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On Jan 25, 7:31*pm, Jim Logajan wrote:
Phil J wrote: Imagine that you had a couple of tall jack stands that you could place under the wings to elevate the airplane a foot or so off the ground. *Let's say you place the stands under the wings just back from the CG such that you have to press down on the tail to keep the nosewheel off the ground. *This is similar to the condition of flight since the center of lift is aft of the center of gravity. *Now if you push down on the tail, the airplane will rotate about the center of lift. *Wouldn't it work the same way in the air? They aren't equivalent situations, mechanically speaking. As I understand it, the force of the tail plane's elevators typically moves the center of lift forward and backward along the airplane's axis as the elevators are moved up and down (as well as changing the lift magnitude a little - though that is secondary). One presumably enters stable flight when the center of lift is moved to coincide with the center of gravity. Actually as I understand it in stable flight the CL is aft of the CG. The airplane remains level not because these two are in line, but because the tail is pressing down to counterbalance the offset of the CL. After thinking about this question some more, it strikes me that this situation is equivalent to a lever and fulcrum. The lever doesn't rotate around it's CG, it rotates around the fulcrum point. In an airplane, this point is the center of lift. Regarding the CL moving around, I think even given that complication the airplane would still rotate around the CL. Phil |
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Phil J wrote:
Actually as I understand it in stable flight the CL is aft of the CG. The airplane remains level not because these two are in line, but because the tail is pressing down to counterbalance the offset of the CL. I should have used the term "total lift" so as to avoid confusion with the lift generated only by the main wings. What you state above appears internally consistent and correct with the definitions you are using. After thinking about this question some more, it strikes me that this situation is equivalent to a lever and fulcrum. The lever doesn't rotate around it's CG, it rotates around the fulcrum point. In an airplane, this point is the center of lift. Whether you are talking about center of total lift (that generated by the main wings, tail or canards, and fuselage) or center of lift of the main wings, what you state above is _incorrect_. I know that what you wrote sounds plausible, but the problem is that the main wings are no more a fulcrum than the tail wings. Suppose the main wing and the tail wing are very nearly the same size and produce nearly the same lift and all have elevator controls? Which line is the fulcrum point now about which the airplane rotates? Regarding the CL moving around, I think even given that complication the airplane would still rotate around the CL. Here's a NASA web link that explains where the rotation point is: http://www.grc.nasa.gov/WWW/K-12/airplane/acg.html Try to find some books on flight mechanics and look for the chapters or sections that appear to discuss longitudinal static stability of aircraft. They should all say that the aircraft rotates about the center of gravity. |
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On Jan 26, 1:50*pm, Jim Logajan wrote:
Phil J wrote: Actually as I understand it in stable flight the CL is aft of the CG. The airplane remains level not because these two are in line, but because the tail is pressing down to counterbalance the offset of the CL. I should have used the term "total lift" so as to avoid confusion with the lift generated only by the main wings. What you state above appears internally consistent and correct with the definitions you are using. After thinking about this question some more, it strikes me that this situation is equivalent to a lever and fulcrum. *The lever doesn't rotate around it's CG, it rotates around the fulcrum point. *In an airplane, this point is the center of lift. Whether you are talking about center of total lift (that generated by the main wings, tail or canards, and fuselage) or center of lift of the main wings, what you state above is _incorrect_. I know that what you wrote sounds plausible, but the problem is that the main wings are no more a fulcrum than the tail wings. Suppose the main wing and the tail wing are very nearly the same size and produce nearly the same lift and all have elevator controls? Which line is the fulcrum point now about which the airplane rotates? Regarding the CL moving around, I think even given that complication the airplane would still rotate around the CL. Here's a NASA web link that explains where the rotation point is: http://www.grc.nasa.gov/WWW/K-12/airplane/acg.html Try to find some books on flight mechanics and look for the chapters or sections that appear to discuss longitudinal static stability of aircraft. They should all say that the aircraft rotates about the center of gravity. Ok, I think it see it. There is a difference between the center of lift and the location of the total lift vector (I guess you could call this the net lift). In a non-canard airplane, the main wing is pushing upward and that is the center of lift we have been discussing. But the stabilizer is pushing downward. The net effect of these two forces is to move the location of the total lift vector forward to the CG location, and that results in stable flight. So a rotational force will rotate the airplane around that point just like a lever rotates on a fulcrum. The same thing would happen in a canard, except that the location of the total lift vector would be between the two wings since they both push upward. Phil |
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On Jan 26, 9:52 am, Phil J wrote:
After thinking about this question some more, it strikes me that this situation is equivalent to a lever and fulcrum. The lever doesn't rotate around it's CG, it rotates around the fulcrum point. In an airplane, this point is the center of lift. Regarding the CL moving around, I think even given that complication the airplane would still rotate around the CL. This might hold if the CL (or CG as some would argue) is rigidly fixed. But in flight, we're in a rather elastic medium, and things move around, even leaving out forward motion. Imagine, for example, two kids on a seesaw or teeter-totter or whatever name by which you know that playground thing. Two kids, same distance from the pivot, same weight. The board rotates around the pivot. The CG is at the pivot. No argument there. But suppose we had a different mounting for that pivot, one where the pivot was suspended by a couple of springs. Same kids, same weight, board level and kids motionless. (Yeah, right: motionless kids.) Now I walk up to one kid and shove down on him; where will the board *really* pivot? As i push down, the pivot point will move down some, too, because of the mass and inertia of the kid at the other end. Now the real point of rotation is somewhere along the board between the pivot and the far kid, and it'll move back toward the pivot as that kid starts to move upward. At any instant in this process it's somewhere besides the original CG. We could complicate things: A heavier kid near the pivot, a light kid at the other end, but this light kid is a little too light, so we have a small spring pulling down under his seat, just enough to keep the seesaw level. Just like the engine in our airplane (big kid near the pivot), the mass of the airplane behind the CG (light kid) and the elevator's downforce (little spring). The main pivot, still on big springs (wing in the air) will still move downward at the instant I shove down on the light kid and the real rotational point will be somewhere on the big kid's side of the pivot. Rotation about the CG works if we ignore all the other variables. Trouble is, those variables are with us every time we fly. We can watch an aerobatic airplane twisting around in the air, appearing to rotate around its CG, but is it really? Can we see the small displacement of that point (do we even know exactly where it is just by looking at the airplane?) at the instant of any change in tail forces or flight path? Like I said earlier, CG is probably good enough for our puddle- jumper purposes, but I think the guys who study advanced aerodynamics would have something to add to it. I don't think it's really all that simple. Dan |
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wrote in message ...
On Jan 26, 9:52 am, Phil J wrote: After thinking about this question some more, it strikes me that this situation is equivalent to a lever and fulcrum. The lever doesn't rotate around it's CG, it rotates around the fulcrum point. In an airplane, this point is the center of lift. Regarding the CL moving around, I think even given that complication the airplane would still rotate around the CL. This might hold if the CL (or CG as some would argue) is rigidly fixed. But in flight, we're in a rather elastic medium, and things move around, even leaving out forward motion. Imagine, for example, two kids on a seesaw or teeter-totter or whatever name by which you know that playground thing. Two kids, same distance from the pivot, same weight. The board rotates around the pivot. The CG is at the pivot. No argument there. But suppose we had a different mounting for that pivot, one where the pivot was suspended by a couple of springs. Same kids, same weight, board level and kids motionless. (Yeah, right: motionless kids.) Now I walk up to one kid and shove down on him; where will the board *really* pivot? As i push down, the pivot point will move down some, too, because of the mass and inertia of the kid at the other end. Now the real point of rotation is somewhere along the board between the pivot and the far kid, and it'll move back toward the pivot as that kid starts to move upward. At any instant in this process it's somewhere besides the original CG. We could complicate things: A heavier kid near the pivot, a light kid at the other end, but this light kid is a little too light, so we have a small spring pulling down under his seat, just enough to keep the seesaw level. Just like the engine in our airplane (big kid near the pivot), the mass of the airplane behind the CG (light kid) and the elevator's downforce (little spring). The main pivot, still on big springs (wing in the air) will still move downward at the instant I shove down on the light kid and the real rotational point will be somewhere on the big kid's side of the pivot. Rotation about the CG works if we ignore all the other variables. Trouble is, those variables are with us every time we fly. We can watch an aerobatic airplane twisting around in the air, appearing to rotate around its CG, but is it really? Can we see the small displacement of that point (do we even know exactly where it is just by looking at the airplane?) at the instant of any change in tail forces or flight path? Like I said earlier, CG is probably good enough for our puddle- jumper purposes, but I think the guys who study advanced aerodynamics would have something to add to it. I don't think it's really all that simple. Dan In a sense it is that simple. The CG does move due to accelerations of the aircraft in flight (your spring analogy is close), but the aircraft still rotates around the center of mass at any given moment (no pun intended!). Dan also...dČ |
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