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Freedom of Speech and a Free Press
Freedom of Speech and a Free Press: In the United States, where I live and where I do most of my research and teaching, the press is for the most part free from government controls as a ...
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Sunday, July 5, 2015
FREE AVIATION STUDY: PHYSICS OF FORCE, WORK, POWER, VELOCITY AND ACCELE...
FREE AVIATION STUDY: PHYSICS OF FORCE, WORK, POWER, VELOCITY AND ACCELE...: PHYSICS OF FORCE, WORK, POWER, VELOCITY AND ACCELERATION Physics relating to the force, work, power, velocity and acceleration defines...
FREE AVIATION STUDY: THRUST EQUATION
FREE AVIATION STUDY: THRUST EQUATION: THRUST EQUATION Momentum Thrust: If the condition (area A , pressure P and velocity V) at the engine intake and exhaust are designat...
THRUST EQUATION
THRUST
EQUATION
Momentum Thrust: If the condition
(area A, pressure P and velocity V) at the engine intake
and exhaust are designated with the subscripts 'a' and 'j' respectively, then a
mass of 'air (m) flowing per unit time through the engine will
experience an:
Increase in
velocity = (Vj - Va).
The momentum gain = m (Vj
- Va), where m is the mass flow rate of air through the
engine under steady condition.
= rate of change of
momentum
= Applied force to the air mass flow as
per Newton
According to Newton
Momentum Thrust = m (Vj - Va)
= m Vj - m Va
Consideration may be given to
the fuel mass flow rate (mf) that is mixing with air at
combustion chamber with initial zero velocity relative to the engine, the
thrust equation may be modified as follows:
Momentum Thrust = (m +
mf )Vj – m
Va
= m (Vj-
Va
Pressure Thrust: Considering the engine as a physical body in the air, it
will be subjected to pressures acting at the intake (Pa) and the exhaust (Pj). The pressures will produce a pressure force of (Pj - Pa)Aj
acting on the engine in the forward direction. This force is the result of an
unbalanced pressure and is called the Pressure Thrust. Hence,
Pressure Thrust =
(Pj - Pa)Aj
In most practical cases, pressure thrust exists because all of the
pressure of the engine cannot be converted into velocity at the exhaust (i.e.
gas does not fully expanded to atmospheric pressure). It becomes more pronounced
and significant as the speed of the aircraft becomes supersonic and the exhaust
nozzle becomes choked. At choked nozzle condition, velocity of exhaust gas
cannot exceed M =1, unless it is a C-D duct and invariably there remains
significant amount of unconverted pressure.
Total Thrust: The Total Thrust on a jet engine will be the sum of the
momentum thrust and the pressure thrust.
Total Thrust =
Momentum Thrust + Pressure Thrust
Tt =
m (Vj- Va
In actual practice, fuel flow
is usually neglected when net thrust is computed, because the weight of the air
that leaks from various section of the engine is assumed to the approximately
equivalent to the weight of the fuel consumed. Therefore, the final equation
for computing the thrust by a turbo-jet engine becomes:
Tt
= m (Vj- Va
) + (Pj – Pa) Aj
This is a general thrust
equation and is applicable for all kinds of jet propulsion.
1.5.4 Gross Thrust, Momentum-Drag and Net Thrust: An
analysis of the total thrust of a jet engine will show that it can be grouped
into two parts.
Tt = [m Vj + (Pj
- Pa)Aj] – [mVa]
The forward part composed of the exhaust jet
momentum [mVj] and the
pressure thrust (Pj-Pa)Aj
and is called the Gross Thrust
of the engine, i.e. thrust developed by the engine. The rear part is the
momentum force of the incoming air impinging on the engine intake and is called
the Momentum Drag. Hence the total
thrust is the difference of the gross thrust and the momentum drag and it is
also called the Net Thrust (actual
thrust) of the engine. Hence,
Tgross = m Vj + (Pj - Pa)Aj
Dmomentum = mVa
Net Thrust = Gross Thrust -
Momentum Drag
Gross thrust is actually the thrust
at the static aircraft, with aircraft speed zero.
Power of aircraft gas turbine engines: Turbojet engines are rated on the basis of
takeoff thrust generated at standard atmospheric conditions. This is
conventional, because output of turbojet engines for the aircraft is THRUST
(propulsive force).
Gas turbine engines for
turboprop are the torque turbine engines and the output of the engine is in the
form of TORQUE on the shaft. Hence, the rating of the engine is the Shaft Horse
Power expressed in BHP.
For comparison purpose,
thrust of the turbojets may be converted into horse power, called Thrust Horse
Power (THP).
THP =
For turboprop aircraft,
total power is the summation of BHP at the engine output shaft (input to the
propeller) and the THP from the exhaust thrust. The summation of these two is
termed as ESHP (equivalent shaft horsepower).
PHYSICS OF FORCE, WORK, POWER, VELOCITY AND ACCELERATION
PHYSICS OF
FORCE, WORK, POWER, VELOCITY AND ACCELERATION
Physics
relating to the force, work, power, velocity and acceleration defines the
quantities and establishes their relationship with mathematical treatment. This
helps us establishing thrust formula, power and work expression for aircraft
gas turbine engines.
Force:
Force is
defined as external influence acting on a body to make a change in the state of
rest or state of motion of the body. It is a vector quantity having a magnitude
and direction of action.
Velocity: This is the change in
speed of a moving body per unit time in a specific direction of motion. This is
a vector quantity having a magnitude and the direction.
Acceleration: This is the rate of change of velocity of a moving body.
Relationship of Force, Velocity and Acceleration: The relationship is
established on the basis of Newton
First Law: "A body will
continue its state of rest or of uniform motion in a straight line unless
compelled by some external force to change its state."
This is actually the law of INERTIA. It is due to
the inertia that body at rest tends to remain at rest, and a body in motion
tends to continue its motion with the same velocity (speed and direction), in a
straight line. The law expresses the necessity of an external force to overcome
the effect of inertia.
An aircraft in level flight (cruise) is under zero
resultant force, but it continues to fly at constant speed and direction due to
inertia. To accelerate (or decelerate) the aircraft, Pilot must increase
throttle to create extra thrust as an unbalanced force.
This law has a close relationship with ‘momentum’.
Momentum is the product of mass (m) and velocity (V) and is a vector having
magnitude and direction. The direction of momentum of a body is the same as the
direction of related motion.
From Newton
How much force will be required to make a change
in motion or momentum, or, how much change in momentum will be effected by a
force, is expressed in the 2nd Law.
Second Law: "The rate of change
of momentum of a body is proportional to the applied force and takes place in
the direction in which the force acts."
This law states the relationship between the force
applied to an object and the resultant change of momentum in that
direction.
Normally, the mass of an object is constant and
the relation becomes:
F = (mv-mu)/t = m(v-u)/t =ma
Where, m
is the mass, u is the initial
velocity, v is the velocity after t second, F is the applied force acting in the direction of motion, a is the acceleration, mu is the initial momentum, mv is the momentum after t seconds.
This formula has direct
application in mathematical treatment of jet-propulsion of an aircraft gas
turbine engine.
Third Law: "For every action, there is an equal and opposite
reaction."
This
law gives the mutual relationship between bodies acting on each other with or
without contact. The action and reaction always exist in a pair.
The
condition of a book resting on a table will produce an action and reaction
pair. The weight of the book will exert a force on the top of the table, and
the table will exert a lift on the book to prevent it from falling down under
gravity.
In
the physics of jet-propulsion, the 2nd Law is used in mathematical
formulation of the action force applied by the engine on to the working
fluid (air and gas flow) undergoing change in momentum. According to the 3rd
law, there is a reaction pair of this action force applied on to the engine by
the gas. This reaction is the propulsive force or the thrust. Thus,
the 2nd law action force formula is taken as the reaction force
(thrust) formula.
Work: Work is a quantity found
by multiplying force acting on a body and the distance through which the body
has displaced in the direction of the force due to its action. It is a scalar,
having only the quantity. If there is no displacement in the direction of
force, it is said that the force has not performed any work, or the work
performed is zero.
Energy:
This is
the capacity of doing work.
THEORY OF JET PROPULSION
THEORY OF
JET PROPULSION
Jet propulsion is the method of producing
propulsive force in a device by the reaction of an accelerating mass of air (or
gas) expelled out through a nozzle in the form of a jet. The generated
propulsive force is used to propel the device (or the aircraft) forward in the
air.
Basic Principle: Jet propulsion is a practical application of Sir Isaac
Newton's 3RD Law of Motion which states that: "For
every action, there is an equal and opposite reaction."
For aircraft propulsion, the
'body' is atmospheric air that is accelerated as it passes through the engine.
The force applied to the air giving this acceleration (or changing momentum)
has an equal effect in the opposite direction onto the engine. The effect by
the accelerating air coming out of the engine through its propelling nozzle in
the form of a jet is the ‘jet reaction’ which is conventionally termed as the
‘thrust’.
Jet reaction is an internal phenomenon and does not
result from the pressure of the jet acting on the atmosphere as shown in
balloon example, Figure 1.4, depicting a non-mathematical or mechanical
approach of justifying jet-propulsion. A turbo-jet engine could be considered
as such an arrangement as the compressor and combustion chamber sections having
high pressure air acting on all surfaces, this pressure being dropped through
the exhaust pipe, hence, unbalance pressure forcing the engine forward
internally similar to the toy balloon.
Operating Principle: To
have jet propulsion based on Newton
All
kinds of jet engines, like turbo-jets, ram-jets, pulse-jets etc are designed
for the sole purpose of producing high-velocity gases at the jet-nozzle so that
reaction forces come into play as a result of jet-reaction. But, propulsive
force is also possible by propellers and fans. The basic principle is same,
that is, accelerating or changing momentum of air. So, these are also called
prop-jets and fan-jets, similar to the turbo-jets.
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