Rick F Guyon - Measures of Central Tendency - Richard F Guyon

Measures of Central Tendency

It is often unnecessary to present the experimental data in their entirety, either in tabular or graphical form. In such cases, the data and distribution can be represented by various parameters. One type of parameter is a measure of central tendency, Mode, median, and mean are measures of central tendency.

The mode is the observed value that occurs most frequently. The mode may vary greatly between series of observations. Therefore, its main use is a quick measure of the central value since little or no computation is required to find it. Beyond this, the usefulness of the mode is limited.

The median is the point in the distribution that partitions the total set of observations into two parts containing equal numbers of observations. It is not influenced by the extremity of scores on either side of the distribution. The median is found by counting up (from either end of the frequency distribution) until half of the observations have been accounted for.

Similar in concept tot he median are percentiles (percentile ranks) quartiles and deciles. The median could also have been called the 50th percentile observation. Similarly, the 50th percentile would be the observed value for which the cumulative frequency was 80%. The quartile and decile points on the distribution divide the observations or distribution into segments off 25% and 10%, respectively.

Rick F Guyon - Differential Equations - Application: Mixing - Richard F Guyon

A typical mixing problem involves a liquid-filled tank. The liquid may initially be pure or contain some solute. Liquid (either pure or a solution) enters the tank at a known rate. A drain may be present to remove thoroughly mixed liquid. The concentration of the solution the amount of solute at some given time is generally unknown.

Rick F Guyon - Stopping Distance - Richard F Guyon

Rick F Guyon - Stopping distance includes the distance traveled before the brakes are applied as well as the distance during the breaking manuever. The breaking perception reaction time is also referred to as the PIEV time, using an acronym for perception, identification, emotion, and volition. PIEV time varies widely from person to person. Though the median value is approximately 0.90 sec for unexpected events, individuals with slow reaction times may require up to 2.7 seconds. 2.5 seconds is the value used by AASHTO for determining the minimum stopping sight distances, the value that is appropriate for approximately 90% for the population.

Rick F Guyon - Coefficient of Friction - Richard F Guyon

Rick F Guyon  - In most cases, a vehicle's braking system is able to provide more braking force than can be transmitted to the pavement. Therefore, the maximum deceleration is limited by the coefficient of friction between the tires and pavement.

The coefficient of friction, f, between a vehicle and the supporting roadway is the frictional force divided by the normal force. The normal force is essentially the total weight of the vehicle, w , on all but the most extreme grades. The coefficient of friction is dependent on the condition of the vehicle's tires, the type and condition of the pavement, and the weather conditions. 

There are two coefficients of friction: static and dynamic(kinetic). The coefficients of friction may also be referred to as coefficients of road adhesion. The coefficients of static friction is larger than the coefficient of dynamic friction. While a vehicle's tires are rotating, the relative velocity between a point of contact on the tire and roadway are zero and the coefficient of static friction controls. 

Once a vehicle enters a skid, however the coefficient of dynamic friction controls. Therefore a vehicle is held to its maximum braking deceleration without entering a skid will take less distance to come to a complete stop than if the vehicle locks up its tires and skids to a stop. 

The coefficient of friction is not constant throughout the braking manuever, but varies inversely with speed. This level of sophistication is not normally considered, and an average value that is representative of the speed and conditions are used.

Rick F Guyon - Refresher: Systems of Units - Dimensional Analysis - Richard F Guyon

Dimensional Analysis

Dimensional analysis is a means of obtaining as equation that describes some phenomenon without understanding the mechanism of the phenomenon. The most serious limitation is the need to know beforehand which variables influence the phenomenon. Once these are known or assumed, dimensional analysis can be applied by a routine procedure.

The first step is to select a system of primary dimensions. The dimensional formulas and symbols for variables most frequently encountered are given .

The second step is to write a functional relationship between the dependent variable and the independent variable.

Rick F Guyon - Dimensional Analysis - Richard F Guyon