airfield ‘b’ to a planned diversion airfield ‘c’.

Sufficient for flight from airfield ‘a’ to airfield ‘b’

together with enough extra fuel to allow for bad

weather on route and/or landing delays at airfield

‘b’.

Taking off at airfield ‘a’ and landing at airfield ‘b’ is

classed as a trip or sector

START AND TAXI FUEL 2% of the tank left empty for venting

PIC discretion

FINAL RESERVE

ALTERNATE FUEL

TRIP FUEL

START AND TAXI FUEL

Empty space

It is the commander of the aeroplane’s

responsibility to ensure that there is

sufficient fuel on board the aeroplane to

safely complete the intended flight and

to land with not less than a specified

level of fuel remaining in the tanks –

irrespective of delays and diversions.

The safe operating fuel requirements

defined above are satisfied by filling the

tanks as shown in the table

MASS DEFINITIONS CG CALCULATION

Basic Empty Mass

Dry Operating Mass (DOM)

+ Crew and special equipment

Ramp (block) Mass

+ Useful load+ START & TAXI FUEL

Take off Mass (TOM)

-START & TAXI FUEL

Landing Mass (LM)

- TRIP FUEL and consumed oil

All light aircraft use the Basic Empty Mass (BEM) and

its CG position as the foundation from which to

calculate all relevant masses and CG positions.

Basic Empty Mass is the mass of an aeroplane plus

standard items such as: unusable fuel and other

unusable fluids; lubricating oil in engine and auxiliary

units; fire extinguishers; pyrotechnics; emergency

oxygen equipment; supplementary electronic

equipment.

Traffic Load: is the total mass of passengers, baggage

and cargo

Useful load: Traffic Load + usable fuel

CALCULATION OF BEM AND CG POSITION CG CALCULATION

In order to determine the Basic Empty Mass and CG

position of an aeroplane the aircraft must first be

prepared to the basic empty mass standard which entails

removing all special equipment and useable fuel and

oils.

The aircraft is placed such that its main wheels and the

nose (or tail) wheels rest on the individual weighing

scales which have been calibrated and zeroed.

The readings on the scales are recorded as shown on

picture.

CALCULATION OF BEM AND CG POSITION CG CALCULATION

The Basic Empty Mass is found by adding together the

readings on the scales.

To find the CG position we need to calculate moments

about the datum (forward balance arm and moment

will be negative, balance arm behind the datum -

positive)

CG = Total moment / Total mass

The Basic Empty Mass of the aeroplane is 4500 lb (or 2043 kg)

CG is 24.4 inches behind the datum (as shown by the positive sign)

CALCULATION OF ZFM AND IT’S CG CG CALCULATION

Use actual weight of passengers and cargo

Arm for each load can be found in aircraft

POH

Check MZFM is not exceeded and calculated

CG is in the limits.

ITEM MASS (lbs) ARM (in) MOMENT/100

Basic Empty Mass 2415 77.7 1876.46

Front seat occupants 340 79 268.6

3rd and 4th seat pax 340 117 397.8

Baggage zone A 0 108 0

Baggage zone B 200 150 300

SUB TOTAL: ZERO FUEL

MASS

3295 2842.86

CG = total moment / total mass = 100 * 2842.86 /3295 = 86.27

CALCULATION OF TAKE OFF MASS CG CALCULATION

Add load and arm for fuel to calculate PAMP

MASS and moment.

Subtract fuel for start taxi and run up to get

takeoff mass and moment. Note that

moment for this line is negative too.

Check if the take-off CG is in the CG limits of

aircraft.

*Fuel for start, taxi and run up is normally 13 lbs

for single engine piston aircraft (SEP 1) at an

average entry of 10 in the column headed

moment / 100

ITEM MASS (lbs) ARM (in) MOMENT/100

ZERO FUEL MASS 3295 2842.86

Fuel loading 60 US galls 360 75 270

Oil 8 US quarts (SG 0.9) 15 -48 -7.2

SUB TOTAL: RAMP MASS 3670 3106.66

Subtract fuel for start taxi

and run up*

-13 75 -10

SUB TOTAL: TAKE OFF MASS 3657 3095.66

CG = total moment / total mass = 100 * 3095.66/3657 = 84.65 In

aft of the datum

CALCULATION OF LANDING CG CG CALCULATION

The Landing Mass (LM) is found by

subtracting the fuel and oil consumed

during the flight from the TOM. The CG

position of the LM is found by dividing

moments by LM

Remember to check that the landing mass

and CG position are within the acceptable

limits for the trip.

ITEM MASS (lbs) ARM (in) MOMENT/100

SUB TOTAL: TAKE OFF MASS 3657 3095.66

Trip fuel -240 75 -180

Used oil 8 US quarts (SG

0.9)

-2.8 -48 1.34

SUB TOTAL: Landing Mass 3414.2 2917

LM CG = total moment / total mass = 100 * 2917/3414.2 = 85.44

In aft of the datum

CENTER OF GRAVITY ENVELOPE CG CALCULATION

The CG can also be found by using the Center of Gravity

Envelope. This is a graphical representation of the mass and

center of gravity limits. The vertical axis is the mass in pounds,

the horizontal axis is the CG position in inches aft of the datum

and the slanted lines represent the moment/100

PPL THEORY

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