Mod A, 2011-01-25 Standard 1976 atmosphere. Based on tables built for iOS app, "FlightMechanic", by Bruce Jackson dated 2010-08-07. Data hand-entered from Table I: Geometric Altitude, Metric Units, p53ff Used equation 3.6 on page 48 for relationship between temperature and speed-of-sound
MS 132 NASA, Hampton, VA 23681
Added xmlns="http://www.w3.org/1998/Math/MathML" to [itex] elements as required.
Sea level pressure in lb/ft2 Bias value of deg Rankine at 0 deg Farenheit; needed to calculate speed of sound from temperature Convert input altitude, in feet, to meters, for function independent value $\mathrm{alt_ft}\times 0.3048$ Output from table is metric Output from table, but only used locally to calculate ambient pressure output Direct output from table without conversion Calculated from ambient temperature using equation 3.6 from REF02 C equivalent: *v_sound_fps = 49.02*pow(t_amb_F + DEGR_AT_0_DEGF,0.5); $49.02(\mathrm{t_amb_F}+\mathrm{DEGR_AT_0_DEGF})^{0.5}$ Convert table output, in deg C, to deg F $32.0+\frac{\mathrm{t_amb_C}\times 9.0}{5.0}$ Converts the ambient pressure ratio found in the tables (p_p0) to English units by multiplying by standard ambient sea level pressure (SEA_LEVEL_PRESSURE_psf) $\mathrm{SEA_LEVEL_PRESSURE_psf}\mathrm{p_p0}$ Geometric altitude, Z, breakpoint set in meters -1000.0, -500.0, 0.0, 1000.0, 1500.0, 2000.0, 2500.0, 3000.0, 3500.0, 4000.0, 4500.0, 5000.0, 5500.0, 6000.0, 6500.0, 7000.0, 7500.0, 8000.0, 8500.0, 9000.0, 9500.0, 10000.0, 10500.0, 11000.0, 11100.0, 12000.0, 13000.0, 14000.0, 15000.0, 16000.0, 17000.0, 18000.0, 19000.0, 20000.0, 20100.0, 21000.0, 22000.0, 23000.0, 24000.0, 25000.0, 26000.0, 27000.0, 28000.0, 29000.0, 30000.0, 31000.0, 32000.0, 33000.0, 34000.0, 35000.0, 36000.0, 37000.0, 38000.0, 39000.0, 40000.0, 41000.0, 42000.0, 43000.0, 44000.0, 45000.0, 46000.0, 47400.0, 48000.0, 50000.0, 51000.0, 51500.0, 52000.0, 53000.0, 54000.0, 55000.0, 56000.0, 57000.0, 58000.0, 59000.0, 60000.0, 61000.0, 62000.0, 63000.0, 64000.0, 65000.0, 66000.0, 67000.0, 68000.0, 69000.0, 70000.0, 71000.0, 72000.0, 73000.0, 74000.0, 75000.0, 76000.0, 77000.0, 78000.0, 79000.0, 80000.0, 81000.0, 82000.0, 83000.0, 84000.0, 85000.0, 85500.0 1976 atmosphere table I ambient temperatures in degrees C 21.501, 18.250, 15.000, 8.501, 5.252, 2.004, -1.244, -4.491, -7.737, -10.984, -14.229, -17.474, -20.719, -23.963, -27.207, -30.450, -33.693, -36.935, -40.176, -43.417, -46.658, -49.898, -53.137, -56.376, -56.500, -56.500, -56.500, -56.500, -56.500, -56.500, -56.500, -56.500, -56.500, -56.500, -56.463, -55.569, -54.576, -53.583, -52.590, -51.598, -50.606, -49.614, -48.623, -47.632, -46.641, -45.650, -44.660, -42.177, -39.407, -36.637, -33.686, -31.100, -28.332, -25.566, -22.800, -20.036, -17.272, -14.509, -11.747, -8.986, -6.225, -2.500, -2.500, -2.500, -2.500, -2.741, -4.119, -6.873, -9.626, -12.379, -15.131, -17.882, -20.632, -23.381, -26.129, -28.876, -31.623, -34.369, -37.114, -39.858, -42.601, -45.343, -48.085, -50.825, -53.565, -56.304, -58.887, -60.842, -62.797, -64.751, -66.704, -68.657, -70.609, -72.560, -74.511, -76.462, -78.411, -80.360, -82.309, -84.257, -85.230 1976 atmosphere table I ambient pressure ratios (relative to sea level) 1.1244e+00, 1.0607e+00, 1.0000e+00, 8.8700e-01, 8.3453e-01, 7.8461e-01, 7.3715e-01, 6.9204e-01, 6.4920e-01, 6.0854e-01, 5.6997e-01, 5.3341e-01, 4.9878e-01, 4.6600e-01, 4.3499e-01, 4.0567e-01, 3.7798e-01, 3.5185e-01, 3.2720e-01, 3.0397e-01, 2.8210e-01, 2.6153e-01, 2.4219e-01, 2.2403e-01, 2.2053e-01, 1.9145e-01, 1.6362e-01, 1.3985e-01, 1.1953e-01, 1.0217e-01, 8.7340e-02, 7.4663e-02, 6.3829e-02, 5.4570e-02, 5.3721e-02, 4.6671e-02, 3.9945e-02, 3.4215e-02, 2.9328e-02, 2.5158e-02, 2.1597e-02, 1.8553e-02, 1.5950e-02, 1.3722e-02, 1.1813e-02, 1.0177e-02, 8.7743e-03, 7.5727e-03, 6.5473e-03, 5.6708e-03, 4.9200e-03, 4.2758e-03, 3.7220e-03, 3.2452e-03, 2.8338e-03, 2.4784e-03, 2.1709e-03, 1.9042e-03, 1.6728e-03, 1.4615e-03, 1.2962e-03, 1.0877e-03, 1.0095e-03, 7.8735e-04, 6.9536e-04, 6.5349e-04, 6.1401e-04, 5.4156e-04, 4.7705e-04, 4.1969e-04, 3.6873e-04, 3.2353e-04, 2.8348e-04, 2.4803e-04, 2.1671e-04, 1.8907e-04, 1.6470e-04, 1.4325e-04, 1.2441e-04, 1.0786e-04, 9.3372e-05, 8.0688e-05, 6.9607e-05, 5.9942e-05, 5.1526e-05, 4.4210e-05, 3.7861e-05, 3.2373e-05, 2.7642e-05, 2.3569e-05, 2.0067e-05, 1.7060e-05, 1.4481e-05, 1.2274e-05, 1.0387e-05, 8.7761e-06, 7.4028e-06, 6.3421e-06, 5.2410e-06, 4.3985e-06, 4.0269e-06 1976 atmosphere table I density ratios (relative to sea level) 1.0996e+00, 1.0489e+00, 1.0000e+00, 9.0748e-01, 8.6376e-01, 8.2168e-01, 7.8119e-01, 7.4225e-01, 7.0482e-01, 6.6885e-01, 6.3432e-01, 6.0117e-01, 5.6936e-01, 5.3887e-01, 5.0964e-01, 4.8165e-01, 4.5485e-01, 4.2921e-01, 4.0470e-01, 3.8128e-01, 3.5891e-01, 3.3756e-01, 3.1720e-01, 2.9780e-01, 2.9332e-01, 2.5464e-01, 2.1763e-01, 1.8601e-01, 1.5898e-01, 1.3589e-01, 1.1616e-01, 9.9304e-02, 8.4894e-02, 7.2580e-02, 7.1439e-02, 6.1808e-02, 5.2661e-02, 4.4903e-02, 3.8317e-02, 3.2722e-02, 2.7965e-02, 2.3917e-02, 2.0470e-02, 1.7533e-02, 1.5029e-02, 1.2891e-02, 1.1065e-02, 9.4474e-03, 8.0714e-03, 6.9089e-03, 5.9248e-03, 5.0902e-03, 4.3809e-03, 3.7769e-03, 3.2618e-03, 2.8216e-03, 2.4447e-03, 2.1216e-03, 1.8440e-03, 1.6051e-03, 1.3993e-03, 1.1581e-03, 1.0749e-03, 8.3827e-04, 7.4033e-04, 6.9637e-04, 6.5765e-04, 5.8605e-04, 5.2164e-04, 4.6376e-04, 4.1180e-04, 3.6521e-04, 3.2348e-04, 2.8615e-04, 2.5280e-04, 2.2303e-04, 1.9650e-04, 1.7288e-04, 1.5188e-04, 1.3323e-04, 1.1670e-04, 1.0206e-04, 8.9118e-05, 7.7690e-05, 6.7616e-05, 5.8747e-05, 5.0917e-05, 4.3938e-05, 3.7866e-05, 3.2589e-05, 2.8009e-05, 2.4039e-05, 2.0603e-05, 1.7632e-05, 1.5068e-05, 1.2857e-05, 1.0954e-05, 9.3178e-06, 7.9134e-06, 6.7099e-06, 6.1747e-06 Table lookup for ambient temperature; returns ambient temperature in degrees C (in variable t_amb_C) based on input value of Z_m (geometric altitude, meters) using the breakpoint values in Z_m_pts and the table defined in T_dgC_table. Table lookup for pressure ratio; returns ambient pressure normalized with SL pressure (in variable p_p0) based on input value of Z_m (geometric altitude, meters) using the breakpoint values in Z_m_pts and the table defined in P_P0_table. Table lookup for density ratio; returns density normalized with SL density (in variable sigma) based on input value of Z_m (geometric altitude, meters) using the breakpoint values in Z_m_pts and the table defined in sigma_table. GeometricAltitude ft 0 AmbientTemperature dgF 59 0.4 AmbientPressure lbf_ft2 2116.22 2.5 RatioOfDensityToSeaLevel nd 1 0.002 GeometricAltitude ft 5000 AmbientTemperature dgF 41.2 0.4 AmbientPressure lbf_ft2 1761.12 2.5 RatioOfDensityToSeaLevel nd 0.8616 0.002 GeometricAltitude ft 10000 AmbientTemperature dgF 23.36 0.4 AmbientPressure lbf_ft2 1455.84 2.5 RatioOfDensityToSeaLevel nd 0.73866 0.002 GeometricAltitude ft 15000 AmbientTemperature dgF 5.55 0.4 AmbientPressure lbf_ft2 1194.336 2.5 RatioOfDensityToSeaLevel nd 0.6292 0.002 GeometricAltitude ft 20000 AmbientTemperature dgF -12.3 0.4 AmbientPressure lbf_ft2 972.576 2.5 RatioOfDensityToSeaLevel nd 0.5328 0.002 GeometricAltitude ft 25000 AmbientTemperature dgF -30.2 0.4 AmbientPressure lbf_ft2 785.376 2.5 RatioOfDensityToSeaLevel nd 0.4481 0.002 GeometricAltitude ft 30000 AmbientTemperature dgF -48 0.4 AmbientPressure lbf_ft2 628.416 2.5 RatioOfDensityToSeaLevel nd 0.3741 0.002 GeometricAltitude ft 35000 AmbientTemperature dgF -65.8 0.4 AmbientPressure lbf_ft2 497.952 2.5 RatioOfDensityToSeaLevel nd 0.3099 0.002 GeometricAltitude ft 40000 AmbientTemperature dgF -69.7 0.4 AmbientPressure lbf_ft2 391.68 2.5 RatioOfDensityToSeaLevel nd 0.2462 0.002 GeometricAltitude ft 45000 AmbientTemperature dgF -69.7 0.4 AmbientPressure lbf_ft2 308.016 2.5 RatioOfDensityToSeaLevel nd 0.1936 0.002 GeometricAltitude ft 50000 AmbientTemperature dgF -69.7 0.4 AmbientPressure lbf_ft2 242.208 2.5 RatioOfDensityToSeaLevel nd 0.1522 0.002 GeometricAltitude ft 55000 AmbientTemperature dgF -69.7 0.4 AmbientPressure lbf_ft2 192.24 2.5 RatioOfDensityToSeaLevel nd 0.12082 0.002 GeometricAltitude ft 60695.53806 AmbientTemperature dgF -69.7 0.4 AmbientPressure lbf_ft2 146.0890153 2.5 RatioOfDensityToSeaLevel nd 9.1816E-02 0.002 GeometricAltitude ft 67257.21785 AmbientTemperature dgF -68.9188 0.4 AmbientPressure lbf_ft2 106.7865774 2.5 RatioOfDensityToSeaLevel nd 6.6981E-02 0.002 GeometricAltitude ft 73818.89764 AmbientTemperature dgF -65.3422 0.4 AmbientPressure lbf_ft2 78.22818852 2.5 RatioOfDensityToSeaLevel nd 4.8623E-02 0.002 GeometricAltitude ft 80380.57743 AmbientTemperature dgF -61.7692 0.4 AmbientPressure lbf_ft2 57.47865142 2.5 RatioOfDensityToSeaLevel nd 3.5405E-02 0.002 GeometricAltitude ft 86942.25722 AmbientTemperature dgF -58.198 0.4 AmbientPressure lbf_ft2 42.35825952 2.5 RatioOfDensityToSeaLevel nd 2.5859E-02 0.002 GeometricAltitude ft 93503.93701 AmbientTemperature dgF -54.6286 0.4 AmbientPressure lbf_ft2 31.30524246 2.5 RatioOfDensityToSeaLevel nd 1.8943E-02 0.002 GeometricAltitude ft 100065.6168 AmbientTemperature dgF -51.0628 0.4 AmbientPressure lbf_ft2 23.20223608 2.5 RatioOfDensityToSeaLevel nd 1.3918E-02 0.002 GeometricAltitude ft 103018.3727 AmbientTemperature dgF -49.4572 0.4 AmbientPressure lbf_ft2 20.29560791 2.5 RatioOfDensityToSeaLevel nd 1.2126E-02 0.002 GeometricAltitude ft 106299.2126 AmbientTemperature dgF -46.912 0.4 AmbientPressure lbf_ft2 17.50240913 2.5 RatioOfDensityToSeaLevel nd 1.0393E-02 0.002 GeometricAltitude ft 109580.0525 AmbientTemperature dgF -41.9242 0.4 AmbientPressure lbf_ft2 15.11637108 2.5 RatioOfDensityToSeaLevel nd 8.8688E-03 0.002 GeometricAltitude ft 112860.8924 AmbientTemperature dgF -36.9364 0.4 AmbientPressure lbf_ft2 13.07866284 2.5 RatioOfDensityToSeaLevel nd 7.5829E-03 0.002 GeometricAltitude ft 116141.7323 AmbientTemperature dgF -31.9522 0.4 AmbientPressure lbf_ft2 11.33553243 2.5 RatioOfDensityToSeaLevel nd 6.4956E-03 0.002 GeometricAltitude ft 119422.5722 AmbientTemperature dgF -26.968 0.4 AmbientPressure lbf_ft2 9.84148111 2.5 RatioOfDensityToSeaLevel nd 5.5745E-03 0.002 GeometricAltitude ft 122703.4121 AmbientTemperature dgF -21.9874 0.4 AmbientPressure lbf_ft2 8.558416924 2.5 RatioOfDensityToSeaLevel nd 4.7926E-03 0.002 GeometricAltitude ft 125984.252 AmbientTemperature dgF -17.0068 0.4 AmbientPressure lbf_ft2 7.454808194 2.5 RatioOfDensityToSeaLevel nd 4.1277E-03 0.002 GeometricAltitude ft 129265.0919 AmbientTemperature dgF -12.028 0.4 AmbientPressure lbf_ft2 6.503990548 2.5 RatioOfDensityToSeaLevel nd 3.5611E-03 0.002 GeometricAltitude ft 132545.9318 AmbientTemperature dgF -7.0492 0.4 AmbientPressure lbf_ft2 5.68310881 2.5 RatioOfDensityToSeaLevel nd 3.0774E-03 0.002 GeometricAltitude ft 135826.7717 AmbientTemperature dgF -2.074 0.4 AmbientPressure lbf_ft2 4.973328622 2.5 RatioOfDensityToSeaLevel nd 2.6638E-03 0.002 GeometricAltitude ft 139107.6115 AmbientTemperature dgF 2.8994 0.4 AmbientPressure lbf_ft2 4.358566712 2.5 RatioOfDensityToSeaLevel nd 2.3095E-03 0.002 GeometricAltitude ft 142388.4514 AmbientTemperature dgF 7.8728 0.4 AmbientPressure lbf_ft2 3.825490894 2.5 RatioOfDensityToSeaLevel nd 2.0055E-03 0.002 GeometricAltitude ft 145669.2913 AmbientTemperature dgF 12.8444 0.4 AmbientPressure lbf_ft2 3.362461958 2.5 RatioOfDensityToSeaLevel nd 1.7441E-03 0.002 GeometricAltitude ft 152230.9711 AmbientTemperature dgF 22.7804 0.4 AmbientPressure lbf_ft2 2.60824115 2.5 RatioOfDensityToSeaLevel nd 1.3251E-03 0.002 GeometricAltitude ft 160761.1549 AmbientTemperature dgF 27.5 0.4 AmbientPressure lbf_ft2 1.886715941 2.5 RatioOfDensityToSeaLevel nd 9.4920E-04 0.002 GeometricAltitude ft 175524.9344 AmbientTemperature dgF 17.1338 0.4 AmbientPressure lbf_ft2 1.075801599 2.5 RatioOfDensityToSeaLevel nd 5.5299E-04 0.002 GeometricAltitude ft 188648.294 AmbientTemperature dgF -2.6626 0.4 AmbientPressure lbf_ft2 0.640981876 2.5 RatioOfDensityToSeaLevel nd 3.4377E-04 0.002 GeometricAltitude ft 205052.4934 AmbientTemperature dgF -27.3928 0.4 AmbientPressure lbf_ft2 0.325114879 2.5 RatioOfDensityToSeaLevel nd 1.8434E-04 0.002 GeometricAltitude ft 221456.6929 AmbientTemperature dgF -52.0852 0.4 AmbientPressure lbf_ft2 0.158629735 2.5 RatioOfDensityToSeaLevel nd 9.5490E-05 0.002 GeometricAltitude ft 237860.8924 AmbientTemperature dgF -75.757 0.4 AmbientPressure lbf_ft2 0.074099443 2.5 RatioOfDensityToSeaLevel nd 4.7307E-05 0.002 GeometricAltitude ft 254265.0919 AmbientTemperature dgF -93.6994 0.4 AmbientPressure lbf_ft2 0.033269095 2.5 RatioOfDensityToSeaLevel nd 2.2259E-05 0.002 GeometricAltitude ft 270669.2913 AmbientTemperature dgF -110.8948 0.4 AmbientPressure lbf_ft2 0.014379292 2.5 RatioOfDensityToSeaLevel nd 1.0105E-05 0.002