Introduction regarding calculators

In keeping with the purpose of this manual, and considering the target reader, this section of the manual has been developed to includes hyperlinks and automatic-calculation programs (called "calculators") in various areas of safety. These are listed in alphabetical order below, together with links back to the relevant more detailed text

These equations and calculations have been included based upon recommended values from various countries. National standards vary and will always take precedence over these values. Any significant difference between the values recommended in a country's standards and those specified in this manual are intended to enhance understanding of the fundamental principles involved.

BASIC EQUATIONS (Horizontal Curves)

This calculator allows the user to compute the values of speed V, curve radius R, or friction coefficient f, depending on which two of the three variables are provided. It also enables the estimation of friction as a function of speed, offering input fields to define the parameters for friction, depending on whether it follows a linear, exponential, or Leu and Henry model.

Further details about these calculations can be found in Technical Sheet - Horizontal Alignment.

BEFORE–AFTER TESTS (INDIVIDUAL SITE)

This tool estimates the Crash Modification Factor using the k-test, and the Probability of a Real Change using the Chi-square test (χ²). The input required includes the number of crashes that occurred at the site under study, both before and after the intervention, as well as the number of crashes at comparable sites with similar interventions.

A detailed explanation of the calculations is available Appendix 12.1 - Statistical Tests.

BINOMIAL TEST

This module calculates the probability of observing f_j or more crashes at a site, given the total number of crashes f, the frequency of type i crashes at the site f_i, and the average proportion of this crash type in a population of similar sites p_i.

Further explanation of the underlying computations is provided Section 10.3 - Crash-Based Identification (Reactive approaches).

BRAKING DISTANCE

This calculator determines either the total stopping distance or the deceleration rate of a vehicle on a downhill grade. The stopping distance is divided into reaction distance and braking distance. Inputs include initial speed V_i, final speed V_f, reaction time t, road gradient G, and friction coefficient f (which can be constant or variable with speed). When calculating deceleration, the deceleration rate a must be provided.

More information on the calculations can be found Technical Sheet - Horizontal Alignment, as well as in Technical Sheet - Road Surface Conditions, and in Technical Sheet - Sight Distance.

CONFIDENCE INTERVAL

This tool estimates the margin of uncertainty m for a given number of crashes acc occurring over a period of x years, based on a specified confidence level K.

An in-depth explanation of the methodology is available in Appendix 10.1 - Methodological Aspects.

CRASH RATE

This calculator computes the crash rate R using the following parameters: crash frequency f, analysis period P, average annual daily traffic Q, and section length L. For intersections, L is automatically set to 1.

More details are provided Section 10.3 - Crash-Based Identification (Reactive approaches).

CRITICAL CRASH RATE

This module estimates the Critical Crash Rate R_c using the average crash rate Rrp, analysis period P, average annual daily traffic Q, and section length L, which defaults to 1 for intersections. The user can also specify the desired confidence level K.

Learn more about this calculator Section 10.3 - Crash-Based Identification (Reactive approaches).

DISTRIBUTION TESTS

This calculator allows users to determine whether the mean speed of a set of speed measurements is significantly different from another (i.e. between a before and after study), to input values for two population samples, using either STUDENT’S TWO-TAILED T-TEST or KOLMOGOROV-SMIRNOV test.

This can be done either manually or by importing data from .txt files using the "Import data set" button. The result is generated upon clicking the "Calculate" button. A "Summary" section is also available, where results can be obtained using known values such as the number of before and after observations (n_b, n_a), and the sum and sum of squares of both samples.

Further explanation is available in Section 12.4 - Evaluating Road Safety Infrastructure Interventions.

ECONOMIC ASSESSMENT

Integer linear programming method (ILP)

This criterion determines the combination of projects yielding the highest discounted benefits for a given budget. The result is obtained by using a computer program that completes a series of iterations on possible project combinations.

In the first section, users may assign a name to the project. Inputs include terminal salvage value, analysis period (in years), discount rate (in %), and a set of radio buttons to classify each factor as either a benefit or a cost. A data entry table is also provided. In the second tab, a “Print” button allows users to generate a PDF report. This section displays results such as Present Value of Benefits (PVB), Present Value of Costs (PVC), First Year Rate of Return (FYRR), Net Present Value (NPV), NPV/PVC ratio, Benefit-Cost Ratio (BCR), and Internal Rate of Return (IRR). A graph of benefits and costs is also shown, along with a button to apply the discount from the first year.

Detailed calculations are explained in Section 11.3 - Priority Ranking Methods and Economic Assessment.

EPDO INDEX

This module enables the input of crash weighting factors and crash frequency by type, returning the total number of crashes, the EPDO Index, and the average EPDO value.

Learn more about the calculations in Section 10.3 - Crash-Based Identification (Reactive approaches).

LATERAL CLEARANCE

This tool calculates the lateral clearance (LC) on the inside of a curve based on curve radius R and stopping sight distance S. It can also compute the curve radius given the lateral clearance and stopping sight distance, or calculate the stopping sight distance using the radius and clearance.

Learn more about the calculations in Technical Sheet - Horizontal Alignment, as well as in Technical Sheet - Sight Distance.

MOTION EQUATIONS

This section includes various calculators for motion-related variables, allowing the user to solve for acceleration (a), initial velocity (V_i), final velocity (V_e), distance (x), or time (t), depending on the provided inputs. A toggle is available to switch the velocity unit between m/s and km/h.

OVERTURNING SPEED

This calculator computes the overturning speed (V_t) of a vehicle using the curve radius R, roadway superelevation e, vehicle track width t, and height of the center of gravity h.

Learn more about the calculations Technical Sheet - Horizontal Alignment.

POISSON TEST

This module performs a Poisson test using the provided safety level m and crash frequency to calculate the probability of a given crash frequency (f) when the safety level (m) is known.

Learn more about the calculations in Appendix 10.1 - Methodological Aspects.

REGRESSION TO THE MEAN

This calculator estimates the effect of regression to the mean using the population crash average a, the crash variance Var(a), the site’s observed crash frequency A, and the analysis period n. It also provides the corrected crash frequency for the site.

Learn more about the calculations Appendix 10.1 - Methodological Aspects.

ROAD WIDTH

This calculator estimates the required road width by allowing users to input the dimensions of different vehicle types. Given the curve radius, design speed, and existing tangent width, the tool calculates the additional widening required and the total road width on the curve.

Learn more about the calculations Technical Sheet - Horizontal Alignment.

SPEED DIFFERENTIALS (TWO-LANE RURAL ROADS)

This tool calculates speed differentials on two-lane rural roads by accepting inputs for the length and radius of two consecutive curves, with the option to include a tangent section between them. The user can also specify the design speed, select speed prediction models from various countries, and define acceleration and deceleration rates, as well as tolerance limits between design and operating speeds. A graphical representation is provided under the “Results” tab.

Learn more about the calculations in Technical Sheet - Horizontal Alignment.

SPOT SPEED STUDY

This module is divided into seven tabs.

• The "Data" tab allows entry of key characteristics of the location under study and displays summary results based on later inputs.
• The "Speed Data Table" tab provides a table for manual or imported data input (via .txt files and the “Import speeds” button).
• The "Insert" button enters the posted speed at the current cursor location.
• The "Delete" and "Delete All" buttons remove individual or all data entries.
• The remaining 2 tabs present calculated results and can each be exported as PDF using the “Print” button at the bottom of the interface.

Learn more about the calculations Section 12.4 - Evaluating Road Safety Infrastructure Interventions.