 We have been talking about rockets. In the last class, I introduced to you a number of rockets, missiles, and some of the ones which can be called space crafts that take not only crafts, but even human beings up in the space. The fundamental science that governs the engine of these crafts is more or less the same. So, we have started also talking about the fundamental rocket science and we have got introduced to some of the fundamental parameters that govern these various crafts and their engines and we are talking about the rocket engines. Some of the parameters that we have got introduced to in the last class, we shall continue with those introduction of parameters and the fundamental rocket science. Let us look at what are the issues that we have been talking about. The last lecture the fundamental parameters that have been introduced are the thrust the jet thrust that is created Fj. The exhaust velocity and in the process we also introduced the maximum exhaust velocity that is possible actually in vacuum when the rocket operates in a vacuum atmosphere which means there is no atmosphere and the fundamental parameter ISP which is called specific impulse. Now these parameters are the fundamental parameters of any kind of rocket engine whether we call them rockets or missiles or space crafts they all have to be specified with these parameters to begin with. I will just add another parameter now which is called weight flow. In most of the rocket engines the important flow rate of the propellants and the oxidizers together is often expressed in terms of weight flow rather than mass flow as it is done in most of the air breathing engines. So all the air breathing jet engines that we have studied earlier the mass flow which is going in and coming out of the engine were measured and expressed in terms of mass flow. Most of the time those crafts flow parallel to the surface of the earth and as a result of which the amount of mass flow that is coming out is directly proportional to the thrust that is generated for flying those crafts. In rocket engine most of the time the rocket would be flying in a direction in which it has to support all of its weight most of the time or part of its weight most of the time. As a result of which the amount of mass flow which actually activates the thrust is now measured more in terms of weight flow rather than in mass flow. So in rocket engines the expressive terms of the flow rate which contributes to the thrust making is measured in terms of weight flow and in simple terms it is of course the mass flow into the gravity so m dot into g. So that is the weight flow that normally we would be using in our fundamental rocket science development. Let us look at some of the fundamental parameters that we need to deal with a good part of the rocket trajectory would have to be within the atmosphere. Many of the ballistic missiles work all the time within the atmosphere so the first thing the rocket needs to negotiate in its flight is the atmosphere and hence the first thing that it has to do is to take off or in terms of rockets it is called lift off. So the aircrafts actually take off the rockets normally lift off because the entire rocket goes up vertically it is normally a vertical take off and hence called lift off. Now if we express the exit area of the nozzle of the rocket chamber as E x the exit pressure in terms of P E x and the altitude ambient pressure at which it is operating as P a P subscript a and if it is at C level we would call it P subscript s l a then the altitude thrust is less than the thrust in vacuum by the amount P a. The second term that you see and you are familiar with by now in the jet thrust creation you can see the second thrust is dependent on the pressure that is available or the differential pressure that is available across the exit pressure exit section of the thrust nozzle. Now in case of C level as you can see the exit pressure is P s l a which subtracts from the exit pressure and as a result of which the thrust is so much lesser at an altitude the second term shows P E x minus P a which is P a is the ambient pressure at that altitude and as a result the thrust is lesser by that much. Now this is something which varies with altitude as the rocket is continuously changing its altitude the actual pressure at which it would be operating is continuously changing and hence the second term is actually continuously changing and as a result of which the actual value of the thrust would be a continuously changing phenomenon. We have seen and we shall see more and more that the flow actually is often quite near the maximum value most of the time. However the value of V E x would depend on the exit pressure and if the exit pressure is changing the pressure ratio across the nozzle is changing and then the value of V E x would continuously change also. So from C level to some altitude at which it has to go the target altitude let us say the value of the thrust would be continuously changing from maximum at C level which is normally required for the lift of purpose you need to produce maximum thrust at C level and then at some altitude it would reach its final high level altitude the maximum altitude and then it may take some other trajectory or it may have reached the orbit at which it is going to rotate around the earth. If we write a generalized version of thrust at any altitude we can write down that f j is equal to f s l j plus f a e x into p s l a minus p a. Now this boils down to the second term as if you take out the p s l a out of the bracket you would find a term 1 minus delta and this delta is nothing but the pressure drop in altitude with varying of the altitude of operation. Now this can be obtained from any normal atmospheric charts or tables that are available and hence it is comparatively unknown or easily knowable parameter. So the basic thrust that any rocket creates can now be obtained from this simple equation. If we progress to the thrust that is created in vacuum we see that in vacuum the ambient pressure p a is to be taken as 0 in which case the thrust equation becomes f j equal to m dot into v e x plus p x into a e x the second term is not there anymore. Now as I mentioned right in the beginning today that most of the thrust generated by rockets is normally expressed in terms of weight flow rather than in terms of mass flow and as a result of that the earlier thrust equation can now be expressed in terms of weight flow and that is expressed in as w dot and hence w dot by g is the mass flow and the first term then gets slightly modified. Now if you write the specific impulse the specific impulse that we had introduced in the last class we can write down the expression for specific impulse i s p is equal to f s l j plus p s l a into a e x into 1 minus delta divided by m dot g. Now as you can see this is the i s p term the general i s p term which can be used for finding out the specific impulse at c level and that is the value you need first for the rocket to lift off. So one can find the specific impulse at c level earlier in the last lecture we had written down the specific impulse for vacuum and if we bring that back this equation is i s p is equal to v x by g. So that is a simple and it is expressed in terms of seconds. So i s p is normally given in terms of seconds very soon in a few minutes now we will see what kind of values normally i s p's have and we will get an idea about the kind of values you would expect from a good rocket engine. The another parameter that is quite often used for characterizing the rocket or rocket engine is signified by the parameter called characteristic velocity. Now characteristic velocity v star is expressed in terms of v e which is the exit velocity divided by c f. Now c f is the thrust coefficient it is different from specific impulse and this thrust coefficient is expressed in terms of f j divided by p c into a t in the denominator. So numerator is the thrust the denominator are the two terms the product of two terms p c and a t. Now p c is the combustion chamber pressure that is one of the primary parameters of rocket engine performance and a t is the nozzle throat area. Now this is now being considered as a primary parameter for nozzle operation and nozzle performance. So if we write down that the characteristic velocity is expressed in v star they are now shown in terms of v e the exhaust velocity and c f the thrust coefficient which I mentioned is not same as specific impulse and this thrust coefficient is different from the thrust coefficient we may have defined for other kinds of jet engines. So the rocket engine thrust coefficient is defined somewhat differently. Now if you look at use of the weight flow and we can redesignate with its relationship with ISP we can say that the specific propellant consumption can be written down in terms of weight flow divided by thrust and that would be 1 by ISP or it can be also expressed in terms of G by ISP depending on the units. So the specific propellant consumption or simply what we used to call for jet engine specific fuel consumption can be written down in terms of weight flow rather than mass flow. And the weight flow coefficient which is again as you see different from the specific fuel consumption specific fuel consumption as before is the specific fuel consumption in weight per unit thrust. Weight flow coefficient on the other hand is weight flow divided by p c into a t that is the combustion chamber pressure and the nozzle throat area. So the two coefficient that are now introduced one is the weight flow coefficient another of course is the specific fuel consumption or specific propellant consumption in case of rockets as we know it is fuel plus oxidizer and as a result of which both of them together are here in this specific propellant consumption expressed in terms of weight flow. If we move forward we find that the characteristic velocity that has been expressed can also be expressed in terms of V star and in terms of weight flow coefficient and as a result of which we get an expression which is V star finally would be equal to G into p c into a t which are the combustion chamber pressure and the throat area divided by the weight flow. It can also be expressed in terms of simply G by weight flow coefficient that is C w C subscript w. So these are simple ways of characterizing a rocket engine which sometimes in many literature is often also referred to as rocket motor. So these are the characteristic terminologies which are used to normally characterize a particular rocket engine. Commotion chamber pressure p c which is used here as a normalizing parameter for many of these fundamental parameters is dependent on the chemical properties of the propellant and it is also dependent on the ignition properties of the propellant. So the way the chemical properties are selected the propellants are selected the oxidizer the fuel and the way the ignition is done or the combustion is done in the combustion zone would create the combustion chamber pressure. So it is to be calculated from the basic propellants that are being used and hence it requires a separate attention. However, as we see here the combustion chamber pressure at any given point of operation is a fundamental parameter of importance and hence we can see that since they are dependent on the fundamental combustion chamber pressure they depend on the propellant chemical properties the basic propellant that is used and hence the rocket engines are very strongly dependent on the basic propellants and their chemical properties that are used. We shall see very soon that we have a large number of actual propellants that are used for various rockets unlike in aircraft where you have only one kind of fuel in rockets you have a large amount of variation of fuel and oxidizer and their combinations and we will have a look at some of them some of them are good some of them are known to be a little toxic and some of them of course, have very high specific impulse as I mentioned they are typified by the specific impulse value and we shall see that we have a large choice there actually and as we go along we shall have a look at some of the not only liquid propellants, but also the solid propellants where also we have large choices. So unlike in aircraft or other kinds of jet engine where you normally use kerosene based hydrocarbon fuel in case of rockets you have a very large choice. The best choice by many parameters is normally hydrogen and oxygen which are the liquids you cannot use them in solids. So, but they are more and more being used, but we have many other options available as far as liquid propellants are concerned and we shall have a look at some of these as we go along today. The ideal characteristic velocity can be expressed in terms of more fundamental parameters in terms of the acoustic velocity of the gas in the combustion chamber. Now, acoustic velocity as you remember is dependent on the local temperature and as a result of which the combustion chamber pressure not only pressure but the temperature will now decide what the acoustic velocity is and as a result of which the characteristic velocity would be decided. The other parameter which will decide the characteristic velocity is the thermodynamic state of the gas as specified in the value of specific ratio k which may be different from gamma which is the ideal value of the gas. Now, the value of k is also dependent on the local temperature in case of combustion chamber the temperatures can be indeed rather high they can be of the order of more than 2000 degree sometimes close to 3000 degree and at that temperature the value of k would be quite different from gamma and we shall see that they actually decide what the characteristic velocity is going to be. So, the ideal characteristic velocity or what can be called the first cut value of characteristic velocity can be simply calculated from the basic specific ratio and the acoustic velocity of the gas in the combustion chamber. So, it is dependent only on two parameters from idealistic point of view. We can take now a look at some of the rocket engines and as some of them are called they are called rocket motors. Now, if you take a liquid rocket motor a very simple version of liquid rocket motor what you see here is you have two tanks which actually store the fuel and the oxidizer. Now, the fuel and the oxidizer are pumped from these tanks with the help of pumps which are run by some turbines and hence they are called turbo pumps. So, they flow from these tanks through these piping the pumps pump them out of the tank and then supply them to towards the rocket engine. Now, this is your rocket engine and you have the nozzle here. So, it comes through the throttle valves and then it is pumped into the combustion zone over here which is the combustion chamber. So, the fuel and oxidizer are pumped in separately they do not mix together as it is done let us say in a normal IC engine in a carburetor. So, there is no carburetor here they are pumped in separately into the rocket chamber and you have two separate sets of pumps and two separate sets of throttle valves to throttle them and we shall see that they actually have different ratios for different kind of fuels and oxidizers. So, these ratios require that they need to be pumped differentially. So, quite often you have some kind of a control unit to control the rate at which they are pumped and the control the rate at which they should be throttled and these need to be controlled continuously during the operation of the rocket starting from the lift off. So, this is a very simple configuration. Now, a liquid rocket motor as you can see here now the rocket combustion chamber is indeed very small it is relatively rather small a very large space is to be allotted to for carrying the fuel that is the oxidizer and the fuel and these tanks need to be housed within the body of the rocket. You also need to carry the pumps the throttle valves all the pipings that are required and of course, the control unit that controls these pumps and throttle. So, you need to carry all this with you all the time during the rockets actual flight which is something means that other than just the combustion chamber you are carrying the whole paraphernalia including the tanks and the turbo pumps and etcetera. Now, the tanks normally house the fuels in liquid form if they are let us say liquid oxygen or liquid hydrogen they are likely to be at very low temperature and at very high pressure. So, the tanks need to be built very strongly to house them and as a result of which the weight that a liquid rocket would have is normally quite high and as a result of that it is necessary that one uses liquid rocket or liquid rocket engine only when the rocket itself is rather big in size normally liquid rockets may not be used unless the rocket itself is rather big in size smaller rockets normally may use solid propellants which we shall be discussing a little later. So, liquid rocket means that you need to carry a lots of things with you besides the rocket engine itself which proportionally is much smaller in size compared to the other things that you need to carry with you. The method by which the liquid combustion chamber operates is somewhat similar to the combustion chamber that we have seen earlier in the other kinds of jet engines. The combustion chamber is designed to do some of the things that we are a little familiar with. Let us look at them one by one the combustion chamber needs to have injectors for both fuel and oxidizer. So, we have two sets of injectors now not one. So, one injecting the fuel and another injecting the oxidizer and both of them have to do injection atomization and vaporization and then mixing of the liquid fuel and the liquid oxidizer in a correct proportion. So, this needs to be done. So, the job here with reference to let us say the jet engines where the fuel was injected into the combustion chamber into air and there only one fuel is to be injected atomized vaporized and mixed with the air. Here two fuels that is a fuel and the oxidizer need to be injected atomized vaporized and then mixed in correct proportion with respect to each other before the combustion can take place. So, these are prerequisites or prerequirements before the combustion can actually take place. Then there is a question of thermal decomposition of the oxidizer to enable chemical reaction with the fuel. This needs to be allowed to happen and then the ignition has to take place the flame needs to be stabilized. Once the ignition takes place and the fuel and the oxidizer have mixed in correct proportion the flame is created. Now, the next job is to stabilize the flame if the flame is subject to large amount of flow of gases and the flame may get extinguished. So, the flame needs to be stabilized. So, you probably would need to have some kind of flame stabilizer or flame holder around there in the combustion zone and then the combustion of fuel and oxidizer would have to be mixed in correct proportion. This mixing would have to continue even after the combustion is over and hence the process of combustion may continue till it hits the exhaust nozzle. Now, through the exhaust nozzle the flow goes out and once the flow goes out a process of motion of the gas or the combusted gas starts happening. So, once that starts happening the combustion products from the combustion zone starts moving towards the nozzle and automatic movement starts initiated and then there is a continuous motion of combustion products from the combustion zone to the exhaust nozzle and it sets up a continuous motion of gas from combustion zone through the nozzle to the exhaust. The volume the length and the shape of the combustion chamber also needs to be selected or design for rocket design. The various fuel oxidizer combination provides for various characteristic length. Now, characteristic length of combustion chamber of a rocket is defined as L star and this is simply defined as combustion chamber volume by the throat area. So, volume of combustion chamber by throat area A t gives us the characteristic length of a rocket. Now, the combustion chamber volume we have seen is somewhat dependent on the combustion chamber pressure, combustion chamber temperature which are also dependent on the chemical properties of the fuel and the oxidizer and as a result of which these are determined independently and hence the value of L star are often found experimentally in the laboratories and then they are characterized. Once they characterized the value of L star for a particular fuel and oxidizer may be selected for a particular kind of rocket from which we can then go on to find out what the combustion chamber volume could possibly be or what the throat area could possibly be for movement of the combustion products. So, these are characteristic parameters that need to be arrived at somewhat early on in the rocket design. Now, let us look at some of the common liquid propellant fuel and oxidizer combinations. These are in terms of oxidizer we have liquid oxygen, nitric acid and hydrogen peroxide. Now, each of these oxidizers can use various fuels. Now, for fuels we have liquid hydrogen, we can have kerosene, we can have fluorine, we can have hydrogen, ethanol, methanol and liquid ammonia. So, all these are possible fuels some of them could be a little toxic and it is something which one has to be little careful while using, whereas kerosene is one which is a very well known hydrocarbon and people have used it quite a lot, but many more and more many of the bigger rocket engines are using liquid hydrogen and liquid oxygen as primary fuel and oxidizer. The other possibilities are if you use nitric acid as oxidizer, you can have hydrogen, you can also have kerosene and you can have liquid ammonia, aniline and turpentine. If hydrogen peroxide is the oxidizer, you can use ethanol, methanol, hydrogen, kerosene and ethylene diamine. Now, you see there are number of possibilities, number of combination that are possible and as I mentioned some of them may have certain amount of toxicity involved and hence they may be somewhat prohibited or objected to for use due to atmospheric pollution, but some of them do have a very good performance indexes. Let us look at one or two of them in terms of how they actually perform. The highest specific impulse values are indeed obtained with hydrogen as fuel and burning it either with oxygen or fluorine. Now, if you use hydrogen as fuel and fluorine, you would get specific impulse of the order of 375. On the other hand, if you use hydrogen and oxygen they are both of them liquid of course, you would get 362. So, you can see with fluorine you can actually get a higher specific impulse and these numbers are arrived at using combustion chamber pressure as 35 kilo newtons. Now, the numbers give just a hint that certain fluid certain fuels actually can give you higher specific impulse than liquid hydrogen and liquid oxygen. However, it is if there is a fear that combination of hydrogen, fluorine could actually give you certain amount of toxicity and that may not be acceptable to many of the environmentalists. So, more and more people are using hydrogen and oxygen because they are clean fuels and their product normally is in terms of steam which is largely water. So, hydrogen and oxygen give very good specific impulse not the best, but very good and they are normally clean fluids. Now, if you take all this into account, we can talk in terms of what can be called certain desirable properties of the liquid propellants. You see the rocket has to operate very quickly at high altitude and very soon it has to the atmosphere there is at very low temperature and of course, very low pressure and as a result of which it needs to be ensured that it operates with a characteristic property which has a low freezing point. Then it should have high specific gravity, it should have very good chemical stability during storage. Now, this is a problem because when the rocket fuel is stored in a tank, it could over a period of time lose its chemical properties. So, if that happens then it will not perform as per the desired predictions of the rocket engine. Hence, it is necessary that the rocket fuel preserves its chemical stability and properties during the storage. It should have high specific heat, high thermal conductivity for the heat to be conducted through its operation during the combustion and high decomposition temperature that means, it should not very quickly decompose before the actual combustion is initiated. Now, you need to realize that combustion is a process which we mentioned has three or four steps. It requires injection, it requires atomization, it requires vaporization and then it requires good mixing between the fuel and the oxidizer. Only when they are mixed in correct proportion, you have the combustion. If the proportion is very bad, you may not have any combustion at all and as a result of all this, there is a certain time period during which in the combustion zone, the temperature which is already been created by the combustion products may travel into the products which are just being injected into the combustion chamber. As a result of which, it is entirely possible that some of the fuels or oxidizers may be subjected to decomposition and it is important that they do not decompose before the combustion actually takes place. So, these are chemical properties. These need to be built into the chemical properties of the fuels and oxidizers that are selected. The ones we looked at in the previous slide actually have some of those properties already built into them. But if you are looking for new fuels and new oxidizers, you need to make sure that they carry these properties that we are discussing right now. The next property that you need to look at is the flow ability. Now, you see when the rocket is flying, it does not fly straight and level like an aircraft. It flies in a trajectory. It initially flies straight up and then it flies in some trajectory and during which the liquid has to be pumped from the tanks into the combustion chamber and this means that the liquid should flow during its various flight trajectories and during which you have a strong force of gravity, you have the motion of the rocket which itself creates a certain motion and all this and then of course, it flies to very high altitude where quickly the temperatures available are very low and as a result of which the flow ability of the fuel and the oxidizer need to be ensured during the entire time during which the rocket is expected to operate and be operational. This is specifically true when the rocket needs to operate for quite some time in very low temperatures definitely sub zero and those are what is known as cryogenic conditions. In the cryogenic conditions, you need to ensure that the fuels that are used retain their property. They can be taken from the tank to the combustion chamber. They can be injected. They can be vaporized. They can be atomized. They can be vaporized. So, all this has to happen under cryogenic operating condition and hence the entire rocket engine needs to be built and the fuels that are used need to be used in a manner that is conforming to cryogenic operation. So, cryogenic rocket engine is a slightly specialized field of rocket engine and hence that needs to be built and designed separately for cryogenic operation and as a result of which the cryogenic engines are the modern versions of the rocket engines which need to be designed keeping in mind that most of the time the rocket may be actually operating under cryogenic conditions. This leads us to the last point that is the temperature stability of the physical properties. You need to ensure that the physical properties of the fuel and the oxidizer are stable. We mentioned the chemical properties. We now have to look into the physical properties of the viscosity, the vapor pressure and these also need to be looked into during the cryogenic operation. So, it is necessary that the rocket engines do look into these aspects before the rocket is actually designed before the fuels are put in place and the rocket is operated. The viscosity and the vapor pressure are some of the elements of physical properties that would have to be built into the fuel and the oxidizer that are used for rocket engine operation. If we may now look into various kinds of solid propellants, we can see that solid propellants by basic definition instead of liquid fuels you have solids. Now, which essentially means that you have bodies that are placed inside the combustion chamber or what is called pre fitted propellants inside the combustion chamber. Now, this also of course means that there are no pumps, no valves, no pipelines, no injectors, no control systems and all the paraphernalia that we saw with the liquid rockets is completely dispensed with in solid propellant rockets. So, solid propellant rockets are by very nature are much simpler devices and in some sense the solid propellant rockets have been around for many, many years probably centuries. For many centuries people have been using one variety or the other of solid propellant rockets mainly for various military purposes. Now, the shape and the size of the combustion chamber is decided by the shape and size of the propellant. This is unlike in a liquid fuel where the shape and size as we just saw it decided by the combustion characteristics and the fuel characteristics, but here the shape and size is decided by the shape and size of the rocket propellant itself and which needs to be given particular shape and particular size. We will have look at some of the shapes in a few minutes. Now, this means that the shape and the size is decided by the burning characteristics of the propellants. The propellants are the fuel and oxidizer. In case of solid there is a mixture of fuel and oxidizer and the desired combustion characteristics the required thrust specific impulse the fundamental parameters are decided by the burning characteristics of the propellant where in case of solids is the mixture of fuel and oxidizer. This is a solid which has a shape which has a size and all this is housed or stored or prefitted inside the combustion chamber of the rocket and hence all this together decide what the combustion characteristics is going to be, what the burning rate is going to be and what is the time during which we will have the rocket operational. We shall look at some of the rocket propellant shapes and sizes. These propellants are technically often known as grain. So, the various grain sizes we shall see in the next slide and these are designed for controlling the burning in a desired manner to achieve certain specific impulse value starting with at sea level lift off and at various altitudes where you need specific impulse of certain amount for the trajectory to be carried out in a desired manner. Now, you need to control the burning as we know very well combustion is fundamentally a controlled burning process a controlled fast burning process and as a result of which you need to have controlled burning and in solid propellant rockets the control of the burning is built into the shape and size of the propellants which as we as we now see are called grains. Now, these are fabricated since they are solid bodies they have to be fabricated they would need to be handled stored after the fabrication in a factory and then later on fitted inside the combustion chamber of the rocket rocket motor and hence there are lot of steps involved before which this propellants are used actually in a rocket. Some of these have serious engineering issues there is a lot of mechanical engineering involved here and the mechanical properties we have talked about the chemical properties and the physical properties, but now we see there are mechanical properties that are required of these solid propellants which need to be taken care of and there is a lot of mechanical serious mechanical engineering involved here that will need to be taken care of and some of it could be quite expensive. Now, due to the shape and sizes of the propellants some of the propellants are designed for what is known as restricted burning and others undergo what is known as unrestricted burning we shall see what these mean actually that some of the surfaces of the grains are restricted from burning whereas, in some other designs all the surfaces are open to burning. So, we shall have a look at these shapes in the next slide and the other fact is once the propellant is ignited it should burn smoothly along its exposed surfaces without any detonations we certainly do not want an explosion or a small detonation anywhere during the combustion it should be smooth combustion and as I mentioned it should be smooth fast controlled combustion. These are some of the cross sectional designs and the side wise views of the so called grains of the solid propellant rockets. Now, you can see here some of them are mentioned as restricted burning types the restricted burning times have these solid and linings around them. So, A and B in this figure are restricted burning. So, around this these are the linings which restrict the burning they do not allow those surfaces to be participating in the combustion process and hence this is called a N burning that means only one end is open for combustion or burning all the other surfaces are close to the burning process. Now, in this in the second one in B we have internal burning which means the internal surface which actually has a star shape this star shape is open to combustion or open to burning all the other surfaces including the two ends especially this end is restricted and is not allowed for combustion or burning only the internal star shaped cross section is open for burning. Now, the question here is why this star shape the star shape or any such shape is created essentially if you look in closely compared to let us say a circle if you have a circle over here the surface area of this star shape is substantially more than any shape that you put here whether circle or ellipse or square a star shape would have more surface area of burning and this more surface area actually gives you a faster burning. So, the star shape has been created for enhanced burning capability of the rocket. The third one which you see here is one of unrestricted burning in which you as you can see the number of surfaces are open to burning the two ends have certain amount of restriction, but all the other surfaces are open to burning the outer annulus and the inner hole is open to burning you have three supporting structures over here to hold the grain in place you know otherwise they will move around or they may move off. So, you need to hold them there very fast strongly and this is where mechanical engineering comes in very strongly rest of the surfaces are open to burning and through this hole as well as through this outer annulus the burnt gas is continuously coming out. So, this burnt gas is released through this open spaces at the ends and it goes to the combustion chamber. Let us take a look at some more of these grains again as we can see here this one has again a lot of restricted burning whereas, the D one which has however the main fuel is over here and these are the surfaces which are open to burning. So, this is a cruciform or cross type of shape in which these surfaces are open to burning and these are inhibitors which are also used for holding the propellant in place firmly otherwise they are likely to move. So, these are the restrictions restricted surfaces these are the unrestricted surfaces through which the burning can take place. Now, here you can see in type E there are restrictions put in the inner circle there are restrictions put in the outermost circular shape. So, the inner one actually has a supporting rod to hold the propellant in place the propellant is now built around the rod and this surface is not open to burning. There is an annulus over here inner annulus which is open to burning. So, the inner annulus surfaces are open to burning. So, this is another type of design in which some surfaces are restricted some other surfaces are indeed unrestricted. And here you have a multiple tubular ones where you have more or less unrestricted burning all the surfaces are open to burning outer as well as the inner surfaces are open to burning. The last one G is a multiple perforated grain again it has lot of surfaces that are open to burning. Here it is more solid and as a result there is a lot of propellant in this particular shape, but there are lot of surfaces that are open to burning. So, all these surfaces actually contribute to the formation of the gas that finally would go out through the nozzle for creation of thrust. Now, the solid propellant as we mentioned would have an oxidizer it has to have a fuel, but it also needs a chemical compound which binds them together. So, it is a mixture so primarily it can be a mixture, but it needs to have a chemical compound which will bind the fuel and the oxidizer together. It also often has number of additives which actually contribute to the control of the burning process and facilitate the fabrication process. As I mentioned the fabrication is a mechanical engineering issue and some of it is quite tricky issue really and some additives are often used for giving those shapes to rendering those shapes through fabrication process and as a result of which some of them are for facilitating the fabrication some of them for control of the burning. There are some components of the propellant which are inhibitors they control in a sense they control the burning process. Now, each of these components which are mentioned here need to have a correct proportion. We know that the fuel and the oxidizer need to have correct proportion their proportion is decided by the chemistry of their mixing, but there are other components here we have the additives we have the inhibitors we have the binders these require also to be included in correct proportion. So, that we have a solid propellant which caters to the combustion process without getting disturbed by any other mechanical or chemical issues. So, there are proportion that need to be adhered to very strongly. By their chemical composition and fabrication method the solid propellants are three types you have the double base type you have the composite propellants and you have multiple base propellants where you can have 4 to 8 different chemicals mixed together into one solid propellant rocket. The double base propellants are the old ones they have been used for many years in military purposes mainly and missiles up to weight of about 10,000 kg and can produce actually pretty good specific impulse up to 250 seconds which is considered a good specific impulse, but most of the modern rockets actually use composite propellants because you need to have more control over the whole business of propulsion, whole business of combustion and all the things that we are talked about you need to have more control. So, most of the modern rockets do use composite propellants the desirable properties of the solid propellants are again we had desirable properties of the liquid propellants the desirable properties of the solid propellants are high release of chemical energy they should have lower molecular weight no deterioration of mechanical and chemical properties during storage. Most of the solid propellant rockets are created in factories specialized factories and they have to be stored for long period during which there should not be any drop in the mechanical or chemical properties because they need to retain them during their actual operation inside the rocket chamber. They also need to be ensured that during the storage period which could be many months they are unaffected by the atmosphere or atmospheric conditions and of course, they should be amenable to they should not be amenable to high temperature and pressure for combustion initiation combustion needs to take place at certain temperature and pressure it should not get into combustion before that temperature or pressure is arrived. So, these are some of the basic properties for solid propellant rockets that are used for choosing the solid propellants the propellant that we talked about already are selected for these properties, but if some new propellants are coming in you need to ensure that these new propellants conform to the properties that we have listed here. We will continue with the rocket science and we will bring in the nozzles that we used for creation of thrust in the next lecture and we shall have some background of the theory of the liquid propellant and theory of the solid propellants that in the next lecture.