 We had looked at all the air breathing systems now let us take a look at what are the non air breathing systems okay why do you think we need this I thought we had covered a large Mach number range with the air breathing system itself why do we think why do you think we need the non air breathing system okay that is one part yes travel beyond sensible atmosphere the other reason that exist is suppose you need a large thrust for a very short duration even within the atmosphere then you tend to go in for non air breathing propulsion okay because if you look at everything propulsion other than the ramjet engine most others are very bulky right so if you are looking for a large thrust for a very short time you cannot use a large dead weight to propel the system if you are looking at a turbo jet engine to propel it if you are looking for a large thrust for a short time then you cannot use it and then discard it right therefore we tend to go in for rockets or non air breathing propulsion even within the sensible atmosphere typically missiles tend to make use of this remember I said any of the ramjet engines are not self-starting and they need to be taken to a Mach number range beyond one for them to be operational usually rocket engine is used to take it to that because you can get to that very quickly right if you use a rocket engine now most of these ramjet engines are used either as an interceptor missile right then you are looking at a very short response time that you have once the enemy is intruded into a territory territory you want to find out how to go about neutralizing the enemy right it it has a very short time you have a very short response time that is available to you so if you have to respond within that time then you need a rocket engine and then a ramjet engine okay now in non air breathing propulsion there are three kinds one as solid rockets then there is liquid rockets and lastly hybrid rockets the classification is done based on the physical state of the fuel and oxidizer remember in a non air breathing propulsion system you need to carry the oxidizer on board right see so in this case the oxidizer carried on board okay so in this case fuel and oxidizer are solids and here fuel and oxidizer are liquids and in this case typically you will have fuel as solid oxidizer as liquid okay now just to look at how these systems developed over a period of time remember we started our discussions with firstly fixed wing design how fixed wing design came about and how it took us 100 years after that to develop the first flight so similarly let us look at how these things have a what over a period of time now most of you must have played with these Diwali rockets right these Diwali rockets use something known as gunpowder salt Peter now this was discovered by the Chinese around the 11th of the 12th century so a typical composition of this is it has potassium nitrate around 75% then sulphur 15% and lastly charcoal 10% this is a typical composition of a gunpowder and this was discovered in the 11th and 12th century after that they have been used as explosives but their first use or first known military use as source to speak as rockets was somewhere in the 1700s by Tipu Sultan of my source state he used this against the British in the third war between the British and the Tipu Sultan so these were you know he had fairly decent systems but one of them was something like 2 meters long and weighed about 3.5 kgs and had a range of something like 3 km he had another system which was of a shorter range of 2 kgs and 1.5 meter and 2 km range so he had essentially two systems if you look at what these things did these were glorified current day rockets right but if you look back at a time when these were not known to people okay and suddenly you have something firing and coming at you you would be very very scared and this would this would be typically used to break up the cavalry ranks if the enemy is approaching you in a rank formation and if you want to break it up and make them go helter skelter that is when you fire these things at them and that makes them really scared and more on these were not really killing machines as such okay now after the British won the final war of Mysore around 1799 they actually took all these things to Britain and there was a person by name William Congrave he developed these systems further he made a systematic study of them and developed this further and they were used in a few other wars fought by the British somewhere in Europe but never really took off beyond that and unfortunately we do not have any of these specimens that Tipu Sultan built anywhere in India now they are only available in the British Museum in Britain okay but after the development by William Congrave it never really took off as a large system okay they were used in battles essentially to break the ranks the cavalry and things like that and they were later on discarded because liquid rockets became more prominent as the 19th century arrived or the 20th century arrived liquid rockets became more prominent and one would find that liquid rockets began to be developed and talked about in the 20th century and the solid rockets made only a comeback after the Second World War somewhere in the 1950s as large systems otherwise they were relegated to the use of being used as flares and ships right or they were used as useful jet assisted take off that is if you have an aircraft that needs to take off within a short runway length typically in a battle operations the enemy will first come and try to bomb your airfields so that your aircraft cannot take off so then your operational length of the airfield somehow becomes smaller and if you want to take off within that small length then you need an extra thrust that probably the afterburner might not also be able to provide in such cases you use the solid rockets and you can drop them as soon as you take off you can drop them so you do not need to carry them so they were essentially used for flares on ships or jet assisted take off okay and only in the 1950s they started getting developed into large systems okay now let us look at what this solid rocket looks like you have an igniter this is known as the head end and this is known as the nozzle end and you have a convergent divergent nozzle here okay this is the solid propellant and this is known as port okay and you have a layer of inhibitor here this layer here is the insulation and this is the motor casing so this is a schematic of a it has an igniter a propellant grain that is the solid propellant grain and has a port where in the propellant burns and the gases fill up this place and it has a convergent divergent nozzle and the whole thing is cased inside a motor casing typically made of steel right or other material metals off late people are planning are trying to use FRPs or fiber reinforced plastics here just to save weight and you have a layer of insulation here what does an insulation do insulation prevents heat from being transferred or inhibits transfer of heat okay now there is something known as inhibitor now what this inhibitor does is although there are high temperature gases here all through this it prevents the burning from taking place in this direction okay it does not allow burning to take place in that direction that is the role of a inhibitor and typically silicon oxides are used as inhibitors and the igniter is typically a solid propellant itself with a slightly higher loading of metal we will discuss that when we discuss about solid propellants in a little more detail as we go along and you have a heat sensitive material here as soon as you apply some voltage across the two terminals this catches fire and as this burns the hot gases and metal fall on the propellant and the propellant gets ignited remember a solid propellant has both fuel and oxidizer okay so this catches fire as soon as this starts to burn the pressure inside the chamber keeps on increasing okay because you only have one port and all the gases need to go out through that port and the pressure will keep on rising till the outflow and the inflow matches okay and that pressure is known as equilibrium pressure that is if you take a pressure versus time graph the pressure keeps on rising and shoots beyond the equilibrium pressure and comes back to this pressure is known as equilibrium pressure it pressure increases and increases beyond the equilibrium pressure and comes back to this value okay so then this high pressure high temperature gases okay that are formed here typically the pressures can be of the range of 30 to 120 bar in the combustion chamber here and temperatures can be in the range of 2600 to 3600 Kelvin so this high temperature high pressure gases are then expanded through a convergent diversion nozzle why are we using a convergent divergent nozzle here why not a convergent nozzle because if you look at it the pressure upstream of it is very large and then you have a large pressure ratio between the ambient and the pressure here so you can expand it through a convergent divergent nozzle and that is why we use a convergent divergent nozzle in any of the rocket motors okay so if you look at a TS diagram for this how will it look like you were to sketch a TS diagram for the processes in till there is combustion at high pressure and there is expansion through the right through the nozzle it is a self-pressurized system because of burning the system pressurizes itself it does not need any compressor and the high pressure high temperature gases expand through the nozzle thrust producing the required moment okay now let us look at how to derive the thrust equation for this remember we derived the thrust equation for a air breathing system let us do the same for this non air breathing system I will take the entire rocket motor as a box and it has only one exit it does not have any inlet because it does not need to take in air so it has only one exit and let me call the conditions here as row II or let me call the mass flow rate that is coming out as M M dot and pressure as PE and area as AE okay fine and the ambient pressure is okay now with this you will you will find that if we were to find the sum of the forces in the x direction that is the negative x direction there is thrust acting in this direction okay thrust must be equal to force must be equal to rate of change of right I did not put one more quantity that is the exhaust velocity PE okay now force must be equal to rate of change of momentum right what is the rate of change of momentum here firstly let us look at what is the forces F-AE PE-PA right there is a pressure differential across this PE-PA and this area is AE so this is acting in the opposite direction as F so I have taken the minus sign must be equal to what is rate of change of momentum here M dot into PE because there is no intake at all right so you have therefore F is equal to this is the thrust equation for a rocket motor it does not matter what kind of rocket motor you have liquid or solid or hybrid this is the thrust equation okay now if you remember we had defined a quantity called specific fuel consumption right when we talked about gas turbine engines or turbojet engines and turbofan engine similarly we can define a quantity called specific impulse here okay what is impulse impulse is force into time right so specific impulse is force into time divided by mass okay so if you look at the expression it is F by M dot that is nothing but force per unit mass flow rate and the units of this is Newton second per kg this is the ISP and SFC is ISP is nothing but 1 by SFC if you remember SFC was nothing but mass flow rate per unit thrust mass flow rate of fuel per unit thrust in this case it is the combined mass flow rate of fuel plus oxidizer this includes mass flow rate of fuel plus mass flow rate of oxidizer whereas SFC is nothing but M dot F by F okay now a couple of classes back you had asked me how is it that you can say that you get optimal thrust when PE is equal to PA right you had asked me how that is optimal now let us take the case when PE is equal to PA right what happens then the flow is said to be optimally expanded if you look at this convergent divergent nozzle or I will draw a different sketch here okay now just like probably some of you are aware of this in aerodynamics you get the lift on the airfoil by integrating all the pressure over the airfoil okay similarly you can get the thrust produced by a rocket motor by integrating the pressure acting on the surface of the rocket motor so if you take a look at this the pressure acting on this direction in this direction cancels each other out because of symmetry so we are only interested in pressure acting in this direction so you will have pressure acting on this surface and then nozzle okay what do we mean by optimally expanded when ambient pressure is equal to exit pressure so pressure here is I will draw only the top half it is symmetric about it pressure goes on decreasing as you go from the convergent portion to the exit right pressure in decreases and velocity increases and let me take it that at the exit it is equal to the ambient pressure okay the ambient pressure is a constant right now this is the nozzle when it is optimally expanded what happens when PE is greater than PA and what happens when PE is less than PA is what we need to look at if we are able to show that in both these cases it is less than the thrust produced by this case when PE equal to PA we have proved our point okay now let us take a look at when PE is greater than PA how does that happen if I cut off a portion of the nozzle here right if I were to cut off a portion of the nozzle remove a portion of the nozzle then the pressure here is greater than the ambient pressure right but what have I done I have cut off a portion if you look at this the pressure on the inside is greater than the pressure on the outside so there is a net force in this direction which you can resolve in these two perpendicular directions now this force cancels each other out because of symmetry and you get only this right so if I removed a portion here in order to make PE greater than PA I am taking out essentially a portion that was producing thrust which means the thrust is going to be smaller than what it was when PE equal to PA now let us consider the other case when PE is less than PA now if you see this the ambient pressure is constant but the pressure inside is decreasing below the ambient pressure when that happens which side is the net force acting on if you look at the rest of the portion up to this point this is the point where PE is equal to PA right up to this portion the net force was acting in this direction now the pressure on the inside surface is less than the pressure on the outside surface so the net force will be acting in this direction which if you resolve will give rise to forces in these two directions perpendicular directions now this is producing a negative thrust right so if we add a portion of the nozzle so that PE is less than PA we are adding a portion which will produce negative thrust and therefore it will be not the highest so the maximum thrust that you can get is when PE is equal to PA if you look at it the other way round one can argue that if PE keeps on decreasing is when the velocities will keep on increasing okay and therefore if PE decreases and goes to zero is when velocities will reach a maximum okay now let us look at what are the yes in the in the process if we cut that nozzle like we have a super conventional nozzle and rocket is flying suppose we cut that nozzle and only the conversion part is there so it will produce negative thrust no just getting something here there is a thrust acting here no this surface over see this surface you can yes you are right the pressure here is acting in a in this direction fine but this area is whereas a small area wherein it is acting in this direction right this this direction will be greater than what is on this direction if you integrate the pressures yes if you integrate the pressures that is if you cut off the nozzle here yes the conversion portion if you look at it from that perspective is producing only a negative thrust and a component of it is what you are looking at but there is a throat right and there is a portion in this direction and remember always the throat pressure is much less than the chamber pressure so therefore you will get a positive thrust even if you have just a conversion now okay now I am looked at how to get the thrust and what is ISP let us look at what are all the different kinds of solid propellant that are available to us or that are currently being used there are three kinds of solid propellants the first is homogenous or double base and lastly composite modified double base now if you look at solid propellants there is a problem in regards to solid propellant the fuel and oxidizer need to be in close proximity with each other and yet not react okay over a period of time so that is that restricts us from using any solid fuel and oxidizer because they have to be compatible right they should not react with each other and in addition they should have good mechanical properties so that they can be used in larp rocket motors so homogenous propellant or double base propellant in this the fuel and oxidizer are mixed at a molecular level that is even if you take a small portion of it you would not be able to make out which is fuel which is oxidizer if you take a double base propellant the typical fuels and oxidizers are fuel less nitrocellulose oxidizer is nitroglycerine they are used nearly in the same proportion and that is why the name double base two bases is what it indicates okay now different as different from this in a composite propellant fuel and oxidizer are mechanically mixed that is if you take a small portion of the propellant you will be able to identify what is a fuel and what is a oxidizer and typical fuels are HTPB or hydroxy terminated poly butadiene and oxidizer is ammonium per chlorate and we also add aluminum in these propellants which is essentially if you will discuss this in a great detail a little later in the course now the essential difference between these two propellants is because this needs to be mixed at a molecular level there is a stronger restriction on this and therefore the specific impulse that we discussed a little earlier is low for if I were to ISP for double base is lower than ISP for composite propellants because in this case you can mechanically mix them there is a lesser restriction and therefore you can find suitable chemicals that you can mix and get a slightly higher performance typically the performance of this is this is around you get an ISP of around 2000 2300 Newton seconds per kg and this can go up to 2500 Newton second per kg why another is one would have thought that because this is superior in terms of performance we should be using this at all why do we have both of them still survive one of the reasons is if you look at in a military application essentially what happens is if you take a composite propellant the composite propellant has aluminum if you see here and there is aluminum oxide produces a strong thermal signature and in addition the ammonium perchlorate that we using has as in the exhaust products HCL which reacts with water in the atmosphere and also gives a strong exhaust signature if you are looking at a short range missile right or a tactical missile as it is called battlefield missile you would not want the enemy to know from where you have fired it right because then the enemy can come back and hit you so which is why you would not want to use these propellants for short range missiles or tactical missiles so for short range or tactical missiles you end up using double base propellant okay because this does not have such a heat signature and a composite modified double base propellant is simply you add HMX or RDX to double base propellant that gives you composite modified double base propellant that will also not have a heat signature but will have a higher performance and therefore it will give you a better performance but it will not have a strong signature like composite propellants and sometimes people use ammonium perchlorate also in this okay in the composite modified double base propellant the typical uses of heterogeneous propellant are for long range missiles launch vehicles okay long range missiles you do not care about what happens whether the enemy detects you because you are separated by a large distance from the target now if you look at this table here I put together thrust different kinds of propellants and ISP here you look at the last few ones they are very large motors that produce very large thrust this has 139 tons of propellant the PSLV stage one and produces something like 4.5 mega Newtons of thrust okay you look at ISPs it is of the first ones are the first two are double base propellants it is around 210 to 1100 Newton second per kg and it can go up to something like 2500 for a composite propellant okay we will stop here and continue in the next class where we will discuss about liquid propellant rockets thank you.