With TechEditor, empirical formulas are no longer a problem!

Hi, you're on the Dystlab channel for engineers. Today we're going to talk about empirical formulas.

Empirical expressions are an important component of applied science. They emulate physical relationships and mathematical laws that are accurate but currently unknown or difficult to use in practice.

Empirical formulas can summarize the results of laboratory research or physical testing. For example, to model the behaviour of a particular material under load. That is why such dependencies have become an integral part of many regulations and design standards. It can be said that empirical formulas create a conditional bridge between complex theory and simpler engineering practice.

But apart from their simplicity, empirical formulas have a downside. They require special attention from the engineer because they do not contain a clear and understandable relationship between the parameters. Such formulas cannot be verified like traditional ones, for example, by comparing units of measurement. The relationship between physical quantities, which is inherent in strict physical laws, may be violated in empirical formulas. The correct result in such expressions is usually achieved by using numerical factors (coefficients).

Let's take a look at the formula contained in Eurocode 1991-2 “Traffic loads on bridges”:

This is a classic example of an empirical formula: to get the load in kilonewtons per square meter, you need to enter the length in meters. The numbers "2", "120", "30" in this formula have no dimensions and are constants. Let's first try to calculate this expression "as is".

As you can see, the TechEditor indicates a mismatch in the units of measurement. To eliminate this problem, we use the special function "empiric", which separates the numerical value from the physical quantity. The units of measurement are cut off and the physical quantity becomes a real number, which can then be used in calculations (including as a coefficient to other physical quantities).

The resulting value is correct, but dimensionless. Add the necessary units of measurement. We could stop here, but there is one significant problem: in our formula, the length must always be in meters. Here's what happens if you pass the length in other units.

We got an incorrect value. In programs that don't work with units of measurement or don't have tools for working with empiricism (such as spreadsheets), the user needs to keep track of these things and use only the right units for parameters.

TechEditor allows you to get rid of this limitation. It is enough to specify in which units you want to work with certain parameters, and you will always get the correct result.

We hope this information was helpful. We wish you successful work! Good luck!