Navigation is very important in aviation and shipping to determine a required heading to reach a given destination or to calculate an estimated position, given a used heading. The core of all navigation calculations is a triangle having speed vectors as its sides and angles derived from given direction angles from the North, which can be mapped to the angles of that triangle. So, a navigation problem is actually solving the missing items (sides and angles) from a triangle.

This package consists of a base module and a navigation module. The base module solves two cases for a triangle with sides and angles:

  1. Solving a triangle if three items out of six (3 sides and 3 angles) are given and the three other must be calculated. There are 20 different combinations possible, each of which can be solved or recognized as special cases without a solution or with an unlimited number of solutions.
  2. Solving a triangle if four items out of six (3 sides and 3 angles) are given and the two remaining must be calculated. There are 15 different combinations possible, each of which can be solved or recognized as special cases without a solution or with an unlimited number of solutions.

Using this base module, the navigation module offers to solve navigation problems. The sides of this triangle are speed vectors and the angles are directions measured from the North. Given four navigation data, it calculates the remaining two data or detects special cases of degenerated triangles.

Both modules are extensively documented, with detailed descriptions of special cases. They also come with demonstration programs in VCL (Windows only) and Firemonkey (Windows, MacOS, iOS and Android), allowing to enter sides or angles and calculate the missing data, both for a simple triangle as well as for a navigation wind triangle. The picture below is a screenshot of both parts of the demonstration program: at the left the solution of a simple triangle with three data given and three remaining to calculate. At the right a navigation triangle with four given data and two to calculate.



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Engineering projects use different units e.g. temperature, speed, diameter, and so on. In addition, these values must also display in different dimensions, e.g. a temperature in °C or °F, a speed in m/s or ft/s, a diameter in mm or inch, and so on. To avoid possible conversion errors and reduce rounding and truncation errors, such calculations must be organized methodically. For example, for each unit used in the project, a dimension is chosen (e.g. °C for a temperature unit) and all calculations are done using this dimension. When retrieving data from the user or from a database, the values are converted to the selected dimensions and when displaying results, the dimensions used internally are converted to the required dimensions.

The modules offered here are highly standardized: all offer the same functions, making it simple to create engineering projects requiring many different units. This product consists of 28 portable, well documented and extendible Delphi Pascal modules for the following units: air density, airflow, specific air volume, altitude, climbrate, ΔT temperature, (pipe) diameters, device dimensions, distance, energy, enthalpy, heat transfer, humidity, length, liquid volume, mass, moist rate, power, pressure, small length, small surface, sound power, speed, surface, temperature, velocity, volume and waterflow.

Each of these module offer the most common dimensions in SI and Imperial units. Adding a dimension only required two extra lines.

Demonstration programs in VCL (Windows only) and Firemonkey (Windows, MacOS, iOS and Android) illustrate how to use the functions in these modules. The picture below is a screenshot of the demonstration program with a selection of 6 different units and the available dimensions per unit. It shows how a value in a selected dimension is displayed in the other dimensions for that unit.