Tilting trains such as the Acela Express that serves the Northeast Corridor in the Northeast United States, 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 tilted 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 Fs (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. Required:
For a train traveling at 100 mi/h on a curved section of track banked through an angle θ = 6° and with a rated speed of 65 mi/h, determine the required angle of tilt Φ if passengers are to feel side forces equal to 10% of their weights.