 Remember, we have to proceed from 2D to 3D, so the information that we have seen so far is mainly for 2D, if you look at 3 dimensional effects, generally what happens is that if you have low quarter chord sweep, if you have reasonably high aspect ratio and if you have a taper of nearly 0.5 and large flaps, then the loss because of the 3D effects is only around 10%, so therefore the wing CL max would be approximately 0.9 of the CL max of the aircraft and most airliners will fall in this category, so the most airliners will, you can assume for most airliners that the 3D effects are only about 0.9. Now when you use partial span flaps, then it is possible to use this formula assuming that 0.9 is what you will get, but this particular additional term helps you to identify the effect of flap and the unflap area and just to show you that the flap and the unflap area are the areas which are under the influence of the flap, so if you have a trailing edge flap, then the area ahead of it also becomes a part of the flap area and if you have leading edge flaps, then the area behind it also is a part of the unflap area, of the flap area, so you have to use these ratios and notice if you have almost full span flaps, for example, suppose you have a wing where you have full span flaps, then the ratio between the two is going to be almost equal to 1. In military aircraft, we sometimes see streaks mounted at the root of the fuselage of the wing near the fuselage and these streaks create a vortex, so we call them as leading edge extensions, LEX or streaks and the effect of the streaks is to create an increase, a non-linear increase in the lift curve flow, so with no streaks even you have a linear curve, with streaks it becomes little bit non-linear and it is beneficial. So the steel alpha with streaks can be simply estimated as the steel alpha without streaks that you already know multiplied by the summation of the streak area and the wing reference area upon the wing reference area, this formula can give you an information regarding the streaks. But this is only applicable for low angle of attacks at which the streaks are not very effective because then we assume them to be like additional area of the wing itself. Now the presence of tail whether the horizontal tail or a canard also affects the lift that is produced, so the delta Cl because of horizontal tail is equal to the Cl alpha of the tail into 1 minus dou epsilon by dou alpha into ST by S where dou epsilon by dou alpha is the effectiveness of the flap or its influence. So this is obtained using a formula which relates to the geometry of the flap. This effect is created because there is always a downwash acting behind the wing and so the angle at which the air comes onto the tail is not the free stream but there is some kind of a downwash and this particular downwash angle changes with the angle of attack alpha also. So the effect of high lift devices, most flaps they increase the alpha at alpha lift equal to 0 but they do not change DCL by D alpha. Basically it is like an equivalent increase in the alpha that is why if you notice the line was parallel for full span flaps there is hardly any effect. So the delta alpha 3d is same as delta alpha 2d but if you have partial span flaps then you can use this formula to get the value of the delta alpha increase and notice that these formulae are going to help you to acquire the information that you need for your calculation. And notice that the delta alpha 2d is 10 degree at takeoff and 15 degree at landing as we saw in the curve in the figure behind. Thanks for your attention, we will now move to the next section.