 In the last class we had talked about how the plug nozzle would have a better performance of design performance let us look at it in this graph if we have PC by PE on the x-axis and CF on the y-axis this is a log scale if you have a nozzle design for some high altitude conditions somewhere here a conventional nozzle or a conical nozzle will go like this whereas a plug nozzle will have a superior performance throughout this is so the conical nozzle has a much inferior altitude at conditions other than the design conditions its performance is not as good as a plug nozzle or an aerospike nozzle so next we move on to the other topic that is thrust vectoring right thrust vectoring is something that is used by all missiles as well as launch vehicles if you look at the tactical missiles that is these are small rockets and if you look at what is the level of thrust that they produce the accelerations that they have initially is of the order of 10g so they very quickly go to a very high velocity so which is why you do not need any control in the boost phase they usually have something known as a boost phase wherein the thrust is very very large and it goes to very high accelerations due to gravity the acceleration achieved a very high and after which they will have a sustained phase which will essentially keep it at that particular Mach number okay. So for such rockets or tactical missiles aerodynamics is a very good aerodynamics offers very good way to control the motion of this as in if you wanted to wear around to a target and other things you can have fins and you can make it make it go towards the target very easily but if you look at launch vehicles and strategic missiles that is long range missiles when they take off their accelerations are very very small typically of the order of 1.6g to 2g right they are not very large so as they are going up they are going up very slowly and cross wins can take them in a direction that is not intended if you have strong cross wins launch vehicle you can put off the launch by a few hours you can say till the weather gets into some kind of reasonable conditions you are not going to launch it and you will wait for that time to launch it but missiles you cannot afford to do that because you need to be ready every time okay. Even in launch vehicles you would still want some kind of control in this period of launch wherein the velocities are very small up to it the time that it reaches a Mach number of around 0.5 aerodynamic control will not be very very effective right. So it is unlike aircrafts where unlike aircrafts will have a very large surface area right the wingspan is very large so it can produce substantial lift here you do not want it to have so much drag associated with any control surfaces you want it to be minimal so you will have very small things. So a for under these conditions you would need something known as thrust victory that is can you change the direction of the thrust itself says to take the vehicle in the direction that you wanted to go in. In addition if you have looked at launch vehicles let us say PSLV or something like that you will find that it has a main core and on the side it has small strap-ons right PSLV has 6 strap-on motors. Now the nozzle of all these boosters are in such a way that they are canted away that is the thrust that it produces is at some angle to the vertical axis right. So if this is the axis then the thrust produced is not parallel to it but at some angle right. So if all of the thrust vectors meet at some common point on the axis then it is perfectly balanced otherwise there is some imbalance and you need to have a counter force to overcome this right. You need to have a control force capable of overcoming this otherwise the vehicle could wear in a direction that is not intended. So for all these things you need this thrust vectoring okay now thrust vectoring can do all this that is it can allow the vehicle to rule yeah and pitch in this class we will concentrate on what are the ways in which we can vector this thrust what are the means that are available and what is it that is practiced and what can also be done okay. Now typically thrust vectoring there are three modes that are usually followed one is jamboling of thrust chamber or nozzle or introducing mechanical control surfaces or second wave fluid injection in the exit cone we will look at each of them in a little more detail in this class. Now firstly jamboling the thrust chamber or the nozzle if you look at a liquid engine liquid engines typically the propellants are not stored in the engine or in the chamber where it produces thrust that is the fuel and oxidizer makes an burn so it is stored in a separate chamber so the engine it is as itself will be very small so you can look at moving the engine in two different planes to get the control force that you require okay that is possible in a liquid engine that is if the engine were hinged on this you could move it around by an angle alpha in either direction and if you have something known as a universal joint is nothing but if you have two hinges right if you have two hinges like this using one of them you can move it in one plane using the other one you can move it in the other plane right so using both of them you can move it in two different planes that is what is a universal joint if you have the entire engine mounted on a universal joint then you can move it in this plane by alpha and also in the plane perpendicular to the board by an angle alpha okay so that is what a jambolar hinge will do as you can see if the engine is moved overall engine is itself moved by an angle then the thrust produced will be the cause of this angle right so it will be lesser than the actual thrust so you are going to lose some amount of thrust by vectoring the thrust itself so you can using this move the entire vector the thrust by plus minus 12 degrees and there will be a small thrust loss and this is typically used in only liquid engines that is because as I said earlier if you look at solid engines the entire propellant is also inside the motor so it would be very difficult to move the entire motor because the weight of the propellant is also there whereas in a liquid engine the propellant is stored elsewhere and only thing is you need to have flexible hosing otherwise it will not allow this kind of movement okay so you need and you need also large actuators to move this okay and the critical thing is if you look at this the entire thrust of the engine is transferred through this hinge or the jambolar so this needs to be very carefully designed because this is a very critical parameter I mean very critical element because the entire thrust is transferred through this element to the rest of the vehicle okay so this needs to be carefully designed instead of jamboling the entire engine the other option is can we just move the nozzle itself and that is called as flexible nozzle so if you have an actuator and move this nozzle alone right then you can get the same desired effect of vectoring the thrust only thing is this joint needs to be flexible here and allow for movement okay this can also give plus minus 12 degrees and again there will be a small thrust loss because you are anyway vectoring the thrust so the cause of the thrust is the only one that is available in the axis along the axis this has also been used in both solids and liquid rockets here you can use it in solid rockets primarily because you do not have to move the entire motor you are only moving the nozzle but still the actuation force required here is also quite significant you need the last of this variety is again if you have something like a ball and a socket joint instead of this one you can move the nozzle if you have it mounted on a bearing then you can move it and therefore get the required thrust vectoring now in both these methods the nozzle in some sense is submerged inside the motor and this leads to something known as submergence loss primarily if you look at the gases coming out they need to you would also have propellant stored in this direction if it is coming in this direction it is a lot easier otherwise the propeller the gases coming from burning of the propellant in this region will have to turn through a large angle and that will lead to some losses because the flow will now have to turn through a large angle to get to the nozzle and that is given by something like it varies between 0.4 to 1.2 % loss in ISP and if you remember the discussions that we had in the morning that is if this propellant were aluminized propellant right then we discussed that the particles do not or condensed particles do not expand and they cause loss right this gets coupled with that and depending on the percentage of aluminum present in the propellant and the amount that the nozzle is submerged the loss could be higher I mean this it is within this range it could be higher if it is more submerged lesser if it is less submerged okay the next set of control that we can get is from mechanical control surfaces here if you are using mechanical control surfaces what you will have is something jetting into the exit flow and therefore you are going to obstruct the flow and cause the require thrust it okay jetter waiters are something like this if you have a rocket motor this at its normal position it is something like this and if you want to have a side force you could change its position to something like this so this does not protrude into the flow in its normal position but when you change its position on one side you get over expansion and on the other side you get a little bit of under expansion this causes a side force okay so you are going to get small amount of thrust vectoring if you are using this you will get something like plus-7 degrees of thrust vectoring and compared to the previous ones this is a lot better in that sense that firstly it does not require a very large actuation actuation power right because you are only looking to actuate a small surface and therefore the power required is smaller here these are used in solid rockets yeah this small portion this dotted line it is it is in line with the nozzle when it is not doing anything right you can then rotate it and on one side it will it will be flush with the nozzle so it will act as on one side it will over expand and on the other side it will under expand and therefore give you the required side force okay then there are some things known as jet tabs now if we were looking at it from the bottom it would look like this now you could move this into the flow as per requirement okay and depending on the amount this up steps the flow you will get the thrust force proportional to that okay so as such this does both these do not obstruct the flow in their normal position so they did not add to any loss in their normal operation but when they are used they will lead to a small loss with this you can get plus-14 degrees of change in the thrust and whenever this is in use it leads to something like 1% loss and thrust per degree of deflection and the actuation power here is also very small because you are only trying to actuate a small tab so the actuation power required is smaller here the last in the mechanical control surfaces is something known as a jet vane these jet vanes are in the exhaust gas flow so because they are present in the exhaust gas flow itself even without actuation they are going to lead to some kind of thrust loss okay so they are going to have you are going to have some thrust loss you can get thrust vectoring of the order of plus-9 degrees and the thrust loss will be more when it is actuated okay it will it is there even without actuation in this case and it will be more when it is actuated so this needs pretty good heat resistant material because it is always in the exhaust flow right what is usually done in the case of jet vanes is you might need this for a small period of time during takeoff or during some critical operation after which you can throw them away okay so these are used in some examples where in your launching something from a ship or launching a missile from a ship or something like that then it has to turn by a large angle so you can use this and then throw this away and for the rest of the flight this is not useful okay so it is used for a very small period of time okay now the last thing that is used actually in rockets is the liquid injection remember in a earlier class we said if you have an oblique shock the flow separates and it will introduce a side force right in this method of controlling or thrust vectoring we actually make use of that and we inject a liquid at some known point in the divergent portion that is let us say if we inject the liquid at this portion because of the liquid coming out here the an oblique shock develops upstream of this liquid injection point and because of this you will get a side force right because in this portion it actually acts as a nozzle being cut off and after some length and therefore it get gets you the required side force okay SIT VC is used in PSL is stage one motor for thrust vector control in this case because of the liquid injection there is a small amount of thrust augmentation that is happening the liquid that is used is strontium work flow rate now the reason for using such a liquid is if you look at the momentum of the jet that is coming through if you are injecting this jet this jet needs to have a higher momentum than the jet okay so rho j vj square must be comparable to rho g vg square now if you notice here the density of the gas is very small and but the velocity is a very large and that is squared right whereas here the liquid velocities are not going to be so large so you need to make it up with a higher density liquid which is why this strontium per chlorate is used people have also thought about using a fraction of the exhaust gases themselves taking a certain bleed from the combustion chamber and using it but the trouble with that is you have to have leak proof valves that operate not only at high temperature but also at high pressure which is not very easy okay otherwise if there is a leak there will be always a side force so you do not want that and therefore this kind of taking a certain bleed from the combustion chamber has not been pursued so therefore you have to have a large tank containing this strontium per chlorate primarily because if it needs to be injected at some velocity the pressure here of the jet must be greater than the pressure here so this tank needs to be pressurized okay and then the liquid has to be expelled under pressure so that makes it a little more bulkier as I said if you want to use gas injection then hot gas handling is not very easy in liquid engines in some of the liquid engines you usually have something known as a gas generator which is used to run the turbine which in turn runs the pumps okay this gas generator also has an exhaust which can be used in auxiliary nozzles to provide the kind of thrust vectoring that we want so you will have small motors for that if this is the main engine you could have small engines that can be moved okay you could have these small thrust chambers which you can control and move it move the entire thrust chamber that will give you the required side force that is required okay but in this case the thrust vectoring that is possible is very small not very large okay so the only other thing that people have kind of thought of using but not yet looked at is in this case instead of using a liquid it is a one has a liquid rocket motor a small liquid rocket motor and inject the exhaust gases here that could also give you the required side force primarily because you will have a very high jet velocity okay and if you want to switch off and switch on this it is not very difficult because you are only going to operate the liquids right switching on and switching off a liquid rocket motor is not a problem but this is something that has not been pursued and probably could be pursued sometime later there is also another method wherein if you have four rocket motors okay and the exhaust coming out through canted nozzles right something like this let us say you had four rocket motors liquid rocket motors that are providing you the thrust then you could have a situation wherein if you look at it from the bottom let us say these are the exhaust ports of these four motors you could increase the thrust and decrease the thrust in two of them to get your required control force that is let us say if you want to pitch up and pitch down right so you could actually increase the thrust of this to pitch up and reduce the thrust in this so that it will this will cause a this will make the pitch which if you are looking into the board this will cause pitch pitch down okay if you are looking into the board this will cause the vehicle to pitch down okay and similarly you can have this is for pitch for yeah increase the thrust in these two or the other two to get the required yeah motion and you could also have rule using two of them in this fashion if you increase the thrust in these two then you can have this is only possible if you have a liquid rocket motor and if you have four of them okay if you have this is canted nozzle so the thrust vectors will not be parallel I mean perpendicular to the board it is at an angle so you will have that role till now we have looked at this rocket propulsion course in this fashion that is we have not looked at what is the thing that is there in the thrust chamber right we have looked at nozzle we have tried to derive equations to get the specific impulse of the nozzle we have not bothered ourselves about what is the kind of engine that is there liquid solid or hybrid now let us look at in the next class we will start looking at the different kinds of engines that is solid liquid and hybrid motor okay thank you