Dieter Scholz Drag Estimation - HAW Hamburg
Dieter ScholzDrag EstimationBased on the Aircraft Design Lecture Notes and Master Thesis of Roberto Segovia García.Hamburg University of Applied Sciences. 2017In cruise we calculate the drag coefficient from: Zero lift drag: Wave drag(Chapter 1)(Chapter 2)For cruise,but for take-off (with initial climb) and landing (with approach) the zero lift drag coefficienthas further components, because high-lift devices may be deployed and/or the landing gearmay be extended. Especially the landing gear adds a considerable amount of drag.For cruise the Oswald Factor e is calculated from the presentation "Estimating the OswaldFactor from Basic Aircraft Geometrical Parameters" (see under http://OPerA.ProfScholz.de"Method only"). Without any further calculation e eCR 0.85 can be taken as a standardparameter (for moderate cruise Mach numbers).For take-off (with initial climb) and landing (with approach) the Oswald Factore eT/O 0.7 can be taken as a standard parameter together with eCR 0.85. However, anyother values of eCR : eT/O eCR . 0.7/0.85 .1 Zero Lift Drag"clean" means: neither flaps, slats, nor the landing gear are extended.
V / Vs 1.2 for take-off and initial climbV / Vs 1.3 for approach and landingEstimating CD0 "clean" from Emax :CD , 0 A e(for Emax see Chapter 3)4 Em2axEstimating CD0 "clean" from wetted areaSee: Aircraft Design Lecture Notes, Section 13 for wetted area calculation.Estimating CD0 in more detail from a drag built up:See: Aircraft Design Lecture Notes, Section 13 for all required parameters.
2Wave Drag2.1IntroductionThe aim of this Section is the analysis of the wave drag of the aircraft. The initial calculationof the wave drag in PrOPerA was based on the Boeing and Airbus philosophy (Scholz 1999),so the tool considers that the cruise Mach number was equal to drag divergence Mach numberand the wave drag coefficient was a constant. For turbofans, this concept can be correct, butfor the turboprops it is unknown if the aircraft flies at the drag divergence Mach number. Forthis reason, a method for the calculation of the wave drag is needed. With thisimplementation, the previous assumption is not needed and the wave drag is calculated foreach design.2.2Calculation of the Drag Divergence Mach Number2.2.1Equation obtained from ShevellShevell 1980 describes an analytical method for the calculation of the crest critical Machnumber,.Figure 2.1Wave drag curve obtained from Shevell 1980
From the Figure 2.1, the relation betweenis represented with, which is the critical Mach number, and(2. 1)The mathematical approximation for the Shevell’s curve that has been realized is the Equation2.2. The curve is represented in the Figure 2.2.(2. 2)Whereand.Shevell curve0.0080.007ΔcD,wave .820.860.900.940.981.021.061.10M/M CCFigure 2.2Representation of the approximation of the Shevell’s curveThe definition that has been taken for the calculation ofis given by Boeing andisdefined as the Mach number for which the wave drag coefficient has an increment of 0.002,or 20 drag counts [CTS] (2.3). The Equation 2.4 represents the calculation of.(2. 3)(2. 4)
2.3Calculation of the Wave Drag Curve2.3.1Analysis of the Real Wave Drag CurvesThe calculation has been based on experimental data from some aircraft. The aircraft thathave been studied are: A320-200, B727-200, B737-800, C-130H and BAe 146-200. The wavedrag curves of B727-200, C-130H and BAe 146-200 have been obtained from Roskam II1985, Figure 2.3.Figure 2.3Wave drag curves of B727-200, C-130H and BAe 146-200, obtained from Roskam II1985.With this empirical information,andhave been measured. The values offor the five airplanes are represented in the Table 2.1.Table 2.1Values ofA 320-2000.600.80andandfor the aircraft that have been 0.64BAe 146-2000.530.67The wave drag curves have been approximated with equations that have the same structure as2.5.(2. 5)Due to the conditions of the problem,. The resultant equation is 2.6.has to be zero at, soand
(2. 6)The values of the constants and are given in the Table 2.2 for each aircraft. The curvesfor the A320-200, B727-200, B737-800, C-130H and BAe 146-200 have been represented inthe Figure 2.4. The representation is based on the Equation 2.6 with the constants of the Table2.2.A320-200: Wave DragB727-200: Wave 1.51M/Mcrit1.21.3M/McritC-130H: Wave DragB737-800: Wave 4M/McritM/McritBAe 146-200: Wave 4M/McritFigure 2.4Wave drag curves for A320-200, B727-200, B737-800, C-130H and BAe 146-200
Table 2.2Values of and for the approximation of the wave drag curves of the aircraft thathave been analyzedA 345.2573.5432.3.2C-130H0.0012013.126BAe 1460.0017653.457Tangent Equation with the Effect of the Sweep Angle for theCalculation of the Wave Drag CurveThis equation has been developed based on the approximation of the Shevell’s curve (2.2).The equation is represented by 2.7.Limitation of the method:M M crit (1 pi/(2B) )(2. 7)The constants and are represented in the Table 2.3 and the SEE is represented in theTable 2.4, in [CTS]. The curve defined by 2.7 and the real curves (approximated with theEquation 2.6) are shown in the Figure 2.5.Table 2.3Values of andfor only one "optimized" Tangent Equation for all aircraft listed inTable 2.2 represented by Equation 2.7Result0.0012723.477Table 2.4SEE [CTS]Use these values for all aircraft not given in Table 2.2.SEE obtained for each aircraft, using the Tangent Equation based on Shevell’scurve (Shevell 1980), Equation 2.7A 320-2009.44B727-2007.41B737-8001.55C-130H23.83BAe 146-2006.99
Mach number Drag rise6050ΔcD,wave/cos3(φ25) [CTS]A320-200B727-20040B737-80030C-130H20Bae 146-20010Tangent equationwith ritFigure 2.5Representation of the Tangent Equation based on Shevell’s curve (Shevell 1980),Equation 2.7, and the real curves (approximated with the Equation 2.6)2.4Calculation of the Critical Mach Number,2.4.1Calculation ofobtained from the Tangent Equation with theEffect of Sweep AngleThe critical Mach number is obtained from the Equation 2.7. The resultant equation for thecalculation ofis 2.10.(2. 8)(2. 9)Calculate M crit for Equation 2.7for all aircraft not in Table 2.2.The constantsandare given in the Table 2.3.(2. 10)
3 Estimating Maximum Glide Ratio, Emaxfor typical passenger jets (see Fig. 1.1).Fig. 1.1Aircraft plan forms and their relative wetted area Swet / SW
kE calculated:Oswald Factor e in cruise (see above).kE given as:kEkE14.9 when calculated for standard parameters,which are considered to be: e 0.85,see Table 1.115.8 according to data in Raymer’s bookfrom our own statistics:kE15.15 short range aircraftkE16.19 medium range aircraftkE17.25 long range aircraft4 Calculating the Glide Ratio, EFor any lift coefficient (which may not be the optimum one):0.003.
: Zero lift drag (Chapter 1) : Wave drag (Chapter 2) For cruise, but for take-off (with initial climb) and landing (with approach) the zero lift drag coefficient has further components, because high-lift devices may be deployed and/or the landing gear may be extended. Especially the landing gear adds a considerable amount of drag.
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The drag curve of a bullet is determined by measuring its drag at multiple flight speeds; measure enough points at different speeds and connect the dots to make a drag curve. It's important to know what the drag curve is not: A drag curve is not a trajectory path for a bullet. A drag curve is not a series of 3 or 4 banded BC's .
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The materials used for components of drag chain are as follows- Table 1:- Materials of drag chain conveyor components. Sr. No. Name of Drag Conveyor Chain Part Material 1. Inner Link Plate C45 2. Outer Link Plate C45 3. Flights C45 4. Pin 40Cr1Mo60 5. Bush 40Cr1Mo60 6. Split pin M.S. II. DESIGN OF DRAG CONVEYOR CHAIN 2.1 Chain Velocity (v):
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