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空气动力学·飞行
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空气动力学·飞行
12
engines
机翼升力方程 L = ½·ρ·v²·S·C_L
Wing lift equation L = ½·ρ·v²·S·C_L
L=½ρv²S·CL · 动压q=½ρv² · 60m/s→17.6kN
How lift scales with air density, speed², wing area and the lift coefficient
迎角与失速:C_L–α 曲线
Angle of attack & stall: the C_L–α curve
CL~0.11/度线性 · 临界~15° CLmax~1.5 · 失速骤降
Lift coefficient rises linearly with angle of attack, then collapses past the critical angle
翼型表面压强分布(C_p)
Airfoil pressure distribution (C_p)
上表面吸力峰Cp<0 · 压力中心 · 面积∝升力
Strong upper-surface suction (negative C_p) with a leading-edge peak; the enclosed area ∝ lift
阻力极曲线(升阻特性)
Drag polar (lift–drag characteristic)
CD=CD0+CL²/πARe · (L/D)max=1/2√(CD0·k) · 寄生+诱导
CD = CD0 + CL²/(π·AR·e): parasite drag plus induced drag, and the maximum lift-to-drag ratio (L/D)max
诱导阻力与展弦比
Induced drag and aspect ratio
Di∝CL²/AR · AR=b²/S · 翼尖涡 · 展向效率e
CDi = CL²/(π·AR·e): raising the aspect ratio AR = b²/S reduces the lift-dependent induced drag
滑翔比与滑翔性能
Glide ratio and glide performance
L/D=水平/下降 · 3000m@15→45km · 滑翔机50/客机17
Glide ratio = L/D = horizontal distance / height lost; best glide occurs at (L/D)max
平板边界层增长
Flat-plate boundary-layer growth
层流δ=5x/√Re · 湍流δ=0.37x/Re^0.2 · 转捩5e5
Slide the probe along the plate to watch δ, the local Reynolds number Re_x and the skin-friction coefficient Cf evolve
马赫数与压缩性效应
Mach number & compressibility
M=v/a · 亚/跨/超/高超 · P-G CL/√(1−M²)
Vary the Mach number to see the flow regimes, the Prandtl–Glauert compressibility correction and the Mach cone
斜激波与 θ–β–M 关系
Oblique shock & the θ–β–M relation
θ-β-M关系 · 弱/强解 · M2/β40°→θ10.6° · 脱体
For a fixed upstream Mach M₁, vary the deflection θ to solve for the shock angle β and the property jumps
机翼载荷与失速速度
Wing loading & stall speed
v失速=√(2(W/S)/ρCLmax) · W/S500→23.3m/s · 襟翼
Stall speed from wing loading W/S: V_stall = √(2·(W/S)/(ρ·C_L,max))
普朗特升力线理论
Prandtl lifting-line theory
椭圆环量e=1诱阻最小 · 下洗 · 有效迎角 · (1+δ)
An elliptical spanwise lift distribution minimises induced drag (span efficiency e = 1)
推重比与爬升角
Thrust-to-weight ratio & climb angle
sinγ=(T−D)/W · 剩余推力爬升 · T/W>1垂直爬升
In a steady climb: sin γ = (T − D) / W = T/W − D/W