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Induced Drag is defined as drag due to the production of lift. If you think about that it is a very strange thing.
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The picture to the left shows the relative wind striking an airplane horizontally. So, we can tell that the airplane is in level flight. The lift vector is shown in green, at right angles to the relative wind. If there is such a thing as induced drag then it must be the case that the actual force created by the wing is inclined from the relative wind, as shown in the picture. But why would this happen? |
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The picture to the reminds us that lift is at 90 degrees to the relative wind. The extra angle - between lift and the actual force created by the wing is know as the induced angle of attack (induced AOA.)
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I have mentioned earlier in the course that physics is not exactly intuitive. The induced angle of attack is a good example. Most people accept it very easily, but if you think about it, it is a contradiction of Newton's Law of Reactions. Remember that Newton said that for every action there is an equal and opposite reaction. He did not say that for every action there is a roughly equal but not exactly opposite reaction. So, if lift is a reaction to the wing pushing on the air and deflecting it (as we said it is in the lift chapter) why doesn't the reaction occur exactly at right angle to the relative wind?
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In simple Newtonian terms all the wing does is deflect the relative wind, as shown in the picture to the left. To do that a force must be applied at right angles to the relative wind. Lift should then be the reaction force and as Newton said it will be equal and opposite to the force the wing applies to the airflow. In other words it should be at right angles to the relative wind, as drawn to the left. |
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The picture to the left shows what Mr Newton would expect to happen. The deflecting force (shown in red) must act at right angle to the relative wind if the airflow is to be deflected. The result will be a lift force exactly at right angle to the relative wind. In this picture the red deflecting force is shown as acting at one spot and common sense tells us that it will actually consist of a series of smaller forces acting along the chord of the wing. But does that change the analysis? More on that in a moment or two. |
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Common sense tells us that as the wing acts on the airflow to deflect it there will be friction, as shown to the left. It should also be fairly obvious that since the deflecting force is "spread out" over the length of the chord there will be more friction than if the same deflecting force had been imparted to the air with one great "whack" like a baseball bat hitting a ball. But the friction force that our common sense tells us will exist is Parasite Drag, which we have already thoroughly discussed. If you are starting to find my fascination with induced drag boring think about this. All life on earth would end within a few days if a force acting at right angles to an object created a force parallel to the objects motion. Why? Well, the earth pulls on the moon, but in doing so it does NOT slow the moon down. And the sun pulls on the earth, and in doing so does not slow the earth down. If pulling on these celestial bodies at right angles to their motion slowed them down the moon would spiral down into the earth and kill us all, unless the earth spiraling down in to the sun got us first. So why does a wing pushing down on the air slow it down - above and beyond friction that is? After all we are claiming that deflecting the airflow, in and of itself, causes drag - that is the definition of induced drag - drag due to producing lift. Induced drag is NOT the friction force. It is something else. But what?
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The answer is that the airflow ahead of the airplane undergoes what we call an upwash. As a consequence the air that actually flows over the wing arrives there at a deflected angle. We already defined the induced angle of attack above, and now you can see that it is the same as the upwash angle. So, the wing really does create a force at exactly right angles to the airflow that it is deflecting, the problem is that the airflow doesn't actually arrive at the wing in the direction of the relative wind. It is deflected by a small angle what we are calling the induced angle of attack. |
We still haven't really explained why there is an induced AOA, but at least now we know where to start looking for an explanation. There must be some reason why the airflow ahead of the wing rises. In other words we need an explanation for "upwash."
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The picture to the left shows a side view of a wing producing lift. The relative wind is deflected, as shown. As we learned earlier when we studied lift, a pressure difference forms between the top and bottom of the wing. As any meteorologist will tell you, air flows from areas of high pressure to areas of low pressure. So, the high pressure area below the wing creates pressure waves that cause the air below the wing to start moving forward to a location where the pressure is lower (because the air ahead of the wing is at atmospheric pressure.) At the same time the low pressure above the wing causes air ahead of and above the wing to start moving rearward, as shown. As a result an upwash ahead of the wing is created, as shown. The process that creates the upwash is known as "circulation." Circulation is the explanation we sought for upwash. We now need to explore the phenomenon a bit more with a view to predicting what factors will increase or decrease the circulation. |
The first thing that common sense tells us is that the pressure waves described above will spread out at the speed of sound. So we can predict that induced drag must be a phenomenon of sub-sonic flight. Later when we discuss supersonic flight we will return to this point, but for now we can say that induced drag is only a factor if the airplane flies slower than the speed of sound (sub-sonic flight.)
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The picture to the left shows the wingtip vortex of a business jet sending cloud tops into swirls. Normally the wingtip vortex is not visible, but it is always there. |
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The picture to the left shows that the wingtip vortex is caused by the air flowing around the wingtip from the high pressure area below the wing to the low pressure area above the wing. A clockwise (as viewed from the rear) vortex forms at the left wingtip and a counter-clockwise vortex forms at the right wingtip. You can see this quite clearly in the clouds of the photograph above. You can easily see that the net result of the vortex is an upward movement of the air near the wingtips, which will enhance, i.e. increase the upwash. Therefore we can predict that the upwash (and induced drag) will be greater near the wingtip than it is near the root of the wing. |
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Upwash reduces the effective angle of attack that the wing flies at. As we have seen, that is bad because it causes induced drag, but there is one benefit from it. The induced angle of attack increases the stalling angle of attack. Because the upwash (induced AOA) is greatest near the wingtip the the wing root tends to stall before the tip. You can see this effect in the photograph to the left. The picture shows the top surface of a wing with short pieces of yarn taped to it. The pilot was just pulling the airplane into a stall as the picture was taken. Near the wing root you can see that the boundary layer flow has been reversed, but near the wingtip the boundary layer is still flowing normally. In the lift chapter we mentioned that this favorable stall pattern can be accomplished using washout, but we now know that even without washout it will happen naturally. |
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The picture to the left shows that if a wing is swept back the vortex can form not just at the wingtip, but all along the span of the wing. Therefore we predict that swept wing airplanes will experience more induced drag. As a side effect of swept wings we should also predict that the stall angle of attack will be increased. Previously in the lift chapter we saw that the CL vs AOA graph has a lower slope, and the stall angle of attack is greater for swept wing airplanes. Now we know why.
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We also saw previously that the CL vs AOA graph has a lower slope for low aspect ratio airplanes. We can now reason that this is due to the greater influence of the wingtip vortex. Obviously the longer the wingspan the less the wingtip vortex will affect the average upwash of the wing. The picture to the left shows why this is so. Assume that each airplane in the picture is the same weight and has the same wing area. Also assume that each airplane is flying at the same airspeed. From our previous analysis in the lift chapter we know that all the airplanes are flying at the same angle of attack. As we know, also from the lift chapter, the pressure difference between the top and bottom of the wing will be the same in all three cases. So, common sense tells us that all three wingtip vortexes will be the same in strength and size. But, just as clearly the vortex will affect a larger percentage of the wing on the low aspect ratio airplane. On the high aspect ratio airplane most of the wing is unaffected by the extra upwash caused by the wingtip vortex. So we can predict that the high aspect ratio airplane will suffer LESS induced drag. In summary, if the wing is NOT swept then the longer the wingspan the less induced drag there will be. This is an important airplane design point. Whenever we see an airplane with very long wings we know that the designer was trying to reduce the induced drag. Unfortunately the long wingspan increases the parasite drag. |