Sunday, September 8, 2013

response to 9%

The "grade" of a road can essentially be thought of as the "tangent" trig function of a right triangle. Grade = rise/run x 100, which can also be looked to ask sin/cosine x 100, or the hypotenuse of a right triangle since it is the slope in comparison to a flat, horizontal surface. We usually consider how large the grade of a road is by thinking about its steepness. For instance, my mother really does not like driving on highways or roads that are very "steep," especially if we have to drive downhill. The steeper the road is, the greater its grade. 

When I ride my bike around my neighborhood, I usually abhor going up really steep hills with large grades, since going uphill requires a lot more energy and tires me out more quickly (but it is the better workout)! A road with a 0% grade is the best since it does not rise any feet for every 100 feet! I remember riding my bike all the time with my friends in elementary school and during this time they took out the speed bumps on the biggest road in my neighborhood, thus making our rides downhill so smooth and fun (since we could zoom down the road really, really fast)! 

An "angle of repose" is "the steepest angle at which a sloping surface formed of a particular loose material is stable." According to this site, railroad grades have to have really low values and it's usually preferred that these values range from zero to 1.5%, since "the friction coefficient of steel wheels on steel rails is low." With higher railroad grades, such as those of 2%-4%, the train has to have stronger locomotives and must be operated with a significant increase of care and financial expense.

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