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Aero Engineering 315

Aero Engineering 315. Lesson 23 Introduction to Aircraft Performance. Intro to performance outline . Define the following terms: Flight path, flight path angle, and thrust angle Given Fig 5.1 from the text write general equations of motion Simplify general EOMs to SLUF

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Aero Engineering 315

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  1. Aero Engineering 315 Lesson 23Introduction to Aircraft Performance

  2. Intro to performance outline • Define the following terms: • Flight path, flight path angle, and thrust angle • Given Fig 5.1 from the text write general equations of motion • Simplify general EOMs to SLUF • Know what thrust required is for SLUF • List factors effecting thrust required • Sketch curves for induced, parasite & total drag versus velocity Lsn 23 #2

  3. Aircraft Performance • These are the “specs” that “sell” an aircraft • How Fast? • How Far? • How High? • How Far Can It Glide? • How Long Can It Stay Up? • How Long of a Runway Does It Need? • How Well Can It Turn? • How Does It Compare to Adversary? Lsn 23 #3

  4. Equations of Motion • For now we’re concerned withtranslational degrees of freedom • For instance--up/down & fore/aft • Later we’ll include rotational movement • Also, for now we’ll treat the aircraft as a point mass • Later we’ll include its moments of inertia • Approach: Sum forces and examine aircraft flight path Lsn 23 #4

  5. a a a T T Relative g Wind • = angle of attack (between aircraft reference and relative wind) • = flight path angle (between horizon and velocity vector) = thrust angle (between thrust vector and velocity vector) Angles and Forces (Fig 5.1) Forces on an Aircraft in a Climb Aircraft Reference Line L T V∞ D Horizon W Lsn 23 #5

  6. a T Relative Wind g Forces Parallel to Flight Path Aircraft Reference Line L a T V∞ g D Horizon SFll = ma W Tcos aT – D – Wsin g = ma Lsn 23 #6

  7. a T Relative Wind Centripetal acceleration SF = ma V2 r Tsin aT + L – Wcos g = m – Forces Perpendicular to Flight Path Aircraft Reference Line L a T V∞ g D Horizon g W Lsn 23 #7

  8. L = W = CL½ r V2 SF-16 slow down example… Lsn 23 #8

  9. Forces || to Flight Path T – D – W sin g = m a Forces ┴ to Flight Path L – W cos g = m (V2/r) Note: r ~ Simplifying Assumptions Assume: αT = 0 What happens if SLUF (=0, no acceleration)? And W = We (empty weight) + Wf (fuel) + Wp (payload - incl. pilot & crew) T = D and L = W Lsn 23 #9

  10. Drag Polar--Review(Two different graphical views) Induced drag Parasite drag Slope = k = 1 / (p eo AR) CD vs CL CD vs CL2 Standard Drag Polar Linearized Drag Polar Lsn 23 #10

  11. 1 k = TR = CD0q S + p eo AR Total Parasite Drag Total Drag due to lift Thrust Required “derivation” Remember? NOTE: The “thrust required” for SLUF is simply the drag at that flight condition -- THUS: (TR = D) kCL2 q S Lsn 23 #11

  12. L 1 W CL= = q = rV2 2 q S q S Thrust required in terms of V Since and Drag due to Lift finally Parasite Drag varies with V2 varies with 1/V2 Lsn 23 #12

  13. Parasite Drag Thrust Required (Parasite) Let’s Look at Parasite Drag First… TR = ½ r V2 S CD,0 + TR or D V (or M) Lsn 23 #13

  14. Drag due to Lift Thrust Required (+Induced) And add in Induced Drag TR = ½ r V2 S CD,0 + 2 kW2 / (r V2 S) Parasite Drag TR or D V (or M) Lsn 23 #14

  15. TR,MIN VMin Thrust Thrust Required (Combined) Then add themtogether…Thrust Required = Total Drag TR = ½ r V2 S CD,0 + 2 kW2 / (r V2 S) Parasite Drag TR or D Drag due to Lift V (or M) Lsn 23 #15

  16. Thrust Required Assumptions • Configuration (Gear, Flaps, Etc.) • Wing Geometry • Altitude • Weight Besides velocity Thrust Required (drag) depends on: - CDo - S, eo, AR (eo and AR in “k”) - - W Lsn 23 #16

  17. Thrust Required (Another Way) Thrust & Lift Required for SLUF: TR = D = CDq S (1) W = L = CLq S (2) so Lsn 23 #17

  18. Maximize Lift/Drag To minimize Thrust Required Minimum Thrust Required The same equation, again: By rearranging we get another useful concept Lsn 23 #18

  19. Example: T-38 Using chart from Supplemental Data Given: W = 10,000 lbs. h = 10,000 ft Find: Min TR Mach at Min TR L/Dmax Lsn 23 #19

  20. = 850 lbs T-38 Chart from Supplemental Data W = 10,000 lbs. Min TR Mach at Min TR L/Dmax Lsn 23 #20

  21. = 0.45 T-38 Chart from Supplemental Data W = 10,000 lbs. Min TR = 850 lbs Mach at Min TR L/Dmax Lsn 23 #21

  22. T-38 Chart from Supplemental Data W = 10,000 lbs. Min TR = 850 lbs Mach at Min TR = 0.45 L/Dmax = W/(TRmin) = 10,000/850 = 11.77 Lsn 23 #22

  23. Note: Parasite = Induced at min drag TR,min or Dmin Thrust Required TR,min = Dmin = W/(L/Dmax) TR or D Parasite Drag Induced Drag V (or M) Lsn 23 #23

  24. CL = (CD,0 /k)1/2 Minimum Thrust Required at L/Dmax At Min Drag Parasite Drag = Induced Drag CD,0 = CD,i or CD,0= k CL2 so: CDmin = CD,0 + CD,i = 2 CD,0 = 2 k CL2 solving for CL: Lsn 23 #24

  25. Example: T-37 Using CD = 0.02 + 0.057CL2 (from whole aircraft lesson), S = 184 ft2 and W = 6,000 lb. @ SL (SA) Find L/Dmax,, TRMIN, and V @ TRMIN CL = (CD,0 /k)1/2 V = (2W/rSCL)1/2 CD = 2CD,0 TRMIN = CD q S Lsn 23 #25

  26. Next Lesson (T24)… Thrust Required and Thrust Available • Review applicable portions of text 5.1 – 5.3 • Read 5.4 • Review/attempt problems 26, 27, 28 • In Class • Discuss Thrust required (ie Drag) versus Thrust available (ie what you’re engine is doing) Lsn 23 #26

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