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Title: Physics and Aerodynamic book 2
Description: KINEMATICS, DYNAMICS, GYROSCOPIC PRINCIPLES

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-Physics & Aerodynamics KINEMATICS
(The study of motion)
LINEAR MOTION
This is motion in a straight line and it is important to understand the difference between speed and
velocity
...

Consider a body (figure 1), moving from A to B (distance in meters) in a time ‘t’ (seconds)
...
Thus if the curved path AB is denoted by‘s’ and the time taken is‘t’
...

Speed, as a scalar quantity possesses magnitude only, velocity however being a vector quantity
possesses both magnitude and direction
...
If ‘x’ is the
displacement, then since average velocity is defined as the displacement divided by the time taken
...


-1-

x
t

m/s

-Physics & Aerodynamics The following examples should reinforce the difference between speed and velocity
...
A helicopter leaving point ‘A’ travels due east, a distance of 18km
...
The whole journey from A to B
taking 15 minutes
...

(b) The average velocity
...
4 m/s

(a) average speed =

(b) average velocity =

total displacement
total time taken

total displacement AB = 40 2 + 182 using Pythogoras theorem
= 1600 + 324
= 43
...
86 × 103 m
15 × 60 s
= 48
...
22
then θ = 65
...
7 m/s acting from A to B at 65
...
The compass reading on the aircraft (and hence the aircraft heading) would be read as 65
...
Traveling due east the heading would be 90°, traveling due south it would be 180° and
traveling due west it would be 270°
...

Example 2
...
DME = Distance Measuring Equipment, a ground based radio navigation aid
...
7 m/s (about 218mph)

Average speed =

In this example the displacement would be the same as the distance covered and so the magnitude of
the average velocity would also be 97
...
However, for it to qualify as a vector quantity the
direction (from A to B) must also be stated
...

change of velocity
time
if u = initial velocity in m/s
if v = final velocity in m/s

In terms of a formula, acceleration (a) =

then acceleration =

-3-

v −u
t

-Physics & Aerodynamics The units would be
Can be written as

m/s
(ie meters per second per second)
...

2
s

If a body is slowing down, or decelerating, the value of v will be less than U, resulting in a negative
value of acceleration
...
For a body accelerating uniformly, the velocity-time diagram would be shown
in figure 2
...
As the ‘s’ on the top line cancels with the ‘s’ on the bottom line, it
leaves ‘m’ the units of distance
...
The symbol given to distance is ‘s’
...

∴ s = 1/2 (v+u)t

Equation 2

The third equation is obtained by substituting Equation 1 into Equation 2
...

ie

from Equation 1

and from Equation 2
∴ (v-u)(v+u) =

v -u = at
v+u=

2s
t

2s
at
t

v 2 - u 2 = 2as

Equation 4

Example
...
It starts from rest and
accelerates uniformly for 30 seconds before becoming airborne
...
97 m/s 2
(b) using s = 1/2(u+v)t
= 1/2(0+59)30
= 885m
=

FREE FALLING BODIES

Between all masses there is a natural force of attraction
...
Sir Isaac
Newton English physicist 1642-1727)
...

This force, known as a ‘gravitational force will cause bodies entering is sphere of influence, to
accelerate towards the earth
...
This is
known as the body’s terminal velocity and depends, amongst other things, on air resistance (drag
force)
...
When the drag force eventually reaches the same value as the force of
gravity the body has reached its Terminal Velocity
...

However, for most general calculations related to free falling bodies, air ) resistance is ignored and the
body is considered as falling in a vacuum, where its acceleration is uniform having a value of 9
...
81m/s every second
...
The preceding equations 1 to 4 may be used to solve problems involving free falling
bodies by substituting ‘g’ for ‘a’ in the previous equations
...
An aircraft ejector seat is projected vertically upwards, rising freely, after the initial
explosive charge has been fired
...

Determine

(a) The maximum height that the seat will reach
...


-6-

-Physics & Aerodynamics u = 40 m/s
v=0
g = -9
...
81)s
402
= 81
...
81
v = u + gt
0 = 40 - (9
...
1 seconds
9
...
However, when a body moves in a circular path its
angular distance is measured in ‘radians’
...


The number of radians in a circle is 2it radians (since it = 3
...


-7-

-Physics & Aerodynamics Angular distance may be envisaged as ‘wedges’ and a body moving in a circular path would move
through a number of these wedges
...

In figure 4, a circle is divided into six to roughly represent its division into radians (rads)
...
Both will
move through the same number of wedges and hence through the same number of radians, here,
approximately 4
...

If the time taken to move through this angular distance is now considered, then this allows for the
angular velocity ‘ω’ (omega) to be calculated:

ω=

θ rads
t

s

Angular acceleration is defined as the rate of change of angular velocity and is given the symbol α
(alpha)
...
The format of these is identical to those of linear motion, only the symbols have changed
...
Had they been moving together, perhaps as points on a circular
disc or arm, then the time taken to move from OX to OY would have also been the same
...
The two
velocities are therefore related by the radius such that:
Linear velocity = angular velocity × radius
v = ω r (m/s)
Linear acceleration = angular acceleration × radius

α = α r (m / s 2 )
Example
...
Determine its angular velocity in rad/ s and
the linear speed of the propeller tip
...
45rad / s
2850rev / min = 2850 ×

v = ωr
v = 298
...
5
v = 447
...
It follows that to cause a body to deviate from this straight
line path and move in a circular one, that a force must be present
...
To think of it another way - it is you
holding onto the end of the string that keeps the body going round
...
This force in the piece of string is known as ‘centripetal force’ (figure 5), and may be
calculated using either the linear velocity (v m/s) of the rotating body or its angular velocity (ω rad/s)
...
No outward force acts on the body
...
It does not fly outward from the centre of rotation
...
Instead it acts at the centre of rotation and acts in the opposite direction to centripetal
force - ie outwards (see figure 6)
...

r

A centripetal force is required to make any object go round a bend
...
When the vehicle is steered from a straight
line the front wheels turn towards the centre of the bend creating a frictional force in that direction
...
If there is no frictional force (as when driving on ice)
the vehicle does not respond
...
Instead he/she uses the most powerful force
available for control of the aircraft
...
On a large aircraft (A380 for example) this
would be in the region of 300 tonnes (about 300 tons) or 2
...
If the pilot banks the aircraft
then the lift force is inclined to the vertical (as viewed from the front) and the horizontal component of
this force (W TAN 0) is the centripetal force to bring the aircraft round the bend (figure 7)
...
An example of this would be the movement of a piston along the cylinder of an internal
combustion engine (figure 8)
...
Its linear velocity, through one complete revolution of the crank varies
from zero at both bottoms (BDC) and top dead centre (TDC) (both ends of the cylinder), to a
maximum at the midpoint of its travel, ie the linear velocity is continuously changing, it is never
constant
...
At the
extremes of travel, ie at BDC and TDC, the acceleration is a maximum that is when the velocity is
zero
...


Simple Harmonic Motion

The periodic reciprocating motion of the piston is complex but if the connecting rod is long when
compared to the crank, then it approximates to a simpler, but important motion known as Simple
Harmonic Motion (SHM)
...
The acceleration is always directed towards a fixed point in the path of the object
...
The acceleration is proportional to its distance from that point
...

The pendulum arrangement is one with which we are all familiar with
...
The cord is supported at a point Q (figure 9)
...

In figure 9 the vertical projection of point P onto line AB, as it revolves in a circular path, satisfies
both the required conditions of SHM, ie its acceleration is always directed to point 0, and the
acceleration is proportional to the displacement x, being zero at 0 and a maximum at both A and B
...


VIBRATION

Vibration is the rapid to and fro motion in a fluid or elastic solid whose equilibrium has been disturbed
from its original position of rest by some forcing function
...

Aircraft structures (which have mass and elastic properties) are capable of vibration in response to
dynamic inputs from rotating masses such as engines and other inputs such as aerodynamic loads
...

On aircraft, vibration can come from many sources including:


The engines - piston or jet
...
It is kept to a minimum by dynamic balancing of
propellers and rotating parts of the engine
...




Aircraft wheels
...
In sever cases can cause structural damage
...
When it occurs it is called Shimmy
...
The airframe/flying controls are buffeted by the air as it flows passed
...
Static balancing (mass balancing) of the control surfaces and correct airframe
design can help reduce this
...


Vibration monitoring equipment is fitted to many engines and some helicopters
...

Vibration is usually considered to he- a form of wasted energy and is generally to be avoided
...

Usually associated with vibration is the term ‘frequency’
...
Frequency is given the unit of Hertz, (German physicist
Heinrich Hertz 1857 — 1894)
...

To reduce vibration to an acceptable level, rotating components can be both statically and
dynamically balanced
...
Damping may come from friction damping or inertia loading
...
Some parts of the structure (and flying control surfaces) may be
damped by the use of mass balance weights
...
This natural frequency is generally dependant on the mass of the vibrating item
...
When friction is considered, then the
frequency of vibration is referred to as ‘damped natural frequency’
...
If the frequencies of vibration are in the audible frequency range, between
approximately 20 and 20,000 Hz, then a range of sounds will be produced - the slower vibrations
producing low pitch sounds and higher vibrations high pitch sounds
...
A whole series of harmonics exists
...

The harmonic series is a sequence of frequencies which is all whole number multiples of the
fundamental frequency, the second harmonic being twice the frequency of the first, and so on
...
It occurs when the frequency
of the exciting vibration (the forcing function that causes the vibration in the first place) coincides with
the natural frequency of the item, often as a result of the damping forces being small
...
If uncorrected this may, in turn, lead to possible failure of the
part often by fatigue
...


VELOCITY RATIO, MECHANICAL ADVANTAGE AND EFFICIENCY

We all understand the meaning of work in the general sense, however in engineering, work is related
to force and distance such that work is done when a force moves through a distance in the direction of
the force
...


- 15 -

-Physics & Aerodynamics The following section deals with the relationships that emanate from devices that helps man to do
work more easily
...

One useful task that a machine is able to achieve is to move a large force by the application of a
relatively small effort
...


Mechanical Advantage =

Load
Effort

The greater the MA the greater is the load that can be moved by a given effort
...
This is partly because, except in an ideal machine (no friction),
the effort required to overcome frictional forces varies with the magnitude of the load applied
...

Figure 10 shows a simple lever and the MA can be worked out by the ratio of the length of the lever
from the pivot to the small force to the length of the lever from the pivot to the end lifting the heavy
load (in this case about 4:1)
...

What you should note from figure 10 is that the amount of movement of the input force is larger than
the amount of movement of the 1oad
...


- 16 -

-Physics & Aerodynamics The ratio of input movement to output movement is called the Velocity Ratio (VR) or ‘Movement
Ratio’
...


Velocity Ratio (VR) =

input distance moved
output distance moved

Since both movements occur in the same time this is also the ratio of the input and output velocities
...

Any practical machine will have energy ‘losses’, often occurring in the form of heat (friction for
example)
...
As a result of
this the work output from a machine will always be less than the work input
...

work output
work input
(the symbol η is pronounced eta)
efficiency may be expressed as
MA
η =
VR
efficiency (η ) =

This must always be less than unity (1), or less that 100% expressed as a percentage, since energy will
always be used to overcome friction and other losses
...


- 17 -

-Physics & Aerodynamics DYNAMICS

For something to exist it is usual to assume that it possesses ‘mass’
...

The basic unit of mass in the SI system is the kilogram (kg) (about 2
...

When larger quantities are involved the mass may be quoted in terms of ‘tonnes’ — called the metric
tonne
...

The mass of a body, once stated, is considered to be constant no matter where it is located, or what
state it is in
...
If this 5kg mass is a solid, it will
also be 5kg when melted to a liquid and if heated to a vapor state, will produce 5kg of vapor
...
This force of attraction is known as ‘gravitational force’
...

It is this force of attraction acting on these bodies that give them weight
...
As the earth is not truly spherical, being flatter at the poles, then the
weight of a body varies around the Earth’s surface
...

To determine the weight of a body the following formula is used
...
81m/s2
...

Describe the differences between these terms (10 mins)
...
Weight and force are units of
measurement used to describe the force that that mass will exert
...
Place it on your hand and it will
exert a force downwards of about 1ON
...
Weight is really another name for force
...
This, in turn, is calibrated to read the weight (or more
correctly the mass) of the body being measured (figure 11)
...

Doubling the mass will cause double the extension
...

- 19 -

-Physics & Aerodynamics A balance scale (figure 12) compares an unknown mass to a known mass
...


Inertia
All bodies seek a state of equilibrium and are reluctant to change their present state of rest or uniform
motion
...
Only the application of a force will cause it to accelerate, decelerate or change
direction
...
Inertia is dependent on the mass of the
body, the larger the mass the greater the inertia, ie the more difficult it is to move when at rest or to
stop when in motion
...


On the take-off run the thrust of the engines must overcome the inertia of the aircraft
...
Equating these forces T D + ma
...
Equating these forces ma = TR + D + B
...
The most effective being the wheel
brakes, the next being reverse thrust putting the propeller into reverse pitch and revving up the
engine/s, or moving cowlings into the jet efflux of a jet engine to direct the thrust rearwards and
opening up the throttles)
...
This may
be increased by the use of flaps, spoilers, airbrakes and parachutes (parachutes on military aircraft
only)
...

Note that in figure 14 that the word “acceleration” is used and not “deceleration”
...


POWER
Power is defined as ‘the rate of doing work’
...
(To give you some idea of the ‘size’ of a watt — a television on
standby would consume about 1W of power, a light bulb would be about 60 to 100W, a small motor
car would be about 50kW (50,000W)
...
5kN
...

Power

= force x speed
= 24
...
125 MW (Mega Watts)

ENERGY
Energy is defined as ‘the capacity to do work’, and in its many forms the unit is the same as that for
work, ie the Joule
...
Energy cannot be made or destroyed but can only be changed from one form to
another - as occurs in an engine for example, where the chemical energy of the fuel is released to
provide heat energy (and sound energy etc)
...

However, the total energy in the system remains unchanged, even though many changes of form
occur
...

Two forms of energy that are of particular importance are Kinetic Energy (energy of motion) and
Potential Energy (energy of position)
...

Potential energy

=

mgh
- 22 -

-Physics & Aerodynamics Where ‘g’ is gravitational acceleration (9
...

Changes of energy between these two forms often occur, and in some situations are continuous such as
with a pendulum
...

At the highest point of its swing, the pendulum is at rest for an instant, it has no motion and so no
kinetic energy (KE)
...

As the pendulum starts to descend, this height ‘h’ decreases resulting in a subsequent reduction in PE
...
At the lowest point in its swing
all the height ‘h’ is lost and the PE is zero, but the velocity of the pendulum is now at its maximum
producing the maximum KE
...


As the pendulum passes through the lowest point, it starts to ascend, gaining PE as ‘h’ increases, but
loosing KE as it slows down
...
If one can determine the work
done on or by a body then this can be equated to the amount of energy possessed or expended by the
body
...
Consider a body of mass 5kg raised a vertical distance of 8m above a datum
...
81m/s2 x 8m

=

392
...
4J
...
4J of energy
...
4J
...

since KE = 392
...
4J
v =

392
...
4 × 2
5
v = 12
...

Example 2: (a) What is the total kinetic energy of a commercial airliner of 200 tons lands at a velocity
of 120mph at an actual angle of 5°? (b) Of this total energy how much energy will the brakes have to
absorb? (c) How much energy will have to be absorbed by the main oleos (shock absorbers)
...
This method provides a close approximation for the energy absorbed by
the brakes — given by the horizontal component (290MJ) and the amount of energy to be absorbed by
the shock absorbers — given by the vertical component (3OMJ)
...

However, using trigonometry will provide an accurate answer:
296cos 50o
294
...
8MJ

Momentum

Momentum is defined as ‘the quantity of motion’ possessed by a body
...

ie, momentum = mass (kg) x velocity (m/s)
Its units are therefore kgm/s, however, you may find Ns (Newton seconds) also used
...


- 25 -

-Physics & Aerodynamics -

However, although the momentum of both bodies is the same, each possesses a different amount of
kinetic energy (‘/2mv2)
The 20kg mass possesses 1/2 x 20 x 0
...
5J of energy
...
5kg mass possesses 1/2 x 0
...


Newton’s Laws of Motion

As we are considering motion, it is a convenient point to state some important fundamental laws Newton’s Laws of Motion
...
The first states that ‘Unless there is resultant external
force acting upon it, a body will move with a constant speed in a straight line’
...
To alter this state a force must be applied, ie to produce acceleration (positive
[+] or negative [-]) or to alter its direction
...

The second law of motion states that ‘The rate of change of motion of a body is proportional to the
resultant force acting on the body and takes place in the direction of the force’
...
Let the final velocity be ‘v’
m/s
...


mv − mu
t
⎛ v−u ⎞
F = m⎜

⎝ t ⎠
v −u
= acceleration 'a' m/s 2
t

Hence F =
or
now

Therefore, F = ma
If the contact time‘t’ between the bodies involved is very small (st), such as occurs when a body is
struck suddenly, then the force applied is known as an ‘impulsive force’
...

impulse

=

impulsive force x δ t

=

ie

change in momentum
...
In other words ‘To every action there is an equal and opposite reaction
...
Each leg has an ‘action’ going downwards into the floor (about
a ¼ of the total mass of the chair and person)
...

These three Laws of Motion can be used to solve most of the problems that arise in mechanics
...

Consider two bodies of mass mA and mB, moving in the same straight line, with mass A, moving at a
greater speed (uA) m/s than mass B, which is moving at UB m/s
...
At collision, each delivers the same impulsive force ‘F’ to the other, present for a
very small time period 6t
...


- 28 -

-Physics & Aerodynamics From Newton’s third law, it can be seen that at impact the impulse received by
B

=

Fδt

=

change of momentum of B

=

mBvB — mBuB

The impulse received by A = -Fδt (the negative sign, indicating the opposite direction of this force)
...
e

Total Momentum Before Impact = Total Momentum After Impact

GYROSCOPIC PRINCIPLES
A gyroscope is basically a spinning mass
...
Most gyros that are designed to
be gyroscopes are mounted in a pivoted frame called gimbals (figure 20)
...
When the wheel is spun it will exhibit properties that are unique to spinning masses
...

The mathematics associated with gyroscopes is fairly complicated, but a knowledge of a few basic terms
is necessary
...
An understanding of vectors is also essential
...
So setting a top spinning on a
flat surface will mean that is will stand upright, even if the surface on which it rests is moved —
provided the top remains spinning
...

The amount of rigidity is directly related to the:
(i) Mass of the rotor
...

(iii) Radius of Gyration or Monient of Inertia of the rotor
...
In
fact it is the radius at which all the mass of a segment of the wheel is said to act when it is rotating
...
If the
two gyros in figure 21 both have the same mass and the same outer diameter then the right hand gyro
will have the greater rigidity than the left hand gyro for the same rpm because its mass is more
concentrated towards the outside of the rotor
...

(ii) Are acting with opposite sense
...

(iv) Are equal in magnitude
...


As the two forces (F) are equal in magnitude but of opposite sense, then the total resultant force is zero
and there is no tendency for the key to move up or down
...
This resultant moment, or couple, is called the Torque produced by the
couple
...

ie

Torque = F x d (Newton metres)

In previous work we came across momentum or more specifically ‘linear momentum’ for bodies
traveling in straight lines and for a change of linear momentum to occur a force had to be applied over a
period of time
...

ie Torque =

change of angular momentum
t

If as, with linear momentum, the time involved is very small then
Angular impulse

=

torque x t

=

change of angular momentum

Consider a stationary flywheel or rotor as shown below in figure 23
...
Let a couple, as shown
by the two vertical forces F, be applied to the shaft
...
Now let the rotor be spinning about its shaft axis with angular speed ‘ω’ rads per second when
the couple is applied
...
First of all the rotating assembly maintains
its rigidity so the shaft will not move up or down at the ends
...
The
assembly rotates with constant angular speed in a horizontal plane, at right angles to the forces ‘F’
...

It appears to defy Newton’s laws in that it will not move in the direction of the applied forces - but at
right angles to them
...
To try and understand why this motion occurs, it is best to
restate Newton’s second law as it applies to rotational motion
...

When the rotor is stationary, the initial angular momentum is zero, so no special arrangement is needed
in interpreting the law, but when the rotor is rotating the system starts with a quantity of angular motion,
to which the change must be added
...

Initially then, the angular momentum of the rotor is represented by a vector perpendicular to the plane of
rotation, ie parallel to the axis of the shaft, and in the direction in which a right hand screw thread would
travel
...

The applied couple, of magnitude T, is similarly represented by a vector perpendicular to the plane of
these forces, shown as T in figure 24 and it is at right angles to oa
...
The result is to alter the
direction of the angular momentum vector by an amount δθ, without altering its magnitude: and the
physical interpretation is that the axis of the shaft rotates with the vector but that the speed of the rotor is
unaltered
...

(ii) Speed of the rotor - the higher the speed the less the precession
...

So:
Any spinning mass has gyroscopic properties
...

A gyro will exhibit rigidity - the tendency for the rotor axis to stay pointing to a distant star in space even when acted on by a force
...
This property is called precession
...
A simple rule of thumb
(Sperry’s Rule of Precession) can be used
...
Modern aircraft have replaced the conventional gyro with
the laser gyro
...

Figure 25 shows a rotor mounted in a single gimbal ring, which itself is pivoted in a supporting frame
...


- 34 -

-Physics & Aerodynamics The rotor has freedom to rotate about just one axis at right angles to the spin axis so the gyro is said to
have “one degree of freedom”
...
The rotor is
now free to turn relative to the frame about two axes B-B and C-C
...

Gyros are classified as either a displacement gyro or a rate gyro
...
A rate gyro has a
spring or some other restraint mechanism against which rate is measured
...
The rotor of the motor driven gyro being the actual rotating mass
...
The property of rigidity is used extensively
in aircraft gyros
...


- 35 -

-Physics & Aerodynamics Figure 26 shows a two degree freedom of movement gyro
...


Precession

This is movement of the spin axis when a force is applied to a gimbal ring
...

Figure 27 shows a force applied to the spin axis of a gyro
...
As a theoretical model continue the movement of the force in the same direction onto the rotor (point
A)
...
Allow the force to move 90° in the direction of the rotor rotation to
point B
...
Imagine the force pushing at this position on the rotor and this is how the gyro would move
...

1
...

2
...


- 36 -

-Physics & Aerodynamics 3
...
This is where the precessional force
will act causing the outer gimbal to precess
...
)

Sperry’s Rule enables the direction of precession to be founc provided the direction of the applied torque
and the direction of rotation f the rotor is known
...

Visualise transferring this force onto the rotor, move it around 900 in the direction of rotation of the
rotor, and the precessional force will be applied at the top of the rotor, causing the inner gimbal to
precess
...

Note that a force applied to the outer gimbal of a two-degree of freedom gyro causes the inner gimbal to
precess and a force applied to the inner gimbal causes the outer gimbal to precess
...

A free gyro is one that its axis will point to a star infinitely far away in space
...

A tied gyro is one that is “tied” to some reference point
...
Note - in this context do not confuse the term ‘Earth” with the termed “earthed”
...

A good illustration of a tied gyro is that fitted to an artificial horizon
...
If it were a free gyro then, if at the
north pole it pointed vertical it would be horizontal when the aircraft got to the equator
...


Methods of Spinning Gyro Rotors

Early gyros and some standby instruments today are driven by air
...
5” Hg
...

Air enters the otherwise sealed instrument case via a filter
...

Most mechanical gyros these days are driven by an electric motor
...
If it is an ac motor it will be of the basic induction type or hysteresis motor
...


- 38 -

-Physics & Aerodynamics -

As the rotor is the rotating mass it is put on the outside of the stator
...

(Typical speeds are 23,000rpm for induction motors, 12,000 — 24,000rpm for hysteresis motors)
...


- 39 -

-Physics & Aerodynamics REFERENCES ESTABLISHED BY GYROS
Displacement Gyros
For use in aircraft this gyro must be able to sense pitch and roll attitude changes and heading (yaw)
changes
...
Usually called a vertical gyro
...


- 40 -

-Physics & Aerodynamics It does this by keeping its spin axis vertical (rigidity) to ensure that the horizon bar stays level compared
to the aircraft symbol which is painted on the glass cover of the instrument
...
Gravity switches operate small motors
from time to time to move the spin axis so it keeps vertical
...
As the aircraft turns so the gyro spin axis
(and the compass card) stays pointing in the same direction (rigidity)
...
This
gyro is called a directional gyro or horizontal gyro
...

This gyro is used to sense rate of angular displacement and would be used in the turn and slip indicator,
autoflight systems and INS
...
This precession is resisted by a spring
...


- 41 -

-Physics & Aerodynamics -

Gyro Errors

The following must be taken into consideration with an earth gyro: real wander and apparent wander
...

Real Wander
...
The gyro ought not to wander away
from its original axis position but various forces may act on the gyro and cause it to precess
...
Such things as friction in the rotor bearings, friction
in the gimbal pivots, unbalanced rotor or unbalanced gimbal rings will all produce a force on the gimbal
rings causing precession
...
As the term suggests the gyro spin axis does not physically wander away from its
original spin axis datum and yet to an observer it appears to have changed its direction
...
The
gyro then appears to wander — in fact it does not, the observer does
...
Apparent wander is due to the effect of the earth’s rotation and the effect of moving
over the curved surface of the earth
...
Wander can be broken down into two
components ‘drift’ and ‘topple’
...
Topple is
movement of the spin axis in the vertical plane
...
An observer at A vertically above the north pole is
looking down the axis of the gyro at a certain point in time
...
It will appear that the gyro has moved
clockwise in the horizontal plane by 90°
...
After 24 hours the observer will be back to the original position
...
So at the poles the
horizontal gyro has a drift rate of 360° in 24 hours
...


- 43 -

-Physics & Aerodynamics Six hours later the earth will have moved from A to B and when looking at the gyro it will appear to the
observer as a vertical gyro
...

Note there is no apparent movement in the horizontal plane
...


Horizontal Gyro (Earth’s Curvature Effect)

Figure 38 shows a horizontal gyro at the equator with its spin axis pointing to a fixed point in space
...
Notice no deviation has taken place
...


Vertical Gyro (Earth’s Rotation Effect)

Figure 39 shows a vertical gyro at the North pole, if you rotate with the earth no apparent movement of
the gyro will appear to take place, ie no drift and no topple
...

To summarise; at the poles there is no drift and no topple and at the equator no drift and maximum
topple
...
What is required is that the
vertical gyro remains vertical in the aircraft at all times, ie to eliminate real and apparent wander effects
and similarly the horizontal gyro must be kept horizontal at all times
...

Note the vertical gyro has no drift
...

An erection system is fitted to the vertical gyro which achieves what we require and the gyro now
becomes an earth tied
...

In the horizontal gyro two systems are fitted one to counteract drift and one for topple, again the gyro
now becomes an earth tied gyro
Title: Physics and Aerodynamic book 2
Description: KINEMATICS, DYNAMICS, GYROSCOPIC PRINCIPLES