Yaw mark formula

CPSC 5360 - Software Engineering

Spring Semester, 2020

Project Specifications and Instructions

Submission date: the last two weeks of the semester

Project Description (‘Estimating a vehicle’s velocity (that is, speed) based on skid marks, yaw marks and vault case’):

This project (‘Estimating a vehicle’s velocity (also known as speed) based on skid marks, yaw marks and vault case’) requires you to adopt a use-case driven object-oriented approach to develop a system to support the estimation of a vehicle’s velocity based on skid marks, yaw marks and vault (that is, when the vehicle is airborne) case.

Motivation:

We live in a society where vehicles play a very important role. Since the beginning of car industry, there were numerous efforts to traffic accident reconstruction based on skid marks, yaw marks and vault case. This particular software’s main purpose is the estimation of a vehicle’s velocity based on skid marks, yaw marks and vault case. The second purpose of the software is to publish the relevant data onto a website for the world to see the past accidents reconstruction and an automated velocity calculator based on various factors involved such as skid distance, drag factor, acceleration of gravity, radius of the yaw marks, horizontal and vertical distances, the takeoff angle and potential other data.

Difficulties:

Some of the challenges in analyzing accidents are the measurements’ accuracy and the time needed to deviate the traffic so that incoming traffic will not be derailed. In addition, there are a lot of environmental factors in determining the correct coefficient of friction also known as drag factor (table below):

image1.png

For example, the drag factor on a road made up of asphalt, dry weather and speed more than 30mph could be taken as f = 0.83.

The structure and the logic of the software:

The software should calculate the velocity for three cases: based on skid marks, based on yaw marks (when a vehicle negotiates a curve) and when a vehicle becomes airborne during some phase of the accident. The formula specifications have been taken from the following reference (The author of this Master Thesis “agrees that the Library shall make it freely available for reference and study”):

Karoly William Krajczar: A rule-based system for preliminary accident reconstruction. Master of Applied Science's Thesis at the University of British Columbia, 1986, retrieved from https://pdfs.semanticscholar.org/be65/5e2252deb670253b4330fc46b82ccf904ab8.pdf

The first case, velocity calculation based on skid marks, is given by the equation: vi = √(2fgd+vf2), where vi is the initial velocity (m/s), vf is the final velocity (m/s), d is the skid distance (m), f is the drag factor and g is the acceleration of gravity (m/s2). Note that vf may be set to 0 after impact, acceleration of gravity is set to 9.8 m/s2 (in fact, at the surface of Earth shortest radius, g = 9.83, and on high mountains g can be as low as 9.76. We have already explained the values of the drag factor (above table). Your software tool may use the following flow diagram:

image2.png

The second case, velocity calculation based on skid marks, is given by the equation: vc = √(Rg(f+e)/(1-fe)), where vc is the critical curve velocity (m/s), R is the radius of the yaw mark (m), e is the super-elevation (%/100), f is the drag factor and g is the acceleration of gravity (m/s2). For a precise estimate, the first one-third of the yaw marks should be used to calculate R.

The third case, vault calculation, is needed if a vehicle becomes airborne during some phase of the accident. In this case, it is possible to calculate the vehicle’s speed at the point of takeoff using kinematics. The vault formula to calculate the vehicle’s velocity is v = √(gD2)/(2(H+De)), where v is the velocity at takeoff (m/s), D is the horizontal distance (m), H is the vertical distance (m) and e is the takeoff angle (%/100). For a better understanding of the vault parameters, please see the below figure: