Communiqué Issue # 5 Volume # 1 Some thoughts on A reproduction project The Lockheed Little Dipper Model 33, Vega Model 308, 1943-45 The beginning . . . . John Thorp, young WWII Lockheed engineer, showed his “after-hours” design to Mac Short, head of Special Projects. Mac took the design to Lockheed head Robert Gross, who decided to sell it to the Army as a flying motorcycle. Thorp put in charge of Lockheed Model 33. 2-cylinder 50hp engine ordered from Franklin. Five designer-draftsmen and five prototype mechanics built the ship in three months, June - September 1944 Specifications •Empty weight . . . . . . . . . . . .. 439 lbs •Gross weight . . . . . . . . . . . . . 710 lbs •Useful load . . . . . . . . . . . . . . .271 lbs •Wing loading . . . . . . . . . . . . ..6.83 lbs/sq ft •Power loading . . . . . . . . . . . . 14.2 lb/hp •Limit loads . . . . . . . . . ……… 4.03 pos, 2.37 neg •Span . . . . . . . . . . . . . . . . . . . 25 feet •Chord, constant . . . . . . . . . . . .51 inches •AR. . . . . . . . . . . . . . . . . . . . . .. 5.88 •Airfoil . . . . . . . . . . . . . . . . . . .. .NACA 4415 •Dihedral . . . . . . . . . . . . . . . . . . 6 degrees Still More Specs •1st “all-flying” horizontal tail, Thorp patent assigned to Lockheed. •All-metal. •Tricycle gear. •Hayes wheels, hydraulic brakes. •Steerable nose wheel •Slotted Flaps, 15 and 45 degrees •Side-hinged canopy. •Sensenich 60” wooden prop. Performance •Max speed . . . . . . . . . . . . . . . . ..99 mph •Cruise . . . . . . . . . . . . . . . . . . . . .90 mph •Landing (with power) . . . . . …....3? Mph •Stall, power off, flaps. . . . . . . . . .36 mph •Stall, power on, flaps . . . . . . . . ..29 mph •R/C, sl. . . . . . . . . . . . . . . . . . . . . 800 fpm •Range, VFR reserve . . . . . . . . . .230 miles •Landing run . . . . . . . . . . . . . . . . 125 ft •T/O run . . . . . . . . . . . . . . . . . . . 140 ft Unstoppable Swarms Each Air Trooper carries one infantryman, his weapon, pack and equipment. Thousands fly over enemy lines and attack his strong points from behind. Cheaper and safer than paratroops or glider troops, after taking into account all system costs. First Flight was at the old Newhall CAA emergency field by Vega chief test pilot Bud Martin, September, 1944. Second flight by Lockheed chief of flight testing Milo Burcham. Word got around that it was a sweet ship and everyone found a reason to fly it: LeVier, Salmon, Hawkins, Margwarth. Thorp was planning to fly it
Transcript
CommuniquéIssue # 5 Volume # 1
Some thoughts on A reproduction project
The Lockheed Little Dipper Model 33, Vega Model 308, 1943-45
The beginning . . . . John Thorp, young WWII Lockheed engineer, showed his “after-hours” design to Mac Short, head of Special Projects. Mac took the design to Lockheed head Robert Gross, who decided to sell it to the Army as a flying motorcycle. Thorp put in charge of Lockheed Model 33. 2-cylinder 50hp engine ordered from Franklin.
Five designer-draftsmen and five prototype mechanics built the ship in three months, June -September 1944
Unstoppable Swarms Each Air Trooper carries one infantryman, his weapon, pack and equipment. Thousands fly over enemy lines and attack his strong points from behind. Cheaper and safer than paratroops or glider troops, after taking into account all system costs.
First Flight was at the old Newhall CAA emergency field by Vega chief test pilot Bud Martin, September, 1944. Second flight by Lockheed chief of flight testing Milo Burcham. Word got around that it was a sweet ship and everyone found a reason to fly it: LeVier, Salmon, Hawkins, Margwarth. Thorp was planning to fly it
inside the temporarily empty huge Constitution hangar but management got wind of the plan and nixed it. He regularly took off and flew for 1/2 hour in a 300’circle until he got dizzy.
Pilot Comments All pilots are very enthusiastic about the airplane and its handling qualities . . . The maneuverability and visibility are considered exceptionally good and are best described by one report that ‘It’s more like flying yourself around than flying an airplane.’”
•-Lockheed Report 5519, September 27, 1945
Tony LeVier’sReport “We [ Milo Burcham and Tony] both thought the Little Dipper flew real easy. It could turn on a dime and give you nickel change. Landing was easy and could land easily in a couple hundred ft.”•-----Notes on back of photo of Tony and Milo at Newhall with the Dipper, 1944.
Ease of Flying At Ft. Benning, GA, summer ‘45, a Pfc with no flying experience was given ground instruction; then, with the aid of a walkie-talkie, took off, flew a pattern and landed. Exhilarated, he took off again, flew around, and again landed safely. It was a “great landing,” as in “you could use the plane again.”
Resources for Project The Good News: the original drawings are still in existence, located at LM Aircraft & Logistics Centers, Greenville, South Carolina. The Bad News: The Little Dipper drawings are one of Lockheed Martin’s most closely guarded secrets. “Red-Flagged” by the Legal Department, they are available to no one.
Solution: Reverse Engineering For starters: a good 3-view. R/C Modeler Magazine has 1/4 scale model plans drawn by Richard Tichenor decades ago when Lockheed was not so secretive. Tichenor had access to original drawings. His model plans reviewed and endorsed by John Thorp and Tony LeVier. The 3-view appears quite accurate. They can be cross-checked with 3-views in “Specification.”
Next Resource: Lockheed “Airplane Model Specification” Spec. 2-1104 for Model No. 33-82-01, dated 3-5-45. 48 ages including two photos, 3-view, inboard profile.
This was filed with CAA in anticipation of certification. There are detailed specifications on dimensions and area, structure, powerplant, instrument installation, surface controls, systems, heating and cooling, and so on. Also, rigging data and weight data for each major group.
Good photos. There are a number of close up photos which show the location of structure by rivet lines, as well as other features.
Other Resources: Thorp T-11
After WWII, Thorp completed and certified his original 2-place, the Thorp T-11 Sky Skooter. Safe to assume that many structural features are same as Dipper. Homebuilt versions of T-211 derivative produced until recently. Assembly manuals, etc., show much of this detail. Assembly Manual for T-211 includes clear, if undimensioned drawings.
“Little Dipper Replica” plans.
Emerson Stevens, aero engineer for Curtiss-Wright and Bell, among others, commissioned by Robert Dart to design replica of Little Dipper. The results, 94 vellum pages, have been acquired by a friend and fellow Little Dipper enthusiast, who dreams of commercial exploitation. However, they may be available for my non-commercial use.
Published reports and descriptions. Example: Lockheed’s Lil ’Darlin’, Air Progress, June-July 1963, by John Underwood, who interviewed Thorp: “Basically the fuselage consisted of ten stamped sectional formers and
two pairs of longitudinal stringers running from the firewall to the fifth and sixth stringers . . . The 2024-T3 external skins were formed in halves, the larger panels having external dorsal and ventral flanges. . . .” “The wing was constructed in two units each panel consisting of four stamped ribs supported by a single truss-type spar of channel section with extruded angle caps . . . Reinforcement of the .020 skin was accomplished by riveting four internal stiffeners between each pair of ribs.” John is looking for his notes.
Possible Modifications: Fuel (13 gallon) is right behind pilot’s head, no rollover structure. Fuel gauge recessed in headrest. “Specification” says this is “visible from the cockpit,” on which Willis Hawkins wrote in pencil, “By the eyes in back of your head.” Relocate fuel to wing roots? Should increase safety but adds numerous complexities. Add rollover structure?
Design challenge: Weight control. Original engine (2AL-112, or O-110) weighed 117 lb, plus 7 lbs of accessories, 2 lbs of lubricating system, total 126 lb; prop 10 lb. 49 hp @ 3,000 rpm. I have Franklin 2A-120-A engine, as fitted to Bellanca 7ACA Champs. Weight is 133 lbs with accessories, which includes starter (implies battery), alternator, fuel pump. 60 hp @ 3,200 rpm. 7 lbs gain. Will wish to add lightest, simplest GPS-com, transponder. Pilot seat was simple bucket for parachute. Wing tanks, rollover structure?
A puzzle: The “Pilot Comments” include the following under “Stalling Characteristics: The airplane nose tends to drop quite rapidly and quite far, but usually straight ahead . . . . The stall is not on a par with the best of small airplanes. Due to the exceptionally confident feeling that the pilot acquires in this plane, there is a tendency to
‘horse it around’. . . A very mild type of stall would tend to minimize the danger of . . . stalling in turns or by landing several feet above the runway.” Why the abrupt stall, with a 4415 airfoil?
This photo appears to show round rivet heads every six or so inches, right at the leading edge, or a little above the stagnation point in slow flight. The wing had internal stiffeners riveted chord wise. Could these have disrupted the air flow?
With a little help from my friends Step one: Learn CAD Step two: Produce plans Step three: Show plans to qualified friends Step four: Redo plans (Repeat steps three and four as necessary) Step five: Learn sheet metal forming basics Step six: Begin to produce smaller parts. This Is to maintain morale of troops. Steps seven: Learn welding, forming, drilling, riveting, etc. etc. etc.
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Expanded History of John W. Thorp and the
Lockheed Model 33A Little Dipper
John W. (for Willard) Thorp came from an old California family, in Lockeford, California, founded by his grandfather, Dr. Dean Jewett Locke. The old family home is now a bed & breakfast run by Richard C. Eklund, a former Piper engineer who spent many years with Thorp and now controls the plans for the Thorp T-18 and other Thorp legacies. (http://www. theinnatlockehouse.com/about.html).
Before WWII Thorp was in Oakland, a partner with Rudy Paulic in various designs designated T-1 through T-6. When the war started he went to work for the Vega division, or subsidiary, of Lockheed Aircraft Company, as a preliminary design engineer, and later Assistant Chief of Preliminary Design. In his spare time he was designing a two-place light airplane for postwar production.
Between himself and his boss, Mac Short, the idea arose that this could be converted to a
single-place and used by the army as a kind of flying motorcycle to launch thousands of troops over enemy lines. Calculations showed that if produced in large quantities, this would be much cheaper than training and delivering airborne or glider troops and would have a substantially lower casualty rate.
Key design criteria, therefore, were ease and cheapness of manufacture and extreme ease of flying so that otherwise untrained GIs could learn to fly with reasonable safety. Short showed the project to Robert Gross, Lockheed President, and received a go-ahead. At that time (April, 1944) the War Department had to approve all such projects even if privately funded.
The government approval was obtained, for Lockheed to proceed with design and prototyping at its own expense. In June, 1944, the idea officially became Lockheed Model 33, Vega Project No. 305 (also 308), the Air Trooper.
A preliminary design section, inboard arrangement, is in the files section of this group, and shows a determined-looking soldier aboard the then-open cockpit job. Five designers and five prototyping mechanics were put on the project and the first prototype, NX18935, was ready to fly by late August of 1944.
Specs were essentially the same as they remained: Span 25 feet, length 17 feet 6 inches, wing area 104 square feet, empty weight 425 lb., gross weight 725 lb., useful load 300 lb., payload (13 gal fuel, 3 qt.oil) 217 lb., wing loading 7 lb/sq ft, power loading 14.5 lb/hp, cruise 90 mph, initial rate of climb 900 fpm, range 210 miles, endurance 2 1/4 hour.
Two of the photos in the photos section show the ship in its first configuration with an open cockpit, and a windshield installed in a hinged throw over frame. The gentleman sitting in the cockpit in the latter is Rudy Thoren, chief of engineering flight test at Lockheed. The engine was a specially made Air-Cooled Motors (Franklin) two cylinder, the 2A-4. The cylinders were from larger engines (4A4 or 464), bolted to a specially cast crankcase with a two-throw crankshaft. It displaced 111.3 cu.in. And produced 45 hp @2,650 rpm, weighing 116 pounds without starter or generator. A later version used in the Little Dipper, the 2A120, displaced 17.6 cu.in. and weighed 117.6 pounds. Franklin obtained a type certificate for this engine, No. T.C. 240, which expired in 1950. (In 1971, Franklin produced and certificated an upgraded version of this engine, the 2A-120-A,
Type Certificate E24EA. This engine was used on the Bellanca Champion 7ACA, a Champ with Wittman-type spring gear and other improvements, the cheapest production airplane in the early 70s. Even though the little Franklin in this version produced an alleged 60 hp at 3,200 rpm, it was not enough for the Champ and most of those produced have been re-engined with Continental 65s or 85s. This means that there should be a bunch of these Franklins
stuffed in the back of hangars.)
First flight of the Model 33 Little Dipper took place in September, 1944, with Vega chief test pilot Bud Martin in charge, at the old CAA emergency field at Newhall, California. A few days later it was flown by famous Lockheed test pilot Milo Burcham. Several pictures in the photo section were taken at the Newhall field. Milo Burcham is enjoying himself and in two photos he is sitting on Tony LeViers lap in the single-place ship (see article). These photos show a later style full canopy replacing the open cockpit but still in the same throw over frame. The prop has also been changed to a more tapered design than in the first pictures.
At some time after this, exact date unknown to author, a determined effort was made to sell the airplane to the Army Air Force. A Lockheed or Vega test pilot, whose name is mercifully unknown to me, flew the little plane back to Wright-Patterson field for evaluation.
Being nordo (no radio) he did not have an exact appointment. When he got there he observed to his delight that a large wooden platform had been set up with bleachers on one side, and the
bleachers were filled with people. Seeing his chance to demonstrate the amazing short-field performance of the Little Dipper he landed on the platform with lots of room to spare. Looking over at the spectators he saw, instead of enthusiasm, expressions of horror and gestures to look up. He did and saw a helicopter descending vertically on him, the platform having been erected for one of the first demonstrations of helicopters. He gunned it and made it off the platform in time but was figuratively sent to Siberia for the exploit.
After cooling his heels for some days, he decided to go on to Washington to show the really big brass. As part of the departure formalities at Wright-Pat he was escorted to the tower, where he was shown a long and convoluted taxi route clear across the field to an outlying runway where he could wait until it pleased the powers to give him a green light. A little later the controllers saw the Little Dipper taxiing rather faster than normal on the assigned route and on closer examination determined that it was flying to the assigned runway. This brought the injunction never to come back. The plane went on to Washington and further disgrace by one account (unsubstantiated by me) is that he landed on the lawn of the Pentagon, failing to impress Hap Arnold, and was ordered back to the West Coast where he took up another line of work. (The foregoing is from conversations in 2003 and 2004 with Willis Hawkins, Lockheed Engineer and one-time President of Lockheed California).
By the time of this snafu, the European invasions were old news and the limited range of the Little Dipper made it an unlikely candidate for the planned invasion of Japan. However, thoughts were turning to the postwar boom, and it did not hurt that Lockheed President Robert Gross lived on a ranch in Chatsworth, in the Northwest San Fernando Valley, and had to drive to work every day to Burbank at the Southeast end of the Valley. It was determined to evaluate the airplane as a civilian commuter, renamed the Little Dipper, and to start work on a larger version, the Model 34 Big Dipper (see photo together with a car). One of the pictures in the photo section shows the Little Dipper sitting under a Constellation, like a duckling under a duck, and was obviously taken for the anticipated publicity campaign.
The flight tests of the airplane all went very well. Before the military market was abandoned, a GI with no flying experience (a PFC by some accounts and a sergeant by others) was taught in one day ground school and a part of a morning cockpit check to take off, circle and land, and then to take off, fly around for a while and come back. Back at Burbank, the still-nordo plane was assigned a flight area which was a long triangle bounded on the east by the north-south runway, on the south by the east-west runway, and on the west by Vineland, all with a ceiling of 500 feet agl. Willis Hawkins was asked by John Thorp if he would like to fly it and on being shown the limited area expressed some trepidation. Thorp told him he would have no trouble, but that if he felt he wasn’t getting off soon enough he could pop one notch of flaps and the ship would
jump off. Willis started from the north end of the area, and as soon as he had the throttle full open glanced down to put his hand on the flap handle. When he looked up he was already twenty feet in the air, and indeed had no trouble staying in the constricted area. Thorp could fly for fifteen minutes in a 300-foot radius circle, until he got dizzy.
In September, 1945, Lockheed produced a report of pilot comments on the airplane. The comments were those of Rudy Thoren, Herman Fish, Salmon, Willis Hawkins, and John Marqwarth, then Vega Flight Test Supervisor and later chief Safety officer. All of them were very enthusiastic. One of them commented It’s more like flying yourself around than flying an airplane. Stall was recorded as 36 mph IAS with full flaps, 42 mph IAS with flaps retracted, power-on stall 29 mph IAS with full flaps. The stall was thought to be a little abrupt, however. (This is puzzling because the airfoil is thought to have been a NACA 4415, known for its gentle stall. However, there is no apparent washout, and no stall strips, so it may have been just that the design and construction were so good and symmetrical that the whole wing let go at once.) Maximum level speed was recorded as 98 mph, and cruise was 90 mph. The only adverse comments were the stall, as mentioned, and high friction in the rudder control owing to the direct connection with the nose wheel steering.
It soon became apparent that the postwar boom, at least for single-place jobs, was not going to materialize. Piper (with its Skycycle), Luscombe (with its Model 10), and Lockheed retired from the field leaving it all to Mooney and the Mite.
At that time the Internal Revenue Code did not permit the deduction of research and development expenses. Such expenses were suspended until such time as the project became commercial, at which time they were capitalized and amortized, or was abandoned, at which time they could be deducted. To prove abandonment, it was required that all tangible products be destroyed. Alas, this required the destruction of the Little Dipper and a partially completed second prototype.
John Thorp went on to design and certify the Thorp T-11 Sky Scooter. This became the T-111 and then the T-211, and is still in play as a potential certificated airplane and as a kit. Later he designed the T-18, the first all-metal homebuilt to be built in large numbers, first homebuilt around the world, and holder of other records. Throughout his design career, Thorp was unexcelled in the simplicity of his designs. For this reason he was recruited by Piper to do most of the design of the PA-28 Cherokee line. Many features of the Little Dipper were carried over to later designs of Thorp and others. For example, the Little Dipper had the first all-flying tail or stabilator, which was patented by him and assigned to Lockheed which collected royalties from Piper and others for many years. For another, the Little Dipper only had three ribs in each wing (four if you count a root rib). At one point, a colonel got to horsing around a little at
low altitude and dug in a wingtip. (The pilots report cited above contains the caution that due to the exceptionally confident feeling that the pilot acquires in this airplane, there is a tendency to horse it around and to disregard the usual conservative procedures of safe flying. The wing was crumpled but when the legal department was consulted as to whether it was required to report the accident to the CAA, it was determined that it was not because wingtip damage was not then reportable unless it involved more than three ribs, and that’s all there were. In the photo section the ribs are at the tip, abeam the junction of the flaps and the aileron, and at the landing gear, location marked by a fairing over the attach hardware. It can also be seen that internal stiffeners were installed at what appears to be about 6-inch intervals.
The airplane remains, sixty years later, a remarkable achievement in fun flying, and a good performer. There are several two-cylinder, 60hp engines in production, and there appears to be nothing exotic about the design which would require quantities of unobtainium for building, except the drawings themselves, which are a closely guarded secret. The little beauty is still such stuff as dreams are made on.
John D. Lyon, June 2004
Sources (partial): Conversations with: Willis Hawkins, former President of Lockheed California, who flew it;
George Robertson, who worked with John Thorp building tooling for the T-11 Sky Scooter in the 1940s, and who built his own single-place version, the Sky Skeeter, N100GR, still flying;
Richard Eklund, keeper of the Thorp legacy and the T-18 plans;
and others.
Dick Tichenor, A Lockheed Little Dipper, Radio Control Modeling magazine, June 1984. This article accompanies quarter-scale plans of a Little Dipper model, which are still available from RCM. Tichenor had access to the Lockheed drawings at the time and the plans are believed to be accurate three views in the side and top views, although the airfoil is not to scale.
Rene J. Francillon, Lockheed Aircraft since 1913, Putnam. Badrocke and Gunston, Lockheed Aircraft Cutaways, Osprey, 1998. John Underwood, The Lightplane, Heritage Press 1970.
FAA type certificates, at http://www.airweb.faa.gov/Regulatory_and_Guidance_library/rgMakeModel.nsf/MainFrame?OpenFrameset
That valuable website, www.aerofiles.com.
Lockheed Model 33 “Little Dipper” AKA the “Air Trooper”
By, Ken Adams, Jr. 2004 The Little Dipper was a single seat aircraft which began its life as a personal design of John Thorp in 1942. However, with WWII still ongoing at that time, "sport planes" were not allowed to be built because the metal necessary to build them was required to build war planes.
John actually wanted to make the Little Dipper a two seat aircraft but when Lockheed got involved, his boss (I think Mac Short - don't have my info handy) suggested that it would be a better single seat design and also suggested that it be brought into the Lockheed fold and developed as an "aerial trooper" for the U. S. Army Air Corp. The Army wanted to use the Model 33 which was then renamed the “Air Trooper”, as a flying motorcycle to serve as the mount for a “flying cavalry”.
The prototype Little Dipper (NX18935) had a Franklin 4 cylinder engine that was cut in half to form a two cylinder opposed 4-stroke engine of approximately 50 hp. Franklin went on to produce this engine as the 2cyl 2A4-45, 2A4-49 series with 45hp at 2650rpm, 49hp at 3000rpm and a weight of 116lbs. The airplane was a single seat conventional low wing aircraft with a tricycle landing gear, flip over bubble canopy, and tractor engine. It had a wing span of 25’, a length of 17’ 6 ½”, 6 degrees of dihedral, and a 60” propeller and no electrical system. It had an empty weight of 425 pounds, a gross weight of 700 pounds, and could fly a distance 210 Nautical Miles. The service ceiling was said to be 16,000’ but I have only seen a figure of ~13,000’ used in documentation. Instead of a "conventional tail" John used an "all flying wing" in the place of the horizontal stab and elevator. This flying tail was an invention of John’s and he held the patent on this design. You can see the
“all flying tail” in the homebuilt designs of the Evans VP-I & VP-II, and in Gene Turner’s T-40 series of aircraft. Mr. Turner told me that John Thorp saw his patented “all flying wing” on the T-40 back in 1962 at the annual EAA Fly-in convention and seemed to be pleased that it was being used. This fly in event was also the same year that Pete Bower brought his “Fly Baby” design to the meeting and won the EAA sponsored aircraft design contest.
After the Army Air Corp decided not to pursue the “Air Trooper” (long story), Lockheed decided to make this plane the "every man's plane" and sell it to the civilian market. But the market for small planes never materialized due to the large number of surplus military training aircraft available at very low prices after the end of the war. The Little Dipper (Lockheed Model L-33) and an unfinished second craft were scrapped 10 years after the prototype testing stage was completed and this ship was lost to the history books.
RRaarree OOppppoorrttuunniittyyThe following is an opinion. John has presented the Design Group with a rare opportunity to receive many benefits from the Little Dipper Project. This opportunity can be assessed in terms of a helpful benefit to the Design Group. We have an opportunity to contribute fully and positively towards an excellent education on designing and returning a historical aircraft back to life. The foundation of this opportunity has a straightforward meaning – an opportunity to participate. The aim of this process is to develop some expertise which can be used in aircraft design methodology. In particular it should help the Design Group to understand the concepts, methods, formulas, and pitfalls. An added bonus would be the fun the group would have in participating. Could it be possible that as a Design Group we are staring right into an exciting opportunity of experience and learning?
NX100GR (cn 1) The sign on the propeller said this is the Lockheed Air Trooper (of which only one was built), but this is actually the Robertson Sky Skeeter. On display at the EAA Arlington Fly-In. This is George Robertson's "Sky Skeeter." George worked for John Thorp immediately after the war at John's T-11 Sky Skooter production facility on San Fernando Boulevard. He was mechanic, machinist, and all-round go-to guy. He especially remembers producing the ribbed wing skin which he describes as a real knuckle-buster to make; he tried to get John to go back to the internal stiffeners of the T-10 (Little Dipper) with no success. George, with John's approval, made extra Sky Skooter parts but converted it back to a single-place and called it the "Sky Skeeter." He lives in Sun City, AZ, He has no drawings, documents, etc. When he stopped flying, not so many years ago, he sold the airplane to James Fernandez of Kirkland, WA, who has given it this spiffy new paint job.
The picture Show
At meeting number five we viewed another video program by brilliant German
aeronautical engineer Dr. Alexander Lippisch, explaining Fluid Motion phenomena from program
number two. We witnessed actual wind tunnel photography of air flowing around a wing. Pulsed smoke streams illustrate that the parcels of air which are divided by the leading edge DO NOT recombine at the trailing edge. Therefore the "wing shape" explanation of lifting force falls apart.
Actual wind tunnel photograph of air flowing around a wing. Pulsed smoke streams illustrate that the parcels of air which are divided by the leading edge DO NOT recombine at the trailing edge. Therefore the "wing shape" explanation of lifting force falls apart. (This image was made by late Aerodynamicist Alexander Lippish, The German Me-163 creator, at Collins Radio wind tunnels, USA, in 1953. It was published in his book. Alexander Lippish was an expert on smoke in wind tunnels and his smoke trails were world-famous.)
A film clip of a wind tunnel experiment depicts a single "plane" of smoky air as it approaches a thin airfoil and is sliced into upper and lower portions. Note that this airfoil is NOT "curved above and flat below." Instead the upper and lower surfaces are approximately equal in length. Note that the air flowing above the wing quickly outraces the air flowing below. The air flowing above and below the wing never rejoins again. The real reason for the rapid flow of air above the wing is never explained in textbooks using the "wing shape" explanation of lift. (This image is made by Aerodynamist Martin-Ingelman Sundberg at KTH windtunnels in 1992. Sundberg, who first saw synchronized smoke pulses when visiting a wind tunnel maker in USA 1962, made this smoke pulse video to show how ICAO pilot education was wrong in explaining wing lift with "airflow longer path over wing".)
A film clip of a wind tunnel experiment depicts a single "plane" of smoky air as it approaches an airfoil and is sliced into upper and lower portions. Note that the air flowing above the wing quickly outraces the air flowing below. The air flowing above and below the wing never rejoins again. The real reason for the rapid flow of air above the wing is never explained in textbooks using the "wing shape" explanation of lift. The confusing aspects of "airfoil shape" shown here can totally obscure the true nature of aerodynamic lift.
Many authors point out that asymmetrical airfoils give positive lift even if the angle of attack is zero. They offer this in order to prove that "wing shape", and not "attack angle" should be the explanation of choice. But there is a problem here. To determine if an airfoil is tilted, we cannot rely on construction of the geometrical attack angle. Geometrical attack angle is very sensitive to tiny bumps on the wing's leading edge, since tiny bumps can change where we draw the main 'chord.' Yet tiny bumps on the leading edge can have little effect on deflection of air, while the tilting of the airfoil shown in the fourth section can have an enormous effect upon the deflection of air and upon lifting force. "Kutta Condition" shows that the angle of the trailing edge is critical to production of lifting force. SMALL FEATURES ON THE LEADING EDGE CAN CAUSE US TO TILT THE ENTIRE WING, WHILE WE DENY THAT WE HAVE DONE SO. To determine the effective attack angle, we cannot trust the simple geometrical rules. To determine whether an asymmetrical wing is REALLY set to zero angle of attack, we instead must take seriously the concept of "Kutta condition," and inspect the trailing edge of the airfoil to see if it directs the air downwards. Or put simply: the angle of the trailing edge IS the angle of attack, and the angle made by the main chord of the airfoil has little effect on the lifting force. The explanations used to teach the principles of flight more often than not merely propagate long-held myths. Discussions should focus on the angle of attack and not the shape of the wing. By explaining flight as an application of Newton’s principles, one can understand lift, power, wing efficiency and other principles of flight. The Newtonian description of lift and an understanding of flight are presented in an attached paper to this newsletter. The myths and some misconceptions of the application of Bernoulli's equation are also discussed.
This material can be found in more detail in "Understanding Flight", byDavid Anderson and Scott Eberhardt, McGraw-Hill, 2001, ISBN: 0-07-
136377-7
This article was written for "Fliegermagazin" (Flyer's Magazine) published inMunich Germany
Almost everyone today has flown in an airplane. Many ask the simple question "what makes anairplane fly?" The answer one frequently gets is misleading and often just plain wrong. We hopethat the answers provided here will clarify many misconceptions about lift and that you willadopt our explanation when explaining lift to others. We are going to show you that lift is easierto understand if one starts with Newton’s laws rather than the Bernoulli principle. We will alsoshow you that the popular explanation that most of us were taught is misleading at best and thatlift is due to the wing diverting air down. Most of this diverted air is pulled down from above thewing.
Let us start by defining three descriptions of lift commonly used in textbooks and trainingmanuals. The first we will call the Mathematical Aerodynamics Description of lift, which is usedby aeronautical engineers. This description uses complex mathematics and/or computersimulations to calculate the lift of a wing. It often uses a mathematical concept called"circulation" to calculate the acceleration of the air over the wing. Circulation is a measure of theapparent rotation of the air around the wing. While useful for calculations of lift, this descriptiondoes not lend themselves to an intuitive understanding of flight.
The second description we will call the Popular Description, which is based on the Bernoulliprinciple. The primary advantage of this description is that it is easy to understand and has beentaught for many years. Because of its simplicity, it is used to describe lift in most flight trainingmanuals. The major disadvantage is that it relies on the "principle of equal transit times", or atleast on the assumption that because the air must travel farther over the top of the wing it mustgo faster. This description focuses on the shape of the wing and prevents one from understandingsuch important phenomena as inverted flight, power, ground effect, and the dependence of lift onthe angle of attack of the wing.
The third description, which we are advocating here, we will call the Physical Description of lift.This description of lift is based primarily on Newton's three laws and a phenomenon called theCoanda effect. This description is uniquely useful for understanding the phenomena associatedwith flight. It is useful for an accurate understanding the relationships in flight, such as howpower increases with load or how the stall speed increases with altitude. It is also a useful toolfor making rough estimates ("back-of-the-envelope calculations") of lift. The PhysicalDescription of lift is also of great use to a pilot who needs an intuitive understanding of how tofly the airplane.
The popular description of liftStudents of physics and aerodynamics are taught that an airplane flies as a result of the Bernoulliprinciple, which says that if air speeds up the pressure is lowered. (In fact this is not always true.The air flows fast over the airplane’s static port but the altimeter still reads the correct altitude.)The argument goes that a wing has lift because the air goes faster over the top creating a regionof low pressure. This explanation usually satisfies the curious and few challenge the conclusions.Some may wonder why the air goes faster over the top of the wing and this is where the popularexplanation of lift falls apart.
In order to explain why the air goes faster over the top of the wing, many have resorted to thegeometric argument that the distance the air must travel is directly related to its speed. The usualclaim is that when the air separates at the leading edge, the part that goes over the top mustconverge at the trailing edge with the part that goes under the bottom. This is the so-called"principle of equal transit times".
One might ask if the numbers calculated by the Popular Description really work. Let us look atan example. Take the case of a Cessna 172, which is popular, high-winged, four-seat airplane.The wings must lift 2300 lb (1045 kg) at its maximum flying weight. The path length for the airover the top of the wing is only about 1.5% greater than under the wing. Using the PopularDescription of lift, the wing would develop only about 2% of the needed lift at 65 mph (104km/h), which is "slow flight" for this airplane. In fact, the calculations say that the minimumspeed for this wing to develop sufficient lift is over 400 mph (640 km/h). If one works theproblem the other way and asks what the difference in path length would have to be for thePopular Description to account for lift in slow flight, the answer would be 50%. The thickness ofthe wing would be almost the same as the chord length.
But, who says the separated air must meet at the trailing edge at the same time? Figure 1 showsthe airflow over a wing in a simulated wind tunnel. In the simulation, smoke is introducedperiodically. One can see that the air that goes over the top of the wing gets to the trailing edge
considerably before the air that goes under the wing. In fact, the air is accelerated much fasterthan would be predicted by equal transit times. Also, on close inspection one sees that the airgoing under the wing is slowed down from the "free-stream" velocity of the air. The principle ofequal transit times holds only for a wing with zero lift.
Fig 1 Simulation of the airflow over a wing in a wind tunnel, with "smoke".
The popular explanation also implies that inverted flight is impossible. It certainly does notaddress acrobatic airplanes, with symmetric wings (the top and bottom surfaces are the sameshape), or how a wing adjusts for the great changes in load such as when pulling out of a dive orin a steep turn?
So, why has the popular explanation prevailed for so long? One answer is that the Bernoulliprinciple is easy to understand. There is nothing wrong with the Bernoulli principle, or with thestatement that the air goes faster over the top of the wing. But, as the above discussion suggests,our understanding is not complete with this explanation. The problem is that we are missing avital piece when we apply Bernoulli’s principle. We can calculate the pressures around the wingif we know the speed of the air over and under the wing, but how do we determine the speed? Aswe will soon see, the air accelerates over the wing because the pressure is lower, not the otherway around.
Another fundamental shortcoming of the popular explanation is that it ignores the work that isdone. Lift requires power (which is work per time). As will be seen later, an understanding ofpower is key to the understanding of many of the interesting phenomena of lift.
Newton’s laws and liftSo, how does a wing generate lift? To begin to understand lift we must review Newton’s first andthird laws. (We will introduce Newton’s second law a little later.) Newton’s first law states abody at rest will remain at rest, or a body in motion will continue in straight-line motion unlesssubjected to an external applied force. That means, if one sees a bend in the flow of air, or if airoriginally at rest is accelerated into motion, a force is acting on it. Newton’s third law states thatfor every action there is an equal and opposite reaction. As an example, an object sitting on atable exerts a force on the table (its weight) and the table puts an equal and opposite force on theobject to hold it up. In order to generate lift a wing must do something to the air. What the wingdoes to the air is the action while lift is the reaction.
Let’s compare two figures used to show streamlines over a wing. In figure 2 the air comesstraight at the wing, bends around it, and then leaves straight behind the wing. We have all seensimilar pictures, even in flight manuals. But, the air leaves the wing exactly as it appeared aheadof the wing. There is no net action on the air so there can be no lift! Figure 3 shows thestreamlines, as they should be drawn. The air passes over the wing and is bent down. Newton’sfirst law says that them must be a force on the air to bend it down (the action). Newton’s thirdlaw says that there must be an equal and opposite force (up) on the wing (the reaction). Togenerate lift a wing must divert lots of air down.
Fig 2 Common depiction of airflow over a wing. This wing has no lift.
Fig 3 True airflow over a wing with lift, showing upwash and downwash.
The lift of a wing is equal to the change in momentum of the air it is diverting down. Momentumis the product of mass and velocity (mv). The most common form of Newton’s second law is F=
ma, or force equal mass times acceleration. The law in this form gives the force necessary toaccelerate an object of a certain mass. An alternate form of Newton’s second law can be written:The lift of a wing is proportional to the amount of air diverted down times the vertical velocity ofthat air. It is that simple. For more lift the wing can either divert more air (mass) or increase its
vertical velocity. This vertical velocity behind the wing is the vertical component of the"downwash". Figure 4 shows how the downwash appears to the pilot (or in a wind tunnel). The
figure also shows how the downwash appears to an observer on the ground watching the wing goby. To the pilot the air is coming off the wing at roughly the angle of attack and at about the
speed of the airplane. To the observer on the ground, if he or she could see the air, it would becoming off the wing almost vertically at a relatively slow speed. The greater the angle of attackof the wing the greater the vertical velocity of the air. Likewise, for a given angle of attack, thegreater the speed of the wing the greater the vertical velocity of the air. Both the increase in thespeed and the increase of the angle of attack increase the length of the vertical velocity arrow. It
is this vertical velocity that gives the wing lift.
Fig 4 How downwash appears to a pilot and to an observer on the ground.
As stated, an observer on the ground would see the air going almost straight down behind theplane. This can be demonstrated by observing the tight column of air behind a propeller, ahousehold fan, or under the rotors of a helicopter; all of which are rotating wings. If the air werecoming off the blades at an angle the air would produce a cone rather than a tight column. Thewing develops lift by transferring momentum to the air. For straight and level flight thismomentum eventually strikes the earth in. If an airplane were to fly over a very large scale, thescale would weigh the airplane.
Let us do a back-of-the-envelope calculation to see how much air a wing might divert. Take forexample a Cessna 172 that weighs about 2300 lb (1045 kg). Traveling at a speed of 140 mph(220 km/h), and assuming an effective angle of attack of 5 degrees, we get a vertical velocity forthe air of about 11.5 mph (18 km/h) right at the wing. If we assume that the average verticalvelocity of the air diverted is half that value we calculate from Newton's second law that theamount of air diverted is on the order of 5 ton/s. Thus, a Cessna 172 at cruise is diverting aboutfive times its own weight in air per second to produce lift. Think how much air is diverted by a250-ton Boeing 777 on takeoff.
Diverting so much air down is a strong argument against lift being just a surface effect (that isonly a small amount of air around the wing accounts for the lift), as implied by the popularexplanation. In fact, in order to divert 5 ton/sec the wing of the Cessna 172 must accelerate all ofthe air within 18 feet (7.3 m) above the wing. One should remember that the density of air at sealevel is about 2 lb per cubic yard (about 1kg per cubic meter). Figure 5 illustrates the effect of theair being diverted down from a wing. A huge hole is punched through the fog by the downwashfrom the airplane that has just flown over it.
Fig 5 Downwash and wing vortices in the fog. (Photographer Paul Bowen, courtesy of CessnaAircraft, Co.)
So how does a thin wing divert so much air? When the air is bent around the top of the wing, itpulls on the air above it accelerating that air downward. Otherwise there would be voids in theair above the wing. Air is pulled from above. This pulling causes the pressure to become lowerabove the wing. It is the acceleration of the air above the wing in the downward direction thatgives lift. (Why the wing bends the air with enough force to generate lift will be discussed in thenext section.)
As seen in figure 3, a complication in the picture of a wing is the effect of "upwash" at theleading edge of the wing. As the wing moves along, air is not only diverted down at the rear ofthe wing, but air is pulled up at the leading edge. This upwash actually contributes to negativelift and more air must be diverted down to compensate for it. This will be discussed later whenwe consider ground effect.
Normally, one looks at the air flowing over the wing in the frame of reference of the wing. Inother words, to the pilot the air is moving and the wing is standing still. We have already statedthat an observer on the ground would see the air coming off the wing almost vertically. But whatis the air doing below the wing? Figure 6 shows an instantaneous snapshot of how air moleculesare moving as a wing passes by. Remember in this figure the air is initially at rest and it is thewing moving. Arrow "1" will become arrow "2" and so on. Ahead of the leading edge, air ismoving up (upwash). At the trailing edge, air is diverted down (downwash). Over the top the airis accelerated towards the trailing edge. Underneath, the air is accelerated forward slightly.
Fig 6 Direction of air movement around a wing as seen by an observer on the ground.
So, why does the air follow this pattern? First, we have to bear in mind that air is considered anincompressible fluid for low-speed flight. That means that it cannot change its volume and thatthere is a resistance to the formation of voids. Now the air has been accelerated over the top ofthe wing by of the reduction in pressure. This draws air from in front of the wing and expels ifback and down behind the wing. This air must be compensated for, so the air shifts around thewing to fill in. This is similar to the circulation of the water around a canoe paddle. Thiscirculation around the wing is no more the driving force for the lift on the wing than is thecirculation in the water drives the paddle. Though, it is true that if one is able to determine thecirculation around a wing the lift of the wing can be calculated. Lift and circulation are
proportional to each other.
One observation that can be made from figure 6 is that the top surface of the wing does muchmore to move the air than the bottom. So the top is the more critical surface. Thus, airplanes cancarry external stores, such as drop tanks, under the wings but not on top where they wouldinterfere with lift. That is also why wing struts under the wing are common but struts on the topof the wing have been historically rare. A strut, or any obstruction, on the top of the wing wouldinterfere with the lift.
Coanda EffectA natural question is "how does the wing divert the air down?" When a moving fluid, such as airor water, comes into contact with a curved surface it will try to follow that surface. Todemonstrate this effect, hold a water glass horizontally under a faucet such that a small stream ofwater just touches the side of the glass. Instead of flowing straight down, the presence of theglass causes the water to wrap around the glass as is shown in figure 7. This tendency of fluids tofollow a curved surface is known as the Coanda effect. From Newton’s first law we know thatfor the fluid to bend there must be a force acting on it. From Newton’s third law we know thatthe fluid must put an equal and opposite force on the glass.
Fig 7 Coanda effect.
So why should a fluid follow a curved surface? The answer is viscosity; the resistance to flowwhich also gives the air a kind of "stickiness". Viscosity in air is very small but it is enough forthe air molecules to want to stick to the surface. At the surface the relative velocity between thesurface and the nearest air molecules is exactly zero. (That is why one cannot hose the dust off ofa car.) Just above the surface the fluid has some small velocity. The farther one goes from thesurface the faster the fluid is moving until the external velocity is reached. Because the fluid nearthe surface has a change in velocity, the fluid flow is bent towards the surface by shear forces.Unless the bend is too tight, the fluid will follow the surface. This volume of air around the wingthat appears to be partially stuck to the wing is called the "boundary layer" and is less than oneinch (2.5 cm) thick, even for a large wing.
Look again at Figure 3. The magnitude of the forces on the air (and on the wing) are proportional
to the "tightness" of the bend. The tighter the air bends the greater the force on it. One thing tonotice in the figure is that most of the lift is on the forward part of the wing. In fact, half of thetotal lift on a wing is typically produced in the first 1/4 of the chord length.
Lift as a function of angle of attackThere are many types of wing: conventional, symmetric, conventional in inverted flight, the earlybiplane wings that looked like warped boards, and even the proverbial "barn door". In all cases,the wing is forcing the air down, or more accurately pulling air down from above. (Though theearly wings did have a significant contribution from the bottom.) What each of these wings hasin common is an angle of attack with respect to the oncoming air. It is the angle of attack that isthe primary parameter in determining lift.
To better understand the role of the angle of attack it is useful to introduce an "effective" angle ofattack, defined such that the angle of the wing to the oncoming air that gives zero lift is definedto be zero degrees. If one then changes the angle of attack both up and down one finds that thelift is proportional to the angle. Figure 8 shows the lift of a typical wing as a function of theeffective angle of attack. A similar lift versus angle of attack relationship is found for all wings,independent of their design. This is true for the wing of a 747, an inverted wing, or your hand outthe car window. The inverted wing can be explained by its angle of attack, despite the apparentcontradiction with the popular explanation of lift. A pilot adjusts the angle of attack to adjust thelift for the speed and load. The role of the angle of attack is more important than the details ofthe wings shape in understanding lift. The shape comes into play in the understanding of stallcharacteristics and drag at high speed.
Fig 8 Lift versus the effective angle of attack.
Typically, the lift begins to decrease at a "critical angle" of attack of about 15 degrees. Theforces necessary to bend the air to such a steep angle are greater than the viscosity of the air willsupport, and the air begins to separate from the wing. This separation of the airflow from the topof the wing is a stall.
The wing as air "scoop"We now would like to introduce a new mental image of a wing. One is used to thinking of awing as a thin blade that slices though the air and develops lift somewhat by magic. The newimage that we would like you to adopt is that of the wing as a scoop diverting a certain amountof air from the horizontal to roughly the angle of attack, as depicted in Figure 9. For wings oftypical airplanes it is a good approximation to say that the area of the scoop is proportional to thearea of the wing. The shape of the scoop is approximately elliptical for all wings, as shown in thefigure. Since the lift of the wing is proportional to the amount of air diverted, the lift of is alsoproportional to the wing’s area.
Fig 9 The wing as a scoop.
As stated before, the lift of a wing is proportional to the amount of air diverted down times thevertical velocity of that air. As a plane increases speed, the scoop diverts more air. Since the loadon the wing does not increase, the vertical velocity of the diverted air must be decreasedproportionately. Thus, the angle of attack is reduced to maintain a constant lift. When the planegoes higher, the air becomes less dense so the scoop diverts less air at a given speed. Thus, tocompensate the angle of attack must be increased. The concepts of this section will be used tounderstand lift in a way not possible with the popular explanation.
Lift requires powerWhen a plane passes overhead the formally still air gains a downward velocity. Thus, the air isleft in motion after the plane leaves. The air has been given energy. Power is energy, or work,per time. So, lift requires power. This power is supplied by the airplane’s engine (or by gravityand thermals for a sailplane).
How much power will we need to fly? If one fires a bullet with a mass, m, and a velocity, v, theenergy given to the bullet is simply ½mv2. Likewise, the energy given to the air by the wing isproportional to the amount of air diverted down times the vertical velocity squared of thatdiverted air. We have already stated that the lift of a wing is proportional to the amount of airdiverted times the vertical velocity of that air. Thus, the power needed to lift the airplane isproportional to the load (or weight) times the vertical velocity of the air. If the speed of the planeis doubled the amount of air diverted down doubles. Thus to maintain a constant lift, the angle ofattack must be reduced to give a vertical velocity that is half the original. The power required forlift has been cut in half. This shows that the power required for lift becomes less as the airplane's
speed increases. In fact, we have shown that this power to create lift is proportional to 1/speed ofthe plane.
But, we all know that to go faster (in cruise) we must apply more power. So there must be moreto power than the power required for lift. The power associated with lift is often called the"induced" power. Power is also needed to overcome what is called "parasitic" drag, which is thedrag associated with moving the wheels, struts, antenna, etc. through the air. The energy theairplane imparts to an air molecule on impact is proportional to the speed2 (form ½mv2) . Thenumber of molecules struck per time is proportional to the speed. The faster one goes the higherthe rate of impacts. Thus the parasitic power required to overcome parasitic drag increases as thespeed3.
Figure 10 shows the "power curves" for induced power, parasitic power, and total power (thesum of induced power and parasitic power). Again, the induced power goes as 1/speed and theparasitic power goes as the speed3. At low speed the power requirements of flight are dominatedby the induced power. The slower one flies the less air is diverted and thus the angle of attackmust be increased to increase the vertical velocity of that air. Pilots practice flying on the"backside of the power curve" so that they recognize that the angle of attack and the powerrequired to stay in the air at very low speeds are considerable.
Fig 10 Power requirements versus speed.
At cruise, the power requirement is dominated by parasitic power. Since this goes as the speed3
an increase in engine size gives one a faster rate of climb but does little to improve the cruisespeed of the plane. Doubling the size of the engine will only increase the cruise speed by about25%.
Since we now know how the power requirements vary with speed, we can understand drag,which is a force. Drag is simply power divided by speed. Figure 11 shows the induced, parasitic,and total drag as a function of speed. Here the induced drag varies as 1/speed2 and parasitic dragvaries as the speed2. Taking a look at these figures one can deduce a few things about howairplanes are designed. Slower airplanes, such as gliders, are designed to minimize inducedpower, which dominates at lower speeds. Faster propeller-driven airplanes are more concerned
with parasite power, and jets are dominated by parasitic drag. (This distinction is outside of thescope of this article.)
Fig 11 Drag versus speed.
Wing efficiencyAt cruise, a non-negligible amount of the drag of a modern wing is induced drag. Parasitic dragof a Boeing 747 wing is only equivalent to that of a 1/2-inch cable of the same length. One mightask what affects the efficiency of a wing. We saw that the induced power of a wing isproportional to the vertical velocity of the air. If the area of a wing were to be increased, the sizeof our scoop would also increase, diverting more air. So, for the same lift the vertical velocity(and thus the angle of attack) would have to be reduced. Since the induced power is proportionalto the vertical velocity of the air, it is also reduced. Thus, the lifting efficiency of a wingincreases with increasing wing area. The larger the wing the less induced power required toproduce the same lift, though this is achieved with and increase in parasitic drag.
As will be briefly discussed in the section on ground effect, the additional loading on the wing instraight and level flight due to upwash is equal to the weight of the airplane time 2/AR. WhereAR is the wing’s aspect ratio (span divided by the mean chord). Thus, when considering twowings with the same area but different aspect ratios, the wing with the greater aspect ratio will bethe most efficient.
There is a misconception by some that lift does not require power. This comes from aeronauticsin the study of the idealized theory of wing sections (airfoils). When dealing with an airfoil, thepicture is actually that of a wing with infinite span. Since we have seen that the power necessaryfor lift decrease with increasing area of the wing, a wing of infinite span does not require powerfor lift. If lift did not require power airplanes would have the same range full as they do empty,and helicopters could hover at any altitude and load. Best of all, propellers (which are rotatingwings) would not require power to produce thrust. Unfortunately, we live in the real world where
both lift and propulsion require power.
Power and wing loadingNow let us consider the relationship between wing loading and power. At a constant speed, if thewing loading is increased the vertical velocity must be increased to compensate. This isaccomplished by increasing the angle of attack of the wing. If the total weight of the airplanewere doubled (say, in a 2g turn), and the speed remains constant, the vertical velocity of the air isdoubled to compensate for the increased wing loading. The induced power is proportional to theload times the vertical velocity of the diverted air, which have both doubled. Thus the inducedpower requirement has increased by a factor of four! So induced power is proportional to theload2.
One way to measure the total power is to look at the rate of fuel consumption. Figure 12 showsthe fuel consumption versus gross weight for a large transport airplane traveling at a constantspeed (obtained from actual data). Since the speed is constant the change in fuel consumption isdue to the change in induced power. The data are fitted by a constant (parasitic power) and aterm that goes as the load2. This second term is just what was predicted in our Newtoniandiscussion of the effect of load on induced power.
Fig 12 Fuel consumption versus load for a large transport airplane traveling at a constant speed.
The increase in the angle of attack with increased load has a downside other than just the needfor more power. As shown in figure 8 a wing will eventually stall when the air can no longerfollow the upper surface. That is, when the critical angle is reached. Figure 13 shows the angle ofattack as a function of airspeed for a fixed load and for a 2-g turn. The angle of attack at whichthe plane stalls is constant and is not a function of wing loading. The angle of attack increases asthe load and the stall speed increases as the square root of the load. Thus, increasing the load in a2-g turn increases the speed at which the wing will stall by 40%. An increase in altitude willfurther increase the angle of attack in a 2-g turn. This is why pilots practice "accelerated stalls"which illustrates that an airplane can stall at any speed, since for any speed there is a load thatwill induce a stall.
Fig 13 Angle of attack versus speed for straight and level flight and for a 2-g turn.
Wing vorticesOne might ask what the downwash from a wing looks like. The downwash comes off the wing asa sheet and is related to the details on the load distribution on the wing. Figure 14 shows, throughcondensation, the distribution of lift on an airplane during a high-g maneuver. From the figureone can see that the distribution of load changes from the root of the wing to the tip. Thus, theamount of air in the downwash must also change along the wing. The wing near the root is"scooping" up much more air than the tip. Since the wing near the root is diverting so much airthe net effect is that the downwash sheet will begin to curl outward around itself, just as the airbends around the top of the wing because of the change in the velocity of the air. This is the wingvortex. The tightness of the curling of the wing vortex is proportional to the rate of change in liftalong the wing. At the wing tip the lift must rapidly become zero causing the tightest curl. This isthe wing tip vortex and is just a small (though often most visible) part of the wing vortex.Returning to figure 5 one can clearly see the development of the wing vortices in the downwashas well as the wing tip vortices.
Fig 14 Condensation showing the distribution of lift along a wing. (from Patterns in the Sky, J.F.Campbell and J.R. Chambers, NASA SP-514.)
Winglets (those small vertical extensions on the tips of some wings) are used to improve the
efficiency of the wing by increasing the effective length, and thus area, of the wing. The lift of anormal wing must go to zero at the tip because the bottom and the top communicate around theend. The winglet blocks this communication so the lift can extend farther out on the wing. Sincethe efficiency of a wing increases with area, this gives increased efficiency. One caveat is thatwinglet design is tricky and winglets can actually be detrimental if not properly designed.
Ground effectAnother common phenomenon that is often misunderstood is that of ground effect. That is theincreased efficiency of a wing when flying within a wing length of the ground. A low-wingairplane will experience a reduction in drag by as much as 50% just before it touches down. Thisreduction in drag just above a surface is used by large birds, which can often be seen flying justabove the surface of the water. Pilots taking off from deep-grass or soft runways also use groundeffect. Many pilots mistakenly believe that ground effect is the result of air being compressedbetween the wing and the ground.
To understand ground effect it is necessary to look again at the upwash. Notice in Figure 15 thatthe air bends up from its horizontal flow to form the upwash. Newton's first law says that theremust be a force acting on the air to bend it. Since the air is bent up the force must be up as shownby the arrow. Newton's third laws says that there is an equal and opposite force on the wingwhich is down. The result is that the upwash increases the load on the wing. To compensate forthis increased load, the wing must fly at a greater angle of attack, and thus a greater inducedpower. As the wing approaches the ground the circulation below the wing is inhibited. As shownin Figure 16, there is a reduction in the upwash and in the additional loading on the wing causedby the upwash. To compensate, the angle of attack is reduced and so is the induced power. Thewing becomes more efficient.
Fig 15 Wing out of ground effect
Fig 16 Wing in ground effect
The additional load due to upwash is equal to the weight of the airplane time 2/AR. Most smallairplanes have aspect ratios of 7-8. An airplane with an aspect ratio of 8 can experience as muchas a 25% reduction in wing loading due to ground effect. Since induced power is proportional tothe load2, this corresponds to a 50% reduction in induced power. Earlier, we estimated that aCessna 172 flying at 110 knots must divert about 5 ton/sec to provide lift. In our calculations weneglected the contribution of upwash. The amount of air diverted is probably closer to 6 ton/sec.
ConclusionsLet us review what we have learned and get some idea of how the physical description has givenus a greater ability to understand flight. First what have we learned:
• The amount of air diverted by the wing is proportional to the speed of the wing and theair density.
• The vertical velocity of the diverted air is proportional to the speed of the wing and theangle of attack.
• The lift is proportional to the amount of air diverted times the vertical velocity of the air.
• The power needed for lift is proportional to the lift times the vertical velocity of the air.
Now let us look at some situations from the physical point of view and from the perspective ofthe popular explanation.
• The plane’s speed is reduced. The physical view says that the amount of air diverted isreduced so the angle of attack is increased to compensate. The power needed for lift isalso increased. The popular explanation cannot address this.
• The load of the plane is increased. The physical view says that the amount of air divertedis the same but the angle of attack must be increased to give additional lift. The powerneeded for lift has also increased. Again, the popular explanation cannot address this.
• A plane flies upside down. The physical view has no problem with this. The plane adjusts
the angle of attack of the inverted wing to give the desired lift. The popular explanationimplies that inverted flight is impossible.
As one can see, the popular explanation, which fixates on the shape of the wing, may satisfymany but it does not give one the tools to really understand flight. The physical description of liftis easy to understand and much more powerful.
If you are interested in reading more, please see "Understanding Flight", byDavid Anderson and Scott Eberhardt, McGraw-Hill, 2001, ISBN: 0-07-
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