Aeronautical Engineer Data Book Episode 4 ppsx

51 Symbols and notations Table 3.4 Continued b 3 Elevator hinge moment derivative with respect to ␤ ␩ . B Input matrix. Number of blades on a propeller. c Wing chord. Viscous damping coefficient. Pitot tube coefficient. c 0 Root chord. c t Tip chord. c Local chord at spanwise co-ordinate y. y cg Centre of gravity. cp Centre of pressure. C Output matrix. C C Coefficient of contraction. C D Total drag coefficient. C DO Zero lift drag coefficient. C f Frictional drag coefficient. C L Lift coefficient. C LW Wing lift coefficient. C LT Tailplane lift coefficient. C H Elevator hinge moment coefficient. C m Pitching moment coefficient. C MO Pitching moment coefficient about aerodynamic centre of wing. C n Yawing moment coefficient. C Pressure coefficient. Power coefficient for p propellers. C R Resultant force coefficient. C v Coefficient of velocity. CP Centre of pressure. D Drag. Propeller diameter. D' Drag in a lateral-directional perturbation. D Direction cosine matrix. Direct matrix. D c Camber drag. D f Friction drag. D Pressure drag. p D ␣ Incidence drag. f Coefficient of friction. F Aerodynamic force. Feed-forward path transfer function. Fractional flap chord. F c Aerodynamic force due to camber. F r Froude number. F ␣ Aerodynamic force due to incidence. F ␩ Elevator control force g Acceleration due to gravity. G Controlled system transfer function. h Height. Centre of gravity position on reference chord. Enthalpy (specific). h 0 Aerodynamic centre position. h F Fin height co-ordinate above roll axis. h m Controls-fixed manoeuvre point position on reference chord. h' m Controls-free manoeuvre point position on reference chord. 52 Aeronautical Engineer’s Data Book Table 3.4 Continued h n Controls-fixed neutral point position on reference chord. h' n Control-free neutral point position on reference chord. H Hinge moment. Feedback path transfer function. Total pressure. Shape factor. H F Fin span measured perpendicular to the roll axis. H m Controls fixed manoeuvre margin. H" m Controls free manoeuvre margin. i x Moment of inertia in roll (dimensionless). i Moment of inertia in pitch (dimensionless). y i z Moment of inertia in yaw (dimensionless). I" Normalized inertia. I x Moment of inertia in roll. I Moment of inertia in pitch. y I z Moment of inertia in yaw. J Propeller ratio of advance. Moment of inertia. j (or i) The imaginary operator ( ͙ –1 ෆ ). k Spring stiffness coefficient. Lift-dependent drag factor. Interference factor. k Centre of pressure coefficient. cp k d Cavitation number. k Pitch rate transfer function gain constant. M M M M L L L L L l l l K K k k k k q u Axial velocity transfer function gain constant. w Normal velocity transfer function gain constant. ␪ Pitch attitude transfer function gain constant. ␶ Turbo-jet engine gain constant. K Feedback gain. Circulation. Bulk modulus. K Feedback gain matrix. 0 Circulation at wing mid-section. n Controls-fixed static stability margin. K' n Controls-free static stability margin. l Lift per unit span. d Disc loading (helicopter). f Fin arm. t Tail arm. L Lift. Rolling moment. Temperature lapse rate. c Lift due to camber. w Wing lift. F Fin lift. T Tailplane lift. ␣ Lift due to incidence. m Mass. Strength of a source or sink (fluid mechanics). Hydraulic depth. m' Rate of mass flow. M Mach number. 0 Free stream Mach number. crit Critical Mach number. M Pitching moment. 0 Wing–body pitching moment. T Tailplane pitching moment 53 Symbols and notations Table 3.4 Continued n Frequency. Number of revs per second. Polytropic exponent. N Yawing moment. P P P o Origin of co-ordinates. p Roll rate perturbation. Static pressure in a fluid. P Power. Total pressure. 0 Stagnation pressure. s Static pressure. t Total pressure. q Pitch rate perturbation. A propeller coefficient. Discharge quantity. Q Dynamic pressure. r Yaw rate perturbation. General response variable. Radius vector. R Radius of turn. Resultant force. Characteristic gas constant. Re Reynolds number. s Wing semi-span. Laplace operator. Specific U U T T S S S entropy. Distance or displacement. S Wing area. B Projected body side reference area. F Fin reference area. T Tailplane reference area. t Time. Maximum airfoil section thickness. T Time constant. Thrust. Temperature. r Roll time constant. s Spiral time constant. u Velocity component. Internal energy. u Input vector. U Total axial velocity. e Axial component of steady equilibrium velocity. E Axial velocity component referred to datum-path V V earth axes. v Lateral velocity perturbation. v Eigenvector. V Total lateral velocity. e Lateral component of steady equilibrium velocity. E Lateral velocity component referred to datum- V V V V V path earth axes. 0 Steady equilibrium velocity. F Fin volume ratio. R Resultant speed. S Stalling speed. T Tailplane volume ratio. V Eigenvector matrix. w Normal velocity perturbation. Wing loading. W W Downwash velocity. W Total nomal velocity. Weight. e Normal component of steady equilibrium velocity. E Normal velocity component referred to datum- path earth axes. 54 Aeronautical Engineer’s Data Book Table 3.4 Continued y x Longitudinal co-ordinate in axis system. x State vector. X Axial force component. y Lateral co-ordinate. B Lateral body ‘drag’ coefficient. y Output vector. Y Lateral force component. z Normal co-ordinate in axis system. Spanwise co- ordinate. z Transformed state vector. Z Normal force component. Greek symbols ␣ Angle of incidence or attack. Acceleration ␥ ␤ ␤ ␣ ␣ (angular). ␣ ' Incidence perturbation. e Equilibrium incidence. T Local tailplane incidence. ␤ Sideslip angle perturbation. Compressibility. e Equilibrium sideslip angle. ␩ Elevator trim tab angle. ␥ Flight path angle perturbation. e Equilibrium flight path angle. ⌫ Wing dihedral angle (half). Circulation. Strength of vortex. ␦ Airfoil section camber. Boundary layer thickness. ␦ m Mass increment. ⑀ Throttle lever angle. Downwash angle. ␨ Rudder angle perturbation. Damping ratio. ␪ Vorticity. ␩ Efficiency. ␪ Pitch angle perturbation. Angle. e Equilibrium pitch angle. Angular co-ordinate (polar). Propeller helix angle. ␭ Eigenvalue. Wavelength. Friction coefficient in a ␻ ␻ µ µ pipe. ⌳ Wing sweep angle. µ Viscosity (dynamic). 1 Longitudinal relative density factor. 2 Lateral relative density factor. ␯ Viscosity (kinematic). ␰ Aileron angle perturbation. ␳ Density. ␴ Aerodynamic time parameter. Tensile stress. ␶ Engine thrust perturbation. Shear stress. ␾ Phase angle. A general angle. ⌽ State transition matrix. ⌿ Yaw angle perturbation. Stream function. ␻ Natural frequency. Angular velocity. b Bandwidth frequency. n Damped natural frequency. 55 Symbols and notations Table 3.4 Continued Subscripts 0 Datum axes. Normal earth-fixed axes. Straight/level flight. Free stream flow conditions. Sea level. 1/4 Quarter chord. 2 Double or twice. ∞ Infinity condition. a Aerodynamic. Available. b Aeroplane body axes. Bandwidth. c Chord. Compressible flow. Camber line. D Drag. e Equilibrium. E Earth axes. F Fin. g Gravitational. Ground. h Horizontal. H Elevator hinge moment. i Incompressible. Ideal. l Rolling moment. LE Leading edge. L Lift. m Pitching moment. Manoeuvre. n Damped natural frequency. n Neutral point. Yawing moment. p Power. Phugoid. p Roll rate. q Pitch rate. r Roll mode. r Yaw rate. s Short period pitching oscillation. Spiral. Stagnation. Surface. t Tangential. TE Trailing edge. T Tailplane. u Axial velocity. U Upper. v Lateral velocity. V Vertical. w Wing. w Normal velocity. x ox axis. y oy axis. z oz axis. ␣ Angle of attack or incidence. ⑀ Throttle lever. ␨ Rudder. ␩ Elevator. ␪ Pitch. ␰ Ailerons. ␶ Thrust. 56 Aeronautical Engineer’s Data Book 3.5 The International Standard Atmosphere (ISA) The ISA is an internationally agreed set of assumptions for conditions at mean sea level and the variations of atmosphere conditions with altitude. In the troposphere (up to 11 000 m), temperature varies with altitude at a standard lapse rate L, measured in K (or °C) per metre. Above 11 000 m, it is assumed that temperature does not vary with height (Figure 3.1). So, in the troposphere: Temperature variation is given by: T = T 0 – Lh Pressure is given by: where T T 2 ᎏ T 1 p 2 ᎏ p 1 = ΂΃ 5.256 = temperature at an altitude h (m) T 0 = absolute temperature at mean sea level (K) L = lapse rate in K/m p = pressure at an altitude The lapse rate L in the ISA is 6.5 K/km. The ‘tropopause’ Altitude in ’000 m 16 2 4 6 8 10 12 14 The stratosphere: temperature does not The troposphere: temperature lapse rate L = 6.5˚C/km vary with height – 60 –40 –20 0 20 40 60 Temperature, ˚C Fig. 3.1 The ISA; variation of temperature with altitude 57 Symbols and notations In the stratosphere T = T S = constant so: p 1 ␳ 1 p ᎏ = ᎏ and ᎏ = RT p 2 ␳ 2 ␳ where R is the universal gas constant: R = 287.26 J/kg K Table 3.5 shows the international standard atmosphere (ISA). Table 3.6 shows the lesser used US (COESA) standard atmosphere. Table 3.5 International standard atmosphere (sea level conditions) Property Metric value Imperial value Pressure (p) 101 304 Pa 2116.2 lbf/ft 2 Density ( ␳ ) 1.225 kg/m 3 0.002378 slug/ft 3 Temperature (t) 15°C or 288.2 K 59°F or 518.69°R Speed of sound (a) 340 m/s 1116.4 ft/s Viscosity (µ) 1.789 ϫ 10 –5 3.737 ϫ 10 –7 kg/m s slug/ft s Kinematic viscosity 1.460 ϫ 10 –5 1.5723 ϫ 10 –4 ( ␯ ) m 2 /s ft 2 /s Thermal conductivity 0.0253 J/m s/K 0.01462 BTU/ft h°F Gas constant (R) 287.1 J/kg K 1715.7 ft lb/slug/°R Specific heat (C p ) 1005 J/kg K 6005 ft lb/slug/°R Specific heat (C v ) 717.98 J/kg K 4289 ft lb/slug/°R Ratio of specific 1.40 1.40 heats ( ␥ ) Gravitational 9.80665 m/s 2 32.174 ft/s 2 acceleration (g) Table 3.5 Continued Altitude Temperature Pressure ratio Density ratio Dynamic Kinematic a (°C) (p/p o ) (␳/␳ o ) viscosity ratio viscosity ratio (m/s) (m) (ft) (µ/µ o ) (µ/µ o ) 0 0 15.2 1.0000 1.0000 1.0000 1.0000 340.3 152 500 14.2 0.9821 0.9855 0.9973 1.0121 339.7 304 1000 13.2 0.9644 0.9711 0.9947 1.0243 339.1 457 1500 12.2 0.9470 0.9568 0.9920 1.0367 338.5 609 2000 11.2 0.9298 0.9428 0.9893 1.0493 338.0 762 2500 10.2 0.9129 0.9289 0.9866 1.0622 337.4 914 3000 9.3 0.8962 0.9151 0.9839 1.0752 336.8 1066 3500 8.3 0.8798 0.9015 0.9812 1.0884 336.2 1219 4000 7.3 0.8637 0.8881 0.9785 1.1018 335.6 1371 4500 6.3 0.8477 0.8748 0.9758 1.1155 335.0 1524 5000 5.3 0.8320 0.8617 0.9731 1.1293 334.4 1676 5500 4.3 0.8166 0.8487 0.9704 1.1434 333.8 1828 6000 3.3 0.8014 0.8359 0.9677 1.1577 333.2 1981 6500 2.3 0.7864 0.8232 0.9649 1.1722 332.6 2133 7000 1.3 0.7716 0.8106 0.9622 1.1870 332.0 2286 7500 0.3 0.7571 0.7983 0.9595 1.2020 331.4 58 2438 8000 –0.6 0.7428 0.7860 0.9567 1.2172 330.8 2590 8500 –1.6 0.7287 0.7739 0.9540 1.2327 330.2 2743 9000 –2.6 0.7148 0.7620 0.9512 1.2484 329.6 2895 9500 –3.6 0.7012 0.7501 0.9485 1.2644 329.0 3048 10000 –4.6 0.6877 0.7385 0.9457 1.2807 328.4 3200 10500 –5.6 0.6745 0.7269 0.9430 1.2972 327.8 3352 11000 –6.6 0.6614 0.7155 0.9402 1.3140 327.2 3505 11500 –7.6 0.6486 0.7043 0.9374 1.3310 326.6 3657 12000 –8.6 0.6360 0.6932 0.9347 1.3484 326.0 3810 12500 –9.6 0.6236 0.6822 0.9319 1.3660 325.4 3962 13000 –10.6 0.6113 0.6713 0.9291 1.3840 324.7 4114 13500 –11.5 0.5993 0.6606 0.9263 1.4022 324.1 4267 14000 –12.5 0.5875 0.6500 0.9235 1.4207 323.5 4419 14500 –13.5 0.5758 0.6396 0.9207 1.4396 322.9 4572 15000 –14.5 0.5643 0.6292 0.9179 1.4588 322.3 4724 15500 –15.5 0.5531 0.6190 0.9151 1.4783 321.7 4876 16000 –16.5 0.5420 0.6090 0.9123 1.4981 321.0 5029 16500 –17.5 0.5311 0.5990 0.9094 1.5183 320.4 5181 17000 –18.5 0.5203 0.5892 0.9066 1.5388 319.8 5334 17500 –19.5 0.5098 0.5795 0.9038 1.5596 319.2 5486 18000 –20.5 0.4994 0.5699 0.9009 1.5809 318.5 59 Table 3.5 Continued Altitude Temperature Pressure ratio Density ratio Dynamic Kinematic a (°C) (p/p o ) (␳/␳ o ) viscosity ratio viscosity ratio (m/s) (m) (ft) (µ/µ o ) (µ/µ o ) 5638 18500 –21.5 0.4892 0.5604 0.8981 1.6025 317.9 5791 19000 –22.4 0.4791 0.5511 0.8953 1.6244 317.3 5943 19500 –23.4 0.4693 0.5419 0.8924 1.6468 316.7 6096 20000 –24.4 0.4595 0.5328 0.8895 1.6696 316.0 6248 20500 –25.4 0.4500 0.5238 0.8867 1.6927 315.4 6400 21000 –26.4 0.4406 0.5150 0.8838 1.7163 314.8 6553 21500 –27.4 0.4314 0.5062 0.8809 1.7403 314.1 6705 22000 –28.4 0.4223 0.4976 0.8781 1.7647 313.5 6858 22500 –29.4 0.4134 0.4891 0.8752 1.7895 312.9 7010 23000 –30.4 0.4046 0.4806 0.8723 1.8148 312.2 7162 23500 –31.4 0.3960 0.4723 0.8694 1.8406 311.6 7315 24000 –32.3 0.3876 0.4642 0.8665 1.8668 311.0 7467 24500 –33.3 0.3793 0.4561 0.8636 1.8935 310.3 7620 25000 –34.3 0.3711 0.4481 0.8607 1.9207 309.7 7772 25500 –35.3 0.3631 0.4402 0.8578 1.9484 309.0 60 [...]... 143 25 146 30 149 35 15 240 46 000 47 000 48 000 49 000 50000 –56.3 –56.3 –56.3 –56.3 –56.3 0.1387 0.1322 0.1260 0.1201 0.1 145 0.1 845 0.1758 0.1676 0.1597 0.1522 0.7 947 0.7 947 0.7 947 0.7 947 0.7 947 4. 3073 4. 51 94 4. 741 9 4. 97 54 5.2203 295.1 295.1 295.1 295.1 295.1 15 544 15 849 161 54 1 645 9 167 64 51000 52000 53000 540 00 55000 –56.3 –56.3 –56.3 –56.3 –56.3 0.1091 0.1 040 0.9909–1 0. 944 4–1 0.9001–1 0. 145 1 0.1383 0.1318... 4. 694E–2 3 .42 6E–2 2.508E–2 1. 841 E–2 1.355E–2 9.887E–3 7.257E–3 347 .9 340 .3 332.5 3 24. 6 316.5 308.1 299.5 295.1 295.1 295.1 295.1 295.1 296 .4 297.7 299.1 300 .4 301.7 303.0 306.5 310.1 18.51 17.89 17.26 16.61 15.95 15.27 14. 58 14. 22 14. 22 14. 22 14. 22 14. 22 14. 32 14. 43 14. 54 14. 65 14. 75 14. 86 15. 14 15 .43 1.25E–5 1 .46 E–5 1.71E–5 2.03E–5 2 .42 E–5 2.90E–5 3.53E–5 4. 56E–5 6.24E–5 8.54E–5 1.17E 4 1.60E 4 2.22E 4 3.07E 4. .. 3.07E 4 4.24E 4 5.84E 4 8.01E 4 1.10E–3 1.53E–3 2.13E–3 4. 3806E–3 3.2615E–3 2 .44 45E–3 1. 843 8E–3 1.3992E–3 1.0 748 E–3 8.3819E 4 6.5759E 4 5.2158E 4 4.1175E 4 3.2 344 E 4 2.5276E 4 1.9 647 E 4 1.5185E 4 1.1668E 4 8.9101E–5 6.7601E–5 5.0905E–5 3.7856E–5 2.8001E–5 2.0597E–5 1.5063E–5 1.0950E–5 7.9106E–6 5.6777E–6 3.7218E–3 2.8337E–3 2.1708E–3 1.6727E–3 1.2961E–3 1.0095E–3 7.8728E 4 6.1395E 4 4.7700E 4 3.6869E 4. .. 0.2 843 0.2710 0.2583 0. 246 2 0.7 947 0.7 947 0.7 947 0.7 947 0.7 947 2.6751 2.7 948 2.93 24 3.0768 3.2283 295.1 295.1 295.1 295.1 295.1 1 249 6 12801 13106 1 341 1 13716 41 000 42 000 43 000 44 000 45 000 –56.3 –56.3 –56.3 –56.3 –56.3 0.17 64 0.1681 0.1602 0.1527 0. 145 6 0.2 346 0.2236 0.2131 0.2031 0.1936 0.7 947 0.7 947 0.7 947 0.7 947 0.7 947 3.3872 3.5 540 3.7290 3.9126 4. 1052 295.1 295.1 295.1 295.1 295.1 140 20 143 25 146 30... 30000 –36.3 –37.3 –38.3 –39.3 40 .3 41 .3 42 .3 43 .2 44 .2 0.3552 0. 347 4 0.3398 0.33 24 0.3250 0.3178 0.3107 0.3038 0.2970 0 .43 25 0 .42 48 0 .41 73 0 .40 98 0 .40 25 0.3953 0.3881 0.3811 0.3 741 0.8 548 0.8519 0. 849 0 0. 846 0 0. 843 1 0. 840 2 0.8372 0.8 342 0.8313 1.9766 2.0053 2.0 345 2.0 643 2.0 947 2.1256 2.1571 2.1892 2.2219 308 .4 307.7 307.1 306 .4 305.8 305.1 3 04. 5 303.8 303.2 9296 944 8 9601 9753 9906 10058 10210... 2.8 344 E 4 2.1668E 4 1. 646 8E 4 1. 243 9E 4 9.3354E–5 6.9593E–5 5.1515E–5 3.7852E–5 2.7635E–5 2.0061E–5 1 .44 77E–5 1.0384E–5 7 .40 02E–6 5.2391E–6 3.6835E–6 0. 849 6 0.8688 0.8880 0.9072 0.9263 0.9393 0.9393 0.9336 0.9 145 0.89 54 0.8763 0.8573 0.8382 0.8191 0.8001 0.7811 0.7620 0. 743 6 0.7300 0.71 64 0.7029 0.6893 0.6758 0.6623 0. 648 8 244 .8 250 .4 255.9 261 .4 266.9 270.6 270.6 269.0 263.5 258.0 252.5 247 .0 241 .5... 31500 32000 32500 33000 33500 340 00 345 00 35000 45 .2 46 .2 47 .2 48 .2 49 .2 –50.2 –51.2 –52.2 –53.2 – 54. 1 0.2903 0.2837 0.2772 0.2709 0.2 647 0.2586 0.2526 0. 246 7 0. 241 0 0.2353 0.3673 0.3605 0.3539 0. 347 3 0. 340 8 0.3 345 0.3282 0.3220 0.3159 0.3099 0.8283 0.8253 0.8223 0.81 94 0.81 64 0.81 34 0.81 04 0.8073 0.8 043 0.8013 2.2553 2.2892 2.3239 2.3592 2.3952 2 .43 18 2 .46 92 2.50 74 2. 546 3 2.5859 302.5 301.9 301.2... 262.2 249 .2 236.2 223.3 216.6 216.6 216.6 216.6 216.6 218.6 220.6 222.5 2 24. 5 226.5 228.5 233.7 239.3 1.278E+5 1.013E+5 7.950E +4 6.166E +4 4.722E +4 3.565E +4 2.650E +4 1. 940 E +4 1 .41 7E +4 1.035E +4 7.565E+3 5.529E+3 4. 047 E+3 2.972E+3 2.188E+3 1.616E+3 1.197E+3 8.890E+2 6.634E+2 4. 985E+2 1 .47 8E+0 1.225E+0 1.007E+0 8.193E–1 6.601E–1 5.258E–1 4. 135E–1 3.119E–1 2.279E–1 1.665E–1 1.216E–1 8.891E–2 6 .45 1E–2 4. 694E–2... 1 .42 9E 4 1.091E 4 8.281E–5 6.236E–5 4. 637E–5 3 .43 0E–5 2.523E–5 1. 845 E–5 1. 341 E–5 9.690E–6 6.955E–6 313.7 317.2 320.7 3 24. 1 327.5 329.8 329.8 328.8 325 .4 322.0 318.6 315.1 311.5 308.0 3 04. 4 300.7 297.1 293 .4 290.7 288.0 285.3 282.5 279.7 276.9 2 74. 1 15.72 16.01 16.29 16.57 16.85 17. 04 17. 04 16.96 16.68 16 .40 16.12 15. 84 15.55 15.26 14. 97 14. 67 14. 38 14. 08 13.87 13.65 13 .43 13.21 12.98 12.76 12.53 2.93E–3 4. 01E–3... 0.1383 0.1318 0.1256 0.1197 0.7 947 0.7 947 0.7 947 0.7 947 0.7 947 5 .47 73 5. 747 0 6.0300 6.3268 6.6383 295.1 295.1 295.1 295.1 295.1 17068 17373 17678 17983 18288 56000 57000 58000 59000 60000 –56.3 –56.3 –56.3 –56.3 –56.3 0.8579–1 0.8176–1 0.7793–1 0. 742 7–1 0.7079–1 0.1 141 0.1087 0.1036 0.9878–1 0. 941 4–1 0.7 947 0.7 947 0.7 947 0.7 947 0.7 947 6.9652 7.3081 7.6679 8. 045 4 8 .44 16 295.1 295.1 295.1 295.1 295.1 . 263.5 4. 833E+1 6.389E 4 325 .4 16.68 2.61E–2 56 4. 1175E 4 3.6869E 4 0.89 54 258.0 3.736E+1 5. 044 E 4 322.0 16 .40 3.25E–2 58 3.2 344 E 4 2.8 344 E 4 0.8763 252.5 2.872E+1 3.962E 4 318.6 16.12 4. 07E–2. 0.7 947 4. 51 94 295.1 146 30 48 000 –56.3 0.1260 0.1676 0.7 947 4. 741 9 295.1 149 35 49 000 –56.3 0.1201 0.1597 0.7 947 4. 97 54 295.1 15 240 50000 –56.3 0.1 145 0.1522 0.7 947 5.2203 295.1 62 15 544 51000. 8.891E–2 295.1 14. 22 1.60E 4 22 5.2660E–2 3.9 945 E–2 0.7585 218.6 4. 047 E+3 6 .45 1E–2 296 .4 14. 32 2.22E 4 24 3.8316E–2 2.9328E–2 0.76 54 220.6 2.972E+3 4. 694E–2 297.7 14. 43 3.07E 4 26 2.7964E–2 2.1597E–2