Stability and Balance Control

Stability and Balance Control

Balance control refers to the location of the CG of an
aircraft. This is of primary importance to aircraft stability,
which determines safety in flight.
The CG is the point at which the total weight of the aircraft
is assumed to be concentrated, and the CG must be located
within specific limits for safe flight. Both lateral and
longitudinal balance are important, but the prime concern
is longitudinal balance; that is, the location of the CG
along the longitudinal or lengthwise axis.
An airplane is designed to have stability that allows it to
be trimmed so it will maintain straight and level flight with
the aircraft will have to fly at a higher angle of attack, and
drag will increase.

A more serious problem caused by the CG being too far
forward is the lack of sufficient elevator authority. At slow
takeoff speeds, the elevator might not produce enough
nose-up force to rotate and on landing there may not be
enough elevator force to flare the airplane. [Figure 1-3]
Both takeoff and landing runs will be lengthened if the CG
is too far forward.

The basic aircraft design assumes that lateral symmetry
exists. For each item of weight added to the left of the
centerline of the aircraft (also known as buttock line
zero, or BL-0), there is generally an equal weight at a
corresponding location on the right.

The lateral balance can be upset by uneven fuel loading
or burnoff. The position of the lateral CG is not normally
computed for an airplane, but the pilot must be aware
of the adverse effects that will result from a laterally
unbalanced condition. [Figure 1-4] This is corrected by
using the aileron trim tab until enough fuel has been used
from the tank on the heavy side to balance the airplane.
The deflected trim tab deflects the aileron to produce
additional lift on the heavy side, but it also produces
additional drag, and the airplane flies inefficiently.

Helicopters are affected by lateral imbalance more than
airplanes. If a helicopter is loaded with heavy occupants
and fuel on the same side, it could be out of balance
enough to make it unsafe to fly. It is also possible that if
external loads are carried in such a position to require large
lateral displacement of the cyclic control to maintain level
flight, the fore-and-aft cyclic control effectiveness will be
limited.

Sweptwing airplanes are more critical due to fuel
imbalance because as the fuel is used from the outboard
tanks, the CG shifts forward, and as it is used from the
inboard tanks, the CG shifts aft. [Figure 1-5] For this
reason, fuel-use scheduling in sweptwing airplanes
operation is critical.

Weight Changes

Weight Changes

The maximum allowable weight for an aircraft is
determined by design considerations. However, the
maximum operational weight may be less than the
maximum allowable weight due to such considerations as
high-density altitude or high-drag field conditions caused
by wet grass or water on the runway. The maximum
operational weight may also be limited by the departure or
arrival airport’s runway length.

One important preflight consideration is the distribution
of the load in the aircraft. Loading the aircraft so the gross
weight is less than the maximum allowable is not enough.
This weight must be distributed to keep the CG within the
limits specified in the POH or AFM.

If the CG is too far forward, a heavy passenger can
be moved to one of the rear seats or baggage can be
shifted from a forward baggage compartment to a rear
compartment. If the CG is too far aft, passenger weight or
baggage can be shifted forward. The fuel load should be
balanced laterally: the pilot should pay special attention
to the POH or AFM regarding the operation of the fuel
system, in order to keep the aircraft balanced in flight.

Weight and balance of a helicopter is far more critical
than for an airplane. With some helicopters, they may be
properly loaded for takeoff, but near the end of a long
flight when the fuel tanks are almost empty, the CG may
have shifted enough for the helicopter to be out of balance
laterally or longitudinally. Before making any long flight,
the CG with the fuel available for landing must be checked
to ensure it will be within the allowable range.

Airplanes with tandem seating normally have a limitation
requiring solo flight to be made from the front seat in
some airplanes or the rear seat in others. Some of the
smaller helicopters also require solo flight be made from a
specific seat, either the right, left, or center. These seating
limitations will be noted by a placard, usually on the
instrument panel, and they should be strictly adhered to.

As an aircraft ages, its weight usually increases due to
trash and dirt collecting in hard-to-reach locations, and
moisture absorbed in the cabin insulation. This growth in
weight is normally small, but it can only be determined by
accurately weighing the aircraft

Changes of fixed equipment may have a major effect upon
the weight of the aircraft. Many aircraft are overloaded by
the installation of extra radios or instruments. Fortunately,
the replacement of older, heavy electronic equipment with
newer, lighter types results in a weight reduction. This
weight change, however helpful, will probably cause the
CG to shift and this must be computed and annotated in
the weight and balance record.

Repairs and alteration are the major sources of weight
changes, and it is the responsibility of the A&P mechanic
or repairman making any repair or alteration to know the
weight and location of these changes, and to compute the
CG and record the new empty weight and EWCG in the
aircraft weight and balance record.

If the newly calculated EWCG should happen to fall
outside the EWCG range, it will be necessary to perform
adverse loading check. This will require a forward and
rearward adverse-loading check, and a maximum weight
check. These weight and balance extreme conditions
represent the maximum forward and rearward CG position
for the aircraft. Adverse loading checks are a deliberate
attempt to load an aircraft in a manner that will create the
most critical balance condition and still remain within
the design CG limits of the aircraft. If any of the checks
fall outside the loaded CG range, the aircraft must be
reconfigured or placarded to prevent the pilot from loading
the aircraft improperly. It is sometimes possible to install
fixed ballast in order for the aircraft to again operate within
the normal CG range.

The A&P mechanic or repairman conducting an annual or
condition inspection must ensure the weight and balance
data in the aircraft records is current and accurate. It
is the responsibility of the pilot in command to use the
most curre hands off the controls. Longitudinal stability
is maintained by ensuring the CG is slightly ahead of the
center of lift. This produces a fixed nose-down force independent of
the airspeed. This is balanced by a variable nose-up force,
which is produced by a downward aerodynamic force on
the horizontal tail surfaces that varies directly with the
airspeed.

Effects of Weight

Effects of Weight

Most modern aircraft are so designed that if all seats
are occupied, all baggage allowed by the baggage
compartment is carried, and all of the fuel tanks are
full, the aircraft will be grossly overloaded. This type of
design requires the pilot to give great consideration to the
requirements of the trip. If maximum range is required,
occupants or baggage must be left behind, or if the
maximum load must be carried, the range, dictated by the
amount of fuel on board, must be reduced.
Some of the problems caused by overloading an aircraft
are:

• the aircraft will need a higher takeoff speed, which
results in a longer takeoff run.
• both the rate and angle of climb will be reduced.
• the service ceiling will be lowered.
• the cruising speed will be reduced.
• the cruising range will be shortened.
• maneuverability will be decreased.
• a longer landing roll will be required because the
landing speed will be higher.
• excessive loads will be imposed on the structure,
especially the landing gear.

The POH or AFM includes tables or charts that give the
pilot an indication of the performance expected for any
weight. An important part of careful preflight planning
includes a check of these charts to determine the aircraft is
loaded so the proposed flight can be safely made.

Weight and Balance Control

There are many factors that lead to efficient and safe
operation of aircraft. Among these vital factors is proper
weight and balance control. The weight and balance
system commonly employed among aircraft consists of
three equally important elements: the weighing of the
aircraft, the maintaining of the weight and balance records,
and the proper loading of the aircraft. An inaccuracy in any
one of these elements nullifies the purpose of the whole
system. The final loading calculations will be meaningless
if either the aircraft has been improperly weighed or the
records contain an error.

Improper loading cuts down the efficiency of an aircraft
from the standpoint of altitude, maneuverability, rate
of climb, and speed. It may even be the cause of failure
to complete the flight, or for that matter, failure to start
the flight. Because of abnormal stresses placed upon the
structure of an improperly loaded aircraft, or because of
changed flying characteristics of the aircraft, loss of life
and destruction of valuable equipment may result.
The responsibility for proper weight and balance control
begins with the engineers and designers, and extends to the
aircraft mechanics that maintain the aircraft and the pilots
who operate them.

Modern aircraft are engineered utilizing state-of-the-art
technology and materials to achieve maximum reliability
and performance for the intended category. As much
care and expertise must be exercised in operating and
maintaining these efficient aircraft as was taken in their
design and manufacturing.

The designers of an aircraft have set the maximum weight,
based on the amount of lift the wings or rotors can provide
under the operation conditions for which the aircraft
is designed. The structural strength of the aircraft also
limits the maximum weight the aircraft can safely carry.
The ideal location of the center of gravity (CG) was very
carefully determined by the designers, and the maximum
deviation allowed from this specific location has been
calculated.

The manufacturer provides the aircraft operator with the
empty weight of the aircraft and the location of its emptyweight
center of gravity (EWCG) at the time the certified
aircraft leaves the factory. Amateur-built aircraft must have
this information determined and available at the time of
certification.

The airframe and powerplant (A&P) mechanic or
repairman who maintains the aircraft keeps the weight and
balance records current, recording any changes that have
been made because of repairs or alterations.
The pilot in command of the aircraft has the responsibility
on every flight to know the maximum allowable weight
of the aircraft and its CG limits. This allows the pilot to
determine on the preflight inspection that the aircraft is
loaded in such a way that the CG is within the allowable
limits.

Weight Control

Weight is a major factor in airplane construction and
operation, and it demands respect from all pilots and
particular diligence by all A&P mechanics and repairmen.
Excessive weight reduces the efficiency of an aircraft
and the safety margin available if an emergency
condition should arise.
When an aircraft is designed, it is made as light as the
required structural strength will allow, and the wings or
rotors are designed to support the maximum allowable
weight. When the weight of an aircraft is increased,
the wings or rotors must produce additional lift and the
structure must support not only the additional static loads,
but also the dynamic loads imposed by flight maneuvers.
For example, the wings of a 3,000-pound airplane must
support 3,000 pounds in level flight, but when the airplane
is turned smoothly and sharply using a bank angle of 60°,
the dynamic load requires the wings to support twice this,
or 6,000 pounds.
Severe uncoordinated maneuvers or flight into turbulence
can impose dynamic loads on the structure great enough
1–
to cause failure. In accordance with Title 14 of the Code
of Federal Regulations (14 CFR) part 23, the structure of a
normal category airplane must be strong enough to sustain
a load factor of 3.8 times its weight. That is, every pound
of weight added to an aircraft requires that the structure
be strong enough to support an additional 3.8 pounds.
An aircraft operated in the utility category must sustain a
load factor of 4.4, and acrobatic category aircraft must be
strong enough to withstand 6.0 times their weight.

The lift produced by a wing is determined by its airfoil
shape, angle of attack, speed through the air, and the air
density. When an aircraft takes off from an airport with a
high density altitude, it must accelerate to a speed faster
than would be required at sea level to produce enough
lift to allow takeoff; therefore, a longer takeoff run is
necessary. The distance needed may be longer than the
available runway. When operating from a high-density
altitude airport, the Pilot’s Operating Handbook (POH)
or Airplane Flight Manual (AFM) must be consulted to
determine the maximum weight allowed for the aircraft
under the conditions of altitude, temperature, wind, and
runway conditions.

Relation between Pressure, Density, and Temperature of a Gas

 Relation between Pressure, Density, and Temperature of a Gas

AIR AT REST, THE ATMOSPHERE AND STATIC LIFT 13

ii. Relation between Pressure, Density, and Temperature of a Gas

By the experimental laws of Boyle and Charles, for constant

temperature the pressure of a gas is proportional to its density ; for

constant volume the pressure of a gas is proportional to its absolute

temperature. The absolute temperature is denoted by T and, if 6 is

the temperature on the centigrade scale, is given by

T = + 273.

Combining these laws, we have, for a given mass of a particular

gas:

pV^Bt (8)

where V is the volume, or, if V is the volume of 1 lb.,

P/9=gBi: (9)

B is a constant which is made characteristic of a particular gas by

treating 1 lb. of the gas ; it is then evaluated from measurements of

pressure and volume at a known temperature. It follows that B

will vary from one gas to another in inverse proportion to the

density under standard conditions of pressure and temperature.

If N is the ixumber of molecules in V, N will, by Avogadro's law,

be the same for all gases at constant p and T. Hence, writing pV/N

= B'T, B' is an absolute constant having the same value for all

gases. Equation (9) is more convenient, however, and the variation

of B is at once determined from a table of molecular weights.

Some useful data are given in Table II. It will be noticed that, if p

is kept constant, B measures the work done by the volume of gas in

expanding in consequence of being heated through unit temperature

change. The units of B are thus ft.-lb. per lb, per degree centigrade,

or ft. per C.

 

Isothermal Atmosphere

Isothermal Atmosphere

We now examine the static equilibrium of a bulk of gas under

gravity, taking into account its compressibility. Equation (2)

14 AERODYNAMICS [CH.

applies, but specification is needed of the relationship between p

and p. The simple assumption made in the present article is that

appropriate to Boyle's law, viz. constant temperature TO, so that />/p

remains constant. From (2) :

*.-*. 9g From (9) : 1 _ J5r 9g P ' Hence : ,. BiQ = - dh. P

Integrating between levels Ax and h2 , where p = pt and p2 respectively,

BTO log (pjpj = h, - h, . . . (10)

The logarithm in this expression is to base e. Throughout this

book Napierian logarithms will be intended, unless it is stated

otherwise. The result (10) states that the pressure and therefore

the density of a bulk of gas which is everywhere at the same temperature

vary exponentially with altitude.

The result, although accurately true only for a single gas, applies

with negligible error to a mass of air under isothermal conditions,

provided great altitude changes are excluded. The stratosphere is

in conductive equilibrium, the uniform temperature being about

- 55 C. The constitution of the air at its lowest levels is as given

in Article 1. As altitude increases, the constitution is subject to

Dalton's law : a mixture of gases in isothermal equilibrium may be

regarded as the aggregate of a number of atmospheres, one for each

constituent gas, the law of density variation in each atmosphere

being the same as if it constituted the whole. Hence argon and

other heavy gases and subsequently oxygen, nitrogen, and neon will

become rarer at higher levels. The value of B for the atmosphere

will consequently increase with altitude, although we have assumed

it constant in order to obtain (10). The variation of B for several

miles into the stratosphere will, however, be small. At greater

altitudes still the temperature increases again.

The Troposphere

The Troposphere

The atmosphere beneath the stratified region is perpetually in

process of being mechanically mixed by wind and storm. When a

bulk of air is displaced vertically, its temperature, unlike its pressure,

has insufficient time for adjustment to the conditions obtaining at the

new level before it is moved away again. The properties of this

part of the atmosphere, to which most regular flying so far has been

restricted, are subject to considerable variations with time and place,

excepting that B varies only slightly, depending upon the humidity.

There exists a temperature gradient with respect to altitude, and on

the average this is linear, until the merge into the stratosphere is

approached.

Centre of Pressure

Centre of Pressure

Th point on a surface exposed to pressure through which the
resultant force acts is called the centre of pressure. The centres of
pressure with which we are concerned relate to the pressure difference,
often called the gas pressure, unevenly spread over part of an
envelope separating gas from the atmosphere. Gas pressures are
small at the bottom of an envelope and reach a maximum at the top,
as illustrated in Fig. 6, and positions of the centres of pressure are
usually high.

The high centres of the total gas pressures exerted on walls which
restrain a gas-bag, as in the case of the wire bulkheads or transverse
frames of a rigid airship, lead to moments internal to the structure.
BCDE (Fig. 8) is a (full) gas-bag of an airship which is pitched at
angle a from a level keel. The longitudinal thrusts P, P' from the

* gas pressure

' are supported by bulkheads EC and DE of areas A,

A', assumed plane, B and E being lowest and C and D highest points.

The gas is assumed to be at rest, so that pressure is constant over

horizontal planes, and its pressure at B, the bottom of the bag, is

taken as equal to that of the atmosphere. Let p be the excess

pressure at height h above the level of B. Then from (3) p = pigA,

where p x is the difference in the densities of the gas and the surrounding

air.

Lower Bulkhead BC. Let 8A be the area of a narrow horizontal

strip of BC distant y from a horizontal axis in its plane through B.

Then h = y cos a, and the total thrust on BC is given by :

re re P = p dA = pig cos a y dA

JB JB = P!# cos a . AyQ

Balloons and Airships

Balloons and Airships

In balloons and airships the gas is contained within envelopes of
cotton fabric lined with gold-beaters

1 skins or rubber impregnated.
Diffusion occurs through these comparatively impervious materials,

and, together with leakage, contaminates the enclosed gas, so that
densities greater than those given in the preceding article must be
assumed. Practical values for lift per thousand cubic feet are 68 Ib. for
hydrogen and 62 Ib. for helium, at low altitude. Thus the envelope of a
balloon weighing 1 ton would, in the taut state at sea-level, have a diameter
of 39-8 ft. for hydrogen and 41-1 ft. for helium ; actually it would be
made larger, filling only at altitude and being limp at sea-level.\

the variation of atmospheric pressure from the level of the top of

the open filling sleeve S to that of the crest of the balloon, OH the

corresponding variation of pressure through the bulk of helium

filling the envelope.

 The difference between these external arid

internal pressures acts radially outward on the fabric as shown to

the right. The upward resultant force and part of the force of

expansion are supported by the net N, from which is suspended the

basket or gondola B, carrying ballast and the useful load.

Balloons drift with the wind and cannot be steered horizontally.

Airships, on the other hand, can maintain relative horizontal velocities

by means of engines and airscrews, and are shaped to streamline

form for economy of power. Three classes may be distinguished.

The small non-rigid airship, or dirigible balloon (Fig. l(a)} has a

faired envelope whose shape is conserved by excess gas pressure

maintained by internal ballonets which can be inflated by an air

scoop exposed behind the airscrew. Some stiffening is necessary,

especially at the nose, which tends to blow in at speed. A gondola,

carrying the power unit, fuel, and other loads, is suspended on cables

from hand-shaped strengthening patches on the envelope. (Only

a few of the wires are shown in the sketch.)

In the semi-rigid type (b) some form of keel is interposed between

the envelope and gondola, or gondolas, enabling excess gas pressure

to be minimised. Several internal staying systems spread the load

carried by the girder over the envelope, the section of which is not as

a rule circular.

Buoyancy of Gas-filled Envelope

Buoyancy of Gas-filled Envelope

The maximum change of height within a balloon or a gas-bag of an
airship is usually sufficiently small for variation of density to be
neglected. Draw a vertical cylinder of small cross-sectional area A
completely through the envelope E (Fig. 5), which is filled with a
light gas of density p', and is at rest relative to the surrounding
atmosphere of density p. Let the cylinder cut the envelope at a
lower altitude-level ht and at an upper one Aa , the curves of inter-

section enclosing small areas Slt Sa , the normals to which (they are

not necessarily in the same plane) make angles oc lf a8 with the

vertical. On these areas pressures />',, p'2t act outwardly due to the

gas, and^>lf p9 act inwardly due to the atmosphere.

There arises at h2 an upward force on the cylinder equal to

(pi ^a)S2 cos a,.

The similar force arising at h^ may be upward or downward, depending

on the position of Sl and whether an airship or a balloon is

considered, but in any case its upward value is

(Pi P()SI cos i- Since Sa cos oc 8 = A == St cos al, 

the resultant upward force on the

cylinder due to the pressures is

Substituting from (3),