development of design engineer tools

We are lenient when it comes to tools like the slide rule. However, it faithfully served engineers and designers for a long time. With the help of this very line, the Tu-104 and the first space rockets were created. But now developments of such magnitude cannot be imagined without the help of a computer.

In this article for the LANIT blog, I will try to present a retrospective of the development of computing devices.

*Source. Sergei Pavlovich Korolev with a slide rule*

In technical universities in the 50-60s of the last century, a special course was taught during the semester, which made it possible to master the numerous nuances of using a slide rule.

Many will be surprised now, but with its help you can multiply, divide, determine the area of a circle, find squares and cubes of numbers, logarithms, sines and tangents of angles, convert angle values into radians, and at a speed not inferior to modern calculators (Fig. 1) .

*Figure 1. Determining the area of a circle in one motion*

Addition and subtraction operations could not be carried out on it. Another disadvantage of the slide rule is the need to determine the characteristic of the number, and not just its mantissa. Simply put, we had to think about where to put the comma when determining the order of a number. Personally, I don't consider this a disadvantage. It was necessary to turn on the brain so as not to accidentally enter the macro- or micro-world. Now, using a calculator, we immediately get a number with a known order, and we unconditionally trust it. However, in many cases, the need to understand the resulting calculation procedure helps to take a broader look at the problem being solved. With a calculator, the prospect of developing the thinking capabilities of our brain is lost. Ask today's schoolchild to estimate how much 330 g of sausage costs at 750 rubles per kilogram. He will definitely use a calculator, although it is quite enough to divide 750 rubles by three (with an accuracy of one ruble).

The most common type of slide rule has a length of 25 cm, which allows you to obtain the calculation result with an accuracy of up to three digits. A conflict arose between length and accuracy: the longer the ruler, the more accurate it is, but then compactness suffers. Half-meter and even meter rulers were produced in limited copies, even scales were printed for independent production of rulers of various lengths, and round rulers were also created (these are no longer rulers, but “round bars”), but they did not become widespread. However, they were used by specialists who needed compactness, for example, geologists (Fig. 2).

The operations of addition and subtraction were mechanized using adding machines (from the Greek αριθμός – “number”, “counting” and the Greek μέτρον – “measure”, “meter”), created at the turn of the 19th-20th centuries. The Felix adding machine, widespread in our country (Fig. 3), cost 110 rubles in 1956 (approximately 12 thousand at the current exchange rate).

*Figure 3. Felix and Curta adding machines (Contina AG, Liechtenstein)*

The smallest mechanical adding machine, Curta (height 85 mm, diameter 53 mm), was used not only by financiers, but even by civil airline pilots, who calculated alignment and fuel on it.

When working on an adding machine, the order of actions is always set manually – immediately before each operation, you must press the corresponding key or turn the corresponding lever. On the adding machine “Felix» Numbers are entered by moving the levers up and down. The folding operation requires pulling out the handle located on the right and turning it one turn away from you. The subtraction operation is the opposite – turning it one turn towards itself. Multiplication and division are implemented as sequential addition and subtraction by moving the carriage one step to move to the next or previous order (when dividing).

The need to speed up calculations gave rise to electromechanical adding machines, representatives of which are shown below (Fig. 4). The older generation remembers that it was possible to determine the location of the accounting department of an enterprise by the terrible roar that these computers produced. But they were able to multiply and divide without manually converting digits. A variation of this type of device were electromechanical cash registers, which entered the amount of money, the store section number and the receipt (the machine was equipped with an automatic four-digit numerator), as well as entering the date of issue of the receipt (issued manually daily), fixed additional information (for example, the name of the enterprise or cash register numbers). Cars of this type were produced in large quantities, but few have survived, since their write-off is controlled by law.

Figure 4. Electromechanical adding machine

Since the late 70s, the era of electronic calculators and computers began. Making calculations has become simple, fast and to some extent uninteresting from the point of view of getting pleasure from the calculations themselves (they happen too quickly). But it became possible to quickly perform calculations that previously took years.

The advent of personal computers stimulated a huge leap in the development of computing capabilities. If in the 70s of the last century a textbook Kopchenova N.V., Maron I.A. “Computational Mathematics in Examples and Problems” (Nauka, 1972) recommended using the so-called grid method for solving differential equations of applied problems, which involves very cumbersome manual calculations, now this is very simply and elegantly done using Excel, resulting in a mathematical model.

I give an example of calculating the change in hydrogen concentration in a casting with a cross section of 200×200 mm during its cooling in the mold. The calculation is based on the solution of the differential diffusion equation for the two-dimensional case, i.e. when considering the distribution of hydrogen in the cross-section of a casting, if its length is at least five times its cross-section. The diffusion equation for the two-dimensional case has the following form (Source: Batuner L.M., Pozin M.E. Mathematical methods in chemical engineering, Leningrad, “Chemistry”, 1968):

$\frac{∂^2c(xyτ)}{∂x^2}+\frac{∂^2c(xyτ)}{∂y^2}={\frac{∂c(xyτ)}{∂τ}}( 1)$

The solution to equation (1) is a series of the form:

$С(xyτ)=\displaystyle\sum_{i=1}^{\infty} \frac{4}{ㄫ(2i - 1)}e^{- \frac{ㄫ^2}{a^2}(2i -1)^2τ}sin \frac{ㄫ(2i - 1)}{a}x_m \displaystyle\sum_{j=1}^{\infty} \frac {4}{ㄫ(2j - 1)}e^ {-\frac{ㄫ^2}{b^2}(2j-1)^2τ} sin {\frac {ㄫ(2j - 1)}{b}y_n}(2)$

– hydrogen concentration at the current time at a point with coordinates ,.

– step of partitioning by coordinate; – step of partitioning by coordinate ; – casting size by coordinate ; – size by coordinate .

Initial conditions: initial hydrogen concentration in the casting metal – .

Recording (3) means that at the initial moment of time the hydrogen concentration over the cross section of the casting is uniform and equal to the initial concentration ; After a significant period of time, the hydrogen concentration drops to zero.