Top Document: Rec.Bicycles Frequently Asked Questions Posting Part 4/5 Previous Document: 9.2 Mail Order Addresses Next Document: 9.4 Helmet FAQ now online See reader questions & answers on this topic!  Help others by sharing your knowledge The grade of an incline is its vertical rise, in feet, per every 100 horizontal feet traversed. (I say "feet" for clarity; one could use any consistent length measure.) Or, if you will accept my picture below, * d  a  o  y R Theta  *___)______________ x then Grade = y/x (Multiply by 100 to express as a percentage.) and Theta = arctan(y/x) So a grade of 100% is a 45 degree angle. A cliff has an infinite grade. [More from Jobst Brandt <jobst.brandt@stanfordalumni.org>] Date: Mon, 26 Apr 1999 16:11:44 PDT The steepness of a road is generally measured in % grade, which in mathematical terms is the slope, or TANGENT of the angle, measured from the horizontal. This is the ratio of elevation change per horizontal distance traveled, often called "rise over run". Typically a road that rises 1in10, is otherwise called 10% grade. Measuring the distance along the surface of the road instead of horizontally gives practically the same result for most road gradients. The distance along the road surface gives the SINE of the angle in contrast to the horizontal distance that gives the TANGENT. For practical purposes SINE equals TANGENT for small angles (up to ten degrees or so). For instance, a 20% grade (11.3 degrees), whereas measuring along the road surface gives a 19.6% grade. The slope of a road is more useful than its angle because it gives a direct way to assess the effort required to move forward against the grade, whereas the angle in degrees does not readily reveal this information. A 5% grade requires a forward force of approximately 5% of the vehicle weight (above and beyond the force it takes to travel similarly on flat ground). A 15% grade requires a propulsion force of approximately 15% of the vehicle weight. Although the angle may be more easily visualized, it does not convert easily to effort without a calculator. For instance a 20% grade is an 11.3 degree angle and is a steep and difficult gradient. The relationship between angle and slope is non linear becoming 100% (1:1) at a 45 degree angle. In contrast, the SINE of 45 degrees is 70.7% while the SINE of 90 degrees (straight up) is 100% for which the slope (TANGENT) is infinity (or undefined). The most accurate way to measure this without a precision inclinometer, is to use a level, a one meter long bar and a metric ruler. Resting one end of the rod (held level) on the road at a representative spot, measuring the distance down to the road at the other end in centimeters gives the percent grade directly. Using a carpenters level and a one meter long rectangular bar can give accurate readings to a couple of tenths of a percent. User Contributions:Comment about this article, ask questions, or add new information about this topic:Top Document: Rec.Bicycles Frequently Asked Questions Posting Part 4/5 Previous Document: 9.2 Mail Order Addresses Next Document: 9.4 Helmet FAQ now online Part1  Part2  Part3  Part4  Part5  Single Page [ Usenet FAQs  Web FAQs  Documents  RFC Index ] Send corrections/additions to the FAQ Maintainer: iglesias@draco.acs.uci.edu (Mike Iglesias)
Last Update March 27 2014 @ 02:11 PM
