1 ft/s = 0.3048 m/s Supplementary information 1 knot = 0.5144 m/s R=287 J/kg/K for air...

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1 ft/s = 0.3048 m/s Supplementary information 1 knot = 0.5144 m/s R=287 J/kg/K for air = 1 lbf 4.448 N 1 litre = 61.02 in 1 HP = 745.6 W 1 km = 0.6214 miles 1 lbm = 0.4536 kg 1 HP = 550 ft lbf/s 1 US Gallon = 231 in Specific gravity of Avgas = 0.72 = 1.852 km 1 slug = 14.5943 kg 1 nautical mile 1 kg/m = 0.0019403 slug/ft R = V L Winitial In TSFC D W final (T - D) Ps = V. W dV T-D-F dt m Vmindrag Vminpower () max 0.5 2 W K 2 W = CDo K 3CD0 0.5 12 2 KCDo International standard atmosphere Altitude m ft Temperature C Kinematic Speed Pressure Ratio Density Viscosity Viscosity of Ratio Ratio Ratio Sound 0 0 15.2 1.0000 1.0000 1.0000 1.0000 340.3 152 304 500 1000 14.2 0.9821 0.9855 0.9973 1.0121 339.7 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 2133 7000 2286 7500 2438 8000 2.3 0.7864 0.8232 0.9649 1.1722 332.6 1.3 0.7716 0.8106 0.9622 1.1870 332.0 0.3 0.7571 0.7983 0.9595 1.2020 331.4 -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 4114 13500 4267 14000 -12.5 4419 14500 -13.5 4572 15000 -14.5 0.6113 0.6713 0.9291 1.3840 324.7 -11.5 0.5993 0.6606 0.9263 1.4022 324.1 0.5875 0.6500 0.9235 1.4207 323.5 0.5758 0.6396 0.9207 1.4396 322.9 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 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 6858 22500 -29.4 0.4134 0.4976 0.8781 1.7647 313.5 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 7924 26000 -36.3 0.3552 0.4325 0.8548 1.9766 308.4 8077 26500 -37.3 0.3474 0.4248 0.8519 2.0053 307.7 8229 27000 -38.3 0.3398 8382 27500 -39.3 0.3324 0.4173 0.8490 2.0345 307.1 0.4098 0.8460 2.0643 306.4 8534 28000 -40.3 0.3250 0.4025 0.8431 2.0947 305.8 8686 28500 -41.3 0.3178 8839 29000 -42.3 0.3107 8991 29500 -43.2 9144 30000 -44.2 0.2970 0.3953 0.8402 2.1256 305.1 0.3881 0.8372 2.1571 304.5 0.3038 0.3811 0.8342 2.1892 303.8 0.3741 0.8313 2.2219 303.2 Question 1 A reusable spacecraft comes in to land at Mexico City airport (elevation 3930 metres) with a speed of 105 m/s. The spacecraft landing weight is 100000 kg. In order to slow down, the spacecraft uses a parachute (CD = 2) with a reference surface area of 17.3 m. Mexico City airport runway is 3846 m long and has a friction coefficient of = 0.02. If maximum brakes are applied, the coefficient is = 0.4. 1) Will the shuttle stop in time if the brakes have failed? (Ans Sg 2) Will the shuttle stop in time if the brakes are applied? (Ans Sg = 5550 m) = 1170 m) 3) If the brakes have failed coming into landing what is maximum touchdown speed in order to safely stop at Mexico City airport? (Ans 58 m/s) 1 ft/s = 0.3048 m/s Supplementary information 1 knot = 0.5144 m/s R=287 J/kg/K for air = 1 lbf 4.448 N 1 litre = 61.02 in 1 HP = 745.6 W 1 km = 0.6214 miles 1 lbm = 0.4536 kg 1 HP = 550 ft lbf/s 1 US Gallon = 231 in Specific gravity of Avgas = 0.72 = 1.852 km 1 slug = 14.5943 kg 1 nautical mile 1 kg/m = 0.0019403 slug/ft R = V L Winitial In TSFC D W final (T - D) Ps = V. W dV T-D-F dt m Vmindrag Vminpower () max 0.5 2 W K 2 W = CDo K 3CD0 0.5 12 2 KCDo International standard atmosphere Altitude m ft Temperature C Kinematic Speed Pressure Ratio Density Viscosity Viscosity of Ratio Ratio Ratio Sound 0 0 15.2 1.0000 1.0000 1.0000 1.0000 340.3 152 304 500 1000 14.2 0.9821 0.9855 0.9973 1.0121 339.7 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 2133 7000 2286 7500 2438 8000 2.3 0.7864 0.8232 0.9649 1.1722 332.6 1.3 0.7716 0.8106 0.9622 1.1870 332.0 0.3 0.7571 0.7983 0.9595 1.2020 331.4 -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 4114 13500 4267 14000 -12.5 4419 14500 -13.5 4572 15000 -14.5 0.6113 0.6713 0.9291 1.3840 324.7 -11.5 0.5993 0.6606 0.9263 1.4022 324.1 0.5875 0.6500 0.9235 1.4207 323.5 0.5758 0.6396 0.9207 1.4396 322.9 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 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 6858 22500 -29.4 0.4134 0.4976 0.8781 1.7647 313.5 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 7924 26000 -36.3 0.3552 0.4325 0.8548 1.9766 308.4 8077 26500 -37.3 0.3474 0.4248 0.8519 2.0053 307.7 8229 27000 -38.3 0.3398 8382 27500 -39.3 0.3324 0.4173 0.8490 2.0345 307.1 0.4098 0.8460 2.0643 306.4 8534 28000 -40.3 0.3250 0.4025 0.8431 2.0947 305.8 8686 28500 -41.3 0.3178 8839 29000 -42.3 0.3107 8991 29500 -43.2 9144 30000 -44.2 0.2970 0.3953 0.8402 2.1256 305.1 0.3881 0.8372 2.1571 304.5 0.3038 0.3811 0.8342 2.1892 303.8 0.3741 0.8313 2.2219 303.2 Question 1 A reusable spacecraft comes in to land at Mexico City airport (elevation 3930 metres) with a speed of 105 m/s. The spacecraft landing weight is 100000 kg. In order to slow down, the spacecraft uses a parachute (CD = 2) with a reference surface area of 17.3 m. Mexico City airport runway is 3846 m long and has a friction coefficient of = 0.02. If maximum brakes are applied, the coefficient is = 0.4. 1) Will the shuttle stop in time if the brakes have failed? (Ans Sg 2) Will the shuttle stop in time if the brakes are applied? (Ans Sg = 5550 m) = 1170 m) 3) If the brakes have failed coming into landing what is maximum touchdown speed in order to safely stop at Mexico City airport? (Ans 58 m/s)