Welcome to class till time we have seen that

there are different types of arrangements for a gas turbine based power plant. And then

we have seen that there are different attachments also for a gas turbine based power plant.

Now we are going to see in the today’s class what are the different ways by which aircraft’s

performance can be measured? And what are the different types of aircraft engines. So, let us start with the today’s class so

engine performance parameter first is thrust. So, let us consider that we are having an

aircraft let us draw a schematic of an aircraft engine. And this is an aircraft engine where

we are considering it as a control volume or practically a black box where there is

some air which is coming with velocity C a and then there is jet which is going out with

velocity C j and the area of the jet is A j. Further the atmospheric pressure which is

acted upon the aircraft or which is present in the ambience of the aircraft from which

it is breathing the air is pH. And the jet pressure at the exit is P j, so having said

this as the operating condition of an aircraft engine we can write thrust of the engine is

equal to change in momentum. So, thrust of the engine is equal to m dot a which is mass

flow rate of the air into Cj – m dot a into C a. So this is the thrust so m dot a into C j

– C a is the thrust produced by the engine. Further we are assuming here that the pressure

acting on the exit of the jet is almost equal to atmospheric pressure or this is almost

a static trust. However if we consider the pressure component of the thrust then we get

the formula for thrust also having pressure which is P j which is A j into P j – P a,

so this is the trust which accounts the pressure. Pressure is also accounted thus this is the

formula for thrust. Now let us find out what is the thrust power. So, the thrust power

is thrust into velocity and we know that aircraft is moving with velocity C a so thrust power

is equal to m dot a into C j – C a into C a this is the formula for thrust power. Now let us move on and find out what is the

propulsive efficiency of an aircraft. So, here we have to first define what do we mean

by propulsive efficiency. So, it appeal let us say that it is propulsive efficiency of

the aircraft and then that is defined as thrust power which is generated by the engine divided

by change in kinetic energy between inlet and outlet of the engine. So, thrust power

divided by change in kinetic energy is propulsive efficiency looking at the figure we can say

that m dot a and through C j – C a into C a was the thrust. And then the change in kinetic energy was

m dot a into C j square into m dot a C a square divided by 2 was the change in kinetic energy

between outlet and inlet. So, we have m dot a into C j – C a into C a so this 2 will

go to the numerator and m dot can be taken as a common so we are C j square – C a square

further m dot a can be cancelled and then we have C a into C j – C a divided by C j

square – C a square this term we can write out C j – C a into C j + C a. So, propulsive efficiency can be written as

propulsive efficiency can be written as 2 C a divided by C j + C a since C j – C a term

gets cancelled further simplified formula for propulsive efficiency is 2 upon 1 + C

j by C a. So, this is the formula for propulsive efficiency of an aircraft. As per this formula

it is evident that if C a is equal to 0 then propulsive efficiency is equal to 0. Further C j is equal to C a would lead to

propulsive efficiency equal to 1. So, this is the definition of propulsive efficiency

of an aircraft. Propulsive efficiency is one of the performance parameters of the aircraft

engine. Next performance parameter of the aircraft engine is energy conversion efficiency.

Let us define energy conversion efficiency as Eta e and that Eta e is change in kinetic

energy which is taking place between outlet and inlet of the engine divided by input fuel

energy. And input fuel energy is known to us from

the calorific value of the fuel. So, change in kinetic energy is already known to us which

is m dot a into C j square – m dot a into C a square divided by 2 and input fuel energy

is mass flow rate of fuel into calorific value of the fuel which is amount of energy liberated

when you unit kg of fuel is burnt. So, having known this we can write this formula as m

dot a into C j square – C a square divided by m dot f into Q. Further this can written based upon air fuel

ratio of an engine as A by F into C j square – C a square divided by Q. So, this is the

formula for energy conversion efficiency of an engine. So, this is second performance

parameter rather in terms of efficiency of an engine. Now we will define a new parameter

as overall efficiency of the engine and overall efficiency is final output divided by initial

input. And we will rewrite the formula for energy

efficiency as 1 by 2 into A by F into CG square – C a square divided by Q and we will write

overall efficiency is overall efficiency as the ratio of thrust power of the engine which

is final output thrust power which is final output and basic input is input fuel energy

and so this becomes equal to propulsive efficiency into energy conversion efficiency. So, in all we are faced feeling that there

is fuel which has chemical energy in it and this fuel’s chemical energy is used to convert

the kinetic energy of the air and this kinetic energy gives thrust power. So, there is an

efficiency which is between thrust power and kinetic energy that we are calling it as propulsive

efficiency. There is an efficiency between fuel energy and kinetic energy that we are

calling it as energy conversion efficiency. And then there is overall efficiency which

is between thrust power and fuel energy. So, these are the three efficiencies which are

related with the performance of the engine. However we can we should not here that the

onlythermal efficiency of the gas turbine power plant should not be thought for the

best performance parameter. We have seen that there is thermal efficiency of the engine

and which was the W net upon Q in and this should not be thought as the best performance

parameter for the engine. Since there are various requirements for designing a given

aircraft engine so there is a requirement something like static thrust or thrust at

the sea level where we encounter maximum temperature in the engine. Further there is requirement for the takeoff

kind situations. So, in such cases we get different performance parameters and those

performance parameters should also be having equal weightage while designing the aircraft

engine from the thrust equation we can see one more thing that we say that thrust is

equal to m dot a into C j – C a here we can see that thrust of an engine can be increased

by changing the velocity more this is one way to increase the thrust if C g – C a

is high for given m dot a this is one way where we are handling small amount of mass

and increasing large velocity change. And bringing in large velocity change this

is one way to increase the thrust and other way to increase the thrust is to increase

the mass flow rate for small or given velocity change. So, here we are handling more amount

of mass but having small change in velocity change small change in velocity. So, these

two are the basic ways by which we can get different thrusts or we can increase the thrust

and based upon this concept we have different types of aircrafts. So as what we have seen this also becomes

one of the parameters for designing an aircraft. Basically we might need to handle more amount

of mass of air something like if we are travelling at lower altitudes we will handle more amount

of mass of air as it is handled by the turboprop engines or the piston prop engines they handle

more amount of mass but they do not begin more amount of change in velocity. So, but if we consider turbojet like engines

they handle less amount of mass comparatively but they bring in large change in velocity

so only thermal efficiency should not be thought as a basic parameter. Further at cruise speed

or at level flight then at that time economy becomes more important and all such parameters

should be considered. Then in one such parameter is thrust specific fuel consumption. So, SFC

is defined as SFC is defined as mass flow rate of the fuel which is fuel mass flow rate

fuel mass flow rate divided by thrust power divided by thrust divided by thrust. So, this is m dot F divided by T further we

can write down it as m dot F divided by m dot a into m dot a divided by thrust we are

multiplying and dividing by m dot a and this becomes fuel-air ratio of an engine into m

dot a divided by T. So, SFC equal to fuel air ratio into 1 upon t or we will say it

as tau and this tau is specific thrust tau is specific thrust and then that is T upon

m dot a this is also termed as thrust specific fuel consumption TSFC. So, here we can use this thrust specific fuel

consumption to compare between two engines which are operating at two different conditions. Then let us consider our aircraft engine where

we are redefining thrust we neglected few terms and we will redefine the thrust by considering

the terms which we did not account. So, this is an aircraft engine we are seeing that air

is coming with we C a velocity going with C j velocity and then jet area is A j and

then we have m dot a as mass of air but while living we have added m dot F amount of fuel. So m dot e is exit mass flow-rate having said

this we can really find the thrust as change in momentum or between iInlet and outlet so

we have outlet momentum as m dot e into C j – m dot a into C a further the component

of the pressure remains same. So, thrust becomes m dot a + m dot f into C j – m dot a into

C a + A j into P j – P. So, let us take m dot a common and then we get 1 + fuel air

ratio into C j – C a + A j into P j – P. So what did we derive in earlier case a we

said in earlier case was only C j – C i we had not accounted this term which basically

accounts air fuel ratio. Here our assumption was that air fuel ratio is negligible. So,

when we accounted air fuel ratio the formula got changed to T is equal to m dot a into

1 + F by A which is fuel air ratio into C j – C i + pressure component of the thrust. Now let us use this formula for finding out

takeoff thrust where we are again going to discard some more terms. So, takeoff thrust

is also called a static thrust and in that trust is actually obtained at very low speeds

or at the static condition of the engine and then that trust is basically trust upon m

dot a. So, if we neglect if we neglect fuel in a ratio to be 0, if we assume P j – P

j is equal to P a. Then we get formula further we will assume

since we are considering that aircraft is at static condition so C a is equal to 0 considering

these three so this term will go then this term will go and this term will go further

this will get divided by m dot a and this leads to the formula as C j. So, C j is the

jet velocity which is giving us the thrust, C j is the jet velocity which is giving us

the thrust per unit mass flow rate in the static condition of the aircraft. So let us use let us use the energy conversion

efficiency and understand this further. So, energy conversion efficiency is energy conversion

efficiency is equal to half m dot a C j square divided by m dot F into Q we know that the

formula for energy conversion efficiency was change in kinetic energy divided by fuel energy.

But in the change in kinetic energy we are neglecting C a so this formula is basically

for static case, for the static case we have only one-half m dot a C j square divided by

Q. So here this formula leads to C j square equal

to 2 into energy conversion efficiency into Q into m dot F divided by m dot a. So, we

get m dot a into C j is equal to 2 into energy conversion efficiency into Q into m dot F

divided by C j. So, m dot a into C j is basically thrust so this is thrust this is equal to

T, so we know now T is equal to 2 into energy conversion efficiency into calorific value

of fuel into mass flow rate of fuel divided by C j. So, from this formula it is even on that for

given energy conversion efficiency and fuel used and further mass flow rate of fuel thrust

is inversely proportional to the jet velocity. Thus it means that if we handle more amount

of mass and have a smaller velocity jet then we can have more amount of static thrust.

So, this is one of the performance parameters of the aircraft. So next parameter what we can see is called

as aircraft range. So, when we are considering range we are meaning that there is certain

amount of fuel in the aircraft and that aircraft is travelling from a place to the other and

for a given amount of fuel the distance travelled by the aircraft this is what we mean by saying

a range of the aircraft. So, a range of the aircraft we are targeting the cruise condition

or level flight and for the level flight there are two things one is lift is equal to weight. And let L is equal to lift and weight is equal

to mg where m is mass of the aircraft and further there is a drag equal to thrust. So,

let D be the drag and Trust be T, so we can use this and find out the derivation for aircraft

range. So, T is equal to D so D by L into L we are multiplying and dividing by L, so

this gives us this D by L is dragged to lift ratio and L is equal to mg. Further trust becomes mg which is weight divided

by lift to drag ratio. Let us multiply both sides by the aircraft velocity. So, T into

C a is equal to mg into C a divided by L by D and we have seen that this we will number

it as 1 and then let us bring down bring the formula for overall efficiency again. And

then we know overall efficiency was for static condition there was one formula however in

general we know it has m dot a C j – C a into C a which is thrust power divided by m dot

F into Q which was fuel input energy. So, here this part is thrust and this is aircraft

velocity, so this is T into C a divided by m dot F into Q and this leads to T into C

a is equal to overall efficiency into m dot F into Q. So, considering this as formula

2, so considering formula number 1 and 2 we get overall efficiency into m dot F into Q

is equal to mg C a divided by L by D. So, using this we can write down the mass flow

rate of fuel is equal to mg C a divided by L by D into overall efficiency into Q. So this is the formula for mass flow rate

of the fuel but what do we mean by mass flow rate of a fuel so that is what it is getting

consumed and so m dot F we can write it as negative of dm by dt where m is the total

mass of the aircraft. As we have used it for the formula for lift. So, total mass of the

aircraft is changing with respect to time and that is due to the consumption of fuel. Further we are interested in finding out range

let us be the distance travelled in the direction of velocity and then the

D velocity C a is equal to ds by dt so using these two things we can write down m dot F

is equal to – C a m dot f into dm by ds, so this these two things this is formula number

3, equation number 4. So, equation 3 and 4 would lead us to this. Where we will have minus C a into dm by ds

and then that is equal to that is equal to mg C a that is equal to mg Ca divided by L

by D into overall efficiency into Q. So, we can use further and say that dm by m is equal

to ds divided by L by D into overall efficiency into Q into g this will have minus sign here

C i is getting cancelled. So, now let us assume that or let us take it for granted that L

by D overall efficiency and calorific value of fuel and G are constants. So, having said this and further m1 and m2

are initial and final masses having said this we can get it as ln of m1 divided by m2 is

equal to gs divided by L by D into overall efficiency into Q where s is the distance

travelled by the aircraft so s becomes overall efficiency into L by D into Lon of m1 divided

by m2 into Q divided by g. We again will use the formula for overall efficiency which was

TC a divided by m dot F into Q where we will use we will say it as equation number 5. We will say that overall efficiency into Q

was TC a divided by m dot F. So, keeping this equation number 6 in equation number 5 we

will get L by D into Lon of m1 divided by m2 into T by m dot F into C a by g, so this

formula is for range of the aircraft where we can see there is a term which is T upon

mf m dot f so that is basically related with specific fuel consumption and so this is m

dot m1 L by D into Lon of m1 – m2 this is thrust specific fuel consumption raised to

– 1 C by g. Where thrust specific fuel consumption or

specific fuel consumption was m dot F upon thrust. So, it is evident from this formula

that for a given speed of the aircraft range decreases if thrust specific fuel consumption

increases. So, range of the aircraft is inversely proportional to the thrust specific fuel consumption.

So, we have seen that there are different parameters like overall efficiency energy

conversion efficiency thrust. Thrust power then we have overall efficiency

we have specific fuel consumption we are range of the aircraft has different parameters which

are deciding the performance of an engine based upon that there are different engines

which we are going to see the aircraft engines. First is the turbo prop engine where we have

first is piston prop engine where this engine has the piston engine which is ourautomobile

engine and this automobile engine is connected with a propeller and the motion of the propeller

would be governed by the engine and then we have basically thrust generated due to the

motion of the propeller so this engine is piston prop engine basically here we are not

having any jet to produce the thrus. Here thrust is produced from the propeller

this engine is more suitable for lower altitudes and at lower speeds. Further this engine also

cannot be used for high thrust application since those thrust conditions the weight of

the piston increases and this engine also cannot handle large amount of mass flow rate

as what we have seen while differentiating between the reciprocating engines and the

aircraft engines based upon the turbo applications. So second is turbo prop engines so in the

turboprop engine we have major thrust coming from the propeller and and this propeller

is rotated by the turbine we can see here the typical arrangement as what we had seen

earlier and then that arrangement was triple spool arrangement. And in the triple spool

arrangement we are seen that propeller will be connected by lowest speed turbine compressor

low pressure compressor will be connected by entering the intermediate turbine. And high pressure compressor will be connected

by high pressure turbine. So, here we are having propeller and then this unit is the

compressor and then this is combustor and then this is turbine. So, most of the energy

extracted from the fuel and the flow is used to row rotate the propeller and rest is passed

through the nozzle. So, there is partially small amount of thrust generated from the

nozzle as well. So, turboprop engine gets major thrust from the propeller and this engine

also gets used at the low speed applications and lower altitudes. The problem at high speed applications is

for the propulsive efficiency of the aircraft further the noise of the propeller becomes

an issue and it needs to have a special design of the propeller. So, turboprop engines are

not generally used for high speed applications basically if we see the schematic of this

aircraft is as what we could draw this is the propeller and this propeller is connected

with a gearbox to a compressor to a compressor. And then air goes parallel into the compressor

then there will be combustion chamber and then after the combustion chamber then there

will be turbine and an air would be passed from the turbine to the nozzle. And in this

nozzle is low speed exhaust nozzle. So, this is typical schematic of a turboprop engine. So, next is turbofan engine and in the turbofan

engine we have fan which is connected with the low-speed turbine this is fan and then

there will be some air which is going from the fan and getting compressed further and

then it is following a route which is called as cold path and then that is generating a

thrust which is called as cold thrust. But some air will go from the fan into the compressor. So, this is compressor after the compressor

it will go into the combustor and then it will go over the turbine. So, this being a

turbofan so some part of the thrust will be from the fan and rest of the thrust will be

from the jet so that is from the nozzle. So, this aircraft is basically having advantage

of having lower noise due to presence of fan. So, here we can draw schematic of the aircraft

like this so this is fan and this pan is practically connected with a compressor. And then this compressor is passing the air

to the combustion chamber and from the combustion chamber air will go to the turbine and after

the turbine it will go to the nozzle. This is moderate speed nozzle. This engine is generally

used at moderate altitudes and moderately high speeds. Then we have turbo jet engine turbo jet engine

has complete thrust based upon the jet and this has components like compressor and then

it has combustor. And it has turbine and nozzle, so there is no propeller there is no fan.

So, complete thrust it generated using the jet and so this is a turbojet engine and here

this engine is generally used for high altitude and also at very large speed applications.

And then we can draw simplest schematic of this engine where we have compressor which

will take air and it will pass to the combustion chamber. And then it will pass to the turbine after

the turbine it will go into the nozzle where we have this as high speed nozzle. Practically

turbojet engines can operate at supersonic speeds. So, this engine would have nozzle

which would lead to have a set which is a supersonic jet. Then last engine what we will be seeing here

is a ramjet engine basically RAM effect is the effect where the meaning inlet moment

of the air is used to compress it to avoid the rotating compressor which is present at

the intake of the engine or at the entry of the engine. So, this ramjet engine does not

have any moving part. So, it compresses the air with its momentum. So, at the inlet there

will be a duct which will compress the air to the desired pressure and desired temperature. And then fuel will be injected as what we

can see here this is fuel and then this will lead to combustion and then this engine would

generate a jet through the nozzle. Practically ramjet engines who are parasite engines which

would operate at the supersonic speeds since we will have supersonic entry of the air and

then the jet will be obtained after combustion of the fuel into the engine. Having said this there is one more type of

an engine which is called as prop fan or unducted fan. Prop fan or unducted fan so this engine

is basically having a compressor which will take the air. And then it will go to the combustion

chamber and after the combustion chamber there is a turbine

and then there is one more turbine and then there will be one propeller which

will be fitted and connected to the low-speed turbine. And one propeller is connected to the high-speed

turbine like this. So, this engine has propellers which are connected counter-rotating to propellers

with our multi blade propellers which are connected to the turbines and they generate

the thrust. So, this is also called as the prop fan or unducted fan kind of propeller.

However this kind of engines need special intention for design of the Aero foils or

section of the propellers. So, having said this we can note down the

engines and then their corresponding limitations. So, piston prop and then we have turboprop

then we have turbofan then we have turbojet and then we have ramjet. So, these engines

and in this direction we are having increase in speed of aircraft and jet. And in the same

direction however we have decrease in mass of the air handed. So, distant of handles large amount of mass

as equally by the turboprop however ram jet and turbo jet would handle lower amount of

mass than the piston prop engine. So, if we plot a graph of altitude versus mach number

where mach number is defined as speed of the aircraft divided by local speed of sound.

So, this is this is turboprop this is turbofan and here we will get turbojet where this range

we will have a round .5 Mach number. And we can go around 6000 6000 meter of altitude

then it is 10000 meter of altitude and here we will have mach number lower than 1 or around

1 and then turbojet engines would go around 20000 altitude and then they can also go for

the mach number of 2.52 or in that range. So, this is where we can see that turboprop

engines are operating at lower altitudes. Since they handle more mass flow rate and

their thrust is based upon the amount of mass handed. Further if we plot propulsive efficiency versus

flight speed in meter per hour flight speed then we can see that propulsive efficiency

is like this for turboprop engines. But turbojet engines would have this kind of propulsive

efficiency trend and then we have two trends for the turbofan engines. So, this turbofan

engine is low bypass this turbofan engine is high bypass. Basically here we mean by

bypass that the large amount of air the rather the amount of air which were passed through

the cold circuit and generate the cold thrust. A lower amount of air were passed through

the cold circuit and more amount of air would pass through the turbo part and generate more

thrust. So, this is the trend of propulsive efficiency and speed of the aircraft. So,

this is how we have seen that there are different kinds of aircrafts and then there are different

performance parameters which are needed to evaluate performance of an aircraft. So, next

we will see in the next class thank you.