Question

2. Tilting trains, such as the American Flyer which will run from Washington to New York and Boston, are designed to travel safely at high speeds on curved sections of track which were built for slower, conventional trains. As it enters a curve, each car is tited by hydraulic actuators mounted on its trucks. The tilting feature of the cars also increases passenger comfort by eliminating or greatly reducing the side force F, (parallel to the floor of the car) to which passengers feel subjected. Tests carried out with the tilting trains revealed that passengers feel queasy when they see through the car windows that the train is rounding a curve at high speed, yet do not feel any side force. Designers, therefore, prefer to reduce, but not eliminate that force. For a train traveling at 100 min on a curved section of track banked through an angle 8 = 6° and with a rated speed of 63 min, determine the required angle of tito il passengers are to feel side forces equal to 10% of their weights. (Round the final answer to two decimal places.) his

Answer 1

- Date: Rated speed: man w N 2 VR 10+% 2 Car ane v² m = w m] 8 32-2X2522-7 VR = tom 63 mi/h = 92.4ft/s 100 mi/h = 146.67 ft/s Now, of ten o f VR (92.432 . 2522.7ft g tano 32 2 tan6° Let the x-axis be parallel to the floor of the to hx = max! Est W Sin (0+0) = man cos CO+) where I % Fs = mv²cos Co+0) - WsPn (0+0) since 8 fsz wf ut cos(6+2) – sỉn coto)] Lol Fs W! (146.67) cos (O+0) sta(640)] For Fs = 0.10w 0 10w¥ $ 226183 cos (0+0) – stn (8+0) Let shoto) ée cos Cotd) = had 0.10 = 0.26483 1-42 0.26483 1 - 4² o, lotu Squaring both sides 0.070135 (1-4²) = 0.01 +4² + 0.24 1.070135 u' u? +0.24 0.0 60135 =0 U = 0.16136 The positive root of this equation is sa (944) = 0 • 16136 0+ 0 sin (0.16136) 6 + 0 = 9.286 0 = 9.286-6 0 - 3.286 1$ = 3.299 | (Required angle of tilt] el