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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
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<title>Physics Code - Help</title>
<meta property="og:url" content="https://pauld0051.github.io/physics-code/index.html" />
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<meta property="og:title" content="Physics Code" />
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Physics Code
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Don't let physics control you - take control of physics!
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<div class="col-12 title-div">
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<h1>Understanding the Dilemma Zone variables <i class="fas fa-info-circle"></i></h1>
<p class="head-text">When approaching a controlled intersection and the traffic signal changes to yellow, a driver of a vehicle has one of two choices;
firstly, they can continue through the traffic signals and intersection or brake in order to stop before the light changes red at the stop line.</p>
<p class="head-text">A dilemma zone exists where a vehicle would not be able to safely pass through the
intersection nor stop before the stop line if a signal light were to turn yellow on approach.</p>
<p class="head-text">The risk involved to other drivers as well as the driver of the vehicle is significant in a dilemma zone situation. To date, no effective
calculator is available online to estimate if a dilemma zone exists at a particular intersection. This help file will give an understanding of the variables
required and how the results can be evaluated.</p>
</div>
</div>
</div>
</section>
<!--First Set of Cards-->
<section class="container">
<div class="row">
<div class="col-12 title-div">
<div class="container heading-background heading-padding heading-margin">
<h2>Velocity and signal phases</h2>
<p class="card-text">
The best methods to determine initial velocities and traffic light phases.
</p>
</div>
</div>
</div>
<div class="row">
<div class="col-lg-4 content-div">
<div class="card shadow" id="card-help-velocity">
<img class="card-img-top img-fluid" src="assets/images/card-images/velocity.png" alt="Velocity Image">
<div class="card-body">
<h5 class="card-title">Velocity</h5>
</div>
</div>
</div>
<div class="col-lg-8 content-div">
<div class="card shadow" id="card-help-text-velocity">
<div class="card-body">
<p>Velocity is a measure of the amount of distance an object travels over an amount of time in a relative direction.
It is common to use the SI units of ms<sup>-1</sup>, however, our calculator will also accept kilometres per hour (kmh<sup>-1</sup>) or miles per hour (mph).
The conversion into ms<sup>-1</sup> is done for you.</p>
<p>The equation to use: \[velocity = { distance \over time}\]</p>
<p>It is common in this case to begin by using the speed limit at the intersection before trying alternatives such as driving too slow or too fast.</p>
</div>
</div>
</div>
</div>
<div class="row">
<div class="col-lg-4 content-div">
<div class="card shadow" id="card-help-yellow">
<img class="card-img-top img-fluid" src="assets/images/card-images/yellow.png" alt="Yellow Light Image">
<div class="card-body">
<h5 class="card-title">Yellow Light Phase</h5>
</div>
</div>
</div>
<div class="col-lg-8 content-div">
<div class="card shadow" id="card-help-text-yellow">
<div class="card-body">
<p>The yellow light phase (<sub>yp</sub>) is a predetermined length of time controlled at the intersection.</p>
<p>The usual time a light remains yellow can range from 3 to 5 seconds. For best results,
it is ideal to know the length of time the traffic signal remains yellow.</p>
<p>This value, in seconds, gives the variable <em>time</em> in our velocity equation. This is rearranged to solve for distance.</p>
<p>The equation to use: \[dist_{yp} = { velocity \cdot time_{yp}}\]</p>
</div>
</div>
</div>
</div>
<div class="row">
<div class="col-lg-4 content-div">
<div class="card shadow" id="card-help-red">
<img class="card-img-top img-fluid" src="assets/images/card-images/red.png" alt="Red Light Image">
<div class="card-body">
<h5 class="card-title">Interphase</h5>
</div>
</div>
</div>
<div class="col-lg-8 content-div">
<div class="card shadow" id="card-help-text-red">
<div class="card-body">
<p>During the interphase all traffic signals at an intersection are red. This time is predetermined but usually is around 1 to 2 seconds.</p>
<p>The distance a vehicle travels through the duration of the interphase is added onto the yellow phase time.</p>
<p>The equation to use: \[dist_{ip} = { velocity \cdot time_{ip}}\]</p>
<p>The total distance a car travels through the yellow and interphase is: \[dist_{total} = { dist_{yp} + dist_{ip} }\]</p>
</div>
</div>
</div>
</div>
<!-- Second Set of Cards-->
<div class="row">
<div class="col-12 title-div">
<div class="container heading-background heading-padding heading-margin">
<h2>Reaction Time, Friction and Intersection Size</h2>
<p class="card-text">
Here we discuss the best methods to determine the reaction time of a driver, the friction between the vehicle and the road, and the size of an intersection.
</p>
</div>
</div>
</div>
<div class="row">
<div class="col-lg-4 content-div">
<div class="card shadow" id="card-help-reaction-time">
<img class="card-img-top img-fluid" src="assets/images/card-images/stopwatch.png" alt="Stopwatch Image">
<div class="card-body">
<h5 class="card-title">Reaction Time</h5>
</div>
</div>
</div>
<div class="col-lg-8 content-div">
<div class="card shadow" id="card-help-text-reaction-time">
<div class="card-body">
<p>Reaction time is a measure of how quickly a person reacts to a stimulus. In this case, how quickly a person reacts to seeing a yellow signal light.
The unit is almost always seconds, and can commonly be less than 1 second. However, many variables come into play when assessing reaction times.</p>
<p>There is no equation you can use to determine reaction time, other than trying it experimentally. We have designed a reaction time game that may
help determine your reaction time or that of other people. See the <a href="game.html" class="underline" target="_blank">reaction time game</a>
to run various estimates and averages for reaction times.</p>
<p>In order to work out stopping distance, we need to take into account the distance travelled before any action has taken place. To do this we
calculate: \[dist_{reaction} = { velocity \cdot time_{reaction}}\]</p>
</div>
</div>
</div>
</div>
<div class="row">
<div class="col-lg-4 content-div">
<div class="card shadow" id="card-help-friction">
<img class="card-img-top img-fluid" src="assets/images/card-images/friction.png" alt="Friction Image">
<div class="card-body">
<h5 class="card-title">Coefficient of Friction</h5>
</div>
</div>
</div>
<div class="col-lg-8 content-div">
<div class="card shadow" id="card-help-text-friction">
<div class="card-body">
<p>The coefficient of friction (μ) is a unitless number between 0 and 1. The lowest possible friction would be zero, however, this is not
logical or plausible in a real world context as this would suggest a complete frictionless system. Conversely, the highest possible friction
would be one. Again, this would not be plausible as movement would then become impossible. You can estimate μ by using real world data.
Good road conditions and good tires on the vehicle could see a range for μ between 0.70 and 0.90. Icy conditions could see μ as low as 0.1. </p>
<p>For more data you can check our accepted values here:
<button type="button" class="btn btn-link" data-toggle="modal" data-target="#frictionHelp">
<i class="far fa-question-circle"></i></button>
\[μ\]</p>
</div>
</div>
</div>
</div>
<div class="row">
<div class="col-lg-4 content-div">
<div class="card shadow" id="card-help-intersection">
<img class="card-img-top img-fluid" src="assets/images/card-images/intersection.png" alt="Intersection Image">
<div class="card-body">
<h5 class="card-title">Intersection Size</h5>
</div>
</div>
</div>
<div class="col-lg-8 content-div">
<div class="card shadow" id="card-help-text-intersection">
<div class="card-body">
<p>There are a few methods to measuring intersection distances, the most precise method, however, is being at the intersection to measure it physically.
However, scaled maps on Google and Bing have provided a chance to estimate the size of various intersections around the world. Ultimately, the next best method would be to have the
engineering plans of the intersection. If these are available you can use the dilemma zone calculator to plot out the location of dilemma and option
zones. Typically, you'd measure the intersection in metres. However, our calculator can convert yards into metres for you.</p>
<p>An intersection is measured from stop line to opposite stop line. Currently, the calculator is not geared for perpendicular roads.
\[dist_{intersection}\]</p>
</div>
</div>
</div>
</div>
<!--Third Set of Cards-->
<div class="row">
<div class="col-12 title-div">
<div class="container heading-background heading-padding heading-margin">
<h2>Length of vehicle</h2>
<p class="card-text">
Length of vehicles vary depending on make, model and even type.
</p>
</div>
</div>
</div>
<div class="row">
<div class="col-lg-4 content-div">
<div class="card shadow" id="card-help-length">
<img class="card-img-top img-fluid" src="assets/images/card-images/length.png" alt="Length Image">
<div class="card-body">
<h5 class="card-title">Vehicle Length</h5>
</div>
</div>
</div>
<div class="col-lg-8 content-div">
<div class="card shadow" id="card-help-text-length">
<div class="card-body">
<p>The one thing that becomes extremely difficult to account for is the type of vehicle approaching the stop line. For the most part we've been
able to eliminate variables such as the mass of the vehicle. But we can't eliminate the length. A truck has much further to go through an
intersection than a small car meaning the chances of a dilemma zone are now greatly increased for larger vehicles. We've included the average of
4.5 m for vehicle length. However, you may want to input other variables based on manufacture data or experience at the intersection in question.
\[length\]</p><br>
</div>
</div>
</div>
</div>
<!--Fourth Set of Cards-->
<div class="row">
<div class="col-12 title-div">
<div class="container heading-background heading-padding heading-margin">
<h2>Putting it all together</h2>
<p class="card-text">
When you have all your variables you can put them into our
<a href="calculator.html" class="underline" target="_blank"> calculator</a> or work it out yourself with this equation.
</p>
</div>
</div>
</div>
<div class="row">
<div class="col-lg-4 content-div">
<div class="card shadow" id="card-help-final">
<img class="card-img-top img-fluid" src="assets/images/card-images/calculator.png" alt="Calculator Image">
<div class="card-body">
<h5 class="card-title">The Equation</h5>
</div>
</div>
</div>
<div class="col-lg-8 content-div d-none d-md-block d-lg-block d-xl-block">
<div class="card shadow" id="card-help-text-final">
<div class="card-body">
<p>The final equation requires all the inputs for each variable.
\[dist_{final} = { dist_{total} - dist_{intersection} - length}\]
\[dist_{stopping} = { velocity^2 \over 2 \; μ \; g}\]
\[zone = {dist_{final} - (dist_{stopping} + dist_{reaction})}\]
Where g = 9.81 ms<sup>-2</sup></p>
<p>If <em>zone</em> is negative, then a dilemma zone exists. If <em>zone</em> is positive, then an option zone exists.</p>
</div>
</div>
</div>
<!-- Prevent overun for MathJax equation on small screens -->
<div class="col-lg-8 content-div d-xs-block d-sm-block d-md-none d-lg-none d-xl-none">
<div class="card shadow" id="card-help-text-final2">
<div class="card-body">
<p>The final equation requires all the inputs for each variable.
\[dist_{final} =\] \[{ dist_{total} - dist_{intersection} - length}\]
\[dist_{stopping} = { velocity^2 \over 2 \; μ \; g}\]
\[zone =\] \[{dist_{final} - (dist_{stopping} + dist_{reaction})}\]
Where g = 9.81 ms<sup>-2</sup></p>
<p>If <em>zone</em> is negative, then a dilemma zone exists. If <em>zone</em> is positive, then an option zone exists.</p>
</div>
</div>
</div>
</div>
</section>
<!-- Friction help modal -->
<div class="modal fade" id="frictionHelp" tabindex="-1" role="dialog" aria-hidden="true">
<div class="modal-dialog" role="document">
<div class="modal-content">
<div class="modal-header">
<h5 class="modal-title">coefficient of friction list</h5>
<button type="button" class="close" data-dismiss="modal" aria-label="Close">
<span aria-hidden="true">×</span>
</button>
</div>
<div class="modal-body">
Table 1: A list of common coefficient of friction numbers
<table class="table table-hover">
<thead class="thead--blue">
<tr>
<th scope="col">#</th>
<th scope="col">Tire Conditions</th>
<th scope="col">Weather Conditions</th>
<th scope="col">μ</th>
</tr>
</thead>
<tbody>
<tr>
<th scope="row">1</th>
<td>Good</td>
<td>Dry</td>
<td>0.8 - 0.9</td>
</tr>
<tr class="table-info">
<th scope="row">2</th>
<td>Good</td>
<td>Wet</td>
<td>0.6 - 0.7</td>
</tr>
<tr>
<th scope="row">3</th>
<td>Good</td>
<td>Snowy</td>
<td>0.4 - 0.5</td>
</tr>
<tr class="table-info">
<th scope="row">4</th>
<td>Good</td>
<td>Icy</td>
<td>0.1 - 0.3</td>
</tr>
<tr>
<th scope="row">5</th>
<td>Average</td>
<td>Dry</td>
<td>0.75 - 0.8</td>
</tr>
<tr class="table-info">
<th scope="row">6</th>
<td>Average</td>
<td>Wet</td>
<td>0.5 - 0.6</td>
</tr>
<tr>
<th scope="row">7</th>
<td>Average</td>
<td>Snowy</td>
<td>0.3 - 0.4</td>
</tr>
<tr class="table-info">
<th scope="row">8</th>
<td>Average</td>
<td>Icy</td>
<td>0.1 - 0.2</td>
</tr>
<tr>
<th scope="row">9</th>
<td>Bad</td>
<td>Dry</td>
<td>0.7 - 0.75</td>
</tr>
<tr class="table-info">
<th scope="row">10</th>
<td>Bad</td>
<td>Wet</td>
<td>0.4 - 0.5</td>
</tr>
<tr>
<th scope="row">11</th>
<td>Bad</td>
<td>Snowy</td>
<td>0.2 - 0.3</td>
</tr>
<tr class="table-info">
<th scope="row">12</th>
<td>Bad</td>
<td>Icy</td>
<td>0.1</td>
</tr>
</tbody>
</table>
<small>Some estimation is required for the calculation of μ which may lead to slightly altered results comparing to our calculator.
This is because the calculation includes some randomness to account for realistic scenarios.</small>
</div>
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