Show All Work You need to design a highway that has a 300 m

Show All Work

You need to design a highway that has a 300 m radius turn. It is decided to bank the turn so that when there is an ice storm the car can still make the turn if going the speed limit. Plot, using excel, the speed limit vs bank angles ranging from 0 degree to 80 degree.

Solution

radius = 300m speed limit= sqrroot(r*g*tan) g = 9.81 m/sec2 2.236 Banking angle(degrees) angle (in radians) speed limit(metres/sec) speed limit(miles/hr) 0.00 0 0 0 1.00 0.017453293 7.16730466 16.02609322 2.00 0.034906585 10.13764394 22.66777185 3.00 0.052359878 12.41918252 27.76929211 4.00 0.06981317 14.34554312 32.07663443 5.00 0.087266463 16.04615645 35.87920582 6.00 0.104719755 17.58754572 39.32575223 7.00 0.122173048 19.00933883 42.50488162 8.00 0.13962634 20.33744518 45.47452743 9.00 0.157079633 21.58993765 48.27510059 10.00 0.174532925 22.7800418 50.93617346 11.00 0.191986218 23.91780194 53.48020514 12.00 0.20943951 25.01107677 55.92476765 13.00 0.226892803 26.06616747 58.28395046 14.00 0.244346095 27.08823199 60.56928673 15.00 0.261799388 28.08156821 62.79038653 16.00 0.27925268 29.0498136 64.95538321 17.00 0.296705973 29.99608967 67.0712565 18.00 0.314159265 30.92310893 69.14407157 19.00 0.331612558 31.83325566 71.17915966 20.00 0.34906585 32.72864799 73.18125691 21.00 0.366519143 33.61118646 75.15461292 22.00 0.383972435 34.48259246 77.10307674 23.00 0.401425728 35.34443922 79.03016611 24.00 0.41887902 36.19817704 80.93912386 25.00 0.436332313 37.04515404 82.83296444 26.00 0.453785606 37.88663363 84.71451281 27.00 0.471238898 38.72380919 86.58643734 28.00 0.488692191 39.55781664 88.45127801 29.00 0.506145483 40.38974546 90.31147085 30.00 0.523598776 41.22064825 92.16936949 31.00 0.541052068 42.05154934 94.02726432 32.00 0.558505361 42.88345255 95.8873999 33.00 0.575958653 43.71734835 97.75199091 34.00 0.593411946 44.55422051 99.62323706 35.00 0.610865238 45.39505243 101.5033372 36.00 0.628318531 46.24083325 103.3945032 37.00 0.645771823 47.09256384 105.2989728 38.00 0.663225116 47.95126274 107.2190235 39.00 0.680678408 48.8179722 109.1569858 40.00 0.698131701 49.69376434 111.1152571 41.00 0.715584993 50.57974762 113.0963157 42.00 0.733038286 51.47707356 115.1027365 43.00 0.750491578 52.38694397 117.1372067 44.00 0.767944871 53.31061868 119.2025434 45.00 0.785398163 54.24942396 121.301712 46.00 0.802851456 55.20476169 123.4378471 47.00 0.820304748 56.17811953 125.6142753 48.00 0.837758041 57.17108212 127.8345396 49.00 0.855211333 58.18534371 130.1024285 50.00 0.872664626 59.22272219 132.4220068 51.00 0.890117919 60.28517506 134.7976514 52.00 0.907571211 61.3748175 137.2340919 53.00 0.925024504 62.49394299 139.7364565 54.00 0.942477796 63.64504688 142.3103248 55.00 0.959931089 64.83085364 144.9617887 56.00 0.977384381 66.05434831 147.6975228 57.00 0.994837674 67.31881304 150.5248659 58.00 1.012290966 68.62786984 153.451917 59.00 1.029744259 69.98553077 156.4876468 60.00 1.047197551 71.39625709 159.6420309 61.00 1.064650844 72.86502964 162.9262063 62.00 1.082104136 74.39743267 166.3526594 63.00 1.099557429 75.99975472 169.9354516 64.00 1.117010721 77.67911049 173.690491 65.00 1.134464014 79.44358921 177.6358655 66.00 1.151917306 81.30243678 181.7922486 67.00 1.169370599 83.26628077 186.1834038 68.00 1.186823891 85.34741126 190.8368116 69.00 1.204277184 87.56013429 195.7844603 70.00 1.221730476 89.92122133 201.0638509 71.00 1.239183769 92.45048736 206.7192897 72.00 1.256637061 95.17154328 212.8035708 73.00 1.274090354 98.11278844 219.380195 74.00 1.291543646 101.3087395 226.5263416 75.00 1.308996939 104.8018393 234.3369127 76.00 1.326450232 108.6449644 242.9301404 77.00 1.343903524 112.9049755 252.4555253 78.00 1.361356817 117.6678648 263.1053457 79.00 1.378810109 123.046424 275.1318042 80.00 1.396263402 129.1920369 288.8733945