 So, for that I have to thank Vijay Gaikwad and in turn who came this summer from Vijay T.I. Mumbai and helped me prepare the content for this particular presentation in which we will discuss longitudinal stability and neutral point, two important concepts that you will need. So, basically let us see what is the reaction of an aircraft and it is disturbed, so the aircraft is in trimmed condition, forces are in balance, moments are in balance and now some disturbance acts on that particular aircraft, so its reaction determines its stability, so the aircraft is considered to be stable when after disturbing it, it comes back to its initial position without any action of the pilot. So, if the pilot has to bring it to the condition it is called as control, but stability means without pilot input on its own, so therefore if it does not return to the initial position then the aircraft can be considered to be unstable but there is also one step in between called as neutral, so stability is of two types there is static instability in which the aircraft departs from the equilibrium, so it just departs and you also have dynamic instability in which case not only does it depart it also becomes more and more unstable, so the tendency initially is static and the final outcome is dynamic, let us have a look, so in short if you look at static stability the first step it is only a function of the initial reaction the tendency not the final outcome but the initial reaction as you disturb an aircraft what is its initial reaction on its own that determines static stability, so definition is when you disturb an aircraft from a trimmed position or equilibrium position if the aircraft tends to return, it need not return finally but at least the tendency is to return then we call it as a statically stable aircraft, so there are three basic types one can have positive static stability which is illustrated by this kind of a behavior, so you have an aircraft on the extreme left it is disturbed because of which it is pitching up slightly, so the tendency is it is coming down that is the initial tendency, so this is the positive static stability, then you have neutral static stability in which case there will be no attempt to either become undisturbed, so neither will it come back to the position nor will it go away, if it is disturbed it remains disturbed and remains disturbed, this is called as a neutral static stability, it will still stable because it is not going away okay but it is neutral, the third one is of course negative static stability in this case you will notice that if you disturb it it goes to a position of disturbance but then on its own it goes further away, then we call it as a negatively static stability but then why the word stability because we do not know what will be in the end okay right, so let us look at these three steps in some other way okay, first is neutral stability, so we have a ball on a flat table we push it to a position it goes to that position and remains there, you push it towards the left and leave it it remains there, this is neutral okay, now let us look at positive, so this is an example of positive stability, you have original state when the ball is at rest at the centre, you take it to the right and leave it, it does not go further ahead it comes back but it may exceed the position where it was go to the left and then come back and then go and then come back what eventually happens is a function of dynamic stability but the ball is statically stable because it does not go away further away okay and this is negative stability, so you place the ball and now you distribute slightly it will keep on going further and further away either on this side or on the that side this is unstable okay, so these are simple examples but we are concerned about flight not about balls on rotating surfaces, so this is a equilibrium flight the aircraft is at some angle of attack though not shown but it is level, so thrust is equal to drag, lift is equal to weight if it is a level flight and no net movement you could incline it to make it a climbing flight study again it will be in equilibrium, moments are still in balance although lift is not equal to weight lift is in fact less than weight inclined, now this is neutral you fly an aircraft you disturb it it remains disturbed and this one is unstable okay, so I will give you an example a small video clip which shows the behavior of an unstable aircraft, this is a remotely controlled aircraft it takes off goes into nose up some disturbance comes if this aircraft was statically stable then when this pitch up when the pitch down movement came because of the disturbance it would not have just gone down let us see once again observe the motion of the aircraft, so take off is fine it lifts off some disturbance we cannot see there is some disturbance but after that no way of recovery on its own, so if the pilot of this aircraft was highly skilled and very quick in reacting he or she could have avoided a crash when the aircraft is switching down you could have quickly put the elevator and made it pitch up, so you can control an aircraft which is statically unstable, this is what the Wright brothers did when they were flying the first aircraft right flyer it was inherently unstable but they were making it stable or they were making it fly by very skillful flight controls okay but you cannot expect that from every pilot and therefore we want to make the aircraft sufficiently stable if you make it too stable then the pilot has to really work very hard to do any control that is also not desirable, so we need stability but we need adequate amount of stability we do not need the plane to be too stable and obviously we do not want the plane to be unstable, so both extremes are bad, so much about static stability I will just sum up once again static stability is basically only the intention or the initial tendency of the aircraft to respond to disturbance on its own, if the initial response of the aircraft is such that it tends to come back to the undisturbed position it is statically stable, if the response is that it does not either come back or go away it is neutral if the response is it wants to go further away it is unstable statically, now let us come to dynamically, so whereas in static stability the intention or the initial tendency is the only consideration in dynamic stability we want finally the aircraft to come back actually to the original position on its own, so not just intention not just tendency but actually coming back, so the final outcome of disturbing an aircraft depends on its dynamic stability the initial response depends on static stability, so let us see, so an aircraft is going to be positive in dynamic stability if the oscillations after disturbance reduce in amplitude with time, so and the extent by which they reduce is the extent of dynamic stability, if the oscillations damp out very fast it is highly dynamically stable, if the oscillations do not damp out then it is neutrally stable, if the oscillations increase it is unstable, if the oscillations damp but slowly it is less dynamically stable, so you can see in this case you have an aircraft going in level flight there is a nose down pitching moment, so it tends to come up that means it is statically stable but it overshoots again down again up again down finally it comes to the original position after a period of time, hence it is having positive dynamic stability in neutral once again the oscillations are same in the magnitude in the in the amplitude, so you disturb the aircraft it oscillates but it does not either come down or go up it remains this is neutrally stable, it is stable because it is not unstable that is why we say stable and obviously unstable or negative stability is when the oscillations are going to worsen increase further with time, now how do you control this aircraft only by pilot intervention, you can still fly this aircraft but you will need constant and regular pilot intervention, in today's modern aircraft you might be able to control the aircraft by automatic flight control, which senses the position of the aircraft senses the movement acting on it and deflects the control surfaces automatically okay, so you can do that, so a quick summary is basically given by this small video you can actually make out by looking. Stable actually knows down even further, so that is static stability, dynamic stability is the overall tendency for the aircraft to get back to its initial flight path, a dynamically stable aircraft will eventually return to the flight path after a few oscillations, a dynamically neutral aircraft will carry on oscillating like some horrendous roller coaster, a dynamically unstable aircraft will carry on oscillating but with increasingly large oscillations which will probably, okay, so this is a quick summary, remember this video on YouTube is actually 7 minutes long, so what you have seen is only a small clip, it is a very detailed video which talks about stability, static, dynamic, longitudinal, lateral, all stabilites and it gives, it is a very detailed video, I will request you to watch it as a self study but our concern right now is only this, now obviously when you are going to take part in the competition you would like to have a stable aircraft because you do not have any control on it, it is a glider and you are not remotely flying it nor you are sitting in the aircraft to fly it, once you throw it okay, whether you use a rubber band to throw or whether you use hand to throw that is up to you, I have not mentioned but I am allowing you to do anything but when you launch it, it is gone, after that its behavior will depend only on its stability characteristics, so therefore you cannot and some people might have got an idea let us make the aircraft neutrally stable dynamically so that when we throw it will go up and down, up and down, up and down it will spend more time in the air, we might win the endurance flight okay, some people have tried this but try it out at your own risk because if that does not happen the plane will simply crash and you will get neither long distance nor long endurance okay, so it will be safer for you and a good idea for you to make the aircraft adequately stable, not too much stable, now if you want to have a flight of maximum range, actually the aircraft has three kinds of stability, stability in pitch, stability in roll, stability in yaw, so obviously you want aircraft to be stable in all of them but our syllabus does not cover the other three types of, other two types of stability, I will just give you a very brief idea, if you perfectly balance the aircraft, if both the wings are equal weight or when you hold the aircraft it does not have a tendency of imbalance it may not roll okay, it may not do this, remember if the aircraft rolls it will not fly straight because we have seen in the last lecture rolling and yawing are coupled, so if your plane starts rolling and you do not have any control it will definitely see off, if your plane starts yawing it will also roll slightly, so you have to design your plane so that it does not roll it does not yaw only then you can throw on a straight line and hit the pillar because any deviation is going to be subtracted, so what you have to do is from the point of view of yaw stability the only thing you can do is when you throw you ensure that it flies straight it does not have any inbuilt imbalance, so the vertical tail should be perfectly centered to the, if you use one vertical tail if you use two of them then they should be equidistant and they should be perfectly aligned that is all you can do and of course the lateral balance but if you want the aircraft not to roll you have to bring in some roll stability and that I leave it to you how to figure out how to make it stable in roll but I will teach you today how to make your aircraft stable in longitudinal motion so that when you throw it does not go up and then down or it does not go down it flies fairly straight okay, obviously tell me one thing how will you get maximum range for a given amount of throwing capacity what is the condition that you will try to implement right you have to throw it at an angle or you have to make the aircraft act with the wings fixed at an angle so that when you throw horizontally the angle of attack of the aircraft is corresponding to maximum L by D how do you know that you might get the angle for maximum C L by C D for an aerofoil from the data but how about the aircraft so it is not easy okay but at least you should be sure that your aircraft flies fairly straight so let us see how you make to do it the whole game is basically about these three centers okay there are three centers in aircraft design and these three centers have to be located with respect to each other in a specific relative position okay so the first one is center of gravity the center of gravity obviously you know is the place where the moments on the aircraft are acting because it is weight act on it so normally we take the moments about center of gravity one reason is that the heaviest item of the aircraft is the aircraft weight so if you balance you can do about any point actually it is not a problem but normally as a convention we always balance moment about center of gravity so there is one point now these three locations you do not worry right now we will very soon see the relative location so this depends only on mass distribution so this can be controlled by you by adding mass deleting mass you can control the CG position it does not depend upon the aerodynamics although the shape of the wing will affect its CG slightly similarly how long is your huge large how large is the tail all that will affect the center of gravity what material do you use but fairly controllable with you the next one is the center of pressure the center of pressure is the point where the resulting aerodynamic forces are applied these forces are the forces of lift and drag and it depends on the models aerodynamics and on the angle of attack so now this is interesting the location of the center of pressure or the place where the net lift is acting or the net the reaction of the wing is acting that particular point will depend upon two things at what angle you are flying and what are the forces acting on it now controlling the angle of attack at which you fly is very difficult and even if you throw it by some kind of a launcher you know 1 degree 2 degree 3 degree makes a big difference so it will be necessary and interesting for us if we can somehow remove the dependency on the angle of attack would it not be nice if the aerodynamic forces and moments could become independent of the angle of attack so one variable gone so let us see what it is the third important point is called as so let us see now the center of pressure center of pressure you know it is going to change so it depends as I said on the aerodynamic force it changes with the angle of attack so the center of pressure is the average location of the pressure it varies around the object and numerically if you want you have to take the integral of the elemental force acting on elemental pressure acting on specific on small areas into the distance from the nose or a relative point upon the sigma of the pressure okay but this is not of much use to us because it changes with the angle of attack okay then we have a neutral point the third point this is the reference point for which the pitching moment does not depend on the angle of attack right then this depends only on the aircraft geometry not on the aerodynamics not on the center of gravity but only on the external geometry again this is the point which is very difficult to determine is difficult to do calculations and say I calculate and hence NP is here so the location of center of pressure or aerodynamic forces is not in your control it depends upon angle of attack depends on what speed you throw and the aerodynamic coefficients of your aircraft so you might copy an aerofoil very accurately but how do you do the calculations for the fuselage for the tail etc it is not easy interestingly individual values are not important the relative location is important so the neutral point is another good definition of that would be it is that place if the CG comes to neutral point the aircraft becomes neutrally stable so obviously if it goes behind it will be unstable which you do not want but are you okay with a neutrally stable plane are you okay no no because a slight discomfort or a slight miscalculation will make it unstable so it is better to be in the stable domain but do not make it too stable because then it will not be recovering okay so there is a very good book by an author called Andy Lennon on the basics of remote control model aircraft design we have a copy of this book in our departmental library it is also available in the institute library and soft copies are available online so I recommend for those of you who are serious about designing your plane it is a very good book to give you basic ideas it also contains some sample designs which are good well flying glider designs so you can actually borrow from there you can copy from there