ccc ccc Title: A validated model for the dispersion of exhaust emissions from aircraft in their take-off roll ccc Authors: A. Graham1, M. Bennett*2, S. Christie2 and D.W. Raper2 ccc ccc * To whom correspondence should be addressed: m.bennett@mmu.ac.uk ccc ccc Affliation 1: Norwegian Centre of Offshore Wind Energy, Postboks 6031, N-5892 Bergen, Norway angus.graham@uni.no ccc Affiliation 2 Centre for Aviation, Transport and the Environment, Manchester Metropolitan University, Manchester M1 5GD, UK ccc ccc Copyright. Manchester Metropolitan University 2018. ccc ccc ccc ccc nomenclature: t .. exhaust age (s) Xs .. distance source has moved through at time of release (m) delta_xL .. distance of exhausts in release direction from reference point collocated with them at old time but static with respect to undisturbed air (m) xL .. distance of exhausts in release direction from reference point collocated with them at release but static with respect to undisturbed air (m) zb .. lowest height exhausts extend to (m) zt .. greatest height exhausts extend to (m) delta_y .. lateral spread of exhausts (m) conc .. concentration of passive conservative tracer per unit rate tracer-mass release (s m-3) duration of ground run before rotation (s) 25 old time since start of ground run (s) 0 new time since start of ground run (s) 5 number ages tracked 5 t, Xs,delta_xL, xL, zb, zt,delta_y, conc 1 22 40.7 40.7 0.0 0.5 310.6 0.222E-03 2 12 56.9 56.9 0.0 1.3 221.6 0.153E-03 3 5 70.5 70.5 0.0 2.5 181.7 0.125E-03 4 1 82.5 82.5 0.0 3.8 159.9 0.110E-03 5 0 94.5 94.5 0.0 5.4 147.8 0.101E-03 old time since start of ground run (s) 5 new time since start of ground run (s) 10 number ages tracked 10 t, Xs,delta_xL, xL, zb, zt,delta_y, conc 1 110 37.6 37.6 0.0 0.4 298.7 0.192E-03 2 87 51.2 51.2 0.0 1.1 209.5 0.127E-03 3 66 61.9 61.9 0.0 2.0 170.3 0.101E-03 4 49 71.3 71.3 0.0 3.1 147.7 0.865E-04 5 34 80.1 80.1 0.0 4.3 133.0 0.777E-04 6 22 48.2 88.9 0.0 5.8 122.5 0.718E-04 7 12 41.0 97.8 0.0 7.5 114.8 0.678E-04 8 5 36.6 107.1 0.0 9.5 109.1 0.652E-04 9 1 34.5 117.0 0.0 11.7 105.0 0.635E-04 10 0 32.8 127.2 0.0 14.0 104.3 0.609E-04 old time since start of ground run (s) 10 new time since start of ground run (s) 15 number ages tracked 15 t, Xs,delta_xL, xL, zb, zt,delta_y, conc 1 265 35.1 35.1 0.0 0.4 288.8 0.171E-03 2 229 47.1 47.1 0.0 1.0 199.6 0.111E-03 3 195 56.2 56.2 0.0 1.8 160.7 0.865E-04 4 164 63.9 63.9 0.0 2.7 138.5 0.733E-04 5 135 71.1 71.1 0.0 3.7 123.4 0.647E-04 6 110 40.3 77.9 0.0 4.8 112.8 0.590E-04 7 87 33.4 84.6 0.0 6.1 105.0 0.549E-04 8 66 29.4 91.3 0.0 7.6 98.9 0.519E-04 9 49 26.9 98.2 0.0 9.2 94.2 0.497E-04 10 34 25.3 105.3 0.0 11.0 90.4 0.481E-04 11 22 23.9 112.8 0.0 13.1 87.5 0.470E-04 12 12 23.0 120.8 0.0 15.4 85.2 0.464E-04 13 5 22.5 129.6 0.0 18.1 83.5 0.461E-04 14 1 22.0 139.0 0.0 21.0 82.9 0.461E-04 15 0 21.9 149.1 0.0 23.6 84.7 0.441E-04 old time since start of ground run (s) 15 new time since start of ground run (s) 20 number ages tracked 20 t, Xs,delta_xL, xL, zb, zt,delta_y, conc 1 488 33.1 33.1 0.0 0.4 279.9 0.156E-03 2 438 43.9 43.9 0.0 0.9 191.2 0.998E-04 3 391 52.0 52.0 0.0 1.6 152.9 0.773E-04 4 346 58.7 58.7 0.0 2.4 130.9 0.649E-04 5 304 64.8 64.8 0.0 3.3 116.2 0.570E-04 6 265 35.4 70.5 0.0 4.2 105.6 0.515E-04 7 229 28.9 76.0 0.0 5.3 97.6 0.474E-04 8 195 25.2 81.3 0.0 6.5 91.5 0.444E-04 9 164 22.8 86.7 0.0 7.8 86.6 0.421E-04 10 135 21.0 92.1 0.0 9.2 82.6 0.403E-04 11 110 19.7 97.6 0.0 10.8 79.4 0.389E-04 12 87 18.8 103.4 0.0 12.5 76.7 0.378E-04 13 66 18.0 109.3 0.0 14.4 74.6 0.371E-04 14 49 17.5 115.7 0.0 16.5 72.8 0.365E-04 15 34 17.0 122.4 0.0 18.9 71.4 0.362E-04 16 22 16.8 129.6 0.0 21.5 70.3 0.361E-04 17 12 16.7 137.6 0.0 24.5 69.5 0.363E-04 18 5 16.4 146.0 0.0 27.7 69.2 0.365E-04 19 1 16.4 155.4 0.0 31.0 70.0 0.367E-04 20 0 16.6 165.7 0.0 34.0 72.8 0.348E-04 old time since start of ground run (s) 20 new time since start of ground run (s) 25 number ages tracked 25 t, Xs,delta_xL, xL, zb, zt,delta_y, conc 1 779 31.5 31.5 0.0 0.3 271.5 0.144E-03 2 715 41.5 41.5 0.0 0.8 184.2 0.918E-04 3 654 48.7 48.7 0.0 1.5 146.5 0.709E-04 4 596 54.8 54.8 0.0 2.2 124.6 0.592E-04 5 541 60.2 60.2 0.0 3.0 110.2 0.517E-04 6 488 32.1 65.2 0.0 3.8 99.7 0.465E-04 7 438 26.0 69.9 0.0 4.8 91.9 0.426E-04 8 391 22.5 74.5 0.0 5.8 85.7 0.397E-04 9 346 20.2 78.9 0.0 6.9 80.8 0.374E-04 10 304 18.6 83.4 0.0 8.2 76.8 0.355E-04 11 265 17.3 87.8 0.0 9.4 73.5 0.340E-04 12 229 16.3 92.3 0.0 10.9 70.7 0.328E-04 13 195 15.6 96.9 0.0 12.4 68.3 0.319E-04 14 164 15.0 101.7 0.0 14.0 66.4 0.311E-04 15 135 14.4 106.6 0.0 15.8 64.7 0.305E-04 16 110 14.1 111.7 0.0 17.7 63.3 0.301E-04 17 87 13.8 117.2 0.0 19.9 62.2 0.298E-04 18 66 13.6 122.9 0.0 22.2 61.2 0.296E-04 19 49 13.3 129.0 0.0 24.7 60.5 0.296E-04 20 34 13.2 135.6 0.0 27.6 59.9 0.297E-04 21 22 13.2 142.8 0.0 30.8 59.5 0.299E-04 22 12 12.9 150.5 0.0 34.3 59.3 0.303E-04 23 5 13.2 159.1 0.0 38.1 59.8 0.308E-04 24 1 12.8 168.2 0.0 41.6 61.3 0.308E-04 25 0 13.4 179.2 0.0 44.7 64.6 0.288E-04 old time since start of ground run (s) 25 new time since start of ground run (s) 30 number ages tracked 25 t, Xs,delta_xL, xL, zb, zt,delta_y, conc 6 779 28.3 59.8 0.0 1.3 240.0 0.401E-04 7 715 23.3 64.8 0.0 2.1 175.9 0.376E-04 8 654 20.3 69.1 0.0 3.0 143.8 0.352E-04 9 596 18.3 73.1 0.0 3.9 123.9 0.332E-04 10 541 16.8 77.0 0.0 4.8 110.3 0.315E-04 11 488 15.6 80.8 0.0 5.9 100.3 0.301E-04 12 438 14.7 84.6 0.0 7.0 92.7 0.290E-04 13 391 14.0 88.5 0.0 8.2 86.7 0.280E-04 14 346 13.4 92.3 0.0 9.4 81.8 0.272E-04 15 304 12.9 96.3 0.0 10.8 77.9 0.265E-04 16 265 12.5 100.3 0.0 12.2 74.6 0.259E-04 17 229 12.2 104.5 0.0 13.8 71.8 0.254E-04 18 195 11.9 108.9 0.0 15.5 69.5 0.251E-04 19 164 11.7 113.4 0.0 17.3 67.6 0.248E-04 20 135 11.6 118.1 0.0 19.2 66.0 0.246E-04 21 110 11.5 123.2 0.0 21.3 64.6 0.245E-04 22 87 11.4 128.6 0.0 23.6 63.5 0.245E-04 23 66 11.4 134.3 0.0 26.2 62.7 0.246E-04 24 49 11.4 140.4 0.0 28.9 62.0 0.247E-04 25 34 11.5 147.1 0.0 32.0 61.5 0.249E-04 26 22 11.6 154.4 0.0 35.5 61.1 0.253E-04 27 12 11.8 162.3 0.0 39.3 61.0 0.257E-04 28 5 12.0 171.1 0.0 43.4 61.5 0.263E-04 29 1 12.1 180.3 0.0 47.1 63.0 0.264E-04 30 0 11.4 190.5 0.0 50.2 66.0 0.252E-04 old time since start of ground run (s) 30 new time since start of ground run (s) 35 number ages tracked 25 t, Xs,delta_xL, xL, zb, zt,delta_y, conc 11 779 13.6 73.4 0.0 3.1 155.7 0.265E-04 12 715 13.1 77.8 0.0 4.1 133.7 0.259E-04 13 654 12.5 81.5 0.0 5.1 118.5 0.251E-04 14 596 12.0 85.1 0.0 6.1 107.3 0.244E-04 15 541 11.5 88.5 0.0 7.2 98.7 0.237E-04 16 488 11.1 92.0 0.0 8.4 92.0 0.232E-04 17 438 10.8 95.4 0.0 9.6 86.5 0.227E-04 18 391 10.5 99.0 0.0 10.9 82.0 0.222E-04 19 346 10.3 102.6 0.0 12.3 78.2 0.218E-04 20 304 10.1 106.4 0.0 13.7 75.1 0.215E-04 21 265 9.9 110.3 0.0 15.3 72.4 0.213E-04 22 229 9.8 114.3 0.0 17.0 70.2 0.211E-04 23 195 9.7 118.5 0.0 18.8 68.3 0.210E-04 24 164 9.6 123.0 0.0 20.8 66.7 0.209E-04 25 135 9.6 127.7 0.0 22.9 65.4 0.209E-04 26 110 9.6 132.8 0.0 25.2 64.2 0.209E-04 27 87 9.6 138.2 0.0 27.7 63.4 0.210E-04 28 66 9.6 143.9 0.0 30.4 62.7 0.211E-04 29 49 9.7 150.1 0.0 33.4 62.2 0.213E-04 30 34 9.8 156.9 0.0 36.7 61.8 0.216E-04 31 22 10.0 164.4 0.0 40.5 61.7 0.220E-04 32 12 10.2 172.5 0.0 44.5 61.7 0.225E-04 33 5 10.4 181.5 0.0 48.9 62.3 0.230E-04 34 1 10.5 190.8 0.0 52.8 63.8 0.233E-04 35 0 10.0 200.6 0.0 55.8 66.6 0.224E-04 old time since start of ground run (s) 35 new time since start of ground run (s) 40 number ages tracked 22 t, Xs,delta_xL, xL, zb, zt,delta_y, conc 16 779 9.8 83.2 0.0 5.3 118.6 0.205E-04 17 715 9.7 87.5 0.0 6.4 108.5 0.204E-04 18 654 9.5 91.0 0.0 7.5 100.3 0.201E-04 19 596 9.3 94.3 0.0 8.7 93.7 0.197E-04 20 541 9.1 97.6 0.0 9.9 88.2 0.194E-04 21 488 8.9 100.9 0.0 11.1 83.6 0.191E-04 22 438 8.7 104.2 0.0 12.5 79.8 0.189E-04 23 391 8.6 107.6 0.0 13.9 76.6 0.186E-04 24 346 8.5 111.1 0.0 15.4 73.8 0.185E-04 25 304 8.4 114.8 0.0 17.0 71.4 0.183E-04 26 265 8.3 118.6 0.0 18.7 69.4 0.182E-04 27 229 8.3 122.6 0.0 20.5 67.7 0.182E-04 28 195 8.2 126.8 0.0 22.5 66.2 0.181E-04 29 164 8.2 131.3 0.0 24.6 65.0 0.181E-04 30 135 8.2 136.0 0.0 26.8 64.0 0.182E-04 31 110 8.3 141.0 0.0 29.3 63.1 0.183E-04 35 34 8.6 165.5 0.0 41.6 61.6 0.192E-04 36 22 8.8 173.2 0.0 45.6 61.6 0.196E-04 37 12 9.0 181.4 0.0 49.9 61.8 0.200E-04 38 5 9.2 190.7 0.0 54.6 62.6 0.205E-04 39 1 9.3 200.1 0.0 58.8 64.1 0.208E-04 40 0 9.0 209.6 0.0 61.7 66.8 0.202E-04 ages ceased tracking since old time t, Xs, reason 32 87 ambient diffusion underway 33 66 ambient diffusion underway 34 49 ambient diffusion underway old time since start of ground run (s) 40 new time since start of ground run (s) 45 number ages tracked 18 t, Xs,delta_xL, xL, zb, zt,delta_y, conc 21 779 7.9 91.1 0.0 7.8 97.8 0.170E-04 22 715 7.9 95.4 0.0 9.0 92.5 0.170E-04 23 654 7.8 98.8 0.0 10.2 87.6 0.169E-04 24 596 7.7 102.0 0.0 11.5 83.4 0.167E-04 25 541 7.6 105.1 0.0 12.8 79.8 0.166E-04 26 488 7.5 108.3 0.0 14.1 76.7 0.164E-04 27 438 7.4 111.6 0.0 15.6 74.0 0.163E-04 28 391 7.3 114.9 0.0 17.1 71.6 0.162E-04 29 346 7.3 118.4 0.0 18.7 69.6 0.161E-04 30 304 7.3 122.0 0.0 20.4 67.9 0.160E-04 31 265 7.2 125.8 0.0 22.2 66.4 0.160E-04 32 229 7.2 129.8 0.0 24.2 65.1 0.160E-04 33 195 7.2 134.0 0.0 26.3 64.0 0.160E-04 34 164 7.2 138.5 0.0 28.5 63.1 0.161E-04 42 12 8.0 189.5 0.0 55.5 61.7 0.180E-04 43 5 8.3 199.0 0.0 60.5 62.5 0.185E-04 44 1 8.4 208.5 0.2 64.7 64.5 0.189E-04 45 0 8.2 217.7 0.3 67.6 67.3 0.184E-04 ages ceased tracking since old time t, Xs, reason 35 135 ambient diffusion underway 36 110 ambient diffusion underway 40 34 ambient diffusion underway 41 22 ambient diffusion underway old time since start of ground run (s) 45 new time since start of ground run (s) 50 number ages tracked 14 t, Xs,delta_xL, xL, zb, zt,delta_y, conc 26 779 6.7 97.8 0.0 10.5 84.5 0.146E-04 27 715 6.7 102.1 0.0 11.8 81.5 0.147E-04 28 654 6.7 105.5 0.0 13.2 78.4 0.147E-04 29 596 6.6 108.6 0.0 14.5 75.6 0.146E-04 30 541 6.6 111.7 0.0 15.9 73.2 0.145E-04 31 488 6.5 114.9 0.0 17.4 71.0 0.144E-04 32 438 6.5 118.1 0.0 18.9 69.1 0.144E-04 33 391 6.4 121.4 0.0 20.5 67.4 0.143E-04 34 346 6.4 124.8 0.0 22.2 65.9 0.143E-04 35 304 6.4 128.4 0.0 24.1 64.6 0.143E-04 36 265 6.4 132.2 0.0 26.0 63.6 0.143E-04 37 229 6.4 136.2 0.0 28.1 62.6 0.143E-04 49 1 7.6 216.2 1.9 69.3 67.4 0.172E-04 50 0 7.5 225.2 1.9 72.1 70.2 0.169E-04 ages ceased tracking since old time t, Xs, reason 38 195 ambient diffusion underway 39 164 ambient diffusion underway 47 12 ambient diffusion underway 48 5 ambient diffusion underway old time since start of ground run (s) 50 new time since start of ground run (s) 55 number ages tracked 11 t, Xs,delta_xL, xL, zb, zt,delta_y, conc 31 779 5.8 103.6 0.0 13.3 75.3 0.129E-04 32 715 5.9 108.0 0.0 14.8 73.5 0.130E-04 33 654 5.8 111.3 0.0 16.3 71.5 0.130E-04 34 596 5.8 114.4 0.0 17.7 69.7 0.130E-04 35 541 5.8 117.5 0.0 19.2 67.9 0.129E-04 36 488 5.8 120.6 0.0 20.8 66.4 0.129E-04 37 438 5.8 123.8 0.0 22.4 65.0 0.129E-04 38 391 5.7 127.1 0.0 24.1 63.8 0.129E-04 39 346 5.7 130.6 0.0 25.9 62.8 0.129E-04 40 304 5.7 134.2 0.0 27.9 61.8 0.129E-04 41 265 5.8 138.0 0.0 29.9 61.1 0.129E-04 ages ceased tracking since old time t, Xs, reason 42 229 ambient diffusion underway 54 1 ambient diffusion underway 55 0 ambient diffusion underway old time since start of ground run (s) 55 new time since start of ground run (s) 60 number ages tracked 9 t, Xs,delta_xL, xL, zb, zt,delta_y, conc 36 779 5.2 108.8 0.0 16.4 68.5 0.115E-04 37 715 5.2 113.2 0.0 18.0 67.5 0.117E-04 38 654 5.2 116.5 0.0 19.5 66.2 0.117E-04 39 596 5.2 119.7 0.0 21.1 64.9 0.117E-04 40 541 5.2 122.7 0.0 22.6 63.7 0.117E-04 41 488 5.2 125.8 0.0 24.3 62.6 0.117E-04 42 438 5.2 129.0 0.0 26.0 61.7 0.117E-04 43 391 5.2 132.3 0.0 27.8 60.8 0.117E-04 44 346 5.2 135.8 0.0 29.8 60.1 0.117E-04 ages ceased tracking since old time t, Xs, reason 45 304 ambient diffusion underway 46 265 ambient diffusion underway old time since start of ground run (s) 60 new time since start of ground run (s) 90 number ages tracked 0 ages ceased tracking since old time t, Xs, reason 66 779 ambient diffusion underway 67 715 ambient diffusion underway 68 654 ambient diffusion underway 69 596 ambient diffusion underway 70 541 ambient diffusion underway 71 488 ambient diffusion underway 72 438 ambient diffusion underway 73 391 ambient diffusion underway 74 346 ambient diffusion underway