Lift Correction for Finite Chord

Lift Correction for Finite Chord AERODYNAMICS Lift Correction for which, it is noted, is one-eight of the incidence due to the main trailing vortex term. Finite Chord The remaining term also gives a very nearly linear variation of along the chord and taking A Method of Close Approximation that is not Laborious and is as usual the ¾-chord value, we find, for y small, Applicable in General to Wings without Sweep The multi­ plier for c/y is no longer constant as we should like, in order to compare with the ordinary By J. Lockwood Taylor, D.Sc. downwash term, so as if possible to include the effect we are considering along with the usual downwash correction. It is necessary to take a T has been noted by Falkner and others that weighted mean which we will estimate as the ordinary aspect-ratio corrections based on lifting-line theory are not as accurate as had though this will depend to some extent on aspect- The second term is the camber term which, on always been assumed even for normal aspect ratio and will be greater at a smaller aspect- insertion of the limits affords an interesting check ratios of the order of 6. Lifting-surface theory ratio when the smaller values of y are of greater on the two-dimensional constant-velocity aero­ involves heavy calculation, and the present work importance. This represents a 25 per cent increase foil. The first term corresponds with one term of is intended to give at least an indication of the in downwash compared with the lifting line. To the usual trailing vortex field, namely that which magnitude of the finite-chord correction on a offset this we already have a decrease of half this vanishes at the aerofoil. To complete the solution fairly simple basis. amount from the camber term previously con­ it is necessary only to add the remainder of the As a starting point, consider the Velocity field sidered, giving a net increase of 12½ per cent. for a finite rectangular wing with uniform lift So far we have considered only uniform loading trailing vortex, as usual, with circu­ distribution, which can be calculated exactly. The or C.P.·5. It is to be expected that the loss of lift velocity potential can be written in the form and increase in downwash will be greater the lation K=4c. In all, after inserting the limits for x greater the separation of C.P. and ¾-chord. This is confirmed by calculations for a parabolic log chordwise loading (C.P.·25) which gives an increase almost in proportion to (¾—C.P.) in the main term above. The camber term does not lend itself very readily to exact allowance for variation The origin of co-ordinates is taken at the mid­ in chordwise loading, but there is no reason to point of the wing, of span 2s and chord 2c, and suppose it to be unduly critical in this respect. We therefore take for C.P.·25, a 25 per cent the element of Φ is chosen to make increase in effective downwash, or 20 per cent If we concentrate for the present on conditions reduction in effective aspect—ratio at moderate near one wing tip or trailing vortex, and measure values of the latter. which vanishes at the wing surface, y from the tip, the limits for y in the integral Thus at A.R.6 our simple estimate gives z=0, except for small values of may be ignored. is the wing-surface slope, instead of (2π × 6/8) for the lift-slope dCl/dα a value or downwash angle, as the case may be. As y a reduction of about 6 per cent, increases, i.e. as we leave the wing tip, the camber but gives = ± 1 on the upper which agrees well with Falkner. At unit aspect term → log which gives as mentioned a ratio we get about 14 per cent on the same basis but we expect this to be rather an under-estimate and lower surfaces, thus accounting for the of the loss, and it appears to be so from the check on the constant-velocity camber in two- assumed uniform vorticity. Integration gives experimental data. dimensional flow. We are particularly interested in the departure Although the theory is worked out primarily from two-dimensional flow represented by this for a rectangular wing, it applies to the first order to any straight wing (without sweepback) term when y is small, i.e. near the tip, and in since the local chord, 2C, in the calculations, is to be taken between the respective limits of x comparing this departure and the flow-curvature common to the various terms whose magnitudes and y. represented by the second term with the third are compared; it also applies to any spanwise term, which is, of course, the well-known lifting- We are particularly interested in line downwash term. It is quite easy to show loading subject to the approximation noted and numerically that the camber decreases to zero at to the usual lifting-line correction for the reduced which gives the wing surface camber-slope to the tip and that except for very small values of y effective aspect—ratio, as estimated above. The produce the assumed uniform lift, and also the decrease is very nearly linear along the chord allowance for C.P. variation has already been considered. furnishes information about the downwash, viz. and such as to give a reduction in no-lift incidence (d) Powerplants, propellers, instruments, inspections to certain other types, notably the K.L.M. AUTHORIZED TO SERVICE radio equipment and accessories eligible Boeing 'Stratocruiser'. It authorizes K.L.M. to for installation on the aircraft models operate a repair station at Schiphol with the U.S. AIRCRAFT listed above. following ratings: aircraft of all-metal construc­ K.L.M. Royal Dutch Airlines announce from tion ; aircraft engines; aircraft metal propellers 2. Routine inspection to Boeing model 377 and their London Office, 196 Sloane Street, S.W.1, and propeller hubs; and aircraft instruments. Curtiss model C-46. that they have been empowered by the Civil The scope of the ratings is limited to the follow­ Aeronautics Administration of the United States ing: to operate an approved repair station at Schiphol 1. Minor or major repairs and alterations; for the overhaul and inspection of aircraft periodic inspections to : registered in the United States. FIRE RESISTANT FINISHES This means that aircraft and components (a) Douglas models—DC-3 series, DC-4 The Lockheed Aircraft Corporation ask us to belonging to American companies may be DC-6, C-47 series and C-54 series. make it clear that Messrs J. A. Jones and R. V. repaired or altered and returned to service without (b) Lockheed models—49-46, 749-79, 749A- Niswander, the authors of the paper with the above prior inspection by a C.A.A. representative. 79, 12-A and 18 series aircraft. title published in our April issue, are members of The certificate relates primarily to aircraft (c) Consolidated Yultee models 240 series the Corporation's engineering staff at Ausbank, types used by K.L.M., but also authorizes routine California. aircraft. Aircraft Engineering http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Aircraft Engineering and Aerospace Technology Emerald Publishing

Lift Correction for Finite Chord

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Publisher
Emerald Publishing
Copyright
Copyright © Emerald Group Publishing Limited
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0002-2667
D.O.I.
10.1108/eb031910
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Abstract

AERODYNAMICS Lift Correction for which, it is noted, is one-eight of the incidence due to the main trailing vortex term. Finite Chord The remaining term also gives a very nearly linear variation of along the chord and taking A Method of Close Approximation that is not Laborious and is as usual the ¾-chord value, we find, for y small, Applicable in General to Wings without Sweep The multi­ plier for c/y is no longer constant as we should like, in order to compare with the ordinary By J. Lockwood Taylor, D.Sc. downwash term, so as if possible to include the effect we are considering along with the usual downwash correction. It is necessary to take a T has been noted by Falkner and others that weighted mean which we will estimate as the ordinary aspect-ratio corrections based on lifting-line theory are not as accurate as had though this will depend to some extent on aspect- The second term is the camber term which, on always been assumed even for normal aspect ratio and will be greater at a smaller aspect- insertion of the limits affords an interesting check ratios of the order of 6. Lifting-surface theory ratio when the smaller values of y are of greater on the two-dimensional constant-velocity aero­ involves heavy calculation, and the present work importance. This represents a 25 per cent increase foil. The first term corresponds with one term of is intended to give at least an indication of the in downwash compared with the lifting line. To the usual trailing vortex field, namely that which magnitude of the finite-chord correction on a offset this we already have a decrease of half this vanishes at the aerofoil. To complete the solution fairly simple basis. amount from the camber term previously con­ it is necessary only to add the remainder of the As a starting point, consider the Velocity field sidered, giving a net increase of 12½ per cent. for a finite rectangular wing with uniform lift So far we have considered only uniform loading trailing vortex, as usual, with circu­ distribution, which can be calculated exactly. The or C.P.·5. It is to be expected that the loss of lift velocity potential can be written in the form and increase in downwash will be greater the lation K=4c. In all, after inserting the limits for x greater the separation of C.P. and ¾-chord. This is confirmed by calculations for a parabolic log chordwise loading (C.P.·25) which gives an increase almost in proportion to (¾—C.P.) in the main term above. The camber term does not lend itself very readily to exact allowance for variation The origin of co-ordinates is taken at the mid­ in chordwise loading, but there is no reason to point of the wing, of span 2s and chord 2c, and suppose it to be unduly critical in this respect. We therefore take for C.P.·25, a 25 per cent the element of Φ is chosen to make increase in effective downwash, or 20 per cent If we concentrate for the present on conditions reduction in effective aspect—ratio at moderate near one wing tip or trailing vortex, and measure values of the latter. which vanishes at the wing surface, y from the tip, the limits for y in the integral Thus at A.R.6 our simple estimate gives z=0, except for small values of may be ignored. is the wing-surface slope, instead of (2π × 6/8) for the lift-slope dCl/dα a value or downwash angle, as the case may be. As y a reduction of about 6 per cent, increases, i.e. as we leave the wing tip, the camber but gives = ± 1 on the upper which agrees well with Falkner. At unit aspect term → log which gives as mentioned a ratio we get about 14 per cent on the same basis but we expect this to be rather an under-estimate and lower surfaces, thus accounting for the of the loss, and it appears to be so from the check on the constant-velocity camber in two- assumed uniform vorticity. Integration gives experimental data. dimensional flow. We are particularly interested in the departure Although the theory is worked out primarily from two-dimensional flow represented by this for a rectangular wing, it applies to the first order to any straight wing (without sweepback) term when y is small, i.e. near the tip, and in since the local chord, 2C, in the calculations, is to be taken between the respective limits of x comparing this departure and the flow-curvature common to the various terms whose magnitudes and y. represented by the second term with the third are compared; it also applies to any spanwise term, which is, of course, the well-known lifting- We are particularly interested in line downwash term. It is quite easy to show loading subject to the approximation noted and numerically that the camber decreases to zero at to the usual lifting-line correction for the reduced which gives the wing surface camber-slope to the tip and that except for very small values of y effective aspect—ratio, as estimated above. The produce the assumed uniform lift, and also the decrease is very nearly linear along the chord allowance for C.P. variation has already been considered. furnishes information about the downwash, viz. and such as to give a reduction in no-lift incidence (d) Powerplants, propellers, instruments, inspections to certain other types, notably the K.L.M. AUTHORIZED TO SERVICE radio equipment and accessories eligible Boeing 'Stratocruiser'. It authorizes K.L.M. to for installation on the aircraft models operate a repair station at Schiphol with the U.S. AIRCRAFT listed above. following ratings: aircraft of all-metal construc­ K.L.M. Royal Dutch Airlines announce from tion ; aircraft engines; aircraft metal propellers 2. Routine inspection to Boeing model 377 and their London Office, 196 Sloane Street, S.W.1, and propeller hubs; and aircraft instruments. Curtiss model C-46. that they have been empowered by the Civil The scope of the ratings is limited to the follow­ Aeronautics Administration of the United States ing: to operate an approved repair station at Schiphol 1. Minor or major repairs and alterations; for the overhaul and inspection of aircraft periodic inspections to : registered in the United States. FIRE RESISTANT FINISHES This means that aircraft and components (a) Douglas models—DC-3 series, DC-4 The Lockheed Aircraft Corporation ask us to belonging to American companies may be DC-6, C-47 series and C-54 series. make it clear that Messrs J. A. Jones and R. V. repaired or altered and returned to service without (b) Lockheed models—49-46, 749-79, 749A- Niswander, the authors of the paper with the above prior inspection by a C.A.A. representative. 79, 12-A and 18 series aircraft. title published in our April issue, are members of The certificate relates primarily to aircraft (c) Consolidated Yultee models 240 series the Corporation's engineering staff at Ausbank, types used by K.L.M., but also authorizes routine California. aircraft. Aircraft Engineering

Journal

Aircraft Engineering and Aerospace TechnologyEmerald Publishing

Published: Jun 1, 1950

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