16.333: Lecture #1 Equilibrium States Aircraft performance Introduction to basic terms
16.333: Lecture #1 Equilibrium States Aircraft performance Introduction to basic terms
Fa2004 16.3331-1 Aircraft performance Accelerated horizontal flight - balance of forces Engine thrust t Lift l(⊥toV) Drag L(‖tov Weight w T-D=m dt 0 for steady fight and L-W=0 Define l= dev ScI where P-air density(standard tables) s- gross wing area=cx b, c= mean chord wIng span AR-wing aspect ratio=b/c namIc pressure V= speed relative to the air
Fall 2004 16.333 1–1 Aircraft Performance • Accelerated horizontal flight balance of forces – Engine thrust T – Lift L (⊥ to V ) – Drag D (� to V ) – Weight W dV D T mg L T − D = m = 0 for steady flight dt and L − W = 0 • Define L = 1 2ρV 2SCL where – ρ – air density (standard tables) – S – gross wing area = c¯× b, – c¯ = mean chord – b = wing span – AR – wing aspect ratio = b/c¯ ct c0 kc �k edge b = 2.s c Sweepback angle Trailing – Q = 1 2ρV 2 dynamic pressure – V = speed relative to the air
Fa2004 16.3331-2 Y lift coefficient -for low Mach number, CL=CI o a angle of incidence of wind to the wing o ao is the angle associated with zero lift Back to the performance 1v2SCi and L=mg which implies that v so that and we can relate the effect of speed to wing lift o a key number is stall speed which is the lowest speed that an aircraft can fly steadily 2 779 SC where typically get Clma at max= 10
� � Fall 2004 16.333 1–2 – CL lift coefficient – for low Mach number, CL = CLα(α − α0) 3 α angle of incidence of wind to the wing 3 α0 is the angle associated with zero lift • Back to the performance: 1 L = ρV 2 SCL and L = mg 2 2mg which implies that V = ρSCL so that V ∝ C−1/2 L and we can relate the effect of speed to wing lift • A key number is stall speed, which is the lowest speed that an aircraft can fly steadily 2mg Vs = ρSCLmax where typically get CLmax at αmax = 10◦
Fa2004 16.3331-3 Steady Gliding Flight Aircraft at a steady glide angle of y e Assume forces are in equilibrium L-mg cos y =0 D+mg sin y =0 Gives that tan DL >Minimum gliding angle obtained when Cp/Cl is a minimum High L/d gives a low gliding angle Note: typically Cp=CD:+ ARe where ' Dmin is the zero lift( friction/parasitic)drag ii gives the lift induced drag is Oswald's efficiency factor a 0.7-0.85
Fall 2004 16.333 1–3 Steady Gliding Flight • Aircraft at a steady glide angle of γ • Assume forces are in equilibrium L − mg cos γ = 0 (1) D + mg sin γ = 0 (2) Gives that D CD tan γ = L ≡ CL ⇒ Minimum gliding angle obtained when CD/CL is a minimum – High L/D gives a low gliding angle • Note: typically CD = CDmin + 2 CL πARe where – CD is the zero lift (friction/parasitic) drag min – C2 L gives the lift induced drag – e is Oswald’s efficiency factor ≈ 0.7 − 0.85
Fa2004 16.3331-4 Total drag then given by d= Spv SCp=pvS(CDmin+hCl v SCD_ +k (4 Total drag No-lift dra Lift-dependent drag So that the speed for minimum drag is 2m9/k 1/4 min drag
Fall 2004 16.333 1–4 • Total drag then given by 1 1 � � D = ρV 2 SCD = ρV 2 S L CD (3) min + kC2 2 2 1 (mg) 2 = 2 ρV 2 SCDmin + k 1ρV 2S (4) 2 D VE VS1 VEmd Total drag No-lift drag Lift-dependent drag • So that the speed for minimum drag is � � �1/4 2mg k Vmin drag = ρS CDmin