# Widths and lengths

## Introduction

On MiningMath, the **widths are constraints within the objective function**, which means that they are **regarded in the optimization instead of being considered just on the pit design stage,** when roads, access are drawn to conceive an operational feasible to the pit.

The definition of minimum widths is a pretty useful feature to obtain **operational results** and **play with different geometries** accordingly with the project requirements. It is important to understand that they are **very complex parameters** to be respected while** considering 3-dimensional non-linear models, **which also** **influence the runtime of each scenario. Therefore, it is not possible to always guarantee that all minimum widths are respected due to the deposit geometry and also the constraints hierarchy. Thus, **testing different** values **is a great strategy to identify opportunities **that could bring the best mining sequence and NPV.

## What are the bottom widths?

Bottom widths (BW) are the **minimum horizontal distance,** **on the lowest floor of the pit**, as seen in *Figure 1, *it is required to allow mining operations based on the equipment sizing. This parameter is considered the same for all periods and is related to adjacent slopes and applicable in other areas regarded as pit bottoms.

## What are mining widths?

Mining widths (MW) are the minimum horizontal distance that should be respected from a pit to another in every period, which means that this is the * horizontal distance between the walls of two surfaces* that belonged to consecutive periods, as shown in Figure 2.

This feature is **more complex than the minimum bottom width** since it would drastically change the pit shapes to identify the best regions. Note that **wider values** provide** greater mining fronts** and also **better designs** to nested pits, pushbacks, schedules, or any other result that you are looking for.

## What are mining lengths?

The Mining Length (ML) represents a **minimum distance that must exist** between at least two points amidst the walls of surfaces among two consecutive mining periods. This distance is already respected for any values smaller or equal to the MW. Thus, this parameter extends such distance between any two points for a value greater than MW. *Figure 3* depicts an example

## Identifying geometric parameters

*Figure 4 *shows a section view of the McLaughlin deposit, where **each color represents a given period**. The **horizontal arrows** highlight** the bottom and the mining width**, while **others identify the vertical advance. **Mining lengths cannot be depicted in this 2D representation.

## How does it work?

The widths inputted in the interface define a *diameter (d)* of a circle. As **MiningMath does not mine partial blocks**, the software will consider the **block size as a reference** to define whether** ****d**** should be rounded up** to the next integer multiple. The approximated **circle results in a polygon,** whose objective is to select centroids of adjacent cells. Then, MiningMath will **assign the same elevation value to the selected cells** to define mining surfaces.

*Figure 5* shows, in sequence, an example of how the minimum width of 25 meters and possible mining length of 50 meters could be defined over a 10 x 10 meters grid (block’s dimension in *x* and *y* direction).