NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

Transcription

1 r NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS TECHNICAL NOTE 1930 AN ANALYSIS OF THE EFFECT OF LIFT-DRAG RATIO AND STALLING SPEED ON LANDING-FLARE CHARACTERISTICS By J. Calvin Lvell and Stanley Lipsn v Langley Aernautical Labratry Langley Air Frce Base, Va. Washingtn September 1949 ms ciü^l:r INSECTS» 4 Reprduced Frm A Best Available Cpy /j Q /Vl ÖÜ '/ 0-3T?

2 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS TECHNICAL NOTE 1930 AN ANALYSIS OF THE EFFECT OF LIFT-DEAG RATIO AND STALLING SPEED ON LANDING-FLARE CHARACTERISTICS By J. Calvin Lvell and Stanley Lipsn SUMMARY Calculatins f the landing-flare paths f a series f hypthetical airplanes having systematically varying characteristics have "been made t prvide infrmatin cncerning the effects f maximum lift cefficient, wing lading, and lift-drag rati n the landing-flare characteristics. Charts are presented which indicate the effects f current design trends n landing-flare velcity and distance requirements and which permit the rapid estimatin f the flare characteristics f any airplane having an apprximately cnstant lift-drag rati during the landing flare. A methd fr predicting the landing-flare characteristics f an airplane having a variahle lift-drag rati during the flare is given in an appendix. The applicatin f the analysis is demnstrated "by the determinatin f the effects f high-lift devices n landing characteristics f three transnic wing cnfiguratins. Airplanes landing at lw lift-drag ratis will have relatively high sinking speeds at the start f/^he flare and at an altitude f 50 feet, even if the stalling speeds are relatively lw. Airplanes which have relatively lw lift-drag ratis and high stalling speeds will require pwer-ff landing flares t start at relatively high altitudes. These results indicate that pwer-ff landings f sme airplanes designed specifically frm high-speed cnsideratins may nt he feasible at cnventinal airprts. Airplanes having high stalling speeds will require relatively large hrizntal distances fr either pwer-n r pwer-ff landing flares. INTRODUCTION The increased applicatin f airfils and wing plan frms designed, specifically frm high-speed cnsideratins has resulted in airplanes having relatively lw maximum lift cefficients, lw lift-drag ratis, and high wing ladings. These design trends increase the stalling speed and gliding angle f airplanes; hence, an adverse effect n the landing maneuver is indicated. In rder t prvide infrmatin cncerning this effect, the landing flares f a series f hypthetical

3 2 NACA TN 1930 airplanes have "been calculated n the basis f an assumed flare plan. The flare plan assumed is "based primarily n reference 1, in which infrmatin permitting calculatin f the flare characteristics f an airplane was btained frm flight tests. The results f calculatins fr airplanes having cnstant lift-drag rati during the flare are pltted in chart frm. In additin, since the drag increase, ften resulting frm deflectin f high-lift devices, may adversely affect the pwer-ff landing f airplanes which already have lw lift-drag ratis, the effect f the high-lift devices f three transnic wing cnfiguratins n landing-flare characteristics was determined. SYMBOLS C L lift cefficient (L/qS) C T maximum lift cefficient Mmax L lift, punds D drag, 'punds L/D lift-drag rati W weight f airplane, punds S wing area, square feet W/S wing lading, punds per square ft q free-stream dynamic pressure, punds per square ft p mass density f air, slugs per cubic ft v~ f velcity alng the flight path, feet per secnd vertical velcity r sinking speed, feet per secnd 7 flight-path angle, degrees /sin-1 ^

4 NACA TN 1930 V U/S V hnax stalling speed, feet per secnd j^wi factr prprtinal t T B ; at sea level numerically equals ^ s h a Y hrizntal distance, feet vertical distance, feet acceleratin nrmal t flight path, g units SLf> J^max maximum nrmal acceleratin deceleratin alng the flight path, feet per secnd per secnd acceleratin due t gravity, 32.2 feet per secnd per secnd time measured frm end f flare, secnds Subscripts: a b apprach cnditin cnditin at 0.8^0^ LAUDING-MARE CALCULATIONS The landing maneuver "begins with a steady-state apprach t a psitin at a relatively lw altitude and ff the end f the runway frm which the landing flare is executed. The flare is the levelingff phase f the landing maneuver, during which the vertical velcity and altitude are reduced t zer. The accmplishment f an acceptable landing depends primarily n the pilt's ability t execute the landing flare s that cntact with the runway is made at a lw vertical velcity and at a reasnably lw frward speed. The landing apprach, being a steady-state glide, is defined when the speed and equivalent value f LTD f the airplane (equivalent because D may include the effect f thrust) are knwn. The landing flare depends primarily n the aerdynamic characteristics f the airplane and the flare plan used by the pilt. In rder t calculate the effects f nly the aerdynamic characteristics n the flare characteristics, a general landing-flare plan must be assumed.

5 4 NACA TN 1930 It is realized that in a practical case a pilt cannt fllw any predetermined landing plan clsely and that the general flare plan assumed fr the present analysis may nt "be entirely realistic ver a wide range f lift-drag rati. In additin, grund effect has "been neglected in rder t simplify the calculatins. Since the primary purpse f this paper is t present a cmparisn f flare characteristics and illustrate general trends, it is believed that these assumptins d nt significantly affect the results. The assumptins cncerning excess speed and lift-cefficient variatin in the flare, based primarily n reference 1, which define the general flare plan assumed fr the present analysis are as fllws: The speed f an airplane at the start f the landing flare must be sufficiently abve the stalling speed t prvide the acceleratin necessary t curve the flight path s that the runway is apprached tangentially. The degree f curvature r abruptness f the flare Vf - v"s depends n the magnitude f the excess-speed rati 7? v. A starts f-flare (initial) excess-speed rati f 0.25 was used in reference 1 fr the airplane studied. Preliminary calculatins shwed that the initial-excess-speed rati required fr cmpletin f a flare increases a3 the value f L/D decreases and that a value f 0.25 is t lw t permit cmpletin f flares at lw values f L/D. In rder t prvide a cmmn basis fr calculatin and cmparisn f flares f airplanes having a wide range f values f L/D, a fixed end-f-flare (final) excess-speed rati fr all values f L/D was assumed. A value f 0.15 was chsen, based n landing recrds at mderate values f L/D. In rder t facilitate calculatin the flare is cnsidered t cnsist f three phases: Phase I is the transitin perid required t increase the value f C" L frm the value in the apprach t the maximum value reached in the flare. This increase in C L is assumed t be effected in 2 secnds by a sinusidal increase in nrmal acceleratin. Phase II is the perid f deceleratin at the highest lift cefficient reached in the flare, which is assumed t be 0.85C T Hnax The duratin f phase II depends n the vertical velcity at the start f the phase and the rate at which it is being decreased. In the flare calculatins, phase II cntinues until the vertical velcity is decreased t the value which is t be lst in phase III.

6 NACA TU 1930 Phase III-is the transitin perid during which the value f C L is decreased frm 0.85C L t the value fr level flight at the end f the flare where Vf equals 1.15Y a. The change in Cy is assumed t ccur in 1 secnd as the result f a sinusidal decrease in nrmal acceleratin. At the end f phase III the vertical velcity is zer and the flare is cmplete. This general flare plan permits calculatin "by a step-by-step methd f the landing-flare characteristics f an airplane having a knwn stalling speed and L/D plar. An exact slutin is precluded by the inability t write equatins expressing the variatin f the acceleratins with time in all phases f the flare. The step-by-step calculatins are simplified by a slutin starting frm the end f the flare and prceeding cnsecutively thrugh phases III, II,- and I because all the end-f-flare cnditins are knwn, whereas the initial excess speed is unknwn. This methd f calculatin is given in detail in the appendix. KE3ULTS AND DISCUSSION The general landing-flare plan.has been used as a basis fr the calculatin f the landing-flare paths f a series f hypthetical airplanes having a range f lift-drag rati frm 2-5 t 20.0 and a range f stalling speed frm 60 miles per hur t 475 miles per hur at sea level. A cnstant value-f L/D during the flare was assumed fr each airplane. The results f these calculatins have been pltted in chart frm t shw the effect f current design trends n landingflare velcity and distance requirements and t permit predictin f the landing perfrmance f prpsed airplanes. In additin, the pwer-ff landing-flare paths f three transnic wing cnfiguratins have been calculated, and the high-lift devices f each airplane have been evaluated. Landing-Flare Charts The assumptin f a cnstant lift-drag rati during the flare f a particular airplane permits the cmpilatin in chart frm f the results f the landing-flare calculatins. The assumptin f a cnstant value f L/D is feasible fr mst straight-wing airplanes in the landing cnditin as indicated by figure 1, which gives the variatin f lift-drag rati with lift cefficient btained frm wind-tunnel tests, fr sme representative airplanes. Fr sme airplanes, hwever, such as thse having extreme sweepback, the value f L/D ften varies cnsiderably during the flare as shwn in figure

7 NACA TN 1930 In this case, the charts d nt apply and a separate flare calculatin must be made; General trends.- The excess-speed rati required at the start f the flare fr cmpletin f the general flare plan is given in figure 2. The curve shwn is the lcus f the required initial-excess-speed ratis determined by the step-by-step calculatins fr the ranges f i/ and stalling speed used, and it indicates an increasing excess-speed rati with decreasing i/ which is independent f stalling speed. Unfrtunately, extensive flight data are nt available fr cmparisn with the calculated initial-excess-speed-rati curve. Hwever, pilt bservatins during glides and landings f several airplanes having lift-drag ratis "between k and 5 (pwer-ff landings recently made at the Langley Labratry f fighter-type airplanes having prpellers) and the initial-excess-speed ratis given fr the airplane f reference 1 ( = 7-9) indicate that the trend f the curve and rder f magnitude f the required initial-excess-speed ratis are realistic. As the value f i/ decreases belw abut k, the indicated initialexcess -speed rati increases rapidly t values appreciably higher than thse generally assciated with present-day airplanes. A presently prpsed high-speed airplane having a triangular wing (airplane A f fig. l) indicates a pwer-ff initial-excess-speed requirement f 0.57V S, which crrespnds t a speed lss during the flare f 0.^2V g. At relatively high values f L/D the lss in speed during the flare is small and, accrdingly, the excess speed required at the start f the flare is lw. Fr a flare at a value f L/D f 10 the decrease in speed during the flare is 0.05V 3, and at a value f L/D f 20 the decrease is 0.01V 8. Figure 3 shws the effect f lift-drag rati and stalling speed jv a ~ 1 n the flight speed and sinking speed at the start f the hax/ flare. At a cnstant value f L/D the flight speed increases in prprtin t the stalling speed, because the lss in speed during the flare is a cnstant percentage f stalling speed. Crrespndingly, at a cnstant value f L/D the sinking speed at the start f the flare, which is prprtinal t the apprach speed, als varies directly with the stalling speed. Fr a given stalling speed, the sinking speed increases as the value f L/D decreases because f the steepening f the glide-path angle and the increasing excess-speed requirements. The maximum nrmal acceleratin and the time duratin f the calculated flare paths are given in figures k and 5, respectively. Figure k indicates that the maximum nrmal acceleratin is primarily

8 NACA TN 1930 dependent n the lift-drag rati, althugh at a lw value f LTD stalling speed has sme effect. Since the maximum nrmal acceleratin, at a given stalling speed, is prprtinal t the excess-speed rati, the maximum nrmal acceleratin increases as the value f L/D decreases. The calculated landing flares have a minimum-time requirement f 3 secnds because the flare plan assumes a 2-secnd phase I and a 1-secnd phase III. At a cnstant value f L/D, the increase in time required is apprximately prprtinal t the increase in stalling speed (fig. 5) and, at a given stalling speed, the time required decreases as the value f L/D increases. The hrizntal-distance requirements fr the landing flare are shwn in figures 6 and 7, in which the limiting lines (dashed) are vertical-velcity cnturs f 10 and 75 feet per secnd. The hrizntal distance required at a cnstant value f L/D increases at an increasing rate with stalling speed (see fig. 6) "because bth the flight speed during the landing flare and the time required fr the. flare increase with stalling speed. At a cnstant stalling speed,, changes in the lift-drag rati effect relatively small changes in. hrizntal distance "because, as shwn in figures 3 and 5, variatins in the lift-drag rati effect nly small changes in flight velcity and landing-flare time. The hrizntal distance required frm an altitude f 50 feet t the end f the flare (fig. 7) is als primarily dependent n stalling speed. At a given stalling speed, hwever, this distance increases smewhat as the value f L/D increases. The ttal vertical distance required fr the flare, r altitude at which the flare must "be started, is shwn in figure 8 t increase as stalling speed increases and the value f L/D decreases. These results indicate that the cmbinatin f high stalling speed and lw lift-drag ratis encuntered in many prpsed high-speed airplanes will result in relatively high pwer-ff gliding speeds and sinking speeds at the start f the flare and, cmpared with cnventinal airplanes, will require greater vertical and hrizntal distances fr cmpletin f the flare. The cnvergence f the vertical velcity and distance cnturs f figures 3 and 8, respectively, indicates that at lw values f L/D an incremental change in stalling speed effects a relatively large change in the rate f descent and the altitude at which the flare must be started. Vertical velcity-altitude relatinship.- The vertical velcity t be encuntered during the landing f an airplane is an imprtant cnsideratin affecting the pilt's ability t execute successfully the landing flare. High vertical speeds in the apprach cmplicate the judging f the altitude at which the flare shuld be started, and high vertical speeds in the final stages f the landing flare increase the difficulty f simultaneusly decreasing vertical velcity and

9 ö NACA TN 1930 altitude t zer. Because the significance f vertical velcity depends n the crrespnding altitude, the variatin f vertical velcity with altitude is cnsidered an imprtant factr. Fr the airplane f reference 1, sinking speeds abve 25 feet per secnd at the start f the flare (apprx. 50-ft altitude) culd nt he cnsistently handled with safety and accuracy. Figures 9(a) and 9(b) shw the sinking-speed variatin with altitude fr airplanes having cnstant values f LTD f k and 7.5, respectively, and varius start-f-flare sinking speeds (crrespnding t different stalling speeds). The plts indicate that at a cnstant lift-drag rati the vertical velcity remaining at an altitude f 50 feet is virtually independent f the initial vertical velcity. At a lift-drag rati f h- fr varius stalling speeds, start-f-flare sinking speeds varying frm 35 t 75 feet per secnd are reduced t a range frm 33 t abut 38 feet per secnd at an altitude f 50 feet, and likewise at a value f L/D f 7.5, start-f-flare sinking speeds frm 25 t V? feet per secnd are reduced t a range frm 2^.5 t 28.5 feet per secnd at an altitude f 50 feet. Althugh the vertical velcity at an altitude f 50 feet is relatively independent f stalling speed, it increases with decreasing value f L/D. The effect f lift-drag rati n the vertical velcity at an altitude f 50 feet fr a representative stalling speed is shwn in figure 10. The start-f-flare vertical velcities have been included in the figure fr cmparisn. Althugh the vertical velcity lst during the initial phases f the landing flare increases as the lift-drag rati decreases, the vertical velcity remaining at an altitude f 50 feet als cntinues t increase with decreasing value f L/D. The sinking speed at 50 feet increases frm 21 feet per secnd at a value f L/D f 10 t U3 feet per secnd at a value f L/D f 3. These results indicate that airplanes landing at lw values f L/D and having high sinking speeds in the apprach will als have relatively high sinking speeds at an altitude f 50 feet, even thugh the stalling speeds may be lw. Predictin f flare characteristics.- The landing-flare charts can be used t predict the flare characteristics f an airplane having a small-percentage variatin in lift-drag rati during the flare. If the value f L/D is nt apprximately cnstant the charts d nt a PPly, & nd a separate flare calculatin by the methd described in the appendix is necessary. In the case f a pwer-ff landing flare f an airplane having given values f C-r, W/S, and L/D, the flare velcities, distance, and ther flare characteristics are btained directly frm figures 3 t 8. The pwer-n flare characteristics can be predicted by cnsidering that the thrust f the airplane is used t adjust the apprach value f L/D t the value which will give the desired startf -flare vertical velcity. Fr the chsen value f V y and the

10 NACA TN knwn values f W/s and Cj, figure 3 gives the crrespnding. value f L/D, which in cnjunctin with the value f W/S and CT permits the determinatin f the ther flare characteristics frm figures k t 8. The increment "between this value f L/D and the pwer-ff value f L/D at the same lift cefficient is indicative f the thrust required t btain the desired sinking speed. Pwer-Off Evaluatin f High-Lift Devices An analysis by the methd presented herein f the pwer-ff landing-flare characteristics f three transnic airplane wings indicates relative merits f high-lift devices nt apparent frm windtunnel data. Since each f the wings cnsidered had n fuselage, canpy, r landing gear, the results btained are t be used nly n a cmparative basis. The lift cefficients given are nt trimmed lift cefficients- The percentage variatin in L/D during the flare fr sme f these cnfiguratins was appreciable, in which case the charts were inapplicable and individual flare calculatins were made. The details f the cnfiguratins, fr which wing ladings f ko punds per square ft were assumed, and a summary f the results btained are given in table I. Wing swept back 37.- A lw-speed investigatin f a wing with the leading edge swept back 37 had been previusly cnducted t determine the effect f split flaps and duble sltted flaps n the aerdynamic characteristics. The basic wing had a value f C^^. f I.27 and an apprach value f L/D f lu.2, which give a start-f-flare flight speed f 195 feet per secnd at a. sinking speed f Ik feet per secnd. Deflecting the split flaps increased the value f C-r^ t I.65 and decreased the value f L/D in the apprach t 6.3. The net effect is a slight reductin in the start-f-flare flight speed and an increase in sinking speed t 30 feet per secnd, which required starting the flare ^0 feet, higher. The use f the duble sltted flap increased the value f CT t 2.32 at an apprach value f L/D f 8.0 and resulted in a desirable 1+5-ft-per-secnd decrease in apprach flight speed with nly a i4--ftper-secnd increase in sinking speed and an appreciable reductin in the hrizntal distance required fr the flare (see table I). These results demnstrate the imprtance f cnsidering the changes in lift-drag rati ften resulting frm the use f high-lift devices. Wing swept back ^8.- The advantages f leading-edge flaps n a wing with the leading edge swept back ^8 are indicated by predictin f the landing-flare characteristics. The basic wing had start-fflare sinking and gliding speeds f 37 feet per secnd and 263 feet per secnd, respectively, a hrizntal-distance requirement f 1250 feet, and a starting altitude f 90 feet. The deflectin f leading-edge

11 10 NACA TN 1930 flaps increased C T nly abut 0.2 but effected a sizeable increase Tnax in lift-drag rati which reduced the start-f-flare sinking speed t almst ne-half the frmer value and, als, substantially decreased the apprach 3peed and the distance requirements. Trailing-edge flaps installed n this wing gave slightly larger increases in maximum lift cefficient, but crrespnding decreases in the value f L/D nullify any imprvement in flare characteristics. Triangular wing.- The landing flare f a triangular wing f equilateral plan frm indicates pr landing characteristics. The ba3ic wing had a C T f 1.08 and an apprach value f L/D f "-max which give start-f-flare sinking and gliding speeds f Vf feet per secnd and 26k feet per secnd, respectively, and vertical- and hrizntal-distance requirements f 105 feet and 1080 feet, respectively. Semispan and full-span leading-edge and trailing-edge flaps tested n this wing gave slight increases in Cr and decreases in the apprach v -"-"max L/D which effected n appreciable imprvement in flare characteristics. Similar undesirable pwer-ff landing characteristics are predicted fr the triangular-wing airplane (cnfiguratin A f fig. 1 (gear dwn)), which indicates a start-f-flare sinking speed f 70 feet per secnd at an altitude f 176 feet and a sinking speed f ^3 feet per secnd at an altitude f 50 feet. The high sinking speeds in the lwaltitude stages f the flare culd be reduced by the use f a higher initial excess speed and lwer lift cefficients during the flare. This methd f reducing sinking speed, hwever, increases the hrizntaldistance requirement. These results indicate that pwer-ff landings at cnventinal airprts f sme triangular-wing airplanes may nt be feasible. A cmparisn f the distance requirements f the basic triangular wing with thse f a hypthetical wing, having the same value f CT (l.08) and a cnstant value f L/D f ^>.k thrughut the flare, indicates that a decreasing lift-drag rati during the flare reduces the distance requirements. If the value f L/D f the triangular wing had remained cnstant during the landing flare, the vertical and hrizntal distances wuld have been increased t 130 feet and 1250 feet, respectively. In cnnectin with triangular-wing airplanes, the large attitude change likely t be required in the landing flare because f the lw aspect rati and the lw lift-drag rati is cnsidered a factr that may cmplicate the landing technique. The landing-flare calculatins, by giving the lift cefficients and flight path during the flare, permit determinatin f the attitude f the airplane. Figure 11 shws the attitude f the triangular wing at three pints during a pwer-ff landing flare and, fr cmparisn, the crrespnding attitudes during a

12 NACA TN 1930 H pwer-ff flare f a straight-wing airplane (cnfiguratin C f fig. 1). The results indicate an attitude change f l8 fr the triangular. wing, whereas fr the straight-wing airplane (cnfiguratin C) the 1 variatin in attitude is nly 9r. SUMMARY OF RESULTS The results f calculatins t determine the effect f airplane aerdynamic characteristics n landing-flare characteristics are summarized as fllws: V f ' v s 1. The excess-speed rati required at the start f the v s flare increases as the lift-drag rati f an airplane decreases, and at a lift-drag rati belw abut k, initial-excess-speed ratis increase rapidly abve thse generally assciated with present-day airplanes. 2. Fr pwer-ff landings f sme airplanes designed specifically frm high-speed cnsideratins, the changes in lift-drag rati resulting frm deflectin f high-lift devices have first-rder effects n landing-flare characteristics and may nullify the effect f maximum-lift-cefficient increases. The present analysis prvides a basis fr determining the cmbined effect f maximum lift cefficient and lift-drag rati n landing-flare characteristics. 3. Airplanes landing at lw lift-drag ratis will have relatively high sinking speeds at the start f the flare and at an altitude f 50 feet even if the stalling speeds are relatively lw. Fr the landing-flare plan assumed in the present analysis, the magnitude f the vertical velcity at 50 feet is primarily dependent n the lift-drag rati. k. Pwer-ff landing flares f airplanes which have relatively lw lift-drag ratis and high stalling speeds will be required t start at relatively high altitudes. 5. Results 3 and k indicate that pwer-ff landings f sme airplanes designed specifically frm high-speed cnsideratins may nt be feasible at cnventinal airprts. 6. Airplanes having high stalling speeds (lw maximum lift cefficient and high wing lading) will require relatively large hrizntal distances fr either pwer-il r pwer-ff landing flares. Langley Aernautical Labratry Natinal Advisry Cmmittee fr Aernautics Langley Air Frce Base, Va., May 11, 19^9

13 12 NACA TN 1930 APPENDIX METHOD OF CALCULATING LANDING FLARE The methd f calculating the landing flare f an airplane is described herein. In rder t facilitate calculatin the flare is cnsidered t cnsist f three phases as discussed in the sectin entitled "Landing-Flare Calculatins." As an illustratin f the cmputatinal prcedure, the results f step-"by-step calculatins f the landing flare f airplane A (fig. l) are given in table II. The step-"by-step calculatins are "begun at the end f the flare and prgress cnsecutively thrugh phases III, II, and I "because all f the cnditins at the end f the flare are knwn, whereas the start-f-flare excess speed is unknwn. In the discussin which fllws^the numerical subscripts will refer t time in secnds measured frm the end f the flare. The variatin f nrmal acceleratin with time during the flare is shwn in figure 12. Start f flare -Time, t, sec 1 0 End f flare Figure 12.- Variatin f nrmal acceleratin with time during landing flare.

14 NACA TW The cnditins knwn at the start f the calculatins (end f flare) are as fllws: V v. = 0 Vf = 1.15Y S feet per secnd a n =1.0 a^ = feet per secnd per secnd (see frmula given in L sectin entitled "Phase III") Phase III Nrmal acceleratins.- In phase III, the nrmal acceleratin a n increases sinusidally frm 1.0 at t n u t the value at 0.85C T -Hmax at t]» The value f a n at 0.85CT can he estimated frm figure 13 "by use f the average value f L/D crrespnding t CL and 0.85CT. This value f a is checked when the step-hy- 4BX J^l.0 step calculatins have prceeded t 1 secnd. If the value f Y., f 1.0 and the assumed value f a^ d nt crrespnd t 0.85C T, 1.0 -haax a new value f a^ is assumed. This is a cnverging prcess requiring few estimates. The frmula fr a^ during phase III is a n - 1. n 1.0 a = n sin (2t - 1) + 1 where t represents the time in secnds frm the end f the flare. Vertical velcity.- In the calculatin f vertical velcity during the flare, the csine f the flight-path angle is cnsidered unity. (At the maximum flight-path angle cnsidered in the analysis, cs 7 > O.99 during phase III and cs 7 > O.97 during phase II. In phase I, when cs 7 reaches a minimum value f 0.9^, the value f a n is relatively small; thus, the errr in V T is negligible.) The vertical-velcity increase during any time increment At is therefre represented "by the area under the nrmal acceleratin-time curve fr that increment and is given "by the fllwing frmula: a^ AV V = ^ - 1 Pt4Atr 1 + sin (2t - 1) 2 dt

15 11+ NACA TN 1930 The evaluatin f this integral fr the p-secnd time intervals used in the calculatin f phase III gives A V t 0.5 " 2-92 (V " 1 AT '0.5 t 1.0 " 13 - l8 ( a ni. " X ' The vertical velcity at the end f each time increment equals the velcity at the start f the increment plus the velcity change during the increment. Vertical distance.- The vertical distance cvered is given "by the fllwing frmula:, s v = 32.2 an 1.0 ~ 1 t2 sin < 2t - D! The evaluatin f this frmula fr phase III gives As v = ^.79^^ - l) Deceleratin alng flight path.- Deceleratin alng the flight path &f is derived by use f the vectr diagram f figure 12: Then. y Frce in directin f flight = W sin 7 = W V f Frce in drag directin (? L = ( ) a n w c3 y 32.2 sn OOS ' - % In the determinatin f a f frm this frmula at a specific time during phase III, the values f a and V v are knwn, and the values f Vf, D/1, and cs 7 fr the previus increment are used. The time increments are chsen small enugh t permit this apprximatin. Flight velcity.- The flight-velcity increase during a time increment is calculated frm the average f the deceleratins at the

16 KACA TN start and end f the increment. The flight -velcity at the end f each time increment equals the velcity at the start f the increment plus the velcity gained during the increment. Hrizntal distance.- The hrizntal distance cvered during a time increment is calculated frm the average f the hrizntal velcities at the "beginning and at the end f the increment. C^ and l/p. - The values f C L and L/D at any time are determined frm the crrespnding values f Vf, a n, and cs 7. The frmula fr C L is W 2a - cs 7 C L = -^4 pv f 2 Phase II Phase II is calculated "by cnsidering that the values f a n and &f are cnstant ver the time increment chsen fr ne step f the calculatins. Since a^ changes substantially in 1/2 secnd and the acceleratin-time histry is nt predetermined as in phases III and I, -^--secnd time increments were used in the calculatin f phase II. The step-"by-step develpment f phase II is demnstrated "by frmulas fr the first step. Vertical velcity.- The frmula fr btaining the vertical-velcity change during a 2_-secnd time increment is 10 AV, r n,, _ = 32.2/a-,, - ly 'n.0 ta 1.2 = 32l2 (^.0 " f The vertical velcity at end f each time increment equals the velcity at start f increment plus the velcity change during the increment; r T 1.2 v 1.0 V Vl O = V Vl A + A V"v v 1<0 tq lm2

17 16 NACA TN 1930 Flight velcity.- The frmulas fr btaining the flight-velcitychange and the flight velcity at end f each time increment are aa fllws: AV fl.o t 1.2 = a fl.o At V fl.2 =V fl.0 +A7 fl.0tl.2 Vf Nrmal acceleratin. - The value f a^,? can "be calculated when is knwn. At cnstant C-r, a n «Vf2; thus, V.2 ^1.2^ 'fi./ n 1.0 Deceleratin alng flight path.- The value f a f calculated by the frmula derived in the analysis f phase III; thus, is "fl.2 * B "- ~ '«" fe Vertical distance and hrizntal distance.- The vertical and hrizntal distances cvered in ne time increment f phase II are calculated frm the average f the vertical and hrizntal velcities, respectively, at the beginning and at the end f the increment. This prcedure is cntinued in -^--secnd steps until a pint is reached frm which the executin f phase I will result in start-fflare cnditins that satisfy the requirement f zer deceleratin alng the flight path: that is, Zx = 2. cs 7. The pint at which Vf L phase I shuld be started is determined by trial. If phase I is started t early, the value f a^ at the start f the flare is psitive; and if phase I is started t late, the value f a^ is negative. An estimatin f the pint at which phase I shuld be started may be btained as fllws: By use f the value f i/ at 0 -^cl^ajr b* frm figure 2 an apprximate value f initial- excess-speed rati and crrespnding apprach Yf. Then, use this

18 NACA TN value f v> t apprximate Cj, (L/D) and T (subscript a a Ll a a refers t apprach). The vertical velcity at the start f phase I plus the vertical velcity t he gained in phase I (see sectin that fllws) shuld equal V v. a Phase I Nrmal acceleratin.- In phase I, the nrmal acceleratin a n decreases sinusidally frm its value at the start f phase I t 1.0 tw secnds later. The frmula fr a n during phase I is an = -^ 1 + sin (t + 1)] + 1 where subscript P refers t pint at which the calculatin f phase I is started (see fig. 12) and t' is time frm the start f the calculatin f phase I. Vertical velcity.- The vertical-velcity increase during any time increment At is given "by the fllwing frmula: AV V = ~ / 1 + sin (f + 1) dt The evaluatin f this integral fr i-secnd intervals gives AY T first half-secnd f phase I = 15.30(a np - l) AV V secnd half-secnd f phase I = 11.05(a n p - 1) AV V third half-secnd f phase I = 5-05(a n - l) AV V final half-secnd f phase I = 0.8(a n - 1) The vertical velcity at the end f each time increment equals the velcity at the start f the increment plus the velcity change during the increment.

19 18 NACA TN 1930 Vertical distance.- The vertical distance cvered is given "by the fllwing frmula: s v = T v P V a np " 1 -rt - -j sin (* +1) + The evaltatin f this frmula fr phase I gives As v = 2T vp + ^5.25(a np - l Deceleratin alng flight path, flight velcity, and hrizntal distance.- The deceleratin alng the flight path, the flight velcity, and the hrizntal distance are calculated "by the methd used in phase III.

20 NACA TN KEFERENCES Gustaf sn, F. B-, and 0' Sullivan, William J., Jr.: The Effect f High Wing Lading n Landing Technique and Distance, with Experimental Data fr the B-26 Airplane. WACA ARE L4K07, 19^5

21 20 NACA TN 1930 O 00 ON H H ON ^ -P CO th CO CO v in v ON O 8 H v ON a) a) > > ir 3 3 H CO VO OJ v H OJ v" OJ CVJ 3 CO CO H t- c OJ t- r -p -p r "3" II O -d (D m cd ^> Ü 00 9 OJ t- OJ l e v VO VO ON v S> OJ c OJ H c A VO H O ON OJ JP CO A CO CM CO OJ A (D p< a> r pi -p. p ID P) O P P cd (D O P <D ID -P I t CD "rl J ir VJ V ir <D fl <D A -P p S 5 d & -d d.p c* HT i4" S <D -rl P<P m cd HH P< v ir 00 n OJ th «in O O d d 0 O P P Ti ä SI > t» <n ID bl) b(i 1 cd -P -P Ö n <D 0)» 0 fc fh (D a> CM FM

22 HACA TW TABLE II. - STEP-BY-STEP CALCULATIONS OF THE LANDHfG- FLARE OF AIRPLANE A OF FIGURE 1 t L **. AV Vv a f AT f v f s T s h L/D D/L cs I * ' ) x " Based n cnditins at t = 5-42, a^ = 0.

23 22 NACA TN 1930 <H th Q v.

24 NACA TK z?_ I g! -p <0 u 8 & 00 H Pi H -d ö <D TH Al pi a (D U O -P SS <0 Tj P) <l O Ü T «in U P CQ % ^l_^j '0//0J paads-ssexa-/d/j/u/ cu

25 2k NACA TN 1930 P m ID P Ü O H <D > <D ä H s p m P «M O Ö 13 1 PR

26 NACA TN P J N

27 26 NACA TN 1930 <V fz? 1 ^ t ^ ^ P <i ä H v «0 11 > _. 1 ^ v I S» 1 A *»» V I 1 5 0> t v rl I I If > * ^ *v» >j P t t ^j 'H d P ti -P 03 H I 1A <D t *l yaw S/M ^

28 1 NACA TW K 1 1 ^?0 -d d 1-1 A V A A I I V I A w 1 t 1 V 1 ^ i A i *i" R A V. 1 rv- A K ]»0 0 '[V < SM 5 S -4 C t -P <D 'S H Ö d H p -d t (D Ü P 09 Q CY 8H i <l Q ON ^! 8^! ' cvi $ N Ö»a < cvi 00 XDW 1Q S/M f* I VO (D & t

29 28 NACA TW 1930 <D Xi p t-l d Ö JS p O P P <D O in d pi P P d g. ra Hi p ä H d S/M ^

30 NACA TN ? v 1 N I 1 4 >, 1/ L 1 s A V. 1, N V >l v ^ if> ^ ^ > fr A V 1 * Q <i > H^ ^ <A, SK *> v S t <l «0 XDUl l0 ~S7M ^ ] *> A > A W a CM S > Q ^ ^ < 5) t?n» s a t <i d Hi -P ä H t H <D -P CM d 2 a* ö ti -p xa d d -P u Ö Id [ CO u t

31 30 NACA TN (a) k.k. Figure 9.- Variatin f sinking speed in the landing flare with altitude fr several stalling speeds.

32 NACA TN V*. ft/sec I / 21 '4. / 2't 7> / r 1 tf ^ /j ) // // / 20 /y ^ if^, /O V v, ft/sec (T) = T.5. Figure 9.- Cncluded.

33 32 NACA TN Initial v (A V v at 50-ft altitude ::: * C s. ^v ^ 10. L/D NACA,^ Figure 10. Variatin with L/D f the initial sinking speed and the sinking speed at an altitude f 50 feet fr a stalling speed f W 167 feet per secnd. = lj-0 punds per square ft; CT = 1.2.

34 NACA TW M ' A s fa

35 3^ NACA TN 1930 saun 6 'u D NACA-Langley

36 TITLE: An Analysis l the Effect f Lift-Drag Rati and Stalling Speed n Landing-Flare Characteristics AUTHORIS) : Lvell, 3. Calvin; Lipsn, Stanley ORIG. AGENCY : Langley Aernautical Lab., Langley Air Frce Base, Va. PUBLISHED BY : Natinal Advisry Cmmittee fr Aernautics, Washingtn, D. C. Sept' 49 Unclass. ii-s- English ABSTRACT: PAGO 34 luiktoations tables, graphs, drwg ATI (Nne) TOW. AGEKCV NO. Tw-man PUCUSMKO A0BKY MO. (Same) Calculatin results are presented f the landing-flare paths f a series f hypthetical airplanes having systematically varying characteristics t shw the effect f lift-drag rati and stalling speed n landing-flare velcities and distance requirements. Results indicate that airplanes landing at lw lift-drag ratis will have relatively high sinking speeds at the start f the flare and at an altitude f 50 ft, even if the stalling speeds are relatively lw. Airplanes having high stalling speeds will require relatively large hrizntal distances fr either pwer-n r pwer-ff landing flares. DISTRIBUTION: SPECIAL. All requests fr cpies must be addressed t: Publishing Agency DIVISION: Aerdynamics _ SUBJECT HEADINGS: Airplanes - Landing characteristics SECTION: Perfrmance (2) (08470) ATI SHEET NO.: R Cntrl Air Dces%3ta OGc WrieM-Pltcnca Air Ptt Cssa, Dyen. OW AI3 TGCKMXAl IX32X