LESSON 24 Aircraft Performance Climb Glide 1 Aerospace

LESSON 24 Aircraft Performance 상승 (Climb) 하강(Glide) 공군사관학교 항공우주공학과 1 Aerospace Engineering

Lesson Outcomes § Review § Endurance (항속시간) § Range (항속거리) 2 항공공학개론

Review : Climb Exercise 1 Given : T-37 at sea level standard conditions weight = 6, 000 lbs, CD = 0. 02 + 0. 057 CL 2 M = 0. 2, S = 184 ft^2, and TA = 2, 500 lbs. The 880 feet from the end of the runway are several 300 foot tall trees. Find : What coefficient of lift should you fly at? What flight path angle should you fly at? By how much will you clear the trees? CL = 0. 592, g = 20. 1, h = 322 ft (22 ft 여유 있음) 3 항공공학개론

Review : Thrust Specific Fuel Consumption (TSFC or ct) TSFC: Ratio of fuel flow required to thrust produced. TSFC = Ct (Lower is better) Altitude correction: Improves at higher altitude 4 항공공학개론

TSFC - Typical Values Engine type TSFC (lbfuel/hr per lbthrust or 1/hr) Recip Prop Turboprop Turbofan 0. 25 to 0. 60 0. 35 to 0. 60 (high bypass) 0. 39 to 0. 70 (medium bypass) 0. 80 to 1. 00 (low bypass) 1. 00 to 1. 30 1. 80 to 2. 50 (with afterburner) Turbojet 5 항공공학개론

Endurance Method #1 : Average Value v How long will and airplane fly? Endurance = D Wf E= • Wf = Total fuel used in lb Fuel use rate in lb/hr D Wf = ct TR D Wf ct D for steady, level flight v But weight changes cause drag changes, so use the average Drag over the segment E= D Wf ct Davg 6 항공공학개론

Maximum Endurance v Using our average endurance equation To maximize endurance E= D Wf ct Davg Minimize Drag ct is constant for a mission segment and altitude 7 항공공학개론

Endurance Method #2 : Breguet § For a complete endurance solution, integrate over weight changes E = Max E? ct min (High altitude) W fuel max where W 1=initial weight and W 2=final weight 8 L/D)max 항공공학개론

Maximizing Endurance A few things that aircraft designers or operators can do to maximize E. E= • • D Wf ct Davg Maximize fuel capacity & burn Minimize TSFC – engine selection Minimize drag (fly at Dmin speed) Maximize L/D (high aspect ratio) 9 항공공학개론

Example: T-38 Given: Winitial = 11, 000 lb h = 20, 000 ft Fuel Wt = 2, 000 lb Find: Mach for EMAX, Drag Emax, M=0. 54 Drag = 900 lbs 10 항공공학개론

Endurance Example (Average Value Method) T-38 Winitial= 11, 000 lbs Wfuel= 2, 000 lbs h = 20, 000 ft (SDC) What is the max endurance of the aircraft in hours (normal power)? = 1. 09/hr X (447. 4/518. 69)1/2 =1. 012/hr Dmin ave = 900 lbs Emax = 2. 2 hr 11 항공공학개론

Range Method #1 : Average Value Range: Distance to fly Range = Velocity. Endurance (R = EV) TR V The tangent (from the origin) gives the maximum cruise range point. At this point parasite drag is three times induced. CDo = 3 k CL 2 12 항공공학개론

Range T = D for (D/V 1) R= TR D Wf TA (WET) ct (D /V 1 ) TA (DRY) Slope = (D/V 1) For a given velocity, say V 13 항공공학개론

Max Range TR T Slope = (D/V)MIN, avg TA (WET) TA (DRY) = D for (D/V)MIN, avg = V for (D/V)MIN, avg 14 V 항공공학개론

Range Method #2: Breguet § For a complete range solution, integrate over weight changes R = Max R? Vdt = ct min (High altitude) W fuel max CL 1/2 where W 1=initial weight and W 2=final weight 15 CD ) max 항공공학개론

Maximize Range A few things that aircraft designers or operators can do to maximize R. R= D Wf ct (D /V ) avg • • Maximize fuel capacity & burn Minimize TSFC – engine selection Minimize D/V Maximize L/D (high aspect ratio) • Lower air density / higher altitude 16 항공공학개론

Max Powered Endurance Max Glide Range gli d. E E Max Glide Endurance R cruis. ER RE R Max Powered Range 17 항공공학개론

Example: T-38 again Given: Winitial = 11, 000 lb h = 20, 000 ft Fuel Wt = 2, 000 lb Find: RMAX Slope tangent at Mavg = 0. 65 Davg = 1000 18 항공공학개론

Range (Average Value Method) T-38 Winitial= 11, 000 lbs Wfuel= 2, 000 lbs h = 20, 000 ft (SDC) What is the max range of the aircraft in NM? ct =1. 012/hr =0. 0002811/sec Using tangent to the curve: Mave, min =. 65 Dave, min= 1000 lbs V =(M)(a) = 0. 65 (1036. 9 ft/sec) = 674 ft/sec = 0. 1109 NM/sec Rmax = 2000 lb/(. 0002811/sec X 1000 lb/0. 1109 NM/sec) = 783 NM 19 compare to E 항공공학개론 max = 2. 2 hr

Some Relationships Case Equation Relation between CDo & KCL Graphical Max Rate of Climb No Set Relation Find greatest distance between PA and PR Max Climb Angle CDo = k. CL 2 Find greatest distance between TA and TR Max Range Average Value Formula or CDo = 3 k. CL 2 (D/V)Min CDo = k. CL 2 TR, Min (L/D)Max Glide Range CDo = k. CL 2 TR, Min (L/D)Max Min Sink Rate 3 CDo = k. CL 2 PR, Min Breguet Range Eq. 5. 27 Max Endurance Average Value Formula or Breguet Endurance Eq. 5. 27 20 항공공학개론

(3) Drag Polar 문제인 경우: A) Induced drag와 Parasite drag와 관계 찾기 CDo= k. CL 2 or 3 CDo= k. CL 2 or B) Find CL from relationship of CDo and k. CL 2 CDo= 3 k. CL 2 Or C) Find V from: D) Find CD from CD = CDo + k. CL 2 E) TR = D = CD q S 22 항공공학개론

(4) Chart 문제인 경우 glid. ER cruis. ER T Endurance means RODmin E RE R V Chart PR, min (go to Power charts, find the lowest pt) Drag Polar 3 CDo = k CL 2 TR, min and L/D)max D/V)min CDo = k CL 2 23 CDo = 3 k CL 2 항공공학개론

상승 문제인 경우 Max climb angle Max climb rate ROCmax = Px, max / W Gammamax = acrsin(Tx, max / W) Px, max occurs at the pt where a line parallel to PA is tangent to the PR curve Tx, max occurs at TR, min T TR PR P PA TA Tx, max Px, ma x V for TR, min V V 24 항공공학개론