APPENDIX J. WIND EFFECTS ANALYSIS


Given: Vehicle velocity during braking with no wind at 0.1-second intervals
Note: Refer to the following three spreadsheets throughout the process below.

1)    Calculate stopping distance with no wind:

2)    Determine the drag forces caused by head and tail winds:

3)    Calculate the stopping distances as affected by wind:
a)    Add the drag forces by the wind from the stopping force without wind to get the total stopping forces in wind:


b)    Calculate the deceleration rates by dividing the mass of the vehicle from these new stopping forces

c)    Calculate the new velocity profiles using these decelerations:

d)    Using these velocities, calculate the stopping distance in the same way as in step 1-c.
e)    To find the differences in stopping distance due to wind, subtract the no wind stopping distance from each of the two distances:

4)    These results can be further refined by additional iteration. To do this, substitute the results for V2 and V3 into the procedure at step 2-b, and repeat the remaining calculations. Continue to iterate this process until the stopping distance results converge. The results from this analysis converged after three iteration.


Vehicle frontal area (ft^2): 40
Vehicle coefficient of drag: 0.6
Vehicle mass (slugs): 154
Wind velocity (mph): 20
Delta1=          -3.56
Delta2=         2.18		 2nd iter         -3.44
2nd iter         2.16		 3rd iter         -3.45
3rd iter         2.16

                                                                                      1st Iteration
Time v1 v1 a1 F1 Drag(nom) Wind Vel(+) Drag(+) Wind Vel(-) Drag(-) Drag D2 Drag D3 F2 F3 a2 a3 v2 v3 d1 d2 d3
(sec) (mph) (ft/s) (ft/s^2) (lbf) (lbf) (mph) (lbf) (mph) (lbf) (lbf) (lbf) (lbf) (lbf) (ft/s^2) (ft/s^2) (ft/s) (ft/s) (ft) (ft) (ft)
0 61.00 89.66 0.00 0.00 225.76   81.00 398.07   41.00 101.98   -172.32 123.77   -172.32 123.77 0.00 0.00 89.66 89.66 0.00 0.00 0.00
0.1 60.88 89.49 -1.78 -273.47 224.86   80.88 396.89   40.88 101.38   -172.02 123.48   -445.49 -149.99 -2.89 -0.97 89.37 89.56 8.97 8.97 8.97
0.2 59.79 87.89 -15.98 -2460.75 216.90   79.79 386.29   39.79 96.06   -169.39 120.84   -2630.14 -2339.91 -17.08 -15.19 87.66 88.04 17.92 17.90 17.92
0.3 57.61 84.69 -31.96 -4921.95 201.42   77.61 365.52   37.61 85.85   -164.11 115.57   -5086.06 -4806.39 -33.03 -31.21 84.36 84.92 26.70 26.67 26.73
0.4 55.44 81.50 -31.96 -4921.73 186.50   75.44 345.33   35.44 76.21   -158.83 110.29   -5080.56 -4811.44 -32.99 -31.24 81.06 81.80 35.17 35.11 35.22
0.5 52.78 77.59 -39.06 -6015.60 169.05   72.78 321.43   32.78 65.21   -152.38 103.84   -6167.98 -5911.76 -40.05 -38.39 77.06 77.96 43.32 43.21 43.40
0.6 50.49 74.22 -33.74 -5195.19 154.67   70.49 301.48   30.49 56.40   -146.81 98.27   -5342.01 -5096.93 -34.69 -33.10 73.59 74.65 51.08 50.92 51.19
0.7 48.68 71.55 -26.63 -4101.33 143.77   68.68 286.18   28.68 49.90   -142.41 93.87   -4243.74 -4007.45 -27.56 -26.02 70.83 72.05 58.50 58.28 58.66
0.8 46.86 68.89 -26.63 -4101.55 133.27   66.86 271.28   26.86 43.79   -138.02 89.47   -4239.57 -4012.08 -27.53 -26.05 68.08 69.44 65.66 65.36 65.86
0.9 44.93 66.05 -28.41 -4375.02 122.50   64.93 255.83   24.93 37.72   -133.33 84.78   -4508.35 -4290.24 -29.27 -27.86 65.15 66.66 72.55 72.17 72.81
1 42.64 62.68 -33.74 -5195.19 110.31   62.64 238.06   22.64 31.09   -127.76 79.21   -5322.95 -5115.98 -34.56 -33.22 61.69 63.33 79.15 78.68 79.47
1.1 40.22 59.13 -35.51 -5468.66 98.16   60.22 220.06   20.22 24.81   -121.89 73.35   -5590.56 -5395.31 -36.30 -35.03 58.06 59.83 85.42 84.85 85.81
1.2 38.29 56.28 -28.41 -4375.02 88.96   58.29 206.16   18.29 20.30   -117.20 68.66   -4492.22 -4306.36 -29.17 -27.96 55.15 57.03 91.33 90.66 91.79
1.3 36.24 53.27 -30.18 -4648.26 79.67   56.24 191.89   16.24 15.99   -112.22 63.68   -4760.48 -4584.58 -30.91 -29.77 52.06 54.06 96.96 96.17 97.49
1.4 33.82 49.72 -35.51 -5468.66 69.40   53.82 175.76   13.82 11.59   -106.36 57.81   -5575.02 -5410.85 -36.20 -35.14 48.44 50.54 102.29 101.38 102.90
1.5 31.52 46.34 -33.74 -5195.19 60.30   51.52 161.09   11.52 8.06   -100.79 52.24   -5295.98 -5142.95 -34.39 -33.40 45.00 47.20 107.26 106.22 107.95
1.6 29.35 43.15 -31.96 -4921.73 52.27   49.35 147.78   9.35 5.31   -95.51 46.97   -5017.24 -4874.76 -32.58 -31.65 41.74 44.04 111.89 110.72 112.67
1.7 27.54 40.48 -26.63 -4101.55 46.02   47.54 137.13   7.54 3.45   -91.11 42.57   -4192.66 -4058.98 -27.23 -26.36 39.02 41.40 116.21 114.90 117.08
1.8 25.12 36.93 -35.51 -5468.66 38.30   45.12 123.55   5.12 1.59   -85.25 36.71   -5553.91 -5431.96 -36.06 -35.27 35.41 37.88 120.26 118.80 121.22
1.9 23.07 33.91 -30.18 -4648.49 32.29   43.07 112.56   3.07 0.57   -80.26 31.72   -4728.75 -4616.76 -30.71 -29.98 32.34 34.88 123.95 122.34 125.01
2 20.78 30.54 -33.74 -5195.19 26.19   40.78 100.88   0.77 0.04   -74.69 26.15   -5269.89 -5169.04 -34.22 -33.57 28.92 31.52 127.34 125.57 128.49
2.1 18.96 27.88 -26.63 -4101.55 21.82   38.96 92.12   -1.04 -0.07   -70.30 21.89   -4171.85 -4079.67 -27.09 -26.49 26.21 28.87 130.40 128.46 131.65
2.2 16.79 24.68 -31.96 -4921.73 17.10   36.79 82.12   -3.21 -0.63   -65.02 17.73   -4986.75 -4904.00 -32.38 -31.84 22.97 25.69 133.18 131.08 134.53
2.3 14.86 21.84 -28.41 -4374.79 13.39   34.86 73.72   -5.14 -1.61   -60.33 15.00   -4435.12 -4359.80 -28.80 -28.31 20.09 22.86 135.65 133.38 137.10
2.4 12.80 18.82 -30.18 -4648.49 9.95   32.80 65.29   -7.20 -3.14   -55.35 13.09   -4703.83 -4635.40 -30.54 -30.10 17.04 19.85 137.84 135.39 139.39
2.5 10.63 15.62 -31.96 -4921.73 6.86   30.63 56.92   -9.37 -5.33   -50.07 12.18   -4971.80 -4909.54 -32.28 -31.88 13.81 16.66 139.72 137.09 141.37
2.6 8.33 12.25 -33.74 -5195.19 4.21   28.33 48.71   -11.67 -8.26   -44.50 12.47   -5239.69 -5182.72 -34.02 -33.65 10.41 13.29 141.28 138.47 143.04
2.7 6.28 9.23 -30.18 -4648.49 2.39   26.28 41.91   -13.72 -11.42   -39.52 13.81   -4688.00 -4634.67 -30.44 -30.10 7.36 10.28 142.50 139.52 144.37
2.8 4.11 6.04 -31.96 -4921.73 1.02   24.11 35.26   -15.89 -15.33   -34.24 16.35   -4955.97 -4905.38 -32.18 -31.85 4.14 7.10 143.43 140.25 145.40
2.9 1.93 2.84 -31.96 -4921.73 0.23   21.93 29.19   -18.07 -19.81   -28.96 20.03   -4950.69 -4901.69 -32.15 -31.83 0.93 3.92 144.03 140.67 146.11
3 -0.48 -0.71 -35.51 -5468.66 0.01   19.52 23.11   -20.48 -25.46   -23.10 25.47   -5491.76 -5443.19 -35.66 -35.35 -2.64 0.38 144.32 140.76 146.50



2nd Iteration

new V+ new D+ new V- new D- new D2 new D3 new F2 new F3 new a2 new a3 new v2 new v3 new d2 new d3
(ft/s) (lb) (ft/s) (lb) (lb) (lb) (lb) (lb) (ft/s^2) (ft/s^2) (ft/s) (ft/s) (ft) (ft)

119.06

 398.04 60.26 101.97 -172.29 123.79 -172.3 123.8 0.00 0 89.66 89.66 0 0
118.77 396.11 60.16 101.64 -171.25 123.23 -444.7 -150.2 -2.89 -0.98 89.37 89.56 8.97 8.97
117.06 384.80 58.64 96.57 -167.90 120.34 -2628.6 -2340.4 -17.07 -15.20 87.66 88.04 17.90 17.92
113.76 363.39 55.52 86.56 -161.98 114.85 -5083.9 -4807.1 -33.01 -31.21 84.36 84.92 26.67 26.73
110.46 342.62 52.40 77.09 -156.12 109.41 -5077.8 -4812.3 -32.97 -31.25 81.07 81.80 35.11 35.22
106.46 318.23 48.56 66.21 -149.18 102.84 -6164.8 -5912.8 -40.03 -38.39 77.06 77.96 43.21 43.40
102.99 297.83 45.25 57.49 -143.15 97.18 -5338.3 -5098.0 -34.66 -33.10 73.60 74.65 50.92 51.19
100.23 282.10 42.65 51.07 -138.33 92.70 -4239.7 -4008.6 -27.53 -26.03 70.84 72.04 58.28 58.66
97.48 266.82 40.04 45.02 -133.55 88.24 -4235.1 -4013.3 -27.50 -26.06 68.09 69.44 65.36 65.86
94.55 251.03 37.26 38.98 -128.53 83.53 -4503.5 -4291.5 -29.24 -27.87 65.17 66.65 72.17 72.81
91.09 233.01 33.93 32.33 -122.71 77.97 -5317.9 -5117.2 -34.53 -33.23 61.72 63.33 78.69 79.47
87.46 214.81 30.43 26.00 -116.65 72.16 -5585.3 -5396.5 -36.27 -35.04 58.09 59.82 84.86 85.80
84.55 200.72 27.63 21.44 -111.77 67.51 -4486.8 -4307.5 -29.13 -27.97 55.18 57.03 90.67 91.79
81.46 186.31 24.66 17.07 -106.64 62.60 -4754.9 -4585.7 -30.88 -29.78 52.09 54.05 96.19 97.49
77.84 170.12 21.14 12.55 -100.72 56.85 -5569.4 -5411.8 -36.16 -35.14 48.47 50.53 101.40 102.89
74.40 155.42 17.80 8.90 -95.12 51.40 -5290.3 -5143.8 -34.35 -33.40 45.04 47.19 106.24 107.95
71.14 142.11 14.64 6.02 -89.83 46.26 -5011.6 -4875.5 -32.54 -31.66 41.78 44.03 110.75 112.67
68.42 131.44 12.00 4.05 -85.42 41.97 -4187.0 -4059.6 -27.19 -26.36 39.06 41.39 114.92 117.07
64.81 117.95 8.48 2.02 -79.65 36.28 -5548.3 -5432.4 -36.03 -35.28 35.46 37.87 118.83 121.21
61.74 107.03 5.48 0.84 -74.74 31.45 -4723.2 -4617.0 -30.67 -29.98 32.39 34.87 122.38 125.00
58.32 95.50 2.12 0.13 -69.31 26.06 -5264.5 -5169.1 -34.19 -33.57 28.97 31.51 125.62 128.48
55.61 86.83 -0.53 -0.01 -65.01 21.83 -4166.6 -4079.7 -27.06 -26.49 26.27 28.86 128.51 131.63
52.37 77.01 -3.71 -0.39 -59.91 17.49 -4981.6 -4904.2 -32.35 -31.85 23.03 25.68 131.14 134.52
49.49 68.78 -6.54 -1.20 -55.38 14.60 -4430.2 -4360.2 -28.77 -28.31 20.16 22.85 133.44 137.09
46.44 60.55 -9.55 -2.56 -50.60 12.51 -4699.1 -4636.0 -30.51 -30.10 17.11 19.83 135.46 139.37
43.21 52.42 -12.74 -4.56 -45.57 11.41 -4967.3 -4910.3 -32.26 -31.89 13.88 16.65 137.17 141.36
39.81 44.49 -16.11 -7.28 -40.28 11.50 -5235.5 -5183.7 -34.00 -33.66 10.48 13.28 138.56 143.02
36.76 37.95 -19.12 -10.26 -35.55 12.66 -4684.0 -4635.8 -30.42 -30.10 7.44 10.27 139.61 144.35
33.54 31.59 -22.30 -13.97 -30.57 14.99 -4952.3 -4906.7 -32.16 -31.86 4.22 7.08 140.35 145.38
30.33 25.83 -25.48 -18.24 -25.60 18.46 -4947.3 -4903.3 -32.13 -31.84 1.01 3.90 140.77 146.08
26.76 20.11 -29.02 -23.65 -20.10 23.66 -5488.8 -5445.0 -35.64 -35.36 -2.55 0.36 140.87 146.47
                                 
                              -3.44 2.16


3rd Iteration
new V+ new D+ new V- new D- new D2 new D3 new F2 new F3 new a2 new a3 new v2 new v3 new d2 new d3
(ft/s) (lb) (ft/s) (lb) (lb) (lb) (lb) (lb) (ft/s^2) (ft/s^2) (ft/s) (ft/s) (ft) (ft)

119.06

 398.04 60.26 101.97 -172.29 123.79 -172.3 123.8 0.00 0 89.66 89.66 0 0
118.77 396.11 60.16 101.64 -171.25 123.23 -444.7 -150.2 -2.89 -0.98 89.37 89.56 8.97 8.97
117.06 384.81 58.64 96.57 -167.91 120.34 -2628.7 -2340.4 -17.07 -15.20 87.66 88.04 17.90 17.92
113.76 363.41 55.52 86.56 -162.00 114.86 -5084.0 -4807.1 -33.01 -31.21 84.36 84.92 26.67 26.73
110.47 342.65 52.40 77.09 -156.15 109.41 -5077.9 -4812.3 -32.97 -31.25 81.07 81.80 35.11 35.22
106.46 318.27 48.56 66.21 -149.22 102.85 -6164.8 -5912.8 -40.03 -38.39 77.06 77.96 43.21 43.40
103.00 297.88 45.25 57.49 -143.21 97.18 -5338.4 -5098.0 -34.66 -33.10 73.60 74.65 50.92 51.19
100.24 282.17 42.64 51.06 -138.40 92.71 -4239.7 -4008.6 -27.53 -26.03 70.84 72.04 58.28 58.66
97.49 266.90 40.04 45.01 -133.63 88.25 -4235.2 -4013.3 -27.50 -26.06 68.09 69.44 65.36 65.86
94.57 251.13 37.25 38.96 -128.62 83.54 -4503.6 -4291.5 -29.24 -27.87 65.17 66.65 72.17 72.81
91.12 233.12 33.93 32.32 -122.81 77.99 -5318.0 -5117.2 -34.53 -33.23 61.72 63.33 78.69 79.47
87.49 214.93 30.42 25.99 -116.77 72.17 -5585.4 -5396.5 -36.27 -35.04 58.09 59.82 84.86 85.80
84.58 200.86 27.63 21.43 -111.90 67.52 -4486.9 -4307.5 -29.14 -27.97 55.17 57.03 90.67 91.79
81.49 186.46 24.65 17.06 -106.79 62.61 -4755.0 -4585.6 -30.88 -29.78 52.09 54.05 96.19 97.49
77.87 170.27 21.13 12.54 -100.87 56.86 -5569.5 -5411.8 -36.17 -35.14 48.47 50.53 101.40 102.89
74.44 155.58 17.79 8.89 -95.28 51.41 -5290.5 -5143.8 -34.35 -33.40 45.04 47.19 106.24 107.95
71.18 142.28 14.63 6.01 -90.00 46.26 -5011.7 -4875.5 -32.54 -31.66 41.78 44.03 110.75 112.67
68.46 131.62 11.99 4.04 -85.60 41.98 -4187.2 -4059.6 -27.19 -26.36 39.06 41.39 114.92 117.07
64.86 118.13 8.47 2.01 -79.83 36.29 -5548.5 -5432.4 -36.03 -35.28 35.46 37.87 118.83 121.21
61.79 107.22 5.47 0.84 -74.93 31.45 -4723.4 -4617.0 -30.67 -29.98 32.39 34.87 122.38 125.00
58.37 95.68 2.11 0.13 -69.50 26.06 -5264.7 -5169.1 -34.19 -33.57 28.97 31.51 125.62 128.48
55.67 87.02 -0.54 -0.01 -65.20 21.83 -4166.8 -4079.7 -27.06 -26.49 26.27 28.86 128.51 131.63
52.43 77.20 -3.72 -0.39 -60.10 17.49 -4981.8 -4904.2 -32.35 -31.85 23.03 25.68 131.14 134.52
49.56 68.96 -6.55 -1.21 -55.57 14.60 -4430.4 -4360.2 -28.77 -28.31 20.16 22.85 133.44 137.09
46.51 60.73 -9.57 -2.57 -50.79 12.52 -4699.3 -4636.0 -30.51 -30.10 17.10 19.84 135.46 139.37
43.28 52.60 -12.75 -4.57 -45.74 11.42 -4967.5 -4910.3 -32.26 -31.89 13.88 16.65 137.17 141.36
39.88 44.66 -16.12 -7.30 -40.45 11.51 -5235.6 -5183.7 -34.00 -33.66 10.48 13.28 138.56 143.02
36.84 38.11 -19.13 -10.28 -35.71 12.67 -4684.2 -4635.8 -30.42 -30.10 7.44 10.27 139.60 144.35
33.62 31.75 -22.32 -13.98 -30.72 15.01 -4952.4 -4906.7 -32.16 -31.86 4.22 7.08 140.35 145.38
30.41 25.97 -25.50 -18.26 -25.74 18.49 -4947.5 -4903.2 -32.13 -31.84 1.01 3.90 140.77 146.08
26.85 20.24 -29.04 -23.67 -20.22 23.69 -5488.9 -5445.0 -35.64 -35.36 -2.56 0.36 140.87 146.47
                                 
                              -3.45 2.16