Aircraft Arrester Final

8/8/2019 Aircraft Arrester Final

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Aircraft Arrester Sprea

First Cas Second Ca Third Cas

Mass Of Plane [kg] 7000.00 7000.00 7000.00

Plane Speed [km/h]&[m/s]145.00 145.00 145.00

40.28 40.28 40.28

Ship Speed [km/h]&[m/s]0.00 20.00 20.00

0.00 5.56 5.56

Wind Speed [km/h]&[m/s]0.00 15.00 15.00

0.00 4.17 4.17

Wind Direction [degrees] 0.00 45.00

Effective Wind Speed [m/s] 0.00 4.17 2.95

Ramp Pitch [degrees] 0.00 0.00 0.00

Kinetic Energy (plane+ship+wi 5678.05 8750.00 8328.08Kinetic Energy (plane+ship-win 5678.05 6076.39 6437.55

Kinetic Energy (plane-ship+win 5678.05 5293.21 4966.21

Kinetic Energy (plane-ship-wind 5678.05 3267.75 3533.99

Cable Extension In Increments 0.10

Cable Extension [m]

0.00 0.00 0.00 0.00

0.10 2.00 0.10 0.10

0.20 4.01 0.30 0.40

0.30 6.02 0.50 0.90

0.40 8.03 0.70 1.60

0.50 10.04 0.90 2.51

0.60 12.06 1.11 3.61

0.70 14.08 1.31 4.92

0.80 16.11 1.51 6.43

0.90 18.14 1.71 8.14

1.00 20.17 1.92 10.06

1.10 22.21 2.12 12.18

1.20 24.24 2.32 14.50

1.30 26.29 2.53 17.02

1.40 28.33 2.73 19.76

1.50 30.38 2.94 22.69

1.60 32.44 3.14 25.83

1.70 34.49 3.35 29.18

ArresterForce[kN]

Area OfSlice

[kNm]

Cumulative Area[kNm]


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1.80 36.55 3.55 32.73

1.90 38.61 3.76 36.49

2.00 40.68 3.96 40.45

2.10 42.75 4.17 44.63

2.20 44.82 4.38 49.00

2.30 46.90 4.59 53.59

2.40 48.98 4.79 58.38

2.50 51.06 5.00 63.39

2.60 53.15 5.21 68.60

2.70 55.24 5.42 74.02

2.80 57.33 5.63 79.64

2.90 59.43 5.84 85.48

3.00 61.53 6.05 91.53

3.10 63.63 6.26 97.79

3.20 65.74 6.47 104.26

3.30 67.85 6.68 110.94

3.40 69.97 6.89 117.83

3.50 72.08 7.10 124.93

3.60 74.20 7.31 132.24

3.70 76.33 7.53 139.77

3.80 78.45 7.74 147.51

3.90 80.59 7.95 155.46

4.00 82.72 8.17 163.63

4.10 84.86 8.38 172.01

4.20 87.00 8.59 180.60

4.30 89.14 8.81 189.41

4.40 91.29 9.02 198.43

4.50 93.44 9.24 207.67

4.60 95.60 9.45 217.12

4.70 97.76 9.67 226.78

4.80 99.92 9.88 236.67

4.90 102.08 10.10 246.77

5.00 104.25 10.32 257.08

5.10 106.42 10.53 267.62

5.20 108.60 10.75 278.37

5.30 110.78 10.97 289.34

5.40 112.96 11.19 300.52

5.50 115.14 11.40 311.93

5.60 117.33 11.62 323.55

5.70 119.52 11.84 335.40

5.80 121.72 12.06 347.46

5.90 123.92 12.28 359.74

6.00 126.12 12.50 372.24

6.10 128.33 12.72 384.96

6.20 130.53 12.94 397.91

6.30 132.75 13.16 411.07

6.40 134.96 13.39 424.466.50 137.18 13.61 438.06

6.60 139.41 13.83 451.89

6.70 141.63 14.05 465.95


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6.80 143.86 14.27 480.22

6.90 146.09 14.50 494.72

7.00 148.33 14.72 509.44

7.10 150.57 14.94 524.38

7.20 152.81 15.17 539.55

7.30 155.06 15.39 554.95

7.40 157.31 15.62 570.56

7.50 159.56 15.84 586.41

7.60 161.82 16.07 602.48

7.70 164.08 16.29 618.77

7.80 166.34 16.52 635.29

7.90 168.61 16.75 652.04

8.00 170.88 16.97 669.02

8.10 173.15 17.20 686.22

8.20 175.43 17.43 703.65

8.30 177.71 17.66 721.30

8.40 180.00 17.89 739.19

8.50 182.28 18.11 757.30

8.60 184.57 18.34 775.65

8.70 186.87 18.57 794.22

8.80 189.16 18.80 813.02

8.90 191.47 19.03 832.05

9.00 193.77 19.26 851.31

9.10 196.08 19.49 870.80

9.20 198.39 19.72 890.53

9.30 200.70 19.95 910.48

9.40 203.02 20.19 930.67

9.50 205.34 20.42 951.09

9.60 207.67 20.65 971.74

9.70 210.00 20.88 992.62

9.80 212.33 21.12 1013.74

9.90 214.66 21.35 1035.09

10.00 217.00 21.58 1056.67

10.10 219.34 21.82 1078.49

10.20 221.69 22.05 1100.54

10.30 224.04 22.29 1122.82

10.40 226.39 22.52 1145.35

10.50 228.74 22.76 1168.10

10.60 231.10 22.99 1191.09

10.70 233.46 23.23 1214.32

10.80 235.83 23.46 1237.79

10.90 238.20 23.70 1261.49

11.00 240.57 23.94 1285.43

11.10 242.95 24.18 1309.60

11.20 245.32 24.41 1334.02

11.30 247.71 24.65 1358.67

11.40 250.09 24.89 1383.5611.50 252.48 25.13 1408.69

11.60 254.88 25.37 1434.05

11.70 257.27 25.61 1459.66


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11.80 259.67 25.85 1485.51

11.90 262.07 26.09 1511.60

12.00 264.48 26.33 1537.92

12.10 266.89 26.57 1564.49

12.20 269.30 26.81 1591.30

12.30 271.72 27.05 1618.35

12.40 274.14 27.29 1645.65

12.50 276.56 27.54 1673.18

12.60 278.99 27.78 1700.96

12.70 281.42 28.02 1728.98

12.80 283.85 28.26 1757.24

12.90 286.29 28.51 1785.75

13.00 288.73 28.75 1814.50

13.10 291.17 29.00 1843.50

13.20 293.62 29.24 1872.74

13.30 296.07 29.48 1902.22

13.40 298.53 29.73 1931.95

13.50 300.98 29.98 1961.93

13.60 303.44 30.22 1992.15

13.70 305.91 30.47 2022.61

13.80 308.37 30.71 2053.33

13.90 310.85 30.96 2084.29

14.00 313.32 31.21 2115.50

14.10 315.80 31.46 2146.95

14.20 318.28 31.70 2178.66

14.30 320.76 31.95 2210.61

14.40 323.25 32.20 2242.81

14.50 325.74 32.45 2275.26

14.60 328.24 32.70 2307.96

14.70 330.74 32.95 2340.91

14.80 333.24 33.20 2374.11

14.90 335.74 33.45 2407.55

15.00 338.25 33.70 2441.25

15.10 340.76 33.95 2475.20

15.20 343.28 34.20 2509.41

15.30 345.80 34.45 2543.86

15.40 348.32 34.71 2578.57

15.50 350.84 34.96 2613.52

15.60 353.37 35.21 2648.73

15.70 355.90 35.46 2684.20

15.80 358.44 35.72 2719.92

15.90 360.98 35.97 2755.89

16.00 363.52 36.22 2792.11

16.10 366.07 36.48 2828.59

16.20 368.61 36.73 2865.32

16.30 371.17 36.99 2902.31

16.40 373.72 37.24 2939.5616.50 376.28 37.50 2977.06

16.60 378.85 37.76 3014.81

16.70 381.41 38.01 3052.83


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16.80 383.98 38.27 3091.10

16.90 386.55 38.53 3129.62

17.00 389.13 38.78 3168.41

17.10 391.71 39.04 3207.45

17.20 394.29 39.30 3246.75

17.30 396.88 39.56 3286.31

17.40 399.47 39.82 3326.13

17.50 402.06 40.08 3366.20

17.60 404.66 40.34 3406.54

17.70 407.26 40.60 3447.13

17.80 409.86 40.86 3487.99

17.90 412.47 41.12 3529.11

18.00 415.08 41.38 3570.49

18.10 417.69 41.64 3612.12

18.20 420.31 41.90 3654.02

18.30 422.93 42.16 3696.19

18.40 425.56 42.42 3738.61

18.50 428.18 42.69 3781.30

18.60 430.81 42.95 3824.25

18.70 433.45 43.21 3867.46

18.80 436.08 43.48 3910.94

18.90 438.73 43.74 3954.68

19.00 441.37 44.00 3998.68

19.10 444.02 44.27 4042.95

19.20 446.67 44.53 4087.49

19.30 449.32 44.80 4132.29

19.40 451.98 45.07 4177.35

19.50 454.64 45.33 4222.68

19.60 457.31 45.60 4268.28

19.70 459.98 45.86 4314.14

19.80 462.65 46.13 4360.27

19.90 465.32 46.40 4406.67

20.00 468.00 46.67 4453.34

20.10 470.68 46.93 4500.27

20.20 473.37 47.20 4547.48

20.30 476.06 47.47 4594.95

20.40 478.75 47.74 4642.69

20.50 481.44 48.01 4690.70

20.60 484.14 48.28 4738.98

20.70 486.84 48.55 4787.52

20.80 489.55 48.82 4836.34

20.90 492.26 49.09 4885.43

21.00 494.97 49.36 4934.80

21.10 497.69 49.63 4984.43

21.20 500.40 49.90 5034.33

21.30 503.13 50.18 5084.51

21.40 505.85 50.45 5134.9621.50 508.58 50.72 5185.68

21.60 511.32 50.99 5236.68

21.70 514.05 51.27 5287.94


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21.80 516.79 51.54 5339.49

21.90 519.53 51.82 5391.30

22.00 522.28 52.09 5443.39

22.10 525.03 52.37 5495.76

22.20 527.78 52.64 5548.40

22.30 530.54 52.92 5601.32

22.40 533.30 53.19 5654.51

22.50 536.06 53.47 5707.98

22.60 538.83 53.74 5761.72

22.70 541.60 54.02 5815.74

22.80 544.37 54.30 5870.04

22.90 547.15 54.58 5924.62

23.00 549.93 54.85 5979.47

23.10 552.71 55.13 6034.60

23.20 555.50 55.41 6090.01

23.30 558.29 55.69 6145.70

23.40 561.09 55.97 6201.67

23.50 563.88 56.25 6257.92

23.60 566.68 56.53 6314.45

23.70 569.49 56.81 6371.26

23.80 572.29 57.09 6428.35

23.90 575.11 57.37 6485.72

24.00 577.92 57.65 6543.37

24.10 580.74 57.93 6601.30

24.20 583.56 58.21 6659.51

24.30 586.38 58.50 6718.01

24.40 589.21 58.78 6776.79

24.50 592.04 59.06 6835.85

24.60 594.88 59.35 6895.20

24.70 597.72 59.63 6954.83

24.80 600.56 59.91 7014.74

24.90 603.40 60.20 7074.94

25.00 606.25 60.48 7135.42

25.10 609.10 60.77 7196.19

25.20 611.96 61.05 7257.24

25.30 614.82 61.34 7318.58

25.40 617.68 61.62 7380.21

25.50 620.54 61.91 7442.12

25.60 623.41 62.20 7504.32

25.70 626.28 62.48 7566.80

25.80 629.16 62.77 7629.57

25.90 632.04 63.06 7692.63

26.00 634.92 63.35 7755.98

26.10 637.81 63.64 7819.62

26.20 640.69 63.93 7883.54

26.30 643.59 64.21 7947.76

26.40 646.48 64.50 8012.2626.50 649.38 64.79 8077.05

26.60 652.29 65.08 8142.14

26.70 655.19 65.37 8207.51


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26.80 658.10 65.66 8273.17

26.90 661.01 65.96 8339.13

27.00 663.93 66.25 8405.38

27.10 666.85 66.54 8471.92

27.20 669.77 66.83 8538.75

27.30 672.70 67.12 8605.87

27.40 675.63 67.42 8673.29

27.50 678.56 67.71 8741.00

27.60 681.50 68.00 8809.00

27.70 684.44 68.30 8877.30

27.80 687.38 68.59 8945.89

27.90 690.33 68.89 9014.77

28.00 693.28 69.18 9083.95

Notes:

This spreadsheet is to calculate the length of the aircraftarrester cable on an aircraft carrier to successfully stop alanding plane.

To do so we have to calculate the integral of the functionf(x)=0.17x^2+20x.

The integral is the area of a region under a curve.By breaking the region into thin vertical slabs we approximatethis area. (The thinner the slabs are the more accurate resultwe get.)

To stop the plane the cumulative area, in other words thework done by the cable has to equal or to be more than thekinetic energy of the landing plane.For calculating the kinetic energy (KE=0.5mV^2) we need toconsider not only the speed of the plane and the ship buttheir direction as well as the wind`s.


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Fourth Case

7000.00

145.00 x> 22.44

40.28 x< 22.45

20.00

5.56

15.00

4.17

45.00

2.95

15.00

8328.086437.55

4966.21

3533.99

First Case Second Case

(plane) (plane+ship+wi (plane+ship-wi (plane-ship+wi

.17x+20xd(x) = [(17/300)x+10 (17/300)x+1

The true value othe two


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Total Stopping EnergyThird Case

(plane-ship-win(plane+ship+wi (plane+ship-wi (plane-ship+wi (plane-ship-win

0x = 5678

f "x" is betweenvalues.


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Fourth Case

(plane+ship+wi (plane+ship-wi (plane-ship+wi (plane-ship-wind)


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Aircraft Arrester Final

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