Airfoil Lifting Force, miscellaneous discussion from the archive of the Physics Teaching list server PHYS-L, phys-l@atlantis.cc.uwf.edu Date: Sun, 17 Jan 1999 10:22:28 -0800 From: Roger Freedman Subject: Flight references I would like to suggest that the recent discussion of the origin of lift (which seems to be rehashed over and over and over again on this list, as well as elsewhere) could benefit from a consultation of the literature. (Yes, even in the age of the Internet, it serves us well to make careful study of published, peer-reviewed materials.) I recommend the following sources: * Alexander, R. McNeill. Exploring Biomechanics: Animals in Motion. Scientific American Library, 1992. Chapters 4 and 5 of this excellent semi-quantitative introduction to biomechanics describe the gliding, soaring, and flapping flight of birds and insects. There are some nice three-dimensional depictions of the airflow around aircraft and birds in flight. The author is a professor of zoology at the University of Leeds. * Anderson, John D., Jr. A History of Aerodynamics and Its Impact on Flying Machines. Cambridge University Press, 1997. A very extensive technical history (fully half the book covers the centuries before the Wright Brothers). The author is a professor of aerospace engineering at the University of Maryland. * Ashley, Holt. Engineering Analysis of Flight Vehicles. Addison-Wesley, 1974. Reprinted by Dover Publications, 1992. A superb graduate-level textbook that should be accessible to anyone with a physics degree. The book has clear, quantitative discussions of two- and three-dimensional wings. The author was a professor in the Department of Aeronautics and Astronautics at Stanford University (and an excellent teacher, as I can attest from personal experience). * Hubin. W. N. The Science of Flight: Pilot-Oriented Aerodynamics. Iowa State University Press, 1992. Written by a physicist (on the faculty at Kent State) who is also a pilot. The book has a wealth of real-life examples based on data from light airplanes. The extent of quantitative detail should be satisying to anyone reading this list. * Hurt, H. H, Jr.. Aerodynamics for Naval Aviators. U. S. Navy Publication NAVAIR 00-80T-80, 1960. (Reprinted by Aviation Supplies and Academics, Inc., and available from Aviation Book Co., 7201 Perimeter Road S., Suite C, Seattle WA 98108) Very clear textbook with excellent discussions of the three-dimensional aspects of airflow around aircraft. The author was on the faculty of the University of Southern California. As an aside, from my experience as a pilot I can attest that what *really* makes airplanes fly is MONEY! (There is a wonderful T-shirt for pilots that carries the slogan "If God had meant man to fly, he would have given him more money.") +++++++++++++++++++++++++++++++++++++++++++++++++++++++ Roger A. Freedman Department of Physics and College of Creative Studies University of California, Santa Barbara From owner-phys-l@LISTS.NAU.EDU Thu Jan 14 05:30:56 1999 Received: from mailgate.nau.edu (mailgate.nau.edu [134.114.96.19]) by mx1.eskimo.com (8.9.1a/8.8.8) with ESMTP id FAA28731; Thu, 14 Jan 1999 05:30:55 -0800 Received: from mailgate ([134.114.96.19]) by mailgate.nau.edu (PMDF V5.2-29 #31141) with ESMTP id <0F5J001B6X5AL7@mailgate.nau.edu>; Thu, 14 Jan 1999 06:30:51 -0700 (MST) Date: Thu, 14 Jan 1999 07:30:40 -0600 From: jlu Subject: Re: Airfoil lift, new article Sender: "phys-l@lists.nau.edu: Forum for Physics Educators" To: PHYS-L@LISTS.NAU.EDU Reply-to: "phys-l@lists.nau.edu: Forum for Physics Educators" Message-id: <0F5J001DMXJ9L7@mailgate.nau.edu> Status: RO X-Status: DA Hi all- Anderson came and gave a lunch seminar in the high energy physics division. The upshot is that he thinks that downwash is a better prime cause than is the pressure distribution around an airfoil. He did have pictures showing that airflow above and below the wing does not "join" at the trailing edge. Regards, Jack William Beaty wrote: > How Airplanes Fly: A Physical Description of Lift > by D. Anderson, Fermilab, and S> Eberhardt, U. Wash Aero/Astro > > http://www.aa.washington.edu/faculty/eberhardt/lift.htm > > An illustrated preprint, to be published in Sport Aviation magazine's > February issue. It's a "conceptual physics" style of article. The authors > offer a Newtonian description of flight intended to replace the "popular" > explanation of lifting force based on wing shape. > From billbeskimo.com Thu Jan 14 08:58:16 1999 Date: Thu, 14 Jan 1999 08:57:07 -0800 (PST) From: William Beaty To: "phys-l@lists.nau.edu: Forum for Physics Educators" Subject: Re: Airfoil lift, new article In-Reply-To: <0F5J001DMXJ9L7@mailgate.nau.edu> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: On Thu, 14 Jan 1999, jlu wrote: > Hi all- > Anderson came and gave a lunch seminar in the high energy physics > division. The upshot is that he thinks that downwash is a better prime > cause than is the pressure distribution around an airfoil. He did have > pictures showing that airflow above and below the wing does not "join" > at the trailing edge. There is currently a discussion about this paper going on at rec.aviation.piloting newsgroup. The Anderson/Eberhardt paper about how airplanes fly: http://www.aa.washington.edu/faculty/eberhardt/lift.htm John Denker has posted a critique of their paper at: http://www.monmouth.com/~jsd/fly/lift.htm I have a crude "thought experiment" explanation of flight here, see if you can poke holes in my reasoning: http://amasci.com/wing/rotbal.html The newsgroup discussion is typical: most of the people are totally confident that an aircraft can remain suspended entirely because of a pressure difference, and it need not obey F=MA, or change the momentum of the air. The way I see it, an aircraft flys ENTIRELY because it changes the momentum of air: it pushes down on the air, and therefor the air pushes up on the aircraft, THEN THE AIR MOVES DOWN. The pressure difference doesn't just sit there, instead it CAUSES the "downwash." I don't know if PHYS-L people really would want to get involved with that discussion, because we can talk forever and not convince anyone. To convince them, they must confront the fact that they've been visualizing the physics of flight incorrectly, as well as angrily defending an incorrect premise. And these people are pilots! It's far easier to convince a non-expert that their pre-existing concepts are actually misconceptions! :) The discussion thread can be viewed at Dejanews by pasting this huge url into your browser (edit it to remove line breaks): http://x10.dejanews.com/=dnt_test1/dnquery.xp?search=thread&svcclass= dncurrent&threaded=1&ST=PS&CONTEXT=916331856.695009561&HIT_CONTEXT= 916331856.695009561&HIT_NUM=9&recnum=%3c76c4t8$sul$1@ eskinews.eskimo.com%3e%231/1 .. or go to www.dejanews.com and search for these keywords: ~g rec.aviation.piloting lifting force ((((((((((((((((((((( ( ( ( ( (O) ) ) ) ) ))))))))))))))))))))) William J. Beaty SCIENCE HOBBYIST website billbeskimo.com http://amasci.com EE/programmer/sci-exhibits science projects, tesla, weird science Seattle, WA 206-762-3818 freenrg-L taoshum-L vortex-L webhead-L From billbeskimo.com Thu Jan 14 09:38:56 1999 Date: Thu, 14 Jan 1999 09:38:46 -0800 (PST) From: William Beaty To: "phys-l@lists.nau.edu: Forum for Physics Educators" Subject: Re: Airfoil lift, new article In-Reply-To: <0F5J001DMXJ9L7@mailgate.nau.edu> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Some bait to temp the unwary. :) See the message below. Can you see the flaw in Mr. Scarfe's diagram and arguments? It is two-dimensional! In 2D, a wing can push on the distant ground instantly, since the air cannot escape in a direction out of (or into) the plane of the diagram. Wing pushes down on air, air pushes down on Earth, Earth doesn't move. Earth pushes up on air, air pushes up on wing, wing levitates without having to eject any KG of air downwards. Flight by "ground effect," with the altitude made irrelevant. In my opinion, this is the central flaw in conventional aerodynamics' explanation of flight. 2D wings fly, it is true, but they employ a fundamentally different mechanism than 3D aircraft. 3D aircraft fly by conservation of momentum, while 2D aircraft fly by contact forces like a hovercraft. A 3D aircraft ejects KGs of air downwards like a rocket (or helicopter!), while an aircraft in a 2D world interacts with the surface of the Earth. In a 2D world, it doesn't matter how high the airplane flys, it is still essentially riding across the earth's surface, and hence there is no need for it to permanently deflect the streamlines of oncoming air. In a 3D world, an aircraft must permanently deflect the streamlines, otherwise there would be no net change in the momentum of the air, and no F=MA force. "Circulation theory" is flawed. It works great for predicting the lifting force. But if we use it to explain flight, then we are ACTUALLY explaining how wings might function in a vertical version of "flatland." 3D aircraft function by profoundly different principles. If anyone on PHYS-L enjoys "lifting force" debates, please feel free to wade on into the rec.aviation.piloting discussion. ((((((((((((((((((((( ( ( ( ( (O) ) ) ) ) ))))))))))))))))))))) William J. Beaty SCIENCE HOBBYIST website billbeskimo.com http://amasci.com EE/programmer/sci-exhibits science projects, tesla, weird science Seattle, WA 206-762-3818 freenrg-L taoshum-L vortex-L webhead-L Author: Julian Scarfe Email:jas1@scigen.co.uk Date:1999/01/12 Forums:rec.aviation.piloting,rec.aviation.student J Kahn (jkahn@planeteer.com) wrote in response to JSD's critique: > : With all due respect: > > I have a problem with your discounting the upwash bit John... if the upwash > : was beneficial to the generation of lift, the upwash would have to be > : produced by a source *external* to the wing. When you throw the ball > : up to me I benefit from the upward energy because *you* imparted the > : energy, not me. The upwash the wing has to deal with is produced by > : the same wing, not an external source... It's accelerating a mass > : upward, the mass wasn't accelerated by an external source. Mark Mallory wrote: > > This is correct; Denker is in error here. Unlike the situation in the > baseball analogy, the airflow in front of the wing *initially* has ZERO > upward momentum. The upwash represents a *change* (increase) in the upward > momentum of the airflow, which must be accompanied by a *downward* reaction > force on the wing. Similarly, a *downward* change in airflow momentum > must be accompanied by an *upward* reaction force on the wing. The total > lift of the wing will be equal to the NET downward momentum change of the > air as it passes the wing. > > However, it's possible to show that there is ZERO net downward momentum > imparted to the air by the passing of a lift-generating airfoil; You're *all* right: you're just talking about different chunks of air! A' A B B' | | | | | | | | | ^ | | | | ---> | | --------- | | | | AIRFLOW | WING | V | | | | | | | | | | | | | X'-----------------------X-----------------Y-----------------------------Y' Consider a situation where air flows from a plane (in the geometrical sense) A'X' at "forward infinity" through a plane AX just ahead of the leading edge of an aerofoil (loosely a "wing" for consistency), through BY just behind its trailing edge, to B'Y' at "aft infinity". Consider X'XYY' to be the surface of the earth a long way below the wing. Let's look at the vertical component of the momentum flux p of the airflow as it passes each vertical plane, the force f on the wing and the force on the horizontal plane in each region. Conservation of momentum in each zone ("control volume") requires: pA'X' - pAX = fXX' (1) pAX - pBY = f_Wing + fXY (2) pBY - pB'Y' = fYY' (3) Adding 1+2+3 gives fXX' + fXY + fYY' + f_Wing = pA'X' - pB'Y' which tends to zero as the ' planes move away towards forward and aft infinity. So the total force on the imparted on the air by the wing is equal opposite to the total force imparted on the air by the ground; or lift is equal opposite to the total force imparted on the air by the ground, which is what Mallory said. Provided the length (area in 2D) XY is much smaller than X'Y', (2) can be approximated by pAX - pBY = f_Wing which is the momentum argument that Denker puts in point 1 of his critique. The upwash (- pAX) in front of the wing contributes additively to the downwash behind (pBY). Anderson and Eberhardt have "slipped a sign"! I don't like the momentum argument very much on the basis that there's a term like fXY in any control surface that you pick. In the case of the choice XABY, it is vanishingly small and the momentum change pAX - pBY is a way to calculate the lift. But in the case of any surface X'A'B'Y' that fills space, the term is of the same order of magnitude as f_Wing (1/2 in the 2D case and 1/3 if I remember rightly for the 3D case, though it's a somewhat academic point). That's why I think you have to be very careful about using macroscopic conservation of momentum arguments around wings. The only thing that you can be sure of is that the sum of the force on your control volume and the momentum flux into it is equal and opposite to the lift. But if you know the velocity field everywhere anyway, why not just apply Bernoulli at the surface of the wing and calculate the pressure directly, like aerodynamicists have been doing for a century? Bill Beaty made the interesting (but, IMHO, mistaken) point: > Yes, a 2D simulation is equivalent to an infinite wing, and for an > infinite wing, if there is any net change in the air motion after the > wing has passed, then an infinite amount of momentum had to be created, > because all of the air far above and below the wing had to be deflected > as well. Yes, but the "wing" has infinite span: the lift per unit span is finite. > In 2D space, if one streamline is permanently deflected, they ALL must > be permanently deflected. Hence a 2D situation is fundamentally > different than a 3D situation, there are fewer degrees of freedom for > each parcel of air, and the air behind an infinite wing had better NOT > move downwards. To an extent, this is true. Some of the downwash can be attributed to the trailing vortices. Nevertheless, if the 3D to 2D transition so fundamentally changes the physics, how come calculated and measured 2D lift coefficients are equal to the limit of 3D lift coefficients at large span? > Even a "thin slice" 2D simulation is bizarre, because if there is any > net deflection of the air, then ALL the air out to infinite distances > above and below the wing must be deflected too. This represents an > infinite mass and an infinite momentum change. Hence, 2D aircraft can > fly without deflecting any air, but 3D aircraft operate by significantly > different rules. The 2D aircraft "deflect air" just like the 3D ones. At plane BY as seen above, there's a large momentum change over a small area. At plane B'Y', the momentum change is infinitesimal over an infinite area. One highly misleading aspect of the Anderson and Eberhardt paper is the implication that the deflection angle as "permanent", i.e. the same at BY as B'Y'. It's not, in either 2D or 3D. -- Julian Scarfe From owner-phys-l@LISTS.NAU.EDU Thu Jan 14 11:28:44 1999 Received: from mailgate.nau.edu (mailgate.nau.edu [134.114.96.19]) by mx1.eskimo.com (8.9.1a/8.8.8) with ESMTP id LAA23475; Thu, 14 Jan 1999 11:28:42 -0800 Received: from mailgate ([134.114.96.19]) by mailgate.nau.edu (PMDF V5.2-29 #31141) with ESMTP id <0F5K004U5DXJ6Y@mailgate.nau.edu>; Thu, 14 Jan 1999 12:28:35 -0700 (MST) Date: Thu, 14 Jan 1999 11:23:35 -0800 From: James McLean Subject: Re: Airfoil lift, new article Sender: "phys-l@lists.nau.edu: Forum for Physics Educators" To: PHYS-L@LISTS.NAU.EDU Reply-to: "phys-l@lists.nau.edu: Forum for Physics Educators" Message-id: <0F5K004VDE3D6Y@mailgate.nau.edu> Status: RO X-Status: William Beaty wrote: > See the message below. Can you see the flaw in Mr. Scarfe's diagram and > arguments? It is two-dimensional! In 2D, a wing can push on the distant > ground instantly, since the air cannot escape in a direction out of (or > into) the plane of the diagram. Wing pushes down on air, air pushes down > on Earth, Earth doesn't move. Earth pushes up on air, air pushes up on > wing, wing levitates without having to eject any KG of air downwards. > Flight by "ground effect," with the altitude made irrelevant > I won't pretend that I could follow the quoted message, but isn't this treating the air as an incompressible fluid? In that case, the pressure argument would be in deep kimchee too. -- --James McLean jmclean@chem.ucsd.edu post doc UC San Diego, Chemistry From billbeskimo.com Thu Jan 14 13:43:52 1999 Date: Thu, 14 Jan 1999 13:43:44 -0800 (PST) From: William Beaty To: "phys-l@lists.nau.edu: Forum for Physics Educators" Subject: Re: Airfoil lift, new article In-Reply-To: <0F5K00ES2IWR0B@mailgate.nau.edu> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: On Thu, 14 Jan 1999, Michael N. Monce wrote: > I had such a discussion about 6 months ago in the flight simulator > group I belong to (I quit actual flying many years ago due to the high > costs). The heated discussion was with a CFI pilot who now has been hired > by an airline. Nothing I could do would ever convince him that the > Bernoulli equation can be derived from Newton's laws. Even when > confronted with the idea of a symmetrical airfoil and inverted flight he > stuck with his notion of pressure differences as the only route to explain > lift. Heh! There's one argument which defeats all others: sticking fingers in the ear canal, shouting "You're Wrong!", and stalking away. Ooops, there are others too: suddenly and mysteriously changing the subject whenever it looks like your opponent is right. ((((((((((((((((((((( ( ( ( ( (O) ) ) ) ) ))))))))))))))))))))) William J. Beaty SCIENCE HOBBYIST website billbeskimo.com http://amasci.com EE/programmer/sci-exhibits science projects, tesla, weird science Seattle, WA 206-762-3818 freenrg-L taoshum-L vortex-L webhead-L From owner-phys-l@LISTS.NAU.EDU Fri Jan 15 05:39:50 1999 Received: from mailgate.nau.edu (mailgate.nau.edu [134.114.96.19]) by mx1.eskimo.com (8.9.1a/8.8.8) with ESMTP id FAA03865; Fri, 15 Jan 1999 05:39:49 -0800 Received: from mailgate ([134.114.96.19]) by mailgate.nau.edu (PMDF V5.2-29 #31141) with ESMTP id <0F5L008GZSM2K7@mailgate.nau.edu>; Fri, 15 Jan 1999 06:39:44 -0700 (MST) Date: Fri, 15 Jan 1999 07:40:42 -0600 From: "JACK L. URETSKY (C)1998; HEP DIVISION, ARGONNE NATIONAL LAB ARGONNE, IL 60439" Subject: a couple of points on flight Sender: "phys-l@lists.nau.edu: Forum for Physics Educators" To: PHYS-L@LISTS.NAU.EDU Reply-to: "phys-l@lists.nau.edu: Forum for Physics Educators" Message-id: <0F5L008H2SM2K7@mailgate.nau.edu> Status: RO X-Status: A 1. In subsonic flight, air is incompressible to a very good approximation. I worked this out for phys-l a couple of years ago. 2. 2-d airfoil theory explains lift on a wing very well. Wind tunnels (the ones I was introduced to 50 or so years ago) are set up to be 2-d and one has to correct the measurements for wall effects, etc. 3. It is true that the ground effect is related to the wing span in 3-d. In 2-d calculations one doesn't usually introduce a ground plane. If one did, I think the effect probably dies off either logarithmically or as 1/distance. Airfoil theory is, after all, just the same potential theory that we came to know and love in electrostatics - except that circulation must be introduced in order to keep things finite. Regards, Jack ps Anderson does not quarrel with conventional aerodynamics. He just thinks that his explanation is more "physical". I think that the essential physics is contained in the statement that the integrated pressure over the wing surface is related to the net change in airflow (the "downwash"), but that's just a matter of taste. "I scored the next great triumph for science myself, to wit, how the milk gets into the cow. Both of us had marveled over that mystery a long time. We had followed the cows around for years - that is, in the daytime - but had never caught them drinking fluid of that color." Mark Twain, Extract from Eve's Autobiography From billbeskimo.com Fri Jan 15 11:00:52 1999 Date: Fri, 15 Jan 1999 11:00:00 -0800 (PST) From: William Beaty To: "phys-l@lists.nau.edu: Forum for Physics Educators" Subject: Re: a couple of points on flight In-Reply-To: <0F5L008H2SM2K7@mailgate.nau.edu> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: On Fri, 15 Jan 1999, JACK L. URETSKY (C)1998; HEP DIVISION, ARGONNE NATIONAL LAB ARGONNE, IL 60439 wrote: > 2. 2-d airfoil theory explains lift on a wing very well. Wind tunnels (the ones > I was introduced to 50 or so years ago) are set up to be 2-d and one has to > correct the measurements for wall effects, etc. Hi Jack! From what I understand of it, I would say that 2-d airfoil theory ALLOWS CALCULATION of lifting force, but that is contains misleading features which befuddle anyone who is attempting to explain airplanes. See below. > 3. It is true that the ground effect is related to the wing span in > 3-d. In 2-d calculations one doesn't usually introduce a ground plane. > If one did, I think the effect probably dies off either logarithmically > or as 1/distance. Airfoil theory is, after all, just the same potential > theory that we came to know and love in electrostatics - except that > circulation must be introduced in order to keep things finite. Here is a central problem: in 2D, the air far upstream from the wing is flowing horizontally, right? And the air far downstream is also flowing horizontally, correct? These flows come about through the superposition of circulation and constant horizontal flight. It seems to me that this guarantees a ZERO change in momentum of the air. It looks as if the 2D flow diagram is symmetrical about a vertical line, and upwash exactly equals downwash. If the wing lifts the air up, reverses the air's vertical velocity, then pushes it down to exactly the same position again, leaving it with zero vertical velocity, then no net momentum change occurred. For there to be net momentum change, the air would be lifted up at first, but then it would be pushed down AND KEEP MOVING DOWN AFTERWARDS. If wings were to fly by deflecting a horizontal hail of bullets, then a "contrail" of constantly-descending bullets would trail behind the wing. The descending contrail appears to be lacking in 2D circulation diagrams. A constantly-descending contrail appears to be incompatible with the circulation field. This confuses me. I have no idea on how to integrate the net change in the air's momentum in the vertical slices as it passes the circulation field of a wing in 2D. My assertion that the net momentum change is zero is based upon visual reasoning and intuition. Yet I still cannot grasp how a wing can create lift unless either it acts directly against an immobile infinite mass of air, either that or it takes in air having a zero vertical velocity component and then leaves a contrail of air which moves constantly downwards. Can anyone here explain where I've gone wrong about the 2D "potential field" analogy of circulation? If this were electrostatics and a charged metal object was being accelerated in an E-field, I would look to the distant "capacitor plates" where the e-field flux lines ended, there to find the opposite mechanical acceleration and the opposite quantity of momentum. In 2D airfoil diagrams, the opposite momentum seems to be stored on the infinite mass of air which is behind the airfoil and extends to plus and minus vertical infinity. The airfoil trys to accelerate a long horizontal slice of the air downwards, but this is impossible in 2D, therefor the airfoil reacts against an "object" having infinite mass, and the lifting force resembles a contact-force with zero momentum changes, rather than a downwards ejection of massive air parcels (think of a hovering helicopter, then think of a toy boat in a bowl of water resting on scales.) > ps Anderson does not quarrel with conventional aerodynamics. He just > thinks that his explanation is more "physical". I think that the > essential physics is contained in the statement that the integrated > pressure over the wing surface is related to the net change in airflow > (the "downwash"), but that's just a matter of taste. I agree in part. My quarrel is with the folks on newsgroups who point out that in 2D, upwash apparently equals downwash, therefor a pressure- difference can be created without any overall deflection of moving mass being required. I strongly suspect that this argument is flawed because this efect only arises in a 2D "flatland" world, and cannot be used to explain why a 3d aircraft can fly. ((((((((((((((((((((( ( ( ( ( (O) ) ) ) ) ))))))))))))))))))))) William J. Beaty SCIENCE HOBBYIST website billbeskimo.com http://amasci.com EE/programmer/sci-exhibits science projects, tesla, weird science Seattle, WA 206-762-3818 freenrg-L taoshum-L vortex-L webhead-L From owner-phys-l@LISTS.NAU.EDU Fri Jan 15 11:41:18 1999 Received: from mailgate.nau.edu (mailgate.nau.edu [134.114.96.19]) by mx2.eskimo.com (8.9.1a/8.8.8) with ESMTP id LAA04151; Fri, 15 Jan 1999 11:41:13 -0800 (PST) Received: from mailgate ([134.114.96.19]) by mailgate.nau.edu (PMDF V5.2-29 #31141) with ESMTP id <0F5M003JM6B6FO@mailgate.nau.edu>; Fri, 15 Jan 1999 12:40:00 -0700 (MST) Date: Fri, 15 Jan 1999 13:40:56 -0600 From: "JACK L. URETSKY (C)1998; HEP DIVISION, ARGONNE NATIONAL LAB ARGONNE, IL 60439" Subject: Re: a couple of points on flight Sender: "phys-l@lists.nau.edu: Forum for Physics Educators" To: PHYS-L@LISTS.NAU.EDU Reply-to: "phys-l@lists.nau.edu: Forum for Physics Educators" Message-id: <0F5M003HY9AHFO@mailgate.nau.edu> Status: RO X-Status: A Hi all- William Beatty writes: *************************************************************** Here is a central problem: in 2D, the air far upstream from the wing is flowing horizontally, right? And the air far downstream is also flowing horizontally, correct? These flows come about through the superposition of circulation and constant horizontal flight. It seems to me that this guarantees a ZERO change in momentum of the air. It looks as if the 2D flow diagram is symmetrical about a vertical line, and upwash exactly equals downwash. ********************************* Wrong. Newton's laws work very well in both wind tunnels and 2-D aerodynamics. The air downstream of a 2-D ideal lifting airfoil has a net downward component. A classic work is Glauert, "Airfoil and Airscrew Theory", but I'm sure that there are many other texts available. I haven't yet checked Brittannica, but that's usually a good place to start. "I scored the next great triumph for science myself, to wit, how the milk gets into the cow. Both of us had marveled over that mystery a long time. We had followed the cows around for years - that is, in the daytime - but had never caught them drinking fluid of that color." Mark Twain, Extract from Eve's Autobiography From owner-phys-l@LISTS.NAU.EDU Fri Jan 15 13:22:25 1999 Received: from mailgate.nau.edu (mailgate.nau.edu [134.114.96.19]) by mx1.eskimo.com (8.9.1a/8.8.8) with ESMTP id NAA29194; Fri, 15 Jan 1999 13:22:19 -0800 Received: from mailgate ([134.114.96.19]) by mailgate.nau.edu (PMDF V5.2-29 #31141) with ESMTP id <0F5M00K4WDFRF5@mailgate.nau.edu>; Fri, 15 Jan 1999 14:21:43 -0700 (MST) Date: Fri, 15 Jan 1999 13:21:11 -0800 From: John Mallinckrodt Subject: Re: a couple of points on flight In-reply-to: <0F5M003RH7JHFO@mailgate.nau.edu> Sender: "phys-l@lists.nau.edu: Forum for Physics Educators" To: PHYS-L@LISTS.NAU.EDU Reply-to: "phys-l@lists.nau.edu: Forum for Physics Educators" Message-id: <0F5M00KABDZZF5@mailgate.nau.edu> Status: RO X-Status: A On Fri, 15 Jan 1999, William Beaty wrote: > Here is a central problem: in 2D, the air far upstream from the wing is > flowing horizontally, right? And the air far downstream is also flowing > horizontally, correct? These flows come about through the superposition > of circulation and constant horizontal flight. It seems to me that this > guarantees a ZERO change in momentum of the air. It looks as if the 2D > flow diagram is symmetrical about a vertical line, and upwash exactly > equals downwash. Maybe we need to remind ourselves that "horizontal" here means "parallel to the earth's surface." The downward flowing air must eventually meet the earth in which case it pushes on and imparts "downward" momentum to the earth. If you stay in the earth's frame it may look like there has been no change in momentum, but you aren't doing your analysis in an inertial frame. And while 3D may offer another way around the apparent dilemma, I don't think it is necessary in order to resolve the paradox. John ----------------------------------------------------------------- A. John Mallinckrodt http://www.csupomona.edu/~ajm Professor of Physics mailto:ajm@csupomona.edu Physics Department voice:909-869-4054 Cal Poly Pomona fax:909-869-5090 Pomona, CA 91768-4031 office:Building 8, Room 223 From billbeskimo.com Fri Jan 15 16:14:20 1999 Date: Fri, 15 Jan 1999 16:14:01 -0800 (PST) From: William Beaty To: "phys-l@lists.nau.edu: Forum for Physics Educators" Subject: Re: a couple of points on flight In-Reply-To: <0F5M003HY9AHFO@mailgate.nau.edu> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: On Fri, 15 Jan 1999, JACK L. URETSKY (C)1998; HEP DIVISION, ARGONNE NATIONAL LAB ARGONNE, IL 60439 wrote: > Hi all- > William Beatty writes: > *************************************************************** > Here is a central problem: in 2D, the air far upstream from the wing is > flowing horizontally, right? And the air far downstream is also flowing > horizontally, correct? These flows come about through the superposition > of circulation and constant horizontal flight. It seems to me that this > guarantees a ZERO change in momentum of the air. It looks as if the 2D > flow diagram is symmetrical about a vertical line, and upwash exactly > equals downwash. > ********************************* > Wrong. Newton's laws work very well in both wind tunnels and 2-D > aerodynamics. > The air downstream of a 2-D ideal lifting airfoil has a net > downward component. I agree, but that's not the problem. To me it looks like the air upstream from an ideal 2D airfoil has a net upward component which equals the downstream downward component. At the position of the airfoil, the upward velocity of the air changes to downward velocity, and this explains the lift. However, the airfoil caused the oncoming air to rise to meet it, and this subtracts from the lift. Also, the airfoil causes the descending downstream air to deccelerate to a standstill, and this also subtracts from lift. If we look at the entire pattern of air surrounding the airfoil out to a fair distance, it appears that the momentum change in the air is first upwards in the upstream section, then downwards at the airfoil, then upwards again in the downstream section, for a net change of zero. > A classic work is Glauert, "Airfoil and Airscrew > Theory", but I'm sure that there are many other texts available. I > haven't yet checked Brittannica, but that's usually a good place to > start. Thanks, I'll have a look at Brittannica, but I hoped that mine was a typical student question which has been answered millions of times, and somebody here would already know the answer offhand. When I see those nice perfect 2D diagrams for a rotating cylinder in a horizontal wind, the upstream air flow is a mirror image of the downstream, which suggests to me that the net momentum change is zero, even thought the lifting force is large. If I am wrong, where is my error hidden? ((((((((((((((((((((( ( ( ( ( (O) ) ) ) ) ))))))))))))))))))))) William J. Beaty SCIENCE HOBBYIST website billbeskimo.com http://amasci.com EE/programmer/sci-exhibits science projects, tesla, weird science Seattle, WA 206-762-3818 freenrg-L taoshum-L vortex-L webhead-L From billbeskimo.com Fri Jan 15 16:46:22 1999 Date: Fri, 15 Jan 1999 16:46:11 -0800 (PST) From: William Beaty To: "phys-l@lists.nau.edu: Forum for Physics Educators" Subject: Re: a couple of points on flight In-Reply-To: <0F5M00KABDZZF5@mailgate.nau.edu> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: On Fri, 15 Jan 1999, John Mallinckrodt wrote: > On Fri, 15 Jan 1999, William Beaty wrote: > > > Here is a central problem: in 2D, the air far upstream from the wing is > > flowing horizontally, right? And the air far downstream is also flowing > > horizontally, correct? These flows come about through the superposition > > of circulation and constant horizontal flight. It seems to me that this > > guarantees a ZERO change in momentum of the air. It looks as if the 2D > > flow diagram is symmetrical about a vertical line, and upwash exactly > > equals downwash. > > Maybe we need to remind ourselves that "horizontal" here means "parallel > to the earth's surface." The downward flowing air must eventually meet > the earth in which case it pushes on and imparts "downward" momentum to > the earth. Yes, but if the upstream/downstream pattern are mirror images of each other, then the upstream pattern would pull upwards on the earth while the downstream pattern pushes the earth downwards, and the forces and momenta subtract. If somebody standing on the ground was shooting a machine-gun up at a solid object, and the object was reflecting the bullets, the object would experience a lifting force. This situation resembles that with the airfoil in a 2D world. Yet the airfoil seems to be *pulling* its own bullets upwards, then reflecting them downwards to create lift, then *pulling* on the bullets to stop their downward motion. The total momentum change would be zero. What am I missing? Maybe I should try to simulate this with a large spreadsheet. Or, to approach the problem from a different angle, what would happen if we took a horizontal streamline in a 2D world and deflected it downwards? Imagine that the earth is 10000KM below. To deflect one horizontal streamline, won't we also have to deflect each adjacent streamline as well? That takes more momentum. How far up and down must we reach to deflect the streamlines? All the way down to the earth, no? ANd so the earth will push on the bottom streamline, and so all the streamlines will feel this occur. Since the gas is incompressible, it cannot be deflected at all. If the earth was removed, we still would need to change the vertical component of momentum for all of the deflected streamlines (an infinite change in momentum), even though we only want to deflect a single streamline. In a 3D world, this problem does not arise, because deflecting a small sheaf of streamlines would simply cause the air underneath to move in the 3rd dimension to get out of the way. > If you stay in the earth's frame it may look like there has > been no change in momentum, but you aren't doing your analysis in an > inertial frame. Bouyancy forces should eliminate the non-inertial frame's effects upon the air parcels, no? Suppose that instead of an earth-frame, we remove gravity and instead somehow apply a "downwards" force to the airfoil but not to the air. I would think that this would not change the physics, since the airfoil would still have "weight", yet the gas would be "weightless," same as when a 2D airfoil flies over a 2D planet. > And while 3D may offer another way around the apparent > dilemma, I don't think it is necessary in order to resolve the paradox. If a 3D aircraft flys because it flings its wingtip-vortices downwards like I've describe here: http://amasci.com/wing/rotbal.html ...then "flight" in a 2D world is distinct from the "flight" of a real 3D aircraft, and while the 2D model would be convenient for calculating the lifting force, it would be wrong to use it in explanations of the lifting force associated with a real aircraft. ((((((((((((((((((((( ( ( ( ( (O) ) ) ) ) ))))))))))))))))))))) William J. Beaty SCIENCE HOBBYIST website billbeskimo.com http://amasci.com EE/programmer/sci-exhibits science projects, tesla, weird science Seattle, WA 206-762-3818 freenrg-L taoshum-L vortex-L webhead-L From owner-phys-l@LISTS.NAU.EDU Sat Jan 16 05:35:16 1999 Received: from mailgate.nau.edu (mailgate.nau.edu [134.114.96.19]) by mx1.eskimo.com (8.9.1a/8.8.8) with ESMTP id FAA26913; Sat, 16 Jan 1999 05:35:15 -0800 Received: from mailgate ([134.114.96.19]) by mailgate.nau.edu (PMDF V5.2-29 #31141) with ESMTP id <0F5N00KMAN2GXI@mailgate.nau.edu>; Sat, 16 Jan 1999 06:35:10 -0700 (MST) Date: Sat, 16 Jan 1999 07:36:10 -0600 From: "JACK L. URETSKY (C)1998; HEP DIVISION, ARGONNE NATIONAL LAB ARGONNE, IL 60439" Subject: Re: a couple of points on flight Sender: "phys-l@lists.nau.edu: Forum for Physics Educators" To: PHYS-L@LISTS.NAU.EDU Reply-to: "phys-l@lists.nau.edu: Forum for Physics Educators" Message-id: <0F5N00KMDN2GXI@mailgate.nau.edu> Status: RO X-Status: Hi William Beaty- You write- ************************************************************ I agree, but that's not the problem. To me it looks like the air upstream from an ideal 2D airfoil has a net upward component which equals the downstream downward component. At the position of the airfoil, the upward velocity of the air changes to downward velocity, and this explains the lift. However, the airfoil caused the oncoming air to rise to meet it, and this subtracts from the lift. Also, the airfoil causes the descending downstream air to deccelerate to a standstill, and this also subtracts from lift. If we look at the entire pattern of air surrounding the airfoil out to a fair distance, it appears that the momentum change in the air is first upwards in the upstream section, then downwards at the airfoil, then upwards again in the downstream section, for a net change of zero. ********************************** It's a quantitative question that depends upon the "angle of attack" of the airfoil. If the angle is sufficient to give lift, then the downstream deflection is greater than the upstream deflection, giving a net lift. This is apparently illustrated in the Anderson-Eberhart paper. Regards, Jack "I scored the next great triumph for science myself, to wit, how the milk gets into the cow. Both of us had marveled over that mystery a long time. We had followed the cows around for years - that is, in the daytime - but had never caught them drinking fluid of that color." Mark Twain, Extract from Eve's Autobiography From owner-phys-l@LISTS.NAU.EDU Sat Jan 16 07:11:17 1999 Received: from mailgate.nau.edu (mailgate.nau.edu [134.114.96.19]) by mx1.eskimo.com (8.9.1a/8.8.8) with ESMTP id HAA22831; Sat, 16 Jan 1999 07:11:16 -0800 Received: from mailgate ([134.114.96.19]) by mailgate.nau.edu (PMDF V5.2-29 #31141) with ESMTP id <0F5N00NKKRII04@mailgate.nau.edu>; Sat, 16 Jan 1999 08:11:11 -0700 (MST) Date: Sat, 16 Jan 1999 09:10:57 -0600 From: brian whatcott Subject: Re: a couple of points on flight In-reply-to: <0F5N00KOUN2NXI@mailgate.nau.edu> Sender: "phys-l@lists.nau.edu: Forum for Physics Educators" To: PHYS-L@LISTS.NAU.EDU Reply-to: "phys-l@lists.nau.edu: Forum for Physics Educators" Message-id: <0F5N00NKNRII04@mailgate.nau.edu> Status: RO X-Status: At 07:36 1/16/99 -0600, you wrote: [Bill] >... If we look at the entire pattern of air surrounding the >airfoil out to a fair distance, it appears that the momentum change in the >air is first upwards in the upstream section, then downwards at the >airfoil, then upwards again in the downstream section, for a net change of >zero. >********************************** [Jack] > It's a quantitative question that depends upon the "angle of attack" >of the airfoil. If the angle is sufficient to give lift, then the downstream >deflection is greater than the upstream deflection, giving a net lift. This >is apparently illustrated in the Anderson-Eberhart paper. > Regards, > Jack What Jack said....with the proviso, the angle of attack for effective lift can include the angle zero for asymmetric sections. Following along with the earlier discussion I received the uncomfortable image of a moving footprint of air in the shape of the moving wing finally pressing upon the ground. I am more comfortable with an image of molecules of the downwards air parcel sharing their largesse with others, in the manner of a marble running down a (Dalton's??) pinboard. Brian brian whatcott Altus OK From owner-phys-l@LISTS.NAU.EDU Sat Jan 16 09:08:50 1999 Received: from mailgate.nau.edu (mailgate.nau.edu [134.114.96.19]) by mx1.eskimo.com (8.9.1a/8.8.8) with ESMTP id JAA28214; Sat, 16 Jan 1999 09:08:49 -0800 Received: from mailgate ([134.114.96.19]) by mailgate.nau.edu (PMDF V5.2-29 #31141) with ESMTP id <0F5N007H7WYBMQ@mailgate.nau.edu>; Sat, 16 Jan 1999 10:08:43 -0700 (MST) Date: Sat, 16 Jan 1999 12:08:31 -0500 From: "Michael N. Monce" Subject: Re: a couple of points on flight In-reply-to: <0F5N00KMDN2GXI@mailgate.nau.edu> Sender: "phys-l@lists.nau.edu: Forum for Physics Educators" To: PHYS-L@LISTS.NAU.EDU Reply-to: "phys-l@lists.nau.edu: Forum for Physics Educators" Message-id: <0F5N007HAWYBMQ@mailgate.nau.edu> Status: RO X-Status: On Sat, 16 Jan 1999, JACK L. URETSKY (C)1998; HEP DIVISION, ARGONNE NATIONAL LAB ARGONNE, IL 60439 wrote: > It's a quantitative question that depends upon the "angle of attack" > of the airfoil. If the angle is sufficient to give lift, then the downstream > deflection is greater than the upstream deflection, giving a net lift. This > is apparently illustrated in the Anderson-Eberhart paper. > Regards, > Jack > I think this is precisely where the pilots I've had discussion with seem to miss the point. They insist that with zero angle of attack, and with no net deviation of the airstream, that the Bernoulli equation still insists that the airfoil will fly. Mike Monce Connecticut College From billbeskimo.com Sat Jan 16 13:22:53 1999 Date: Sat, 16 Jan 1999 13:22:52 -0800 (PST) From: William Beaty Reply-To: William Beaty To: "phys-l@lists.nau.edu: Forum for Physics Educators" cc: tap-l , scott@aa.washington.edu, Jan-Olov Newborg , dfa@fnal.gov, jefraskin@aol, jsd@monmouth.com Subject: PHYS-L: is Circulation theory "wrong" ???? In-Reply-To: <0F5N00KMDN2GXI@mailgate.nau.edu> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: In PHYS-L on Sat, 16 Jan 1999, JACK L. URETSKY (C)1998; HEP DIVISION, ARGONNE NATIONAL LAB ARGONNE, IL 60439 wrote: > It's a quantitative question that depends upon the "angle of > attack" of the airfoil. If the angle is sufficient to give lift, then > the downstream deflection is greater than the upstream deflection, > giving a net lift. This is apparently illustrated in the > Anderson-Eberhart paper. I totally agree with this reasoning as far as the 3D case is concerned. The Anderson-Eberhart paper (http://www.aa.washington.edu/faculty/eberhardt/lift.htm) argues that 3D aircraft must impose a net downwards deflection upon the air being encountered by the wings, and therefor derive an upwards F=MA lifting force. I agree because there is no way for the aircraft to push upon the earth directly, and because the forces created by the wing must obviously deflect mass (with no "earth's surface" being required.) I agree because the downstream "wake" of a 3D aircraft is totally different than the upstream patterns of air motion: it contains a pair of large wake-vortices which presumably are carrying air downwards, as illustrated in my "disk balloons" example at http://amasci.com/wing/rotbal.html. Clearly a 3D aircraft applies a reaction force between its wings and the oncoming parcels of air, and consequently the air accelerates downwards, and the craft accelerates upwards and therefor opposes gravity and flys horizontally. My conceptual confusion lies with the 2D case. In the 2D "world", it appears to me that the air-flow patterns upstream and downstream of the 2D airfoil are mirror images of each other, and so the airfoil on average does not throw air downwards (nor does it leave air moving downwards.) It appears to me that the wing is directly reacting against an infinite mass of downstream air (or possibly is directly reacting against the distant surface of the earth which blocks the vertical motion of the 2D air). Why do I think this? See below. Since the air in the 2D world is treated as incompressible, then whenever a downward force is applied to a long horizontal downstream parcel of air, this downward force will be instantly communicated all the way down to the earth's surface, and the earth's surface will instantly prevent that chunk of 2D atmosphere from moving downwards. The wing *TRIES* to deflect air downwards, but it only succeeds in creating a circular flow; where every parcel of downward-moving downstream air is match by an upstream parcel which is forced to move upwards. Isn't that what "circulation" means, after all? A tilted airfoil tries to deflect air downwards, but in the 2D world, this air encounters a sort of "solid floor", and as a result, it ends up causing an equal upwash ahead of the wing. Upwash equals downwash, therefor there is no *NET* change in the vertical velocity or vertical momentum of the oncoming air. By conservation of momentum, there must be zero lifting force! Yet the wing does fly. Why? I suspect it works like so: the wing essentially pushes downwards upon a (horizontally wide) "rigid column" of 2D air which is resting upon the earth and prevented from moving downwards. Therefor there is an instantaneous contact-force pair between the wing and the earth; as if the wing was resting upon the earth itself (or was using a pressure-bubble like a hovercraft; in other words, flight by "ground effect.") Another way to think about the problem. It appears to me that the following flow pattern is impossible in the two dimensional world: upstream of downstream of the airfoil the airfoil --------------------- ___ ---___ --------------------- ___ ---___ ---___ --------------------- ___ ---___ ---___ --------------------- ___ ---___ ---___ --------------------- ___ ---___ ---___ ---___ In order to permanently deflect one streamline, the airfoil would have to deflect ALL the downstream streamlines, agreed? This phenomena only arises in a 2D world. The tilted flow in the right-hand diagram would crash into the earth. Or, if the earth was removed and the atmosphere was infinitely tall, then the change from horizontal-flow to diagonal-flow would require an infinite momentum change. The airfoil cannot create the infinite force needed to permanently deflect the infinite mass of two-dimensional air. With no deflection, there is no F=MA force. However, since the airfoil TRIES to deflect the air downards, it is applying a force to the air and therefor to the earth's surface. The earth's surface answers: it applies an upward 3rd-law force to the air and therefor to the airfoil. As a consequence, the two-dimensional airfoil rides indirectly upon the two-dimensional earth: it flies entirely by "ground effect." The airfoil in the 2D world cannot deflect air, however it is allowed to move air around by creating a CIRCULAR flow. The circular flow doesn't impose a permanent net downwards deflection upon oncoming parcels of air in the way that a 3D aircraft does. The circular flow requires that the "upwash" equal the "downwash". If upwash equals downwash, there is no net downwash, and no net F=MA lifting force. In the 2D world, the airfoil cannot fly by deflecting air downwards. Instead there is a contact-force with the earth, and the airfoil "rides on a bubble." This bubble is its circulation pattern which has higher pressure below, and which pushes upon the earth like some vast automobile tire. I conclude that, in the two-dimensional world, an airfoil "flys" by contact forces with the distant earth's surface (or equivalently, by attempting to deflect the entire 2D atmosphere). On the other hand, a 3D aircraft flys by directing a stream of air downwards in three dimensions, and the air far below the aircraft can move aside in order to allow the downwards flow to pass by. Such a thing is not possible in 2D. Hence, aircraft in "flatland" rely on the unique physics of the two-dimensional world, and they essentially are hovercrafts, no matter how high they may fly above the ground. Hey everybody on PHYS-L! Please feel free to find the huge flaw in my reasoning above. I cannot find it. I've cc:'d TAP-L to attract more "opponents." :) I seriously want to get to the bottom of my confusion. Either that, or I want to contribute to a "phase change" where a bunch of people leap onto my bandwagon and stop using 2D circulation theory to explain real-world flight. What I'd REALLY love to see is the graph of net vertical velocity of vertical slices of the atmosphere surrounding a wing in a 2D world. My intuition is that this graph is flat except near the airfoil, and near the airfoil every upward part is matched elsewhere by an equal downward part. If true, then isn't my intuition correct, and the wing causes circulation but no net deflection of oncoming air, and therefor no net change in momentum? "Bill Beaty (and Dr. Weltner, etc.) CANNOT be right, because it would mean that any explanation of flight which is based on 2D circulation is profoundly misleading when used to explain how 3D airplanes fly. That many textbooks and experts cannot possibly be wrong!" My experiences with "educator misconceptions" shows that the above argument is invalid. That many textbooks CAN be wrong, and frequently are. That's why I'm on such a personal crusade! I usually limit myself to K-6 textbook issues. In the case of flight, the (apparent) conceptual garbage from the university level is reaching down and distorting explanations of flight in grade school. Therefor I have no inhibitions about attacking circulation theory. It might after all be "wrong." If I can find the flaw in 2D circulation explanations of flight, then I can weaken their hold on K-6 textbook explanations of flight, and defeat the typical arguments from authority. ( Don't try to reason it out for yourself, instead listen to expert opinions contained in advanced textbooks? NOT! ) The flaw appears to be located in the "flatland physics" which does not apply to any 3D aircraft. My reasoning is obviously oversimplified, and it is possible to argue about all sorts of little issues. However, if my reasoning has a *fundamental* flaw, I need somebody would set me straight. In conclusion, it appears to me that 2D circulation theory is fine when its use is confined to calculations of lifting force of airfoil cross-sections. Local to the airfoil surface, 3D air flows are probably identical to air flows in a 2D world, and so any lifting-force calculations that are based on 2D circulation will match the real-world 3D results. However, since 2D circulation theory only *EXPLAINS* the flight of "flatland aircraft", we should never unthinkingly apply it to 3D craft which fly by an entirely different physical mechanism: by creating downwards-moving 3D trailing vortices. As always, more stuff and old message-threads are available here: Airfoil Lifting Force Misconception in K-6 Textbooks http://amasci.com/wing/airfoil.html "Science Myths" in K-6 Textbooks and Popular culture http://amasci.com/miscon/miscon.html (note the new domain name, but the old will always work) "It is a good morning exercise for a research scientist to discard a pet hypothesis every day before breakfast. It keeps him young." -- Konrad Lorenz "If you make people think they're thinking, they'll love you. If you REALLY make them think, they'll hate you" - D. Marquis ((((((((((((((((((((( ( ( ( ( (O) ) ) ) ) ))))))))))))))))))))) William J. Beaty SCIENCE HOBBYIST website billbeskimo.com http://amasci.com EE/programmer/sci-exhibits science projects, tesla, weird science Seattle, WA 206-762-3818 freenrg-L taoshum-L vortex-L webhead-L From owner-phys-l@LISTS.NAU.EDU Sun Jan 17 11:03:24 1999 Received: from mailgate.nau.edu (mailgate.nau.edu [134.114.96.19]) by mx1.eskimo.com (8.9.1a/8.8.8) with ESMTP id LAA25379; Sun, 17 Jan 1999 11:03:22 -0800 Received: from mailgate ([134.114.96.19]) by mailgate.nau.edu (PMDF V5.2-29 #31141) with ESMTP id <0F5P00H5UWXAAF@mailgate.nau.edu>; Sun, 17 Jan 1999 12:03:17 -0700 (MST) Date: Sun, 17 Jan 1999 14:00:29 -0500 From: "James W. Wheeler" Subject: Re: PHYS-L: is Circulation theory "wrong" ???? In-reply-to: <0F5O00E9E8QOKW@mailgate.nau.edu> Sender: "phys-l@lists.nau.edu: Forum for Physics Educators" To: PHYS-L@LISTS.NAU.EDU Reply-to: "phys-l@lists.nau.edu: Forum for Physics Educators" Message-id: <0F5P00H5YWXBAF@mailgate.nau.edu> Status: RO X-Status: A If one wants to know about the effect of the ground on the system, I suspect the distance to the ground and the speed of sound would be necessary considerations, even in 2-D. On Sat, 16 Jan 1999, William Beaty wrote: > In PHYS-L on Sat, 16 Jan 1999, JACK L. URETSKY (C)1998; HEP DIVISION, ARGONNE NATIONAL LAB ARGONNE, IL 60439 wrote: > > > It's a quantitative question that depends upon the "angle of > > attack" of the airfoil. If the angle is sufficient to give lift, then > > the downstream deflection is greater than the upstream deflection, > > giving a net lift. This is apparently illustrated in the > > Anderson-Eberhart paper. > > I totally agree with this reasoning as far as the 3D case is concerned. > The Anderson-Eberhart paper (http://www.aa.washington.edu/faculty/eberhardt/lift.htm) > argues that 3D aircraft must impose a net downwards deflection upon > the... From owner-phys-l@LISTS.NAU.EDU Sun Jan 17 13:00:31 1999 Received: from mailgate.nau.edu (mailgate.nau.edu [134.114.96.19]) by mx1.eskimo.com (8.9.1a/8.8.8) with ESMTP id NAA00509; Sun, 17 Jan 1999 13:00:30 -0800 Received: from mailgate ([134.114.96.19]) by mailgate.nau.edu (PMDF V5.2-29 #31141) with ESMTP id <0F5Q00H012CKWW@mailgate.nau.edu>; Sun, 17 Jan 1999 14:00:26 -0700 (MST) Date: Sun, 17 Jan 1999 15:01:25 -0600 From: "JACK L. URETSKY (C)1998; HEP DIVISION, ARGONNE NATIONAL LAB ARGONNE, IL 60439" Subject: Re: PHYS-L: is Circulation theory "wrong" ???? Sender: "phys-l@lists.nau.edu: Forum for Physics Educators" To: PHYS-L@LISTS.NAU.EDU Reply-to: "phys-l@lists.nau.edu: Forum for Physics Educators" Message-id: <0F5Q00H042CKWW@mailgate.nau.edu> Status: RO X-Status: Hi William Beaty- Well, I'm willing to give you some hints. ************************************************************ My conceptual confusion lies with the 2D case. In the 2D "world", it appears to me that the air-flow patterns upstream and downstream of the 2D airfoil are mirror images of each other, and so the airfoil on average does not throw air downwards (nor does it leave air moving downwards.) It appears to me that the wing is directly reacting against an infinite mass of downstream air (or possibly is directly reacting against the distant surface of the earth which blocks the vertical motion of the 2D air). Why do I think this? See below. *************************************** Your assumption that upstream and downstream are mirror images is false. The statement that the wing is directly reacting against an "infinite mass of downstream air" (at any instant, at least) is not supportable by any legitimate calculation. The surface of the earth roughly analogous to an infinite conducting plane in 2-D electrostatics. The potential of a 2-D point charge near such a plane is a logarithm. The 2-D wing is like a 2-D charge distribution (plus circulation). ***************************************************************** Since the air in the 2D world is treated as incompressible, then whenever a downward force is applied to a long horizontal downstream parcel of air, this downward force will be instantly communicated all the way down to the earth's surface, and the earth's surface will instantly prevent that chunk of 2D atmosphere from moving downwards. ************************ Also in the subsonic 3-D world is air incompressible. Circulation is, I believe, still accounted for by the Kutta-Jokowski hypothesis, which I will encourage you to learn about for yourself. As I bow out of this discussion, I will remind the list that Aristotelean argument does not replace a successful mathematical description of nature. Regards, Jack "I scored the next great triumph for science myself, to wit, how the milk gets into the cow. Both of us had marveled over that mystery a long time. We had followed the cows around for years - that is, in the daytime - but had never caught them drinking fluid of that color." Mark Twain, Extract from Eve's Autobiography From billbeskimo.com Sun Jan 17 13:10:44 1999 Date: Sun, 17 Jan 1999 13:10:42 -0800 (PST) From: William Beaty To: "phys-l@lists.nau.edu: Forum for Physics Educators" Subject: Re: PHYS-L: is Circulation theory "wrong" ???? In-Reply-To: <0F5P00H5YWXBAF@mailgate.nau.edu> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: On Sun, 17 Jan 1999, James W. Wheeler wrote: > If one wants to know about the effect of the ground on the system, I > suspect the distance to the ground and the speed of sound would be > necessary considerations, even in 2-D. Right! This is taken care of by making the compressibility of the air approach zero, which makes the speed of sound grow very large (or at least that's the way I understand it, perhaps I'm wrong.) ((((((((((((((((((((( ( ( ( ( (O) ) ) ) ) ))))))))))))))))))))) William J. Beaty SCIENCE HOBBYIST website billbeskimo.com http://amasci.com EE/programmer/sci-exhibits science projects, tesla, weird science Seattle, WA 206-762-3818 freenrg-L taoshum-L vortex-L webhead-L From owner-phys-l@LISTS.NAU.EDU Sun Jan 17 15:01:07 1999 Received: from mailgate.nau.edu (mailgate.nau.edu [134.114.96.19]) by mx1.eskimo.com (8.9.1a/8.8.8) with ESMTP id PAA07141; Sun, 17 Jan 1999 15:01:00 -0800 Received: from mailgate ([134.114.96.19]) by mailgate.nau.edu (PMDF V5.2-29 #31141) with ESMTP id <0F5Q00JWX7WIC2@mailgate.nau.edu>; Sun, 17 Jan 1999 16:00:57 -0700 (MST) Date: Sun, 17 Jan 1999 16:59:27 -0600 From: Herb Schulz Subject: Re: PHYS-L: is Circulation theory "wrong" ???? In-reply-to: <0F5Q00H2L2CRWW@mailgate.nau.edu> Sender: "phys-l@lists.nau.edu: Forum for Physics Educators" To: PHYS-L@LISTS.NAU.EDU Reply-to: "phys-l@lists.nau.edu: Forum for Physics Educators" Message-id: <0F5Q00JXB7XGC2@mailgate.nau.edu> Status: RO X-Status: A Howdy, Imagine a VERY LONG wing passing through the air and look at the motion of the air near the center. Symmetry tells me that at least near the center of the wing the air flow should be independent of which plane perpendicular to the wing you pick; i.e., a 2D model should still work. If it would need a 3D analysis then ends of the wing would have to give almost all of the lift; ALL planes would have short stubby wings. Good Luck, Herb Schulz (herbs@interaccess.com) From owner-phys-l@LISTS.NAU.EDU Sun Jan 17 15:26:29 1999 Received: from mailgate.nau.edu (mailgate.nau.edu [134.114.96.19]) by mx1.eskimo.com (8.9.1a/8.8.8) with ESMTP id PAA14949; Sun, 17 Jan 1999 15:26:27 -0800 Received: from mailgate ([134.114.96.19]) by mailgate.nau.edu (PMDF V5.2-29 #31141) with ESMTP id <0F5Q00JWX7WIC2@mailgate.nau.edu>; Sun, 17 Jan 1999 16:12:25 -0700 (MST) Date: Sun, 17 Jan 1999 15:12:14 -0800 From: William Beaty Subject: Re: PHYS-L: is Circulation theory "wrong" ???? (fwd) Sender: "phys-l@lists.nau.edu: Forum for Physics Educators" To: PHYS-L@LISTS.NAU.EDU Reply-to: "phys-l@lists.nau.edu: Forum for Physics Educators" Message-id: <0F5Q00J7D8GKC2@mailgate.nau.edu> Status: RO X-Status: Forward message, NOT from Bill Beaty. ---------- Forwarded message ---------- Date: Sun, 17 Jan 1999 09:44:39 -0600 (CST) From: David_Anderson To: William Beaty Cc: "phys-l@lists.nau.edu: Forum for Physics Educators" , tap-l , scott@aa.washington.edu, Jan-Olov Newborg , jefraskin@aol, jsd@monmouth.com Subject: Re: PHYS-L: is Circulation theory "wrong" ???? Bill, I found your last email somewhat stimulating. I believe that I can shed some light on the situation. I will first start by giving a quote from Elementary Fluid Dynamics, by D.J. Acheson, Clarendon Press, Oxford: Notwithstanding the importance of circulation, the Kutta-Joukowski condition, and the theorem of [the previous section which relates lift to speed and circulation], an aerofoil obtains lift essentially by imparting downward momentum to the oncoming airstream. In the case of a single aerofoil, in an infinite expanse of fluid this elementary truth is disguised, perhaps, by the way that the deflection of the airstream tends to zero at infinity. There should be no question that the net result of lift is that air is given vertical momentum and energy. The confusion comes from the 2D simulations of the aeronautical engineers. I think you will have an easier time visualizing the 2D situation if you keep in mind that a 2D airfoil is really an airfoil of infinite length. This fact is often lost and is the cause of much of the confusion. As Scott and I discussed in our paper, the efficiency for lift of a wing is proportional to its length. A wing of infinite length diverts an infinite amount of air down at zero velocity. Since the work done is proportional to the vertical velocity of the air (squared), the infinite wing develops lift without doing work. It is the loss of the fact that 2D simulations are of infinite wings that give rise to the (silly) misconceptions that lift does not require work (the basis for the book Stop Abusing Bernoulli! How Airplanes Really Fly, By Gail Craig), that if one were to look far enough back there would be no net momentum transfer, that circulation drives lift (rather than the other way around), that a wing with symmetric circulation has lift, and that the induced drag is just due to the nasty wingtip vortices. The point was brought up in the email that many textbooks and expert cannot possibly be wrong. Through the years of developing the view that is presented in our paper, many a time I almost quit because of something that I read from an expert. I would be stopped by the thought that if what was said were true, that I really didn't know how a wing developed lift. Fortunately for me, Scott was there to explain the origin of the misconceptions. This work has been more of an effort in learning where misconception came from than figuring out how planes really fly. I hope this is of some help. David _______________________________________________________________________________ David F. Anderson Fermi National Accelerator Laboratory PO Box 500, MS-220 Batavia, IL 60510 (630) 840-3471; FAX (630) 840-6039 _______________________________________________________________________________ From billbeskimo.com Sun Jan 17 15:35:12 1999 Date: Sun, 17 Jan 1999 15:35:08 -0800 (PST) From: William Beaty Reply-To: William Beaty To: David_Anderson cc: "phys-l@lists.nau.edu: Forum for Physics Educators" , tap-l , scott@aa.washington.edu, Jan-Olov Newborg , jefraskin@aol, jsd@monmouth.com Subject: Re: PHYS-L: is Circulation theory "wrong" ???? In-Reply-To: Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: To everyone on the CC list: Would you be interested if I were to volunteer one of my listservers for use in discussing the lifting force controversy? This would remove the debate to a separate forum and keep phys-L and other groups from being taken over by the "lifting force" discussion. I would demand civilized behavior from all participants, and the discussion would definitely NOT descend to the level of a newsgroup flamewar. I have a disused list called VortexC-L (appropriate name, eh?) The forum would only be worthwhile if opposing sides in the controversy are both interested. There's no point to starting a dedicated "lifting force" forum if it becomes a mutual-admiration society for one side of the debate. On Sun, 17 Jan 1999, David_Anderson wrote: > Bill, > > I found your last email somewhat stimulating. I believe that I can shed > some light on the situation. I will first start by giving a quote from > Elementary Fluid Dynamics, by D.J. Acheson, Clarendon Press, Oxford: > > Notwithstanding the importance of circulation, the Kutta-Joukowski > condition, and the theorem of [the previous section which relates lift > to speed and circulation], an aerofoil obtains lift essentially by > imparting downward momentum to the oncoming airstream. In the case of > a single aerofoil, in an infinite expanse of fluid this elementary > truth is disguised, perhaps, by the way that the deflection of the > airstream tends to zero at infinity. Hey! Maybe all these non-mathematical "Conceptual physics" intuitions are correct after all? :) > There should be no question that the net result of lift is that air is > given vertical momentum and energy. The confusion comes from the 2D > simulations of the aeronautical engineers. I think you will have an > easier time visualizing the 2D situation if you keep in mind that a 2D > airfoil is really an airfoil of infinite length. This fact is often lost > and is the cause of much of the confusion. I agree. However, the infinite length can be eliminated if we imagine that the 2D world is actually 1mm deep, and is trapped between frictionless glass walls (with the airfoil being free to move.) This visual image is how I eliminated my own fuzzy thinking regarding an infinite lifting force applied to an infinitely long wing, resulting in a finite net force. > It is the loss of the fact that 2D simulations are of infinite wings that > give rise to the (silly) misconceptions that lift does not require work > (the basis for the book Stop Abusing Bernoulli! How Airplanes Really Fly, > By Gail Craig), that if one were to look far enough back there would be no > net momentum transfer, I just had a brainstorm yesterday about "looking far back enough." I think I've found the flaw. If we take a vertical 2D slice of the 3D air patterns around a real aircraft, we can find a situation that resembles the world of the 2D airfoil simulation, including the distant starting-vortex. However, that slice exists in a 3D world, and HENCE HAS NO MASS. If the same slice is made thicker and taken in a variety of positions and orientations, it is clear that there IS a net momentum transfer which supports the aircraft. Only in one symmetrical position, a position which avoids intersecting the trailing vortices, does it APPEAR that the 2D model applies to the 3D aircraft. In my opinion this is a weird, nonphysical artifact, and the supporters of the 2D model are moved to grasp it fiercely in an attempt to deny ever admitting that their viewpoint is fundamentally flawed. An unbiased outsider would lack the emotional issues connected with being proved wrong, and therefor wouldn't defend such a nonphysical distortion of reality. In other words, our misconceptions are strong, they are intertwined with our egos, and they fiercely resist being cured by a dose of correct information. > The point was brought up in the email that many textbooks and expert > cannot possibly be wrong. Through the years of developing the view that > is presented in our paper, many a time I almost quit because of something > that I read from an expert. I would be stopped by the thought that if > what was said were true, that I really didn't know how a wing developed > lift. Fortunately for me, Scott was there to explain the origin of the > misconceptions. This work has been more of an effort in learning where > misconception came from than figuring out how planes really fly. This sounds verrrrry familiar. It took me years to realize that textbooks as a whole are just lousy with conceptual errors. Still, I try to confine myself to an area of expertise I can deal with: errors in grade-school texts. (Obviously there are far more errors to fight in those books than in postgraduate texts. Yet the number of errors does not decrease to zero as the level of study advances. Far from it.) Take a look at my website called SCIENCE MYTHS IN K-6 TEXTBOOKS, at http://amasci.com/miscon/miscon.html I had to go through numerous mental "phase changes" in order to clear these misconceptions from my worldview. As a result, my warning bells now go off whenever someone uses arguments from authoritiy, and insist that the authorties confront their OWN misconceptions, no matter what the stature of those authorities. Fortunately, the health of my future career does not depend on my keeping silent about the flaws of others, therefor I have few inhibitions about speaking my mind. Also, I've been wrong so many times in the past, that I'm no longer very embarassed about it. The best way to follow the process of trial and error is to pursue accuracty, yet to unknowningly be flagrantly erroneous in front of a large group of experts, then let them find the weak spot which shatters my flawed reasoning. Here's a quote which you might enjoy. We ignore it at our peril. It is even MORE perilous if we apply it exclusively to our students, but not to ourselves nor to the authors of our textbooks and reference books. "I know that most men, including those at ease with problems of the greatest complexity, can seldom accept even the simplest and most obvious truth if it be such as would oblige them to admit the falsity of conclusions which they have delighted in explaining to colleagues, which they have proudly taught to others, and which they have woven, thread by thread, into the fabric of their lives." - Tolstoy ((((((((((((((((((((( ( ( ( ( (O) ) ) ) ) ))))))))))))))))))))) William J. Beaty SCIENCE HOBBYIST website billbeskimo.com http://amasci.com EE/programmer/sci-exhibits science projects, tesla, weird science Seattle, WA 206-762-3818 freenrg-L taoshum-L vortex-L webhead-L From owner-phys-l@LISTS.NAU.EDU Sun Jan 17 16:26:47 1999 Received: from mailgate.nau.edu (mailgate.nau.edu [134.114.96.19]) by mx1.eskimo.com (8.9.1a/8.8.8) with ESMTP id QAA02808; Sun, 17 Jan 1999 16:26:45 -0800 Received: from mailgate ([134.114.96.19]) by mailgate.nau.edu (PMDF V5.2-29 #31141) with ESMTP id <0F5Q00184BW6JS@mailgate.nau.edu>; Sun, 17 Jan 1999 17:26:39 -0700 (MST) Date: Sun, 17 Jan 1999 18:26:00 -0600 From: brian whatcott Subject: is Circulation theory "wrong" ???? (fwd) In-reply-to: <0F5Q00J9U8GQC2@mailgate.nau.edu> Sender: "phys-l@lists.nau.edu: Forum for Physics Educators" To: PHYS-L@LISTS.NAU.EDU X-CC: David_Anderson , tap-l , scott@aa.washington.edu, Jan-Olov Newborg , jefraskin@aol.nau.edu, jsd@monmouth.com Reply-to: "phys-l@lists.nau.edu: Forum for Physics Educators" Message-id: <0F5Q00187BW6JS@mailgate.nau.edu> Status: RO X-Status: >Date: Sun, 17 Jan 1999 09:44:39 -0600 (CST) >From: David_Anderson > , > tap-l , scott@aa.washington.edu, > Jan-Olov Newborg , jefraskin@aol, jsd@monmouth.com >Subject: Re: PHYS-L: is Circulation theory "wrong" ???? > >... an aerofoil obtains lift essentially by imparting >downward momentum to the oncoming airstream. In the case of a single >aerofoil, in an infinite expanse of fluid this elementary truth is >disguised, perhaps, by the way that the deflection of the airstream tends >to zero at infinity. > >There should be no question that the net result of lift is that air is >given vertical momentum and energy. The confusion comes from the 2D >simulations of the aeronautical engineers. I think you will have an >easier time visualizing the 2D situation if you keep in mind that a 2D >airfoil is really an airfoil of infinite length. This fact is often lost >and is the cause of much of the confusion. As Scott and I discussed in >our paper, the efficiency for lift of a wing is proportional to its >length. A wing of infinite length diverts an infinite amount of air down >at zero velocity. Since the work done is proportional to the vertical >velocity of the air (squared), the infinite wing develops lift without >doing work..... >___________________________________________________________________________ ____ > David F. Anderson While sympathizing completely with Anderson's approach, I had better tighten up an assertion of his which is not quite sturdy enough to serve as a stick for beating aero engineers, namely: "A wing of infinite length diverts an infinite amount of air down at zero velocity." This assertion would doubtless be true for any wing of finite weight. If, however, the wing loading were given in force ( or weight) per unit length of span, then the weight to be reacted, also being infinite would need finite net downwards velocity. I hope and believe that Anderson and his associates would heartily concur with my position. I have copied him on this note as a courtesy. brian whatcott Altus OK From owner-phys-l@LISTS.NAU.EDU Sun Jan 17 17:08:30 1999 Received: from mailgate.nau.edu (mailgate.nau.edu [134.114.96.19]) by mx1.eskimo.com (8.9.1a/8.8.8) with ESMTP id RAA15505; Sun, 17 Jan 1999 17:08:28 -0800 Received: from mailgate ([134.114.96.19]) by mailgate.nau.edu (PMDF V5.2-29 #31141) with ESMTP id <0F5Q001RNDTVJS@mailgate.nau.edu>; Sun, 17 Jan 1999 18:08:25 -0700 (MST) Date: Sun, 17 Jan 1999 17:08:09 -0800 From: William Beaty Subject: Re: PHYS-L: is Circulation theory "wrong" ???? In-reply-to: <0F5Q00JXB7XGC2@mailgate.nau.edu> Sender: "phys-l@lists.nau.edu: Forum for Physics Educators" To: PHYS-L@LISTS.NAU.EDU Reply-to: "phys-l@lists.nau.edu: Forum for Physics Educators" Message-id: <0F5Q001RQDTWJS@mailgate.nau.edu> Status: RO X-Status: On Sun, 17 Jan 1999, Herb Schulz wrote: > Howdy, > > Imagine a VERY LONG wing passing through the air and look at the motion of > the air near the center. Hey, I think my mental model has improved, because I never before saw the flaw in the above. I've heard that irplanes fly by "ground effect" whenever they are within a wingspan or less above the earth. The "2D world" model is a description of ground-effect flight. Therefor it applies whenever the wingspan of an aircraft is lots longer than the altitude of flight. To make an airplane "obey" the 2D model, simply make its wingspan longer than the altitude of flight. Simple, no? And conversely, if you wish to make the 2D model fail, simply make the wingspan far smaller than the altitude of flight, and the craft will be flying only because it is flinging vortex tubes downwards, vortex tubes which constrain a particular mass of air. ((((((((((((((((((((( ( ( ( ( (O) ) ) ) ) ))))))))))))))))))))) William J. Beaty SCIENCE HOBBYIST website billbeskimo.com http://amasci.com EE/programmer/sci-exhibits science projects, tesla, weird science Seattle, WA 206-762-3818 freenrg-L taoshum-L vortex-L webhead-L From owner-phys-l@LISTS.NAU.EDU Mon Jan 18 12:41:06 1999 Received: from mailgate.nau.edu (mailgate.nau.edu [134.114.96.19]) by mx1.eskimo.com (8.9.1a/8.8.8) with ESMTP id MAA29892; Mon, 18 Jan 1999 12:41:04 -0800 Received: from mailgate ([134.114.96.19]) by mailgate.nau.edu (PMDF V5.2-29 #31141) with ESMTP id <0F5R00DG5W3Y8D@mailgate.nau.edu>; Mon, 18 Jan 1999 13:40:54 -0700 (MST) Date: Mon, 18 Jan 1999 14:38:14 -0600 From: Phil Parker Subject: Re: Airfoil lift, new article Sender: "phys-l@lists.nau.edu: Forum for Physics Educators" To: PHYS-L@LISTS.NAU.EDU Reply-to: "phys-l@lists.nau.edu: Forum for Physics Educators" Message-id: <0F5R00DG8W3Y8D@mailgate.nau.edu> Status: RO X-Status: >Date: Thu, 14 Jan 1999 16:01:58 -0500 >From: "Michael N. Monce" > > And I used to think I could generally teach anybody some physics :) > It's the same old problem: one has to *want* to learn before one can learn, and an important part of wanting to learn is being willing to face the possibility that what one thinks one surely knows *might* be wrong. Bill gave two typical implementations of the lack of want. One reason I like this list is that it helps me maintain that honest want. I think I have learned somewhat more than I've unlearned here in the last few years, but sometimes I'm not so sanguine. --------------------------------------------- Phil Parker pparker@twsuvm.uc.twsu.edu Random quote for this second: Honk if you hate bumper stickers that say "Honk if ...." From billbeskimo.com Mon Feb 1 03:05:13 1999 Date: Mon, 1 Feb 1999 03:05:08 -0800 (PST) From: William Beaty Reply-To: William Beaty To: list physics teaching cc: scott@aa.washington.edu, dfa@fnal.gov Subject: a drag equation based on "disk balloons" Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: To PHYS-L aerodynamics people: I used my crude "disk balloons" analogy of airplane flight to predict the induced drag upon an aircraft to be: Drag force = 8 * (M * g)^2 / [ pi * span^2 * V^2 * density ] M * g being aircraft weight, V is velocity of horizontal flight, and "density" is the density of air. How does this match conventional calculations of induced drag? The only reference I have at hand is THEORY OF FLIGHT, in which I don't immediately find a treatment of induced drag. If anyone here has offhand knowledge of this issue, can they tell me if my above equation is totally bogus? Does induced drag increase as aircraft weight^2, and decrease as 1/V^2, and as 1/span^2? The above equation comes from the simplified physical model described here: http://amasci.com/wing/rotbal.txt (Note: I assume that the disk balloons contain "solid air", or that there are membranes within the balloons which force the enclosed air to rotate like a solid disk.) ((((((((((((((((((((( ( ( ( ( (O) ) ) ) ) ))))))))))))))))))))) William J. Beaty SCIENCE HOBBYIST website billbeskimo.com http://amasci.com EE/programmer/sci-exhibits science projects, tesla, weird science Seattle, WA 206-762-3818 freenrg-L taoshum-L vortex-L webhead-L From owner-phys-l@LISTS.NAU.EDU Tue Feb 2 07:42:10 1999 Received: from mailgate.nau.edu (mailgate.nau.edu [134.114.96.19]) by mx1.eskimo.com (8.9.1a/8.8.8) with ESMTP id HAA09114; Tue, 2 Feb 1999 07:42:04 -0800 Received: from mailgate ([134.114.96.19]) by mailgate.nau.edu (PMDF V5.2-29 #31141) with ESMTP id <0F6J001T79F493@mailgate.nau.edu>; Tue, 2 Feb 1999 08:41:53 -0700 (MST) Date: Tue, 02 Feb 1999 07:42:26 -0800 From: Roger Freedman Subject: Re: a drag equation based on "disk balloons" In-reply-to: <199902020857.AAA11541@spacecase.physics.ucsb.edu> Sender: "phys-l@lists.nau.edu: Forum for Physics Educators" To: PHYS-L@LISTS.NAU.EDU Reply-to: "phys-l@lists.nau.edu: Forum for Physics Educators" Message-id: <0F6J0019VA9F93@mailgate.nau.edu> Status: RO X-Status: William Beaty writes: >I used my crude "disk balloons" analogy of airplane flight to predict the >induced drag upon an aircraft to be: > > Drag force = 8 * (M * g)^2 / [ pi * span^2 * V^2 * density ] > >M * g being aircraft weight, V is velocity of horizontal flight, and >"density" is the density of air. > >How does this match conventional calculations of induced drag? The only >reference I have at hand is THEORY OF FLIGHT, in which I don't immediately >find a treatment of induced drag. If anyone here has offhand knowledge of >this issue, can they tell me if my above equation is totally bogus? Does >induced drag increase as aircraft weight^2, and decrease as 1/V^2, and as >1/span^2? The above equation is quite close to the mark. The standard expression for the induced drag in level flight is D = (weight)^2/[pi * e * (span)^2 * q], where q is the dynamic pressure (= 1/2 * density * speed^2) measured far in front of the wing (i. e. in undisturbed airflow) and e is an "efficiency factor" (no greater than 1) which depends on the three-dimensional shape of the wing. The smaller the value of e, the more induced drag is produced for a given situation. That's about all I know on the subject, so for further research I recommend the following references, which I also recommended in a post on Jan. 17: Ashley, Holt. Engineering Analysis of Flight Vehicles. Addison-Wesley, 1974. Reprinted by Dover Publications, 1992. Hubin. W. N. The Science of Flight: Pilot-Oriented Aerodynamics. Iowa State University Press, 1992. +++++++++++++++++++++++++++++++++++++++++++++++++++++++ Roger A. Freedman Department of Physics and College of Creative Studies University of California, Santa Barbara Mailing address: Department of Physics UCSB Santa Barbara CA 93106-9530 E-mail: airboy@physics.ucsb.edu WWW: http://www.physics.ucsb.edu/~airboy/ Voice: (805) 893-2345 FAX: (805) 893-3307 Voicemail: (800) 344-3147 x4322