Wikipedia

User:Mr swordfish/List of works with the equal transit-time fallacy

< User:Mr swordfish
An illustration of the equal transit-time fallacy (from NASA).

This is a partial list of works with the equal transit-time fallacy presented as truth.[1][2][3] The equal transit-time fallacy is a common misconception of how a wing creates lift.[4][5] The misconception is based on the fallacy of an equality constraint on the transit times of air parcels traveling above and below a cambered airfoil, i.e. that the air traveling over the top of a wing must traverse the wing in the same amount of time as the air traveling under the wing. [6][7][8]

There is no physical principle that requires the air to traverse the wing in the same amount of time, and experimental results show that this assumption is false.[9][10] Although the Kutta condition requires the upper and lower surface velocities to be equal at the trailing edge,[11] circulation associated with lift requires the transit times to be different,[12] with the parcel on the longer route arriving earlier.[13][14] The transit time is equal only in the special case where the airfoil is producing no lift.[15]

Although currently accepted theories of aerodynamic lift were developed as early as 1907,[16][17] the incorrect equal transit time fallacy became popularized later, especially after World War II.[18] Despite the obvious problems with this "theory" in relation to lift of flat plates,[19] symmetric airfoils,[12] inverted flight,[20] or sails,[21] this incorrect explanation is often repeated, even in recent works, and in otherwise reliable sources.[4]

Books edit

In reverse order of first publication:

2000s edit

2009 edit

  • Resh, Vincent H. (2009). Encyclopedia of Insects (second ed.). Academic Press. p. 366. ISBN 0-12-374144-0. For the flow to separate under the wing, but meet again at the trailing edge, the upper stream must travel faster than the lower because it travels a greater distance.
  • Sundem, Garth (2009). The Geeks' Guide to World Domination. New York: Three Rivers Press. p. 222. ISBN 0307450341. Due to the curved shape of the wing's top, the air above must travel farther than does the air below to rejoin at the same point at the back of the wing. As this airstream has to rejoin simultaneously (to avoid leaving a vacuum), the air on top has to travel a bit faster than the air below.

2008 edit

  • Henderson, Carrol (2008). Birds in Flight. Stillwater: Voyageur Press. p. 58. ISBN 0760333920. The convex top of the wing presents a longer path for the air to pass over in the same amount of time…
  • Knutzen, Kathleen; Hamill, Joseph (2008). Biomechanical Basis of Human Movement. Hagerstown, MD: Lippincott Williams & Wilkins. p. 380. ISBN 0-7817-9128-6. Molecules of air A and B move from A1, to A2 and B1, to B2 respectively in the same amount of time, but the distance from A1, to A2 is greater…{{cite book}}: CS1 maint: multiple names: authors list (link)

2007 edit

  • Hunter, Hugh (2007). Digital Overdrive: Automotive & Transportation Technology. Burlington, ON (Canada): Eastwood Multimedia. p. 183. ISBN 1897507070. Air speed over the top must be faster than under the bottom in order to meet at the trailing edge.
  • Kessler, Colleen (2007). Super Smart: Science. Prufrock Press. pp. 10–11. ISBN 1593632134. OCLC 85833306. …whether the air goes over or under the wing, it arrives at the other side of the wing at the same instant.
  • Narinder, Kumar (2007). Comprehensive Physics XI. New Delhi: Laxmi Publications. p. 1072. ISBN 8131801969. The air splits up at the leading edge A and meets at the trailing edge B simultaneously. The air molecules…travel a longer distance…in the same time.
  • Miller, Sara Swan (2007). Feet (All Kinds of). Marshall Cavendish Children's Books. p. 32. ISBN 0-7614-2520-9. However, the air flowing over the top reaches the back of the wing at the same time as air moving under the wing.
  • Rogers, Denny (2007). The Illustrated Birds of Prey: Red-Tailed Hawk, American Kestrel & Peregrine Falcon: The Ultimate Reference Guide for Bird Lovers, Artists, and Woodcarvers (The Denny Rogers Visual Reference series). Fox Chapel Publishing. p. 3. ISBN 1-56523-310-7. OCLC 105054698. The upper air current must travel farther and faster to join the underwing airstream as it meets behind the wing.
  • VanCleave, Janice Pratt (2007). Janice VanCleave's Engineering for Every Kid: Easy Activities That Make Learning Science Fun. Science for Every Kid Series. San Francisco: Jossey-Bass. pp. 20–21. ISBN 0-471-47182-8. …airstreams meet at the same time behind the wing.

2006 edit

  • Colton, Raymond H.; Rebecca Leonard; Casper, Janina K. (2006). Understanding voice problems: A physiological perspective for diagnosis and treatment. Hagerstwon, MD: Lippincott Williams & Wilkins. p. 388. ISBN 0-7817-4239-0. This curvature on the upper wing surface means that the air molecules passing over the top of the wing have a greater distance to travel to pass over the wing than those molecules that pass under the wing.{{cite book}}: CS1 maint: multiple names: authors list (link)
  • Griffiths, Iwan W. (2006). Principles of biomechanics & motion analysis. Hagerstown, MD: Lippincott Williams & Wilkins. p. 272. ISBN 0-7817-5231-0. OCLC 61204449. The air molecules travel faster over the upper surface of the airfoil because they have to complete a longer distance in the same time.
  • Mccoy, Mickey (2006). Airline Wings as a Career. Trafford Publishing. p. 26. ISBN 1412062799. OCLC 64669922. The air moving over the top of the curved wing surface must travel farther and faster to reach the back of the wing at the same time as the air on the flat underside of the wing.

2005 edit

  • Busby, John R. (2005). Drawing Birds. Portland, Or: Timber Press. pp. 102, 104. ISBN 0-88192-697-3. Because the air travelling past the wing has further to go along the curved upper surface in the same time, it has to travel faster;
  • Dingle, Lloyd; Tooley, Michael H. (2005). Aircraft engineering principles. Boston: Elsevier Butterworth-Heinemann. p. 548. ISBN 0-7506-5015-X. The air travelling over the cambered top surface of the aerofoil shown in Figure 7.6, which is split as it passes around the aerofoil, will speed up, because it must reach the trailing edge of the aerofoil at the same time as the air that flows underneath the section.{{cite book}}: CS1 maint: multiple names: authors list (link)
  • Halliday, John (2005). Flying through Midnight. New York: Simon and Schuster. p. 139. ISBN 0743281993. Airflow at the wing's leading edge separates into top and bottom airflows that rush to meet each other at the back of the wing.
  • Mayer, Richard (2005). The Cambridge Handbook of Multimedia Learning. Cambridge: Cambridge University Press. p. 188. ISBN 0521838738. The air flowing over the top of the wing has a longer distance to travel in the same amount of time.
  • McGinnis, Peter Merton (2005). Biomechanics of sport and exercise. Champaign, IL: Human Kinetics. p. 206. ISBN 0-7360-5101-5. If the flow is laminar, each molecule on top reaches the trailing edge of the airfoil at the same time as the corresponding molecule on the bottom.
  • Peeters, Hans J.; Pam Peeters; (2005). Raptors of California. Berkeley: University of California Press. p. 25. ISBN 0-520-24200-9. …air molecules must pass over a longer distance crossing the upper surface than they must over the underside before reaching the wing's trailing edge simultaneously.{{cite book}}: CS1 maint: extra punctuation (link) CS1 maint: multiple names: authors list (link)
  • Riley, Peter (2005). Forces and Movement. Mankato: Smart Apple Media. p. 29. ISBN 158340712X. the air rushing over the curved upper surface has farther to travel than the air rushing along the flat surface underneath but has to cover the distance in the same time.
  • Robertson, William (2005). "Chapter 2 : Figure 2.24". Air, water, and weather. Arlington, Va: NSTA Press. p. 33. ISBN 0-87355-238-5. The air moving on the top has to travel a greater distance in the same amount of time.
  • Vecchione, Glen (2005). 100 Amazing First-Prize Science Fair Projects. New York: Sterling. p. 196. ISBN 1402719116. Air flowing over the top has a greater distance to travel in the same time; that's why it flows faster.

2004 edit

  • Conger, David (2004). Physics Modeling for Game Programmers. City: Muska & Lipman/Premier-Trade. p. 448. ISBN 1592000932. The air above the wing must move across the wing in the same amount of time as the air below the wing.
  • Gardner, Joseph Lawrence; McPherson, Stephanie Sammartino (2003). Wilbur & Orville Wright: Taking Flight (Trailblazers Biographies). Minneapolis: Carolrhoda Books. p. 34. ISBN 1-57505-443-4. Sir George Cayley … explained … the other stream, following the upper curve of the wing, had a slightly longer distance to travel. In order to keep up with the lower airstream, it moved faster.{{cite book}}: CS1 maint: multiple names: authors list (link)
  • Clancy, Tom (2004). "Airpower 101 : Lift". Fighter Wing: A Guided Tour of an Air Force Combat Wing. New York: Berkley. p. 3. ISBN 0-425-19370-5. if both air streams are to arrive at the trailing edge at the same time, then the air stream above the wing must have a higher speed.
  • Humphrey, Jay (2004). An Introduction to Biomechanics. Berlin: Springer. p. 425. ISBN 0387402497. Consequently, the air must move faster over the top surface (to reach the trailing edge at the same time as the air traveling along the bottom surface).
  • Jones, Philip (2004). Boomerang. Kent Town: Wakefield Press. p. 31. ISBN 1862543828. Bernoulli's Principle dictates that both parcels of air must arrive on the other side of the airfoil or wing at the same time.
  • Love, Alexander; D. Bailin; Bailin, David; Love A. (2004). Cosmology in gauge field theory and string theory. Bristol: Institute of Physics Pub. p. 48. ISBN 0-7503-0492-8. The upper path is longer and the air therefore has to travel faster to keep up with the other half which has taken the low road.{{cite book}}: CS1 maint: multiple names: authors list (link)
  • Prothero, Donald (2004). Sedimentary Geology. San Francisco: W.H. Freeman. p. 35. ISBN 0716739054. If the two masses of air meet after the airfoil passes through them, the air deflected along the top must move faster to keep up with the air flowing along the bottom, and the two masses of air come together in the same place.

2003 edit

  • Anderson, Bryon D. (2003). The Physics of Sailing Explained. Dobbs Ferry, N.Y: Sheridan House. p. 45. ISBN 1-57409-170-0. Because of the pressure of the air from in front of and around the wing, the flow of air over the top will have a larger speed in order to try to keep pace with the air moving past the wing.
  • Dennis, Johnnie (2003). The Complete Idiot's Guide to Physics: By Johnnie T. Dennis. (Complete Idiot's Guide to). Indianapolis: Alpha Books. p. 133. ISBN 159257081X. I exaggerated those paths to emphasize to you that both paths are traveled by air particles in the same amount of time.
  • Dooley, John W.; Sexton, Matthew G.; Nelson, Steven O. (2003). AP Success: Physics B/C, 4th edition. Princeton, N.J: Peterson's. p. 87. ISBN 0-7689-1265-2. Since the time to travel over/under the wing is the same, the particles traveling over the top of the wing have a larger velocity.{{cite book}}: CS1 maint: multiple names: authors list (link)
  • Eichenberger, Jerry A. (2003). Your Pilot's License. McGraw-Hill Professional. p. 82. ISBN 0-07-140285-3. OCLC 50653696 52347497. For reasons determined by the laws of physics, the molecules that go over the top and those that go under the lower surface of the wing must remain opposite each other as they make their respective trips along both surfaces of the wing. {{cite book}}: Check |oclc= value (help)
  • Fox, Mark (2003). Discovering Science. Melbourne, Australia: Curriculum Corporation. p. 26. ISBN 1876973781. If the wing is curved, the air on top has a lot further to go than the air below. The top air stretches to catch up to the bottom layer.
  • Hidalgo, Maria (2003). Air. Let's Investigate Science. Mankato: Creative Education. p. 4. ISBN 158341231X. The assumption is that the air on top arrives at the back of the wing at the same time as the air underneath.
  • Hise, Phaedra (2003). Pilot Error: The Anatomy of a Plane Crash. Washington: Potomac Books. p. 30. ISBN 1-57488-524-3. As air rushes along the top, it has farther to travel than the air running along the bottom. This makes it run a little faster to meet up with the air at the trailing edge of the wing.
  • Maglischo, Ernest W. (2003). Swimming fastest. Champaign, IL: Human Kinetics. p. 11. ISBN 0-7360-3180-4. Because the upper surface of the wing is rounded, and thus longer than the underside, the velocity of the air flowing over the top must accelerate to reach the back side of the wing at the same time as the air flowing underneath.
  • Parks, Lee (2003). Total Control: High-Performance Street Riding Techniques. Osceola, WI: Motorbooks International. p. 111. ISBN 0-7603-1403-9. Because the air making its way around the motorcycle has a longer distance to travel than the surrounding air, it must accelerate to keep up.
  • Raynes, Sylvain (2003). The Analysis of Structured Securities. Oxford Oxfordshire: Oxford University Press. pp. 315, 439. ISBN 0195152735. The central idea is that in order for the fluid above the airfoil to reach the back of the airfoil (the trailing edge) at the same time as the fluid below it, it has no choice but to accelerate since, in order to do so,* it must travel a greater distance in the same time interval. *This is not quite the whole story, but it will do for our purposes
  • Boy Scouts of America (2003). Webelos Handbook. Irving, TX: Boy Scouts of America. p. 404. ISBN 0-8395-3452-3. An airplane wing is curved on top and flat on bottom. Because of that, air travels a longer distance over the wing in the same amount of time that air moves under the wing, which is a shorter distance.
  • FAA (2003). PILOT’S HANDBOOK of Aeronautical Knowledge. FAA. pp. 2–5. ...the air molecules moving over the upper surface would be forced to move faster than would the molecules moving along the bottom of the airfoil, since the upper molecules must travel a greater distance due to the curvature of the upper surface. This increased velocity reduces the pressure above the airfoil.

2001-2002 edit

  • Fleisher, Paul (2002). Liquids and Gases. Minneapolis: Lerner Publications. p. 41. ISBN 0822529882. Because the airfoil is curved on top, the air passing over the wing has a longer distance to travel in the same amount of time.
  • Marino, Emiliano (2001). Sailmaker's Apprentice. Camden, Maine: International Marine/Ragged Mountain Press. p. 114. doi:10.1036/0071376429. ISBN 0-07-137642-9. …such that air flowing over the curved surface must speed up in order to make that detour and still keep up with air passing below the brolly
  • Trefil, James (2001). "Aircraft". Encyclopedia of Science and Technology. New York: Routledge. p. 19. ISBN 0415937248. Thus, the air that passes over the top of the wing has to travel a greater distance than the air passing under the bottom in the same amount of time.

2000 edit

  • Illman, Paul (2000). The Pilot's Handbook of Aeronautical Knowledge. New York: McGraw-Hill. pp. 15–16. ISBN 0071345191. When air flows along the upper wing surface, it travels a greater distance in the same period of time as the airflow along the lower wing surface.
  • Ed Sobey (2000). Fantastic Flying Fun with Science. New York: McGraw-Hill. p. 14. ISBN 0-07-134800-X. The high speed resulted from air having to travel the longer surface (the bulging top) in the same time as did air traveling the shorter distance underneath.
  • Vasilyev, Mikhail (2000). Matter and Man. Kirill Stanyukovich, Translated by Vladimir Talmy. Seattle: University Press of the Pacific. p. 38. ISBN 0898750512. The part of the stream passing over the wing must move faster than the part passing below so as to cover the distance from the leading to the trailing edge in the same time.
  • World Book, Inc. Staff (2000). "Helicopter : How Helicopters Fly". The World Book Encyclopedia. Vol. 9. Chicago, Ill: World Book. p. 171. ISBN 0-7166-0100-1. In the same amount of time, the air flowing over the curved upper surface travels farther than the air flowing under the wing.

1990s edit

1995-1999 edit

  • Dispezio, Michael (1999). Scott Foresman - Addison Wesley Science Insights : Exploring Living Things. New Jersey: Pearson Education. ISBN 0201332817. OCLC 39783716. The air above the wing must move faster to cover this longer distance in the same amount of time.[22]
  • Webster, John G. (1999). Wiley encyclopedia of electrical and electronics engineering. New York: John Wiley. p. 304. ISBN 0-471-13946-7. Air flowing over the top surface of the wing must reach the trailing edge of the wing in the same time as the air flowing under the wing.
  • Gleim, Irvin N. (2005) [1998]. Learn to fly and become a pilot. Gleim Pub. p. 13. ISBN 1581943814. As the air on top of the wing travels a greater distance in the same amount of time...
  • Love, Michael (1998). Flight Maneuvers. New York: McGraw-Hill. p. 4. ISBN 0070388652. According to Bernoulli's principle, if two air molecules start at the leading edge of the wing, and one flows over the top while the other flows under the wing, they will both reach the trailing edge of the wing at the same time.
  • Bishop, Nic (1997). The Secrets of Animal Flight. Boston: Houghton Mifflin. p. 7. ISBN 0395778484. Air passing over the curved top of an airfoil has to travel farther than the air underneath, so it moves faster to keep up with the air moving under the wing.
  • Kelly, Emery J.; Trombley, Richard (1997). Paper airplanes: models to build and fly. Minneapolis: Lerner Publications. p. 9. ISBN 0-8225-2401-5. The principles of aerodynamics require air moving over the wing to arrive at the trailing edge at the same time as air moving under the wing.
  • Maton, Anthea (1999) [1997]. Prentice Hall Exploring Physical Science (Teacher's ed.). Englewood Cliffs: Prentice Hall. p. 363. ISBN 0134358724. Recalling what you know about speed, what must be true if the air above the wing travels a longer distance in the same amount of time?
  • Allen, Merrill (1996). "General Aviation Accident Investigation". Forensic Aspects of Vision and Highway Safety. Tucson: Lawyers & Judges Pub. Co. p. 21. ISBN 0913875244. In this example, the left aileron has created an area of the wing where there is a greater surface area over which the air must travel to reach the trailing edge at the same time as the air on the other side of the wing.
  • Rod Machado (1996). "Chapter 2 - Aerodynamics: The Wing is the Thing". In Titterington, Diane; Weiss, Brian L. (eds.). Rod Machado's Private Pilot Handbook: The Ultimate Private Pilot Book. Aviation Speakers Bureau. pp. B10. ISBN 0-9631229-9-1. OCLC 36458474. If the wind above is to reach the trailing edge at nearly the same time as the wind below (science and experiments say that it does), it must speed up…
  • Koury, Joanne (1996). Aquatic Therapy Programming. Champaign: Human Kinetics. p. 30. ISBN 0873229711. ...it moves more rapidly over the top or curved part of the wing so that it meets at the same time with the air moving over the shorter underside of the wing.
  • Johnson, Mark (1995). "RACING BASICS". Univ of Iowa. Looking at the top of the foil in figure 1, you can see an air particle will have further to travel than his little twin particle going over the bottom. These two want to reach the back of the sail at the same time, so what gives? The particle over the top needs to travel faster.

1990-1995 edit

  • Cunningham, James; Herr, Norman (1994). Hands-on physics activities with real-life applications: easy-to-use labs and demonstrations for grade 8-12. Jossey-Bass. p. 252. ISBN 0-87628-845-X. The relative speed of air moving over the wing is greater than the speed of air moving under the wing because it must travel a greater distance in the same length of time.
  • Szurovy, Geza ; Goulian, Mike (1994). Basic Aerobatics. Blue Ridge Summit: Tab Books. p. 69. ISBN 0070629269. The greater curvature of the wing's top surface provides a longer distance for the air particles to travel in the same time that particles travel along the wing's underside.{{cite book}}: CS1 maint: multiple names: authors list (link)
  • Wood, Robert (1994). What?: experiments for the young scientist. Blue Ridge Summit: Tab Books. ISBN 0070516367. The air over the top must arrive at the back of the wing at the same time as the air moving under the wing.
  • Jennings, Terry (1993). Planes, Gliders, Helicopters : And Other Flying Machines. London: Kingfisher. p. 10. ISBN 1856978699. The air flowing over the airfoil has to travel farther than the air flowing below, and it has to speed up to keep up.
  • Chase, Carl (1991). An Introduction to Nautical Science. New York: Norton. p. 45. ISBN 9780393028508. Since both the air above and the air below pass the hand in the same amount of time, the upper air must move faster in order to cover a greater distance.
  • Sternstein, Ed (1991). From Takeoff to Landing. New York: Pocket Books. p. 72. ISBN 0671722174. Yet both molecules are going to meet at the trailing edge of the wing at the same time — a property of nature — which means they are moving at two different speeds.
  • Burger, Robert (1990). Cooling Tower Technology. Lilburn: Fairmont Press. p. 82. ISBN 0131732463. ...the air flowing over the wing is divided by the leading edge and the particles of air at the leading edge so split, must rejoin at the trailing edge of the wing at the same time.

Pre 1990 edit

1980s edit

  • Collins, John (1989). The Gliding Flight : 20 excellent fold and fly paper airplanes. Berkeley: Ten Speed Press. p. 12. ISBN 9780898153132. In order to finish even with the runner below, he must run faster along ... The runner (or air) going over the wing has to go faster than the runner below.
  • Wheye, Darryl; Ehrlich, Paul R.; Dobkin, David S. (1988). The birder's handbook: A field guide to the natural history of North American birds: Including all species that regularly breed north of Mexico. New York: Simon & Schuster. p. 161. ISBN 0-671-65989-8. You can think of the upper air thinning out as it races to cover a greater distance in the same time as the air going under the wing.{{cite book}}: CS1 maint: multiple names: authors list (link)
  • Boy Scouts of America (1987). Webelos Scout book. Irving, Texas: Boy Scouts of America. p. 285. ISBN 0-8395-3235-0. The plane flies because the air travels a longer distance over the wings in the same time as the air under the wings.
  • Perrins, Christopher (1987). New Generation Guide to the Birds of Britain and Europe. Austin: University of Texas Press. p. 36. ISBN 0292755325. ...the air which is deflected over the upper surface has to travel faster than the air beneath the wing, because it has further to travel in the same time.
  • Halpern, Richard (1983). Physical science (Barnes & Noble outline series). New York: Barnes & Noble. p. 37. ISBN 0-06-460195-1. Air flowing over the top of the wing has to travel farther, in the same time…
  • Taylor, Glenn (1982). Windsurfing. New York: McGraw-Hill. p. 61. ISBN 0070631581. The air that goes over the top of the wing must travel slightly faster than the air which goes underneath, since it must cover a greater distance in the same length of time, ...
  • Baxter, Gordon (1981). How to Fly: for People Who Are Not Sure They Want to. New York: Summit Books. p. 181. ISBN 0671448013. As the wing is thrust forward with enough airspeed, the airflow passing over the upper cambered surface has farther to go than the air moving straight along the flat bottom surface, so it must move faster to meet at the trailing edge.
  • Boyne, Walter J. (1980). Flying, an introduction to flight, airplanes, and aviation careers. Englewood Cliffs, NJ: Prentice-Hall. p. 35. ISBN 0-13-322644-1. Air flowing over the top surface of the wing must reach the trailing edge of the wing in the same amount of time as the air flowing under the wing.

1970s edit

  • Federal Aviation Administration (1979). How to Become a Pilot. New York: Sterling. p. 4. ISBN 0806983868. When air flows along the upper wing surface it travels a greater distance in the same period of time than the airflow along the lower wing surface.
  • Harrison, Colin James Oliver; Cameron, Ad; Perrins, Christopher M. (1979). Birds--their life, their ways, their world. Pleasantville, N.Y: Reader's Digest Association. ISBN 0-89577-065-2. OCLC 12407468 5352749. In order to travel to the rear of the wing at more or less the same time as the air on the underside, the air on the upper surface must travel faster than the air underneath the wing. {{cite book}}: Check |oclc= value (help)CS1 maint: multiple names: authors list (link)
  • Federal Aviation Administration, Flight Standards Service (1976). Advisory Circular 65-15A: Airframe and Powerplant Mechanics Powerplant Handbook. Washington D.C.: United States Government Printing Office. p. 30. ISBN 0160051452. Air flowing over the top surface of the wing must reach the trailing edge of the wing in the same amount of time as the air flowing under the wing.
  • Jensen, Jens Trygve (1976). Physics for the Health Professions. Philadelphia: Lippincott. p. 91. ISBN 0397541708. Air currents flowing past the wing will separate and rejoin behind the wing. In order for the divided air stream to converge at the back of the wing, the top stream must have a higher linear velocity than the lower stream...
  • Papallo, George (1976). What Makes It Work. New York: Fireside. p. 76. ISBN 0668039639. For these two bodies of air to be re-united at the back of the wing, the upper air has to move faster and so create a deficiency of air known as a low pressure zone.
  • Fuller, R. Buckminster (1975). Synergetics; explorations in the geometry of thinking. New York: Macmillan. p. 350. ISBN 0-02-541870-X. This is simply because, as Bernoulli showed, it is longer for the air to go around the top of the foil than under the foil, and so the same amount of air in the same amount of time had to be stretched thinner, ergo vacuously, over the top.
  • Wood, Elizabeth A. (1975). Science from your airplane window. New York: Dover Publications. p. 4. ISBN 0-486-23205-0. One way in which this difference in pressure is achieved is by shaping the wing so that the air that goes over the top has to go farther… At the trailing edge of the wing the top air must come together again with the bottom air. The greater velocity of the air going over the top has resulted in a lifting force.
  • Drummond, A. H. (1974). Sailboarding : a beginner's guide to boardboat sailing. Garden City: Doubleday. p. 24. ISBN 0385004532. But the air going above the wing must travel a greater distance along the curve than the air streaming over the flat surface along the bottom.... This is easy to see; since the top air must go a greater distance in the same time, it must go faster.
  • Stever, H. Guyford (1973). Flight. Time-Life Books. p. 54. …air molecules moving over the curved upper surface would have farther to go, and would have to move faster to keep pace with molecules moving along the flatter bottom of the wing.
  • Friedl, Alfred (1972). Teaching Science to Children: The Inquiry Approach Applied. New York: Random House. p. 190. ISBN 0394313402. Therefore, the air above has to travel faster to get to the end of the wing at the same time as the air below the wing.
  • Simon, Seymour (1971). The Paper Airplane Book. New York: Viking Press. p. 15. ISBN 0670537977. The air moving over the top reaches the back of the wing at the same time as the air moving across the bottom of the wing.

1960s edit

  • Marks, Robert W. (1969). The new dictionary & handbook of aerospace. New York: Bantam Books. p. 97. ISBN 0275026124. LCCN 79094768. Since the two parts of the air-stream reach the trailing edge of the wing at the same time, the air that flows over the wing must move faster than the air that flows under.
  • Pan American Navigation Service (1968). Flight engineers manual. North Hollywood, Calif. p. 6. LCCN 67030737. Air flowing over the top surface of the wing must reach the trailing edge of the wing in the same amount of time as the air flowing under the wing.{{cite book}}: CS1 maint: location missing publisher (link)
  • Victor, Edward (1965). Science for the elementary school. New York: Macmillan. ISBN 0024228109. LCCN 65010303. OCLC 983725. However, scientific tests show that all of the air flowing over and under the wing reaches the end of the wing at the same time.
  • Caidin, Martin (1963). Flying: principles of flight and the development of aircraft. Holt Library of Science. Vol. 3. Holt, Rinehart and Winston. p. 73. LCCN 63022248. The 'race' between the two streams of air always ends in a tie at the trailing edge of the wing.
  • Navarra, John Gabriel; Zafforoni, Joseph (1963). Today's Basic Science. Harper & Row. LCCN 63007414. The over and under parcels of air start simultaneously from point A (the leading edge). Yet, each arrives at point C (the trailing edge) at the same time.
  • Newman, James Roy (1963). The Harper Encyclopedia of Science (1st ed.). Harper & Row. p. 12. LCCN 62014541. Thus a particle moving over the top of the wing has to travel in the same time a distance greater than that traveled by a similar particle moving under the wing.
  • Air Training Command, United States Air Force & technical staff [of] Aero Publishers, inc. (1960). Fundamentals of Guided Missiles. Aero Publishers. p. 19. LCCN 59014965. Airflow over a wing section wing must reach the trailing edge of the wing in the same amount of time as the air flowing under the wing.{{cite book}}: CS1 maint: multiple names: authors list (link)
  • Bernardo, James V. (1960). Aviation in the Modern World : the dramatic impact upon our lives of aircraft, missiles, and space vehicles. New York: E. Dutton. LCCN 59005824. The airstream that goes over the top travels a bit farther than that which flows under the wing, yet both streams meet at the trailing edge of the airfoil. This means that the air moving over the wing must go faster.

1950s edit

  • Marcus, Abraham (1959). Tomorrow the Moon!: Planes, Missiles, Satellites, Space Travel. Englewood Cliffs, N.J.: Prenctice-Hall. p. 23. LCCN 59008651. Hence, if these two portions of air are to join up, the air flowing over the top of the wing must travel faster than the air flowing along the bottom of the wing.
  • Bavier, Robert Newton (1956). Faster Sailing: New Developments in Yacht Racing. London: N. Kaye. p. 113. LCCN 54006052. The reason for wind velocities being increased (and static pressures decreased) on the leeward side of a sail is the fact that the wind there has to travel further in the same time as the wind on the windward side.
  • Lewellen, John Bryan (1953). Birds and planes: How they fly. New York: Crowell. p. 23. ASIN B0007E69WC. LCCN 52013131. Since the two molecules rejoined each other at the same time, the one that went across the top, having had farther to go, had to travel faster in order to get back at the same time.

1940s edit

  • Norwood, Arthur G. (1949). Private pilot’s handbook. New York: Pittman. p. 8. LCCN 49006987. If the air mass travels a greater distance in the same time it must move faster in order to reach the trailing edge of the wing in time to prevent a vacuum.
  • United States Navy, Bureau of Naval Personnel (1946). Flight Engineering. United States Government Printing Office. p. 40. LCCN 46027976. If two air particles starting at A are to meet again at C—and they DO meet again at the trailing edge—the particle travelling the upper ABC route must travel FASTER to reach C at the same time that a particle travelling the shorter ADC route does.
  • Carlisle, Norman (1945). The Modern Wonder Book of the Air. Philadelphia, Toronto: The John C. Winston Company. p. 47. LCCN 45037891. When two sections of air flow around a wing, they meet again at the wing's trailing edge at the same time…
  • Francis, Devon Earl (1945). Aviation: What everyone should know. Indianapolis, New York: Bobbs-Merrill. p. 22. LCCN 45009859. … giving the air that goes over the wing's top a greater distance to travel. And since that body of air has farther to go in the same length of time, …
  • Dean, Frederick Ernest (1944). Power and speed; the story of the internal combustion engine on land, at sea and in the air. Clymer. p. 103. LCCN 48039837. Moreover, the air passing over the top has covered the increased distance in the same time as the air covering the shorter distance beneath the wing.
  • Railroad Committee for the Study of Transportation (Subcommitte on Air Transport) (1944). Initial study of air transportation. Association of American Railroads. The air above the wing (because of its curved surface) must move a greater distance in the same length of time than the air below the wing...
  • Hall, Charles Gilbert (1942). How a Plane Flies: Are You Sure You Know?. New York: Funk & Wagnalls. p. 51. LCCN 43000367. The difference between that and the well-nigh straight line of the under surface isn't great, but it is enough … as the two flows must meet at the rear edge of the wing at the same time.
  • Manzer, James Gordon (1942). Physical science in the air age: (a teachers' guide). Air-age education series. Prepared with the coöperation of the Civil Aeronautics Administration. Sponsored by the Institute of the Aeronautical Sciences. New York: Macmillan. LCCN 42022003. In the diagram in Figure 20, the airstream is divided at the leading edge into two parts indicated by the lines at A and C. The part marked A flows over the upper camber of the airfoil, and the part marked C flows under the lower surface. These two parts of the airstream meet again at the trailing edge at the point where the streams are marked B and D. {{cite book}}: Cite has empty unknown parameter: |1= (help)
  • Pope, Francis (1941). Elements of Aeronautics. New York: World Book Company. p. 110. LCCN 43018255. but the air that flows over the wing must do so in the same time that is taken by the air that flows under the wing.

1930s edit

  • Burge, Cyril Gordon (1936). Encyclopædia of aviation. London: Pitman. p. 441. LCCN 36002088. … the fact that the air passing over the the hump on the top of the wing will have to speed up more than that flowing beneath the wing, in order to arrive at the trailing edge in the same time.

References edit

  1. ^ "Incorrect Lift Theory". Beginner's Guide to Aeronautics. National Aeronautics and Space Administration. Retrieved 2007-07-07. There are many theories of how lift is generated. Unfortunately, many of the theories found in encyclopedias, on web sites, and even in some textbooks are incorrect...
  2. ^ Knudson, Duane (2003). Fundamentals of Biomechanics. New York: Kluwer Academic/Plenum. pp. 200–201. ISBN 0306474743. Unfortunately, this simplistic explanation is not technically correct. Rather, it's an oversimplification of a complex phenomenon
  3. ^ Babinsky, Holger (2003). "How Do Wings Work" (PDF). Physics Education. Retrieved 2009-07-06. Unfortunately the most widely used explanation of lift is wrong in a number of key points.
  4. ^ a b Technical education research center (2006). Physics That Works. Kendall Hunt Pub Co. ISBN 0787291811. OCLC 61918633. One of the most widely circulated, but incorrect, explanations can be labeled the "Longer Path" theory, or the "Equal Transit Time" theory.
  5. ^ Metcalfe, Peter; Metcalfe, Roger (2004). Excel Senior High School Engineering Studies. Pascal Press. p. 222. ISBN 174125051X. OCLC 224118801 225315292. Erroneous explanations of the Bernoulli principle in relation to lift often state that the airflow is separated at the leading edge of the wing and, under a principle of 'equal transit time', the air travelling over the upper curved surface must travel faster (since it has further to travel) to rejoin the air at the trailing edge. {{cite book}}: Check |oclc= value (help)CS1 maint: multiple names: authors list (link)
  6. ^ Anderson, John (2005). Introduction to Flight. Boston: McGraw-Hill Higher Education. p. 355. ISBN 0072825693. It is then assumed that these two elements must meet up at the trailing edge, and because the running distance over the top surface of the airfoil is longer than that over the bottom surface, the element over the top surface must move faster. This is simply not true
  7. ^ Philpott, D. R.; Barnard, R. D. (1995). Aircraft flight: A description of the physical principles of aircraft flight. Harlow, Essex, England: Longman Scientific & Technical. p. 6. ISBN 0-582-23656-8. It is argued, that the air that takes the longer upper-surface route has to travel faster than that which takes the shorter under-surface route, in order to keep up.{{cite book}}: CS1 maint: multiple names: authors list (link)
  8. ^ Rosa, Aldo (2009). Fundamentals of Renewable Energy Processes, Second Edition. Boston: Academic Press. ISBN 9780123746399. The transit time of air molecules along the path over the airfoil from leading to trailing edge is not the same as that for the flow under the airfoil. Such synchronism, frequently invoked in explanations of wing lift, does, in fact, not occur.
  9. ^ "Although the assumption of equal transit time is wrong and has no basis in known physics, it can be found in books from otherwise reputable publishers..." PHYSICAL PRINCIPLES OF WINGED FLIGHT (c) Copyright 2003, 2008 Gale M. Craig http://www.regenpress.com/aerodynamics.pdf
  10. ^ "... experimental evidence ... disapproves the arguments based on differences in path length." Physics of Flight - reviewed Weltner, Klaus and Ingelman-Sundberg, Martin http://user.uni-frankfurt.de/~weltner/Flight/PHYSIC4.htm
  11. ^ Wegener, Peter (1997). What Makes Airplanes Fly?. Berlin: Springer. pp. 137–138. ISBN 0387947841. ...the streamlines adjacent to the wing, above and below, have identical speeds when they leave the airfoil.
  12. ^ a b Anderson, David (2001). Understanding Flight. New York: McGraw-Hill. pp. 15–16. ISBN 0071363777. The first thing that is wrong is that the principle of equal transit times is not true for a wing with lift. It is true only for a wing without lift.
  13. ^ Vogel, Steven (2003). Comparative Biomechanics. Princeton: Princeton University Press. p. 245. ISBN 0691112975. Were they to arrive at the same time, Bernoulli's principle would predict less lift than we measure and depend upon to keep our aircraft aloft.
  14. ^ Al, Jie-Zhi (2006). Vorticity and Vortex Dynamics. Berlin: Springer. p. 589. ISBN 3540290273. The timelines (Sect.2.1) in Fig.11.2 indicate that the fluid on the upper surface runs even faster than needed for meeting the fluid from the lower surface at the trailing edge.
  15. ^ Flight Physics: Essentials of Aeronautical Disciplines and Technology, with Historical Notes (1st ed.). Springer. 2009. p. 144. ISBN 1-4020-8663-6. In conclusion, there is no possibility that the particles passing above and below the aerofoil would arrive simultaneously at the tail, except for the case that there is no circulation around the section – in this case, there is no lift on it.
  16. ^ Aerodynamics Frederick W. Lanchester 1907
  17. ^ Anderson, John (1997). A History of Aerodynamics and Its Impact on Flying Machines. Cambridge: Cambridge University Press. p. 244. ISBN 0521669553. That man was Frederick W. Lanchester, and he would later formulate the concepts underlying a scientific breakthrough in our understanding and calculation of lift.
  18. ^ Anderson, David (2009). Understanding Flight, Second Edition. City: McGraw-Hill Professional. ISBN 0071626964. Somewhere around World War II this popular assertion began to be taught from grade school to flight training classes.
  19. ^ Nevers, Noel (2004). Fluid Mechanics for Chemical Engineers 3/E with Engineering Subscription Card. City: McGraw-Hill Science/Engineering/Math. p. 284. ISBN 0072976764. In elementary and high-school science classes students are taught that the wing is curved so that the air flow over the top is faster than that over the bottom...but if this were the correct explanation of how lift occurs, then flat-winged aircraft could not fly.
  20. ^ Devlin, Keith (2002). The Millennium Problems. New York: Basic Books. p. 151. ISBN 0465017290. Many books and articles describe this incorrectly in terms of the shape of the wing...since airplanes can fly upside down, this theory is clearly false.
  21. ^ "consider a sail that is nothing but a vertical wing(generating side-force to propel a yacht)... it is obvious that the distance between the stagnation point and the trailing edge is more or less the same on both sides... Thus, the generation of lift does not require different distances around the upper and lower surfaces. Holger Babinski How do wings work? Physics Education Nov 2003 http://iopscience.iop.org/0031-9120/38/6/001/pdf/pe3_6_001.pdf
  22. ^ Bennetta, William J. "On Wings of Ignorance". The Textbook Letter. The Textbook League. Retrieved 2007-07-08.
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