 Today, we will discuss in this lecture, various ways the piston engine supplies power to a aircraft propulsion unit. As we have been discussing in the last one or two lectures, piston engine has been used as a power supplier for aircraft engines for last more than hundred years. And we have been discussing various bases of these piston engines or IC engines as they are often called. And how they have been configured based on certain thermodynamic principles, certain thermodynamic cycles. And we had had look at some of these thermodynamic cycles which actually govern the fundamental concept behind functioning of these engines. Today, we will look at some of the mechanical aspects of how these engines actually work and how they actually create power and how these power is finally, harnessed for flying of the aircraft. So, this is the basic principles under which the piston engine works and that is what we will discuss in this particular lecture. And the mechanical theories, we have we had look at the various thermodynamic cycles and the thermodynamic theories, the cycle theories, how they work, the ideal cycles, the real cycles. Today, we will try to look at the theory of the mechanical engineering that makes these engines work. And exactly how do you go about designing them, how you go about predicting their performance or calculating their performance. And we need to do that to make sure that the engine is working ok. If you look at an engine and if you the first thing that you would see is the power is created within a restricted volume which we call a cylinder. Now, within this cylinder everything that you have seen in a thermodynamic cycle happens. So, thermodynamic cycle is basically is the matrix on which this piston and cylinder combination functions. So, inside the cylinder you have a piston and as the movement of the piston allows certain amount of air which we often call charge that comes in and then the fuel is burnt and what is created is a gas which is a mixture of air and burnt fuel. And when this hot gas starts operating the cylinder moves and that is how the movement of the piston is created inside the cylinder. And this creates the power or work and that is what we are mostly interested in. The fact that we burn fuel, the fact that the burning of the fuel creates hot gas is the reason for which these engines are all called heat engines. So, basically what we are looking at is of course, an heat engine and it is also referred to as an internal combustion engine, IC engine as popularly known as and this internal combustion obviously refers to the fact that we have the combustion or heating inside a restricted identified space and this space is the cylinder and the piston and the volume contained within the piston and the cylinder and this is the space within which the heating is first done and then we see the mechanism by which this heat is converted to work. So, conversion of heat to work is what we are actually dealing with at this moment and that is why this is called generally in a very generic manner a heat engine. Now, what we see here is a piston which is enclosed within a cylinder and then as the ignition occurs the fuel air mixture is burnt and a high pressure is created somewhere at the top of the cylinder over here and that high pressure then activates the piston. So, this movement of the piston is created by the hot gas and that creates what we have already called power stroke. So, it moves the cylinder from the top of this station to the bottom over here which we have called the top dead center and the bottom dead center. Once they reach this top and the bottom they start there the piston starts their journey backward that means from the bottom it starts moving to the top and when it reaches the top after the ignition and the heating it starts moving to the bottom. So, that is a movement of the piston it is move from bottom to top and top to bottom and it keeps doing that all the time and during which we have the execution of the thermodynamic processes which are contained within the thermodynamic cycle which were presented in the last lecture. So, that is the mechanism by which basically the whole thing works. Now, you see the movement of the piston is created from the top dead center and as we know when it moves from the top to the bottom we call it a power stroke. Now, as we know by now that only one leg or one process within the whole thermodynamic cycle actually is a power creating or work creating process. Rest of the processes within that thermodynamic cycle are not power creating processes. So, same thing here typically this ice engines have you know four strokes and these are often called four stroke engines and only one of the stroke is power creating. Now, how does the motion of the piston get sustained over other three strokes and this is normally done through what is known as a flywheel which is in kit of aircraft engines a combination of the crankshaft the propeller and rest of the things which means when once the power stroke is delivered and the power is delivered this entire flywheel motion that is the propeller and crankshaft starts moving that means their rotary motion is initiated. Now, once the rotary motion is initiated that motion is sustained by itself for another three strokes. So, other three strokes are created by the continuous motion of these which we may now call flywheel for the time being let us say and as the flywheel moves the other three strokes are sustained till the next power stroke comes. So, out of the four strokes one stroke is a power stroke other three are sustained by the flywheel. So, that till the next power stroke comes the motion of the entire engine motion of the pistons the motion of the shafts are sustained this is important if you do not do that obviously the engine is going to come to a halt. Once the power stroke is over as we know the next thing that needs to be done is the gases need to be exhausted that means the gases which were burned pressure were created and now the power stroke is over which means the work that we wanted to get out of this high energy gas has been taken out and now actually we do not have any need for this gas anymore. So, we need to get rid of this gas and this is done by what is known as the exhaust stroke. In this exhaust stroke this piston now starts moving upward and as it starts moving upward the gas which contain the entire cylinder gets exhausted through one of the exhaust valves and as a result of which the used up gas is now sent out of the cylinder cylinder is our working space and it is now sent out of the working space and as a result of which this once the cylinder is more or less exhausted fresh charge or fresh air or fuel air mixture can now come in through the inlet valve and fill up the cylinder space all over again for the next four strokes that means the next cycle through which the work is performed. So, this is how the work is actually sustained from one cycle of four strokes to next cycle of four strokes. The linear motion of the piston this is a bit of mechanical engineering which we need to know is sustained through the connecting rod and is transferred to the crankshaft and the crankshaft you see what we have here is a linear motion of the piston it is just moving up and down up and down or if it is positioned horizontally it would be moving sideways. So, what we have here essentially is a linear motion the work is being done simply in the form of a linear motion and this linear motion now needs to be converted to a rotary motion and that is done through this crankshaft and as a result of which the crankshaft that supplies power to the propeller in case of a aircraft engine and that is how the propeller rotates and creates thrust. So, we need to convert linear motion of the piston to a rotary motion and that is done through the system of connecting rods and cams and crankshaft and then we have the concept of flywheel which then sustains the motion or continued smooth motion through the other stroke. So, that we have continuous motion now when you have multiple cylinders as we have seen that many of the aircraft engines actually have more than one cylinder quite often up to 10, 12 or even 16, 18 cylinders and what happens is the supply of power to the central crankshaft every engine has only one single crankshaft and all the cylinders supply power to that crankshaft and as a result of which now that the cylinder power strokes are time staggered the supply of power to the crankshaft is now time staggered as a result of which when one particular cylinder is executing some other stroke let us say exhaust stroke or intake stroke the some other cylinder is probably providing the power stroke. So, as a result of which continuous power is being supplied to the crankshaft and the whole flywheel or the crankshaft propeller combined continues to rotate all the time because some cylinder or the other almost on a continuous basis is supplying power to the main crankshaft and this is how it typically in an aircraft engine a multi cylinder arrangement continues to supply power to the main crankshaft. Now, it means that when you have more number of cylinders there are certain mechanical advantages and today we are discussing some of the mechanical issues involved with the engine it actually creates a little more vibration free or smooth operation. Now, this is very important in a actual operation of an engine if you if you can create a engine that is vibration free because what happens is as we have seen you have four strokes one of them is a power stroke and during the other strokes the engine has to sustain itself in its motion and as a result of which it is possible that there is a uneven application of force or moment on the crankshaft. Now, this uneven application of force and moment on the engine can create certain amount of vibration. If you have more engines more cylinders 6 or 8 or 10 or you know even 12 or as we have seen up to 18 cylinders is possible if you put them together and sometime on the other every split second one of the cylinders is supplying power to the crankshaft then that particular engine is likely to be more vibration free it is likely to be more smooth because the crankshaft is almost getting supply power almost on a continuous basis. So, a multi cylinder arrangement quite often comes out to be a smoother operating engine compared to let us say a single or a two cylinder engine. So, the aggregate power of a reciprocating engine is then normally given in terms of the total volume of all the pistons together that means the displaced volume the amount of volume that is typically created between the top dead center and the bottom dead center. This motion is what the piston is executing every time it moves from one end to another and this is what we call the displaced volume and this is the volume of displacement of the gas and this is the volume which is often coated as a capacity of the engine and this all the cylinders together you can coat a certain total amount of volume and that is often specified as the engine specification and is representative of the engine's capacity to produce power. So, total volume of all the pistons together is often coated as the engine's capacity and is an indicative of the engine's capacity to produce power. Now, let us see actually how the engine as particular cylinder actually creates power. We can put now numbers or simple relations to some of the concept that we have been talking about. You have a piston which we say that it has a piston stroke of length L P and it moves as we see from B D C to T D C and then of course, back from T D C to B D C. Now, when the piston is at T D C from the cycle we have seen it reaches a pressure of P 4 from the cycle diagram we have seen that and this pressure then is very high. It is also hot gas of course, so as a result of which it executes a lot of force on this head of the piston or often is called piston head and this as an area. So, obviously, more this area of the piston head more is likely to be the force, but as we have seen the aircraft engine has to have certain limitation of its size and weight and as a result the size and weight are often a little restricted. So, the pressure here created creates the force which then starts driving the piston to its power stroke. That means, its motion backwards from T D C back from T D C to B D C and it executes the power stroke. Now, the power delivered to the engine by one cylinder is often given by this simple relation which is power is equal to P effective into the power stroke into the area of the piston into N by 2 N by 2 being the power strokes per minute where N is actually the r p m or the motion of the rotary motion of the crankshaft. So, it tells us very quickly that if it is rotating, if we are managing to rotate the crankshaft at high speed, you know we are able to get more power or vice versa whichever way you look at it and as it is obvious that if you have more area of the piston then you get more power, you have a longer piston length which is the force into distance and that is your work done from your Newton's laws of motion and as a result of which you get the power done. Now, P effective is something which we are yet to define actually and mind you P effective is not same as P 4. So, P effective is some kind of an average power that is average pressure that is applied on the head of the piston during its power stroke. So, we will define that a little more formally in a couple of minutes. So, just at this moment remember P effective is not same as P 4 which is the maximum pressure that the piston or the cylinder actually experiences. So, the number of cylinders if it is given by capital N C, the total amount of engine power that one can say is created is given in terms of as we know in terms of I H P which we call indicated horsepower and nowadays of course, they are all mentioned in terms of kilowatts and the N C comes in as the last parameter and hence you get the indicated horsepower or what we can call a mechanical estimation of the ideal horsepower. The total volume displaced which we are talking about just a while earlier is now given in terms of area of the piston head, the length of the stroke into the number of cylinders that is the volume which I was talking about and that is the total displaced volume which is often coated as the engine capacity. You might hear same things about the various automobile engines where the total displaced volume is coated as the engine capacity and hence we can write now I H P in terms of effective power the total displaced volume into the power stroke per minute which is N by 2. So, that gives us an idea about the mechanical estimation of the indicated horsepower as we know we have earlier defined indicated horsepower from the cycle diagram thermodynamic cycle diagram. Now, we can see that we can have an estimation of that from purely from the piston and cylinder configuration point of view. Now, some of the power that is developed in the piston cylinder is actually lost in friction of the piston and the inner surface of the cylinder. Now, this is often referred to as frictional horsepower and this is a continuous affair. This is going on during all the strokes of the piston mind you one of the strokes is only power stroke others are not power stroke and even during the other strokes this friction is continuously happening and as a result of which a lot of power is actually lost in the process of overcoming the frictional friction between the piston and the inner surface of the cylinder and this needs to be this is not a small amount this is a reasonably good amount and this needs to be factored into the actual power availability of the engine. So, actual power available at the end of the shaft may then be called the brake horsepower or BHP and this is of course, IHP minus FHP which we call the frictional horsepower. Now, the BHP can be written in terms of twice pi into rpm into the torque that is produced. We shall see as we go along that the torque produced by the engine is of great importance in running the propeller. The propeller has a certain torque characteristics and we shall discuss that later on in this course that unless you meet those torque characteristics the thrust would not be created. So, the torque of created by the engine needs to match with that of the propeller and as and we know from simple mechanical formulations that the horsepower or the BHP can be actually written down in terms of torque. Now, this torque of course, can be also written down the BHP can also be written down in terms of IHP into the mechanical efficiency of transmission of the crankshaft and that again to the various parameters here the P effective, the total volume, the rpm and as a result of which we get a parameter which we call P effective brake. Now, this is what we had mentioned earlier as P effective and now we call this brake mean effective pressure BMEP actually speaking if you measure it this whole thing with reference to IHP you can actually come up with something which is indicated mean effective pressure IMEP it is possible, but that will be an ideal mean effective pressure. The more useful mean effective pressure is the brake mean effective pressure which is related to the final BHP that is being created and through the piston cylinder arrangement and this is why I said that this is some kind of an average pressure that is actually created by the theoreticians it is not something that you can measure actually and it is not the physically active pressure which is active inside the cylinder. So, it is a kind of measure of the average mean gas load through which the piston actually operates and it is become a widely used index of the engine performance. As a result of which we need to keep an eye on this brake mean effective pressure for our various understanding of how the piston cylinder arrangement actually works. Since the entire objective of an aircraft engine the IC engine or the piston engine that we are looking at is fundamentally to convert the chemical energy contained within the fuel into finally, propulsive thrust. So, what we have first to begin with the input to the engine is the fuel which has chemical energy contained within it. Once it is burned this energy manifests in the form of heat and then the heat is converted to the piston motion linear motion which is converted to the rotary motion. That rotary motion is transmitted through the crankshaft to the propeller and which then creates the propulsive thrusts. So, it is a fairly long drawn out procedure through which finally, thrust is created. So, we have quite a few steps to contain with before we get the thrust and thrust is what makes the aircraft fly. So, the overall efficiency of this entire process needs to be also understood and estimated for us to know what is the energy efficiency of this entire power plant. So, we have an engine which is fed with a mass flow let us say m dot f and which let us say has a thermal input of q f and this mass flow has a thermal input of q f and BHP is normally as I mentioned expressed nowadays in terms of kilowatts and it may also be expressed in terms of kilo joules per hour and where q f is the heating value of the fuel this is a characteristic of the fuel. This is the chemical energy that is expected to be contained with within the fuel it will vary from one fuel to another quite often quite substantially and hence you need to choose your fuel very carefully. You need to choose a fuel that has a good heating value and quite often many other characteristics of the fuel are also taken care of in choosing the fuel, but one of the main things are probably the first thing that makes for the choice of the fuel is the heating value of the fuel. You want to have lot of heat generated by burning the fuel and as I said the fuel is characterized by the heating value it is a typical chemical energy content of the fuel that comes out through the heating value. The ratio of these two quantities that means the chemical energy that we have we can expect to be available in the form of heat and the final power that is created in terms of BHP the ratio of the two is the break efficiency of the engine and this is our break thermal efficiency of the engine which is the most important efficiency parameter that actually is quoted as efficiency of the engine. This can be written in terms of m dot 1 by m dot f by BHP into Q and m dot f by BHP of course is the parameter which is of importance and this is often referred to as break specific fuel consumption and this is given in terms of m dot f by BHP and is often expressed in terms of kg's per kilowatt hour. Now break specific fuel consumption is conceptually based on the BHP where you can again you know conceptually you can have a indicated specific fuel consumption where instead of BHP you can use IHP and you can get that but as I mentioned the more useful one is the break specific fuel consumption. So, when we say BSFC we are talking about the utility of the fuel in terms of the break horse power the final horse power that is available from the engine. Now in most of the modern engines BSFC is quoted as the figure of engine efficiency or figure of merit for the engine efficiency. We have just defined the engine efficiency or break thermal efficiency but most engineers would like to prefer to use BSFC as a measure of the engine efficiency. So, quite often in the engine specifications you may not find the value of engine efficiency actually mentioned anywhere it is more of a theoretical understanding by the designers but the engineers and operators quite often would use BSFC as the measure of the engine efficiency. And now we can also look at the overall efficiency of the piston and propeller combined and this is often given in terms of the overall efficiency which is equal to the break thermal efficiency into eta p which is the propeller efficiency and quite often the propeller efficiency comes out of the propeller understanding which we will probably do you know later on in this course. So, typically when an aircraft is flying at cruise condition the break thermal efficiency is likely to be of the order of 30 percent whereas, the propeller efficiency the aerodynamic efficiency of the propeller functioning it could be of the order of 85 percent and in which case the overall engine thrust producing efficiency could be of the order of 25.5 percent. Now that is the kind of overall thrust production efficiency with which the aircraft power plant functions a word about the fuel some of the fuels that are used in typical aircraft engines are basically the petrol based in some parts of the world they are also called gasoline. Now they have as I mentioned a very high heating value that is how they are chosen and quite often they are to be used under high compression ratios we need to have high power output and of course, as we have just seen the efficiency definition good efficiency at various operating conditions of the aircraft and most specifically at high altitudes where the aircraft actually flies. Now this kind of fuel is typified by what is known as high octane value and octane rating is given in terms of in terms of 100 and the aircraft fuels are often of 100 octane and they often have what is known as a small amount of lead content. This is this lead is tetraethyl lead which is often added to a basic fuel is blended with the basic fuel which is often as I mentioned some variety of petrol and provides a high octane rating. Now we know that in the land based automobiles this addition of tetraethyl is now banned because of the environmental issues, but in aircraft engine it is still being practiced because aircraft mostly flies at very high altitudes and as a result of which we require the high octane rating that is necessary to operate at very high compression ratios at high speeds for producing high power at reasonably good efficiencies. We now see that quite often in a craft engine has to operate at high altitudes where it has to produce good power at good efficiency and for power production at high altitudes we have a few issues. Now if we go back to the cycle diagram which we are familiar with we shall see that the you know the exhaust that starts at the point five well while the cylinder pressure is you know still quite high actually high above the atmosphere. Now you realize the aircraft has gone to high altitude so the atmospheric pressure is rather low. So the exhaust stroke which ends at near atmospheric which as I mentioned by virtue of the inertia of the piston motion happens at a lower pressure. So the difference between the exhaust pressure and the intake pressure starts going up and as a result of which this loop which we see here the intake exhaust loop starts consuming more and more this area becomes higher and higher which is the non productive or non power creating loop of the cycle and as a result of which a lot of power that is produced actually goes into this loop and it is not available at the end as BHP. Now this is a problem and as a result of which the available BHP would go down. Now one of the ways of getting around this is by what is generally known as augmentation procedure and in this an attempt is made to raise this intake pressure to a higher level through a process which is known as supercharging and a device that is called supercharger which raises the intake pressure to a higher value so that this intake exhaust loop again becomes a small one and does not take away a lot of power and as a result of which the BHP available would again become a reasonable value for supplying power to the propeller. So this supercharging is a business which we will look into in some detail in the next class and for the moment just remember that for aircraft engines you need to have this augmentation which is normally not required in land based automobiles but in aircraft without this augmentation procedure or without the supercharger the aircraft would not be able to get sufficient power supply from the engine for executing its flight motions. Now when the cylinder is operational we have just seen that at the end of the exhaust stroke the burnt gases are exhausted from the cylinder. However we have just we also know that the end of the stroke when the piston reaches the top dead center there is a certain amount of volume which is still containing the burnt gases. So all the burnt gases do not go out of the cylinder a very small amount remains and when the intake valve opens and the fresh charge or fresh air comes in it gets mixed with the fresh air and as a result of which what you get finally is a combination of fresh air charge and a certain amount of residual burnt gases that has remained after the exhaust stroke and as a result of which effectively the piston capacity of the volume with which we have been talking about effectively gets reduced. This error is attempted to be now quantified through a term which we call volumetric efficiency. Now volumetric efficiency we shall define in a minute but let us quickly understand what is it all about what happens is the density of the first charge affects the volumetric efficiency and we have seen in a craft engine we need to hike this density through the process of supercharging and then the pressure and the atmosphere the temperature of the outgoing burnt gas which has remained or the residual amount and then of course how quickly or how efficiently the intake and the exhaust valves or manifolds as they are often called open and close. So, the closing of the exhaust and the timing of the exhaust and the intake manifolds is of great importance and this is where the mechanical engineering comes in a big way. So, the engine needs to be designed to create very efficient intake and exhaust manifolds otherwise it will affect the volumetric efficiency and the timing of the opening and closing of these valves. This is the engineering that needs to be engineered into this particular piston cylinder arrangement otherwise it will affect the volumetric efficiency and this needs to be made sufficient attention by the piston designers otherwise the volumetric efficiency as it is defined now would be coming into the picture and it is simply defined as the charge that is coming in or the charge that is now available by the theoretical charge which we assume to have to be effective in the cylinder. So, the ratio of the two is the volumetric efficiency. So, the actual charge is the mass that is you know theoretically estimated from the geometry of the cylinder and the total number of cylinders etcetera which we often quoted as I mentioned earlier as the engine capacity and as we see now quite often that theoretical capacity may not actually be effective or operational during the operation of the engine due to the various factors that we have just mentioned. So, the actual operation of the engine would get affected by the volumetric efficiency of the engine which is typically less than 100 percent. The various power that is created is affected by the various losses that occur. We mentioned one of the losses that is the friction losses due to the motion of the piston. There are other losses which we need to contend with and they all affect the final power supply of the engine. One of the losses is due to the cooling of the cylinder body. Now, you see the cylinder is getting heated. We are burning fuel, the cylinder is getting heated, the piston is getting heated and they get heated to very high temperature in spite of the advancement of the material science and metallurgy. The heat bearing capacity of these metal bodies has certain limitations and if you have to provide them with certain amount of life span or working which is often in terms of thousands of operational hours, then it is necessary that these bodies are cooled on a continuous basis to lend them a certain respectable amount of life. As a result of which a goodly amount of heat is actually lost through the cylinder body through the process of cooling. This cooling is absolutely essential for the life of the engine but it affects the continuous operation of the engine in terms of its actual power supply efficiency. So, a good amount of cooling losses actually take place and as we see in this particular simple graph as the engine speed increases from low to high, the cooling losses actually stay more or less of the same order. The friction losses keep on increasing as the motion of the piston becomes faster and faster, the friction losses are more and that is of course, easy to understand. This is the mechanical friction and the other important loss is due to the radiation of the various heat that is produced within the cylinder due to the exhaust which the gas is going out and it takes away lot of heat with it. So, the exhaust gas when it is exhausted or forced out of the cylinder goes away with a lot of heat. So, that loss of heat, the radiation losses and many other losses such heat related losses put together amount to a large amount of losses. Certain amount of losses are due to the improper inlet and exhaust valve operation. So, when you put all of these are the mechanical functions of the engine and when you put all of them together, we find that the useful work actually is a small amount a little more than 25 percent of the energy that is produced through the burning of the fuel. So, only 25 percent of the energy is finally, probably available as useful work and it goes down a little with the speed of the operation of the engine. So, typically one can say at high speed you can get work done total amount of work, but the efficiency of the work done is likely to be somewhat of the lower order. Now, this is a penalty that you have to pay in a aircraft engine because you do want high work, high amount of work supply and as a result you are consigned to or you have to be content with the fact that you may have to be working at a slightly lower efficiency because the friction losses and other losses are somewhat on the higher side at high speed operation. The other thing that we need to keep in mind is we have talked about ideal cycle and real cycle. One of the main difference between ideal cycle and real cycle is that the ideal cycle is actually operating on air cycle, whereas the real cycle is operating on a gas cycle. Inside the cylinder fuel has been burned, gas has been created and actual operation of the cycle is specially from 0.4 to 0.5 and through the exhaust it is not air, it is gas, combination of air and burned fuel. So, what we have from 4 downwards 4 to 5 and then on to 6 is actually gas. So, this part of the cycle is definitely gas cycle and that is why that is one of the main reasons you see there is a big difference between the ideal cycle which is given from D to E and the gas cycle, gas process from 4 to 5 and there on on to 6. So, this difference is mainly due to the fact that you do not have air and as we know and we can code the numbers now that for air the specific heat ratio given by k in some books it is given as gamma is often is of the order of 1.4 whereas, for the gas it is 1.33 and when you factor them in your some rhyming cycle calculations you will find there is a big difference between these two use of these two values in the power calculation or pressure ratio calculation and as a result of which there is a big difference between these two areas is due to the simple fact that you do not have air here what you have here is gas. Let us look at some of the issues of the engine as a whole what happens when an aircraft engine is of a piston engine is performing for powering an aircraft. As we can see here the air consumption per cycle you know that is given over here as y axis and that goes up with the speed on the other hand the air consumption per unit air consumption per cycle goes up and it reaches a peak summer over here and it goes down whereas, the air consumption per unit time per unit second or minute it actually continues to go up over here and it reaches a peak at a very high speed. So, there is a difference between the air consumption per cycle and the air consumption per unit time the air consumption per cycle peaks at a some lower speed not at the high speed and then it actually starts going down with increase of speed of operation whereas, the air consumption per unit time actually goes up till the a very high speed and then plate goes up and as a result of which IHP the indicated horsepower actually keeps going up and reaches the high value at high speed on the other hand the torque created peaks with the air consumption per charge consumption per cycle and it is approximately around may not be exactly at the same engine speed, but somewhere around and as a result of which the high torque is often created at somewhat lower speed not exactly at high speed, but high power is created at high speed. Now, this is a dichotomy which most engines have to live with that high torque creation which is important for operation of the propeller and high power supply which is also important for creation of the thrust are at two different speeds quite often two very different speeds and as a result of which the engine operation needs to be properly configured or matched with the propeller operation. We shall discuss about some of these later on again in this course. The maximum torque of the engine occurs as we now see at a somewhat lower speed and the IHP keeps going up as we have seen in the last graph whereas, the BHP which takes into account now the FHP actually keeps going up and then somewhere over here the high FHP forces the BHP to level off and it sort of plateaus out and BHP may not increase any further after a certain engine speed. So, every engine has a high speed at which BHP reaches its peak and there is no point operating the engine above that. So, quite often most engine speeds are cut off slightly above this high speed and it does not operate anywhere higher than those speeds and this is found out from this engine estimation before the engine is actually installed. If we look at BSFC we have seen is one of the most important parameters of the engine operation it is indicative of the efficiency of the engine. However, in this graph we see that BSFC and the total fuel consumption are two slightly different issues. BSFC is a unit fuel consumption per unit mass flow or unit power consumption and is indicative of the efficiency and it reaches some kind of a low plateau somewhere in the speed range over here in this particular engine that is being shown. It reaches a low value over here at a lower speeds it has actually a higher BSFC at high speeds again it starts going up and BSFC is no more the lowest. So, engine operation in this range of speed would probably give a low BSFC that is true of most of or almost all kinds of ISA engines or piston engines even in automobile engines that run the cars or vehicles on ground and you know car manufacturers or operators would tell you that car operation at certain median value of speed of rotation often produces the best efficiency of fuel consumption. On the other hand if you take the total fuel consumption and we are talking about full throttle operation it continues to increase with the speed. So, higher the speed of operation higher is the fuel consumption. So, we have to balance between the two we have also seen that higher the engine speed higher the power production. So, there is always a balancing act that operator has to find out between high power consumption high power creation which produces which obviously has high fuel consumption. On the other hand the BSFC also starts going up. So, if you keep an eye on the efficiency of the engine then you would probably like to operate somewhere at a slightly lower values of engine speed and we have seen that at the some of one of these lower values you also get a high torque. So, high torque BSFC fuel consumption power production are four different parameters and engine operators have to keep an eye of all of them while operating the engine to find the best balance during the various course of operation of the engine. So, we see now that maximum torque operates at some speed maximum power operates at another speed minimum BSFC happens at a third speed. So, we have three different speeds and this is true of most of the engines all kinds of engines that I say engines that powered the aircraft power plant and this is what an engine operator will have to quickly figure out and apply his engine control to operate. Typically he would like to do it in such a manner that taken over the entire aircraft light let us say from takeoff to cruise to landing the finally the total fuel consumption would be at a low value. So, this is something which requires a certain amount of control which requires certain amount of engine control propeller control some of which a little bit of which we might discuss later on in this course and the two controls together we will have to find a balance of using the engine for maximum torque or maximum BHP or minimum BSFC. So, that the total fuel efficiency of the engine is quite good and competitive and has an economic repercussion in the operation of the power plant. So, these are the issues that typically an engine operator and engineer would have to deal with in the operation of the engine for flying an aircraft. In file flying of an aircraft engine one of the things that is required is once the engine takes off it has to climb to a cruise and the engine typically needs to provide certain amount of extra power not only for cruising for climbing and this is how the measure of the extra power needs to be quickly arrived at. So, that when an aircraft takes off and then it finally reaches a cruise where the power available and the power required are matched. So, typically cruise would be somewhere here actually little before this and we shall talk about that again later on how the matching of the aircraft and engine is done. This excess power availability from the engine is vitally important because this is what makes the aircraft climb otherwise the aircraft would not be able to climb from low altitude to high altitude to the cruise altitude. So, this excess power requirement needs to be factored into the engine design and this is vitally important for aircraft engines. We have in this lecture we have now looked at various aspects of engine that goes into the aircraft. In the next lecture we shall see various issues that goes into the operational reasons for loss of engine power. We shall see what happens when the engine operates at part load, which is when the engine is not at its full BHP full power creating capacity, but at some kind of a part power creating capacity and what happens during those operations and we shall see that for an aircraft engine for it to operate at high altitudes it is necessary we have a supercharging which creates augmentation of power without supercharging we cannot have an aircraft engine. So, this is these are important issues specifically with reference to aircraft engines and these are the things we shall discuss in the next class.