 Let us have a look at some wing geometry parameters now. The basic geometrical configuration of a wing is supposed to be a trapezoidal wing and these are some of the important geometrical parameters. The first parameter is the root chord which is the chord of the wing not at the place where it attaches with the fuselage but at the location of the extended centerline of the fuselage. So, this is a very common mistake. Sometimes many people take the root chord as the location where the wing and the fuselage are physically meeting but the root chord is defined theoretically as the chord of the wing when it meets the theoretical extended centerline of the fuselage. You also have tip chord which as the name suggests is the chord of the wing when it is at the tip. The distance between the two ends of the wing is called as the span B and half of it is called as the semi-span S. Capital S is normally reserved as the parameter wing reference area which is the area of the wing as viewed in the top view including the part that is submerged inside the fuselage. So, the hashed area in this figure is the definition of wing reference area. It is a reference. So, as long as everyone understands what it stands for there will be no confusion. So, it is important to remember the definition of the wing reference area. You then have thickness T which as you can see in this figure is the maximum distance between the upper and the lower surface of the aerofoil. You have the chord C which is the distance between the leading edge and trailing edge of the aerofoil or the wing and angle of attack is the angle that is made by the ambient wind vector with a reference line on to the aircraft. There are some derived parameters like the taper ratio which is a ratio of the tip chord to the root chord. There is an aspect ratio which is an indication of its slenderness is defined as the square of the span upon the wing reference area. And we have a thickness to chord ratio or the T by C ratio which is the ratio of the maximum thickness divided by the mean aerodynamic chord of the wing. Now, the wing geometrical parameters like the camber of the aerofoil, the thickness ratio of the aerofoil aspect ratio, taper ratio and the leading edge sweep angle they all affect the aerodynamic characteristics and the weight quite substantially and it is summarized in this particular chart. But let us have a look at each of these elements one by one to have a better understanding. The first parameter that affects is the camber. Camber of the aerofoil essentially is an indication of its curvature. So, the black line is for the base aircraft, baseline geometry and the red line is for the effect of change or increase in a particular parameter. So, we notice here that as you increase the camber then the lift coefficient increases. In fact, you have a line which is almost parallel to the original line. So, the lift coefficient increases but the drag coefficient also increases. As far as the weight is concerned effect of camber on the aircraft weight is not that substantial. And the typical values of camber that you see are between 0 percent which is a symmetric aerofoil to around 6 percent of the chord. The aerofoil thickness ratio is another parameter which affects the CL alpha curve mainly it actually increases the angle at which it stalls. So, it increases the CL max but it also increases the drag coefficient. However, when you have a higher thickness to chord ratio you generally can come up with a lower wing weight. This is not very intuitive because many people think that a thicker wing should actually weigh more because they think it is larger in size. However, please remember that one of the main components of the aircraft that is heavy is the main and the rear spar or the spars which are present. And the spars themselves consist of a flange and a web. Now, in a wing with higher thickness to chord ratio these spar flanges are further away because the web is larger in size and because they are larger in there because they are far away they have a it gives a higher moment of inertia and higher moment of inertia gives you a smaller value of the bending moment which is the principle load that a spar has to carry. So, up to a point increasing T by C can actually lead to a reduction in the aircraft weight, wing weight. The range of values for subsonic aircraft is between around 5 to 18 percent and for supersonic aircraft the thickness to chord ratio is kept low because of the high drag between 3 to 7 percent. The next important parameter is the aspect ratio. The aspect ratio is a very important aerodynamic parameter as I mentioned it is an indication of the slenderness of the wing. It improves the induced drag coefficient K and actually it reduces the induced drag because of that. And another problem with the increasing aspect ratio is the more you increase the aspect ratio the more slender the wing becomes and a slenderer wing is going to be more prone to aeroelastic problems because of flexibility and also to make it sufficiently rigid we need to provide huge support and that leads to an increase in the wing weight. In fact, increasing aspect ratio of the wing leads to a very large increase in the wing weight and the wing is approximately 12 percent of the aircraft weight in most cases between 10 to 12 percent. So, it substantially affects the weight of the aircraft. So, the recommend value of aspect ratio is between 7 to 9 or maybe 10 for subsonic aircraft except those which are designed for very long endurance. And for supersonic aircraft the value recommended is between 2 and 4. Taper ratio is another parameter that is very important in reducing both the weight of the wing as well as the induced drag of the aircraft. However, giving large taper is going to create a problem with the lift distribution. So, the taper ratio generally is between 4 to 14 for subsonic aircraft and 2 to 5 for supersonic aircraft. And lastly we look at the leading edge sweep angle. Sweep angle definitely reduces CD naught, but it increases the induced drag coefficient and it makes the wing heavy. So, subsonic aircraft normally we do not see them to be swept more than 35 degrees, but for supersonic aircraft you normally see the sweep from 35 to 70 degrees or even more sometimes. It may be noted that the only advantage of providing wing sweep is to reduce the drag at high speeds and for all other considerations the wing sweep is actually detrimental. So, we sweep should not be provided unless it is essential from pure aerodynamic reasons. The reference wing platform is always considered as trapezoidal and we have already seen the effect of aspect ratio. If you increase aspect ratio we see that the induced drag reduces, but another good thing is that the angle at which the aircraft will stall is also going to reduce. So, the subsonic L by D of the aircraft increases because of the reduced induced drag, but as I already mentioned there is a substantial increase in the wing weight. Sweep, twist, incidence, dihedral are other parameters which are very important as far as the geometrical choice of an aircraft is concerned. So, I did mention to you that taper ratio of the aircraft the benefit of that is that it gives you ease in construction, but it makes the wing heavy. If you do not give taper then you have a rectangular wing and it gives you a heavier wing. When you have a lower taper ratio then you have a lighter wing because the wing root bending movement is reduced. However, the concentration of the lift moves towards the tip. So, therefore, as the value of taper ratio reduces the tips start getting loaded and that means the tips will start stalling first and that is not desirable as far as controllability is concerned. For a good controllability in the post stall scenario we do not want the tips to stall first, we want the root to stall first because when the root stalls first it gives some kind of a vibration and a physical feel to the tail and also if the root stalls before the tip then the ailerons which are normally outboard are in unstalled wing. So, they are still providing the required moment for controllability whereas, if the tips stalls first then the ailerons which are at the tips will also be in the stalled condition and it will be ineffective. So, it will be difficult to recover from a disturbance especially in roll. So, the compromise value of taper ratio is normally between 0.4 to 0.6 in most aircraft. Thanks for your attention. We will now move to the next section.