Flying Low and Slow. (and the Tools for its Calculation) Dieter Scholz. Hamburg University of Applied Sciences

Transcription

1 AIRCRAFT DESIGN AND SYSTEMS GROUP (AERO) (and the Tools for its Calculation) Hamburg University of Applied Sciences 12th European Workshop on Aircraft Design Education (EWADE) 2015

2 (and the Tools for its Calculation) Content with New Aircraft Designs Flight Mechanics Fundamentals Drag Polar Specific Fuel Consumption and the SFC-Paradox with a Given Aircraft Summary and Conclusions , Slide 2

3 with New Aircraft Designs Standard Jet Configuration "The Rebel" Optimization for minimum fuel Standard Prop Configuration "Smart Turboprop" Optimization for minimum DOC Genetic algorithm (Differential Evolution) proposes parameters. Aircraft designed automatically in EXCEL. About 2000 feasible designs tested in one optimization run , Slide 3

4 with New Aircraft Designs Standard Jet Configuration: "The Rebel" Parameter Value Deviation from A320* Main aircraft parameters m MTO kg - 10 % m OE kg -5 % m F 7500 kg - 42 % S W 68 m² - 45 % b W,geo 48.5 m + 42 % A W,eff % E max % T TO N - 20 % Parameter Value Deviation from A320* Requirements m MPL kg 0 % R MPL 1510 NM 0 % M CR % max(s TOFL, s LFL ) 2700 m + 53 % n PAX (1-cl HD) % m PAX 93 kg 0 % Dieter SP Scholz 28 in - 3 % Thrust to Weight Ratio [-] Early conceptual design 0.7 [-] 0.6 tio r a 0.5 t h 0.4 ig e 0.3 -w 0.2 tṯo s 0.1 r u h T Wing loading in kg/m² 25 Contingency: 10 % Alternate: 200 NM [t] 20 s Loiter time: 30 min a 15 Add. tank: 4 m³ m Ref. aircraft: A320 d a 10 lo y a 5 P 0 012th EWADE Range [NM] Payload Mass [t] BPR % SFC 1.03E-5 kg/n/s - 37 % h ICA ft - 23 % s TOFL 2490 m + 41 % s LFL 2110 m + 45 % t TA 32 min 0 % , Slide 4

5 with New Aircraft Designs Standard Jet Configuration: "The Rebel" Parameter Value Deviation from A320* DOC mission requirements R DOC 750 NM 0 % m PL,DOC kg 0 % EIS c fuel 1.44 USD/kg 0 % Results m F,trip % U a,f % DOC (AEA) 93 % -7 % Operating empty mass breakdown Component drag breakdown Direct operating cost breakdown 24% 7% 5% 25% 25% 13% 0.3% 1.0% Wing Fuselage Horizontal tail Vertical tail Engines Landing gear Systems Operator's items 8% 4% 17% 38% 32% Wing Fuselage Horizontal tail Vertical tail Engines 15% 23% 6% 24% 17% 14% 1% Depreciation Interest Insurance Fuel Maintenance Crew Fees , Slide 5

6 with New Aircraft Designs Standard Prop Configuration: "Smart Turboprop" Parameter Main aircraft parameters Value Deviation from A320* Parameter Value Deviation from A320* Requirements m MPL kg 0 % R MPL 1510 NM 0 % M CR % max(s TOFL, s LFL ) 1770 m 0 % n PAX (1-cl HD) % m PAX 93 kg 0 % Dieter SP Scholz 29 in 0 % Natural Laminar Flow (NLF) [-] 400 tio ra 300 s a 200 -m Power to Mass Ratio kw/t rṯo 100 e w o P Wing loading in kg/m² 25 Contingency: 10 % Alternate: 200 NM [t] 20 s Loiter time: 30 min a 15 Ref. aircraft: A320 m d a 10 lo y a 5 P Range [NM] Payload Mass [t] m MTO kg -24 % m OE kg -31 % m F 8400 kg -36 % S W 95 m² - 23 % b W,geo 36.0 m + 6 % A W,eff % E max % P eq,ssl 5000 kw d prop 7.0 m η prop 89 % PSFC 5.86E-8 kg/w/s h ICA ft - 40 % s TOFL 1770 m 0 % s LFL 1300 m -10 % t TA 32 min 0 % , Slide 6

7 with New Aircraft Designs Standard Prop Configuration: "Smart Turboprop" Parameter DOC mission requirements Value Deviation from A320* R DOC 755 NM 0 % m PL,DOC kg 0 % EIS c fuel 1.44 USD/kg 0 % Results m F,trip 3700 kg - 36 % U a,f 3600 h + 5 % DOC (AEA) 83 % - 17 % Operating empty mass breakdown Component drag breakdown Direct operating cost breakdown 26% 6% 7% 1.4% 18% 13% 1.4% 25% 1.0% 1.7% Wing Struts Fuselage Horizontal tail Vertical tail Engines Landing gear Systems Operator's items Soundproofed material 6% 8% 48% 5% 23% 9% Wing Struts Fuselage Horizontal tail Vertical tail Engines 24% 16% 6% 14% 27% 11% 1% Depreciation Interest Insurance Fuel Maintenance Crew Fees , Slide 7

8 Flight Mechanics Fundamentals A/C Performance Often claimed: "There is one speed for minimum drag!" Really only one? flying lower: 1 mg L 2 V C L, md S 2 W , Slide 8

9 Flight Mechanics Fundamentals The Pilot's View of Flying Low and hence Fast Lower altitude => Higher Speed of Sound => Higher True Airspeed (cruise Mach number remains constant High Speed & high density => very low lift coefficient => very low L/D => Extremely high fuel consumption! , Slide 9

10 Drag Polar Drag Polar (Airbus A320, approximated, based on the following equations) Mach number Mach dependent induced drag wave drag C D0 = C D C C D, 0 D, W 2 CL A e , Slide 10

11 Drag Polar Induced Drag Prediction Method (Nita 2012) C D, i 2 CL Ae e Q k e, M PA Q 1 P KC K = 0,38 e theo k D,0 e, F Fuselage: k df 1 b e, F 2 2 from one of many handbook methods Mach: k a e, M e a 0; Generic parameters: e c M M e a b c comp 1 e e e M 1 1 b e 0.3 c comp e f ( for unswept wings: e theo 1 1 f ( ) A Hörner , Slide 11

12 Drag Polar NACA Report 921 for all sweep angles 25 : opt 0.45e opt e in deg e theo 1 f 1 ( ) A 25 f ( ) ( ) ( ) ( ) ( ) , Slide 12

13 Drag Polar Mach Dependent Induced Drag (A320) e_a320 k_e,m,a320 1,1000 1,0000 0,9000 0,8000 Parameters for A320: y y = -8431,955x ,614x ,820x ,125x ,215x ,125x - 408,255 R 2 = 0,998 e_a320 k_e,m k_e,m,a320 Poly: k_e,m Calc: e_a320 0,7000 Calc: e_a320 Polynomisch (k_e,m,a320) 0,6000 0,5000 0,50 0,55 0,60 0,65 0,70 0,75 0,80 0,85 M Parameters for A320: a_e = 0, b_e = 8, , Slide 13

14 Drag Polar Wave Drag Prediction Method Shevell 1980: A = , B = Own proposal of generic parameters (from 5 A/C): A = , B = ,029 0,027 0,025 In case Mcrit is not given: C_D0 + CD,wave 0,023 0,021 0,019 C_D0 A320 C_D0 Calc witha= A, b= B 0,017 A320: C D0 = ,015 0,60 0,65 0,70 0,75 0,80 0,85 M , Slide 14

15 Specific Fuel Consumption The SFC Paradox c T = c : Thrust-Specific Fuel Consumption c T = m F / T c T = kg/n/s (typical for jet) Heating value. Kerosene: H = 42.5 MJ/kg m F H : overall efficiency of the flight = 1: V = 680 m/s, M = 2 (MSL) Efficiency increases to any value if only speed is increased. => Paradox! , Slide 15

16 Specific Fuel Consumption Deriving a Basic SFC as a Function of Speed or Mach Number c P = c' : Power-Specific Fuel Consumption c P = m F / P / t c P = kg/w/s (typical for turboprop) m F c T cp ctv c cv c' is slope a* is slope , Slide 16

17 Specific Fuel Consumption The Basic SFC Function a* is slope Élodie Roux , Slide 17

18 with a Given Aircraft Preparation relative fuel consumption E max C Ae C D0 D0, W E = L/D E E ref k k e, M e, M, ref C C D0 D0 C C D0, W, ref D0, W if the aircraft is unchanged and C L is kept constant E only depends on k e,m and C D0,W , Slide 18

19 with a Given Aircraft The Reference The New Flight Condition , Slide 19

20 with a Given Aircraft More Basics , Slide 20

21 with a Given Aircraft Numbers (A320) , Slide 21

22 with a Given Aircraft Results Reference: long range cruise 0,00% -0,50% -1,00% Delta m_f / m_f,ref -1,50% -2,00% -2,50% -3,00% -3,50% -4,00% 0,60 0,62 0,64 0,66 0,68 0,70 0,72 0,74 0,76 0,78 M , Slide 22

23 with a Given Aircraft Results V m/s rho kg/m³ 0,364 0,378 0,396 0,415 0,435 0,458 0,507 h m T K a m/s M 0,76 0,74 0,72 0,70 0,68 0,66 0,62 k_e_m 0,8450 0,8988 0,9399 0,9651 0,9802 0,9891 0,9970 CD0W 0,0011 0,0009 0,0007 0,0005 0,0004 0,0003 0,0001 E 17,9 18,6 19,1 19,4 19,7 19,8 20,0 c kg/n/s 1,66E-05 1,65E-05 1,64E-05 1,63E-05 1,61E-05 1,60E-05 1,58E-05 Bs m 2,47E+07 2,53E+07 2,56E+07 2,56E+07 2,55E+07 2,52E+07 2,45E+07 Mff 0,893 0,895 0,896 0,897 0,896 0,895 0,892 m_f/m_to 0,1072 0,1048 0,1036 0,1034 0,1040 0,1049 0,1077 fuel saving 0,00% -2,26% -3,39% -3,51% -3,01% -2,11% 0,48% E = L/D increases continuously with flying slower (down to M = 0.3). Thrust-specific fuel consumption c = SFC decreases with flying slower. The Breguet factor B s is proportion to speed and decreases once E stops increasing with substancial rate. Fuel consumption decreases as long as the Breguet factor B s increases , Slide 23

24 Summary and Conclusions Flying slower gets you on a better drag polar (this is true also below the critical Mach number) The best lift coefficient has to be maintained This can be done by letting the design find its optimum condition with respect to altitude and wing area and Given aircraft have to accept the given wing area and can fly lower when slower An example calculation showed fuel burn reduction of 3.5 % at 0.05 Mach less than reference Mach number (0.76) This could be done today(!) with all aircraft(!) and would also reduce contrails But: Productivity goes down and DOC go (most probably) up! This is "only" a financial question, however decisive! , Slide 24