1、NASA Technical Paper 1157Ground Distance CoveredDuring Airborne HorizontalDeceleration of an AirplaneAPRIL 1978V #NASAProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NASA Technical Paper 1157Ground Distance CoveredDuring Airborne HorizontalDecelerati
2、on of an AirplaneWilliam H. PhillipsLangley Research CenterHampton, VirginiaNASANational Aeronauticsand Space AdministrationScientific and TechnicalInformation Office1978Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-SUMMARYAn analysis is presented
3、of the distance an airplane floats with respectto the ground during deceleration at constant altitude, taking into account theeffects of a constant wind. By use of suitable nondimensionalizing parameterssuggested previously in the literature, data applicable to all airplanes arepresented by means of
4、 a single family of curves. The application of thesecurves in a typical example is included.INTRODUCTIONA study of the phase of flight in which an airplane decelerates at constantaltitude has several practical applications. If an airplane completes the land-ing flare with excessive speed, the pilot
5、may elect to hold the airplane off theground until a suitable touchdown speed or attitude is reached. General-aviationairplanes operating at large airports frequently approach at speeds higher thannormal to maintain their spacing in the traffic pattern. Measurements haveshown that, even in routine o
6、perations, many pilots land with excessive speed(ref. 1). The flight path of an airplane after an aborted take-off is anothersituation which may involve deceleration at constant altitude. Some situationsexist involving an excessive tendency to float during a landing. For example,landing with a tail
7、wind increases the distance covered. The effect of encoun-tering a head wind at low altitude is an increased initial airspeed which mayalso lengthen the floating distance. Sailplanes, because of their low drag,may float excessively in landing, particularly if a deceleration device such asa drag para
8、chute fails to work. In all these applications, the presence of windhas an important effect on the ground distance covered.A rational analysis of the landing of an airplane is given in reference 2.This analysis includes the phases of glide, flare, deceleration at constant alti-tude (called the float
9、 phase), and the ground run. Constant deceleration (corre-sponding to constant lift-drag ratio) was assumed during the float phase, anapproximation that was adequate for the purpose under consideration. Approxi-mate methods for the calculation of landing distance sometimes neglect the floatphase ent
10、irely (ref. 3). Some consideration of the role of the float phase indetermining certification standards for the landing distance of transport air-planes is given in reference 4 but again the assumption of constant lift-dragratio was made. In cases in which the flare is completed with considerableexc
11、ess speed, however, a more accurate method for calculating the distancecovered during the float phase would be desirable.A solution of the equations governing deceleration in level flight is pre-sented in reference 5. The analysis of reference 5 shows that by use of suit-able nondimensionalizing par
12、ameters, the solutions for air distance and airspeedmay be expressed by means of a pair of curves applicable to .all types of air-planes. The present report extends these results by including the effects of aProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IH
13、S-,-,-constant wind and solving for the ground distance covered during deceleration atconstant altitude. By use of the same nondimensionalizing parameters as thosesuggested in reference 5, the results for a series of values of wind velocityare given by a single family of curves applicable to all typ
14、es of airplanes.SYMBOLSC constant of integrationCD drag coefficient, pP U2S2CD,o profile drag coefficientCL lift coefficient, LP U2S2CL,max maximum lift coefficientD dragg acceleration due to gravity (Ig = 9.807 m/sec2)K variation of CD with C2L liftlp aerodynamic penetration, 2mPSCD,0m massS wing a
15、reas float distance with respect to grounds1 nondimensional float distance with respect to ground, sO true airspeedUg ground speedUr reference velocity,Os true stall speedUw wind speedProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-U1 nondimensional
16、airspeed, uOrUa nondimensional ground speed, _UrUs nondimensional stall speed, s“rUw nondimensional wind speed, wUrW weightx = U2Y flight-path anglep air densityA dot over a symbol denotes differentiation with respect to time.ANALYSISThe vertical and longitudinal forces acting on an airplane in glid
17、ingflight with wings level are shown in figure 1. The longitudinal equationsin flight-path axes are2U + g sin Y + (CD,0 + KCL2)? = 0 (1)mP 02SUt + g cos Y - CL i _ = 0 (2)mIn level flight, Y = Y = 0- Equation (2) then becomesSubstituting this value in equation (1) gives U2s 2U + CDf0 2 _ + K_Eil_=0
18、(4) . “2sProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-If the velocity over the ground is defined as Ug = U + Uw, where Uw is asteady wind directed along the flight path, the differential equation govern-ing the distance an airplane will float over
19、 the ground at constant altitude isU = u % = 2mpS(Ug .org = CDoPS (Ug - Uw)2 _ 2Kmg2 (5)ds 2m ug pSUg(Ug - Uw)2As shown in reference 5, the solution of this equation may be simplified byexpressing distance in terms of a reference length called the aerodynamic pene-tration which is defined by the fol
20、lowing equation:= 2mc PSCD,0and by expressing velocity in terms of a reference velocity given byThis reference velocity is the speed at which CDfO = KC2 and is thereforethe speed for the maximum ratio of lift to drag. Let s1 = s/Zp, Ug = Ug/Ur,and Uw = Uw/Ur. Equation (5) then becomesd 1), the angle
21、 should be between ir/2 and IT.RESULTSThe curves of figure 2 show in nondimensional form the float distance s1required to decelerate as a function of airspeed U1, for various values of tailwind or head wind. The results, based on equation (12), are presented in termsof the nondimensional parameters=
22、 s U uwJwwhere lp is the aerodynamic penetration defined as 2m/pSCDfO. As wasmentioned previously, these nondimensionalizing parameters are suggested inreference 5.The values of s1 are plotted as positive quantities in figure 2. Thenegative sign of s1 shown in equation (12) is ignored. This negative
23、 signin the formula results from the fact that the distance is increasing in a posi-tive direction as the airplane decelerates. If the point s1 = 0 correspondsto the point where the ground speed is zero, the airplane is, strictly speaking,in the region of negative values of s1 during the period of d
24、eceleration. .The constant of integration C in equation (12) may be used to place thezero of the scale of s1 at some arbitrary location. In the data presented,the value of C is determined such that, for tail winds, the value of s1 = 0when U1 =0, and for head winds, the value of s1 = 0 when U = 0 oru
25、- = -uwUq =Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-In practice, the float distance required is the distance covered betweensome initial and final values of airspeed. This distance may be obtained asthe difference between the values of s1 at t
26、hese values of airspeed. Themaximum float distance is usually obtained if the final airspeed is the stallspeed. The nondimensional stall speed isA vertical line may be drawn in figure 2 showing the airspeed at touchdown tofacilitate reading the values of float distance for various values of windspee
27、d. In the unlikely event that a head wind exists with velocity greaterthan the touchdown speed, the forward progress of the airplane stops whenU1 = -Uw. In this case, the maximum forward penetration of the airplane maybe obtained from the value of s1 at the initial airspeed, inasmuch as thefinal val
28、ue is plotted as zero when U1 = -Uw.DISCUSSIONThe results of this analysis are based on the assumption that the drag isgiven by an expression of the form CD = CDfO + KCj. If the airplane is float-ing at low altitude, the values of CDfO and K may be influenced by groundeffect. Values appropriate to t
29、he altitude under consideration should thereforebe used. The primary effect of proximity to the ground is a reduction in theinduced drag as expressed by the value of K. At high values of lift coeffi-cient, the ground effect may also reduce the effective dynamic pressure. Ifthe airspeed is considered
30、 to be the speed with respect to the distant air mass,as is required for calculation of the distance covered, the effect of thisreduction in dynamic pressure may be approximated by appropriate modificationsin C)fO and K. The effect of an idling propeller or jet engine may intro-duce drag or thrust t
31、erms that differ in form from the assumed expressionCjj = CDfO + KC. A more detailed analysis would be required to account forthese effects.The value of float distance for a particular case may be read from figure 2and converted back to dimensional form. If more accuracy is required, the valuemay be
32、 calculated from equation (12). Alternatively, the entire plot presentedin figure 2 may be converted back to dimensional form for application to a par-ticular airplane. An example is shown in figure 3, which presents the float dis-tances for a general-aviation airplane with the characteristics shown
33、 in thefigure. The drag characteristics assumed correspond to a lift-drag ratio of6.98 at the stall (CL = 1.2). This value of lift-drag ratio is representativeof the condition of flaps and landing gear down.In reference 5, the float distance and time are each given as functions ofairspeed by express
34、ions similar to the first and second terms, respectively, ofequation (12). Both time and distance are involved in the present analysisbecause, with a head wind, the distance the airplane moves with respect to theair must be corrected for the movement of the air with respect to the groundProvided by
35、IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-during the time of flight. In the derivation presented herein, however, theground distance is determined as a function of airspeed directly, without theintermediate step of determining time of flight.CONCLUDING REM
36、ARKSAn analysis is presented of the distance an airplane floats with respectto the ground during deceleration at constant altitude, taking into account theeffects of a constant wind. By use of suitable nondimensionalizing parameters,data applicable to all airplanes are presented by means of a single
37、 family ofcurves. These results provide a rational approach for estimating the contribu-tion of this floating regime of flight to the distance needed for landings oraborted take-offs.Langley Research CenterNational Aeronautics and Space AdministrationHampton, VA 23665March 13, 1978REFERENCES1. Goode
38、, Maxwell W.; OBryan, Thomas C.; Yenni, Kenneth R.; Cannaday, Robert L.;and Mayo, Marna H.: Landing Practices of General Aviation Pilots in Single-Engine Light Airplanes. NASA TN D-8283, 1976.2. Glauert, H.: The Landing of Aeroplanes (Part I). Technical Report ofthe Advisory Committee for Aeronautic
39、s for the Year 1919-20, Vol. II,pp. 513-525. (Also available as R. and Hage, Robert E.: Airplane Performance Stabilityand Control. John Wiley and Korn, Theresa M.: Mathematical Handbook for Scientistsand Engineers. Second “ed. McGraw-Hill BookCo., Inc., c.1968, pp. 934, 938.Provided by IHSNot for Re
40、saleNo reproduction or networking permitted without license from IHS-,-,-Forces acting n anProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2.0cSS12cI -8o.4Nondimensionalwind velocity, Uw Tail wind Head wind0 1 2 3 4Nondimensional true airspeed, UFigu
41、re 2.- Nondimensional float distance required to decelerate as a function ofinitial airspeed for various values of wind, s1 = _; u1 = UV Jw 2mPSCD,OProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-200016001200oo5 800400Stall speed, UCL = 1.2Wind veloc
42、ity, U . m/secw20.91,Tail windHeadwindTrue airspeed. U, m/secFigure 3.- Float distance for a typical general-aviation airplane as afunction of initial airspeed. Cp = 0.1 + 0.050; ra/S = 68.72p = 1.226 kg/m3; lp = 1121 m.10Provided by IHSNot for ResaleNo reproduction or networking permitted without l
43、icense from IHS-,-,-1. Report No.NASA TP-11572. Government Accession No. 3. Recipients Catalog No.4. Title and SubtitleGROUND DISTANCE COVERED DURING AIRBORNE HORIZONTALDECELERATION OF AN AIRPLANE5. Report DateApril 19786. Performing Organization Code7. Author(s)William H. Phillips8. Performing Orga
44、nization Report No.L-120089. Performing Organization Name and AddressNASA Langley Research CenterHampton, VA 2366510. Work Unit No.505-06-63-0211. Contract or Grant No.12. Sponsoring Agency Name and AddressNational Aeronautics and Space AdministrationWashington, DC 2054613. Type of Report and Period
45、 CoveredTechnical Paper14. Sponsoring Agency Code15. Supplementary Notes16. AbstractAn analysis is presented of the distance an airplane floats with respect to theground during deceleration at constant altitude, taking into account the effects ofa constant wind. By use of suitable nondimensionalizin
46、g parameters, data applicableto all airplanes are presented by means of a single family of curves.17. Key Words (Suggested by Author(s)Float distanceLanding distance18. Distribution StatementUnclassified - UnlimitedSubject Category 0519. Security Qassif. (of this report)Unclassified20. Security Clas
47、sif, (of this page)Unclassified21. No. of Pages1022. Price*$4.00* For sale by the National Technical Information Service, Springfield, Virginia 22161 NASA-Langley, 1978Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-National Aeronautics andSpace Admi
48、nistrationWashington, D.C.20546Official BusinessPenalty for Private Use, $300SPECIAL FOURTH CLASS MAILBOOKPostage and Fees PaidNational Aeronautics andSpace AdministrationNASA-451US.MAILNASA POQTM ACTFP If Undeliverable (Section 158rus 1 MA:, i E.K . , Do Not ReturnProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
