Search

The composition, operating principle, and metrological characteristics of GET 130-2019, the State Primary Special Standard of the unit of length in the field of measurements of deviations from straightness and flatness, are described. Results of investigations of the metrological characteristics of the interference measurement system incorporated into GET 130-2019 by means of which reproduction of the unit is realized on the basis of the fundamental physical constants and the properties of matter (interference) are presented, thus eliminating any additional instrumental sources of errors (uncertainty). Transmission of the unit of length in the region of measurements of deviations from straightness and flatness in the range 0–50 μm with length of the measured surface up to 30 m is achieved with the highest accuracy attainable in Russia. Comparisons that were carried out demonstrate that the metrological characteristics of GET 130-2019 correspond to the level of precision of foreign standards in measurements of deviations from straightness on a length up to 30 m and to the measurement capabilities presented in the database of the International Bureau of Weights and Measures.

Precision interference measurement of parameters of form optical surfaces are one of the most important type of the measurement in the field of the geometrical values. In countries-participants of this comparisons the special primary standards in this field of measurements take part in reproduction and transmission the unit of length in this field of measurements ensuring high measuring and calibrating capabilities countries in this type of measurement. In this article presents the result of supplementary comparisons COOMET 570/UA-a/12. The result of comparisons allowed to declare to Belarus and Russia, and to confirm to Ukraine their measuring and calibrating capability in database CIPM MRA.

Length measurement has been an indispensable part of human life since the ancient era till present days. Length and area measurement got importance from very early Indus Valley civilization for construction of roads to measurement of agricultural land. In India, length measurements were defined in Indus Valley civilization and rulers had rules for length measurements. Mughal and British adopted the measurement system contemporary to the international system of units available and were used in the country. During twilight years of the regime of British government, plans for setting up an institute for measurement standards were made and a national institute of measurements was founded in 1942. Within the first decade of laying the constitution of India, SI units were adopted. In this paper, we describe the history and advancements in the progress towards length measurement through its various redefinitions from time to time. It covers the evolution of SI unit of length “Metre” through its diversified redefinitions from the ages of body parts to latest quantum standards.

Space-time symmetries and the principle of relativity alone suffice to obtain Lorentz-like coordinate transformations, in which a free parameter, k, plays the part of c − 2 in special relativity. Several authors have concluded that special relativity does not need the postulate of the constancy of the speed of light (the “second postulate”). I oppose this claim and argue that the transformations have no physical content unless different observers can ensure that they use the same units. The relativity of lengths and durations makes this non-trivial. One usually assumes boostability to solve this problem. I analyze this concept and show it is also non-trivial and cannot be assumed in general. The second postulate offers a way around this, as well as an economical method to match both time and length units. Without it, additional postulates are necessary to ground the physical meaning of the transformations.

A new certified reference material (CRM) for size and shape analysis of elongated nanoparticles has been developed by the European Commission’s Joint Research Centre. The CRM consists of titanium dioxide nanorods dispersed in 1-butanol, was coded ERM-FD103 and has been certified for different electron microscopy–based operationally defined measurands such as the modal and median values of the particle number-weighted distributions of the minimum and maximum Feret diameter, the maximum inscribed circle diameter, the area-equivalent circular diameter and the aspect ratio. The nanorods have nominal dimensions of 15 nm in width and 55 nm in length. Homogeneity and stability measurements were performed using transmission electron microscopy. The relative standard uncertainty for homogeneity ranged from 0.3 to 1.7%. No significant instability was detected for a shelf life of 18 months and a storage temperature of 18 °C. The certified values have been determined from the results of an interlaboratory comparison in which qualified expert laboratories participated with scanning and transmission electron microscopy. The certified values are traceable to the unit of length in the International System of Units, the metre, and the relative expanded uncertainties (confidence level of approximately 95%) range from 4 to 6%. These properties allow the CRM to be used for quality assurance and calibration of electron microscopy methods for nanoparticle size and shape analysis in ranges relevant for the implementation of EU legislation related to nanomaterials. The presented study discusses the purpose and results of the different steps that were followed to turn an industrially relevant raw titanium dioxide nanorod material into a fit-for-purpose CRM. Graphical abstract Electronic supplementary material The online version of this article (10.1007/s00216-020-02984-z) contains supplementary material, which is available to authorized users.

The results of studies aimed at creating a complex of high-precision hardware instruments for reproduction and transmission of the unit of length are described. The composition of the complex is described. The creation of the complex is intended to increase the scientific and technological level of the Russian Federation and support the uniformity of measurements of length. The complex will become the foundation for the further development of the standards base of the Russian Federation in the field of measurements of length and will make it possible to perform reproduction of the unit of length at two wavelengths, 633 and 532 nm, as well as measure the wavelength of laser sources of radiation in a vacuum in the range 500–1050 nm.

Here the debated issue of units of length in building construction practice in ancient Aegean architecture is focused through the case study of the Mycaenean tholos tomb, the Treasury of Atreus. Recent architectural analysis of the monument highlights a geometric mesh underlying its architectural form, which reveals the coexistence of more than one unit of length and the geometric relations among them. These units are consistent with the modular units reported in the literature. Starting from such details, the present study explores the usefulness of the identified mesh for measuring lengths and areas in situ and controlling the construction process. The integrated analysis of length measurement systems and the associated geometric pattern shed light on their strict correlation. The contextualization of the units of length in their systems in multiples and sub-multiples and the aim to compute lengths explain and clarify the co-existence of diverse modular units in Aegean architecture.

GET 183–2019, the State Primary Special Standard of the unit of length in the area of measurements of the parameters of deviations from flatness of optical surfaces, is presented. The standard supports the reproduction, storage, and transmission of the unit of length in the range 0.002–2.000 μm for optical surfaces measuring 50–280 mm in dimension. An interference apparatus incorporated into GET 183–2019 in which a new method of treatment and interpretation of interference patterns is described, the method of phase steps, is implemented. Studies conducted as part of an effort at improving the standard, including theoretical and experimental investigations of the interference apparatus, are described. The selection of the new method is evaluated and a comparative analysis of the calibration and measurement capabilities of foreign metrological devices is performed. The metrological characteristics of GET 183–2019 are presented.

Introduction. Increasing demands of precise geometry measurements by science and industry cause the necessity of improvement in an associated branch of legal and practical metrology. One of the most significant fields is the measurement of internal dimensions and so the issues with the unit of meter transfer. Now we face the situation when the current accuracies of National standards of different levels in corresponding traceability chain (reference rings measurements) get close to each other. This means that we have to make the standard of upper level more precise. One of the obvious ways is to apply the latest ultra-stable laser locked to a frequency comb.Objective. The objective is to propose possibilities for improvement of the National secondary standard of the unit of length by researching its measuring capabilities to minimize measurement uncertainty.Materials and methods. The calculation of expanded uncertainty of internal diameter measurements by the National secondary standard of the unit of length is performed according to the international document «Guide to the Expression of Uncertainty in Measurement» JCGM 100:2008 approved by BIPM. The secondary standard research results represented in previous reports and publications are also taken into consideration.Results. Detailed uncertainty budget for the proposed measuring system is given as well as graphical data representing the accuracy improvement.Conclusion. Actions for minimization of measurement uncertainty components of the National secondary standard of the unit of length in the field of reference ring internal diameter measurements in combination with state-of-the-art laser interferometer system improve it to the next frontiers of accuracy and precision.

Multi-axis electrical discharging machining (EDM) is the main manufacturing approach for shrouded blisks. To maintain a stable discharging, the feedrate of an electrode must be regulated appropriately with respect to a workpiece. The feedrate control in multi-axis EDM is a challenge due to two facts. The first is that the feedrate fluctuations occur at line segment junctions along the feeding trajectory which is expressed in G01 codes. The second is that, with involvement of rotary axes, the feedrate control must consider the nonlinear mapping between the workpiece frame and the machine frame. This paper proposes an extended unit arc length increment interpolation (UALII) for generalized NURBS curves. Given the point coordinates in the machine frame, the coordinates in the workpiece frame can be obtained by the forward kinematics. By using the UALII, the curve parameter is first obtained. To achieve synchronization among involved axes, the curve parameter is substituted into the generalized NURBS curve. Due to the nonlinear mapping, each interpolation of one basic length unit (BLU) can give the axial increments which are more than one BLU. Digital differential analyzer (DDA) is used for a finer interpolation for each axial increment. Machining tests show that the use of UALII for generalized NURBS curves can decrease the machining time by 42.19%, 29.65% and 26.42%, respectively, as compared with the cases of no feedrate planning, the weighted average movement ratio algorithm (WAMRA) and the feedrate post-processing algorithm (FPPA). The extended UALII algorithm can also reduce the electrode wear.

A logical reasoning problem in the Special Relativity interpretation of the Lorentz transformation was discovered and corrected by introducing an alternative interpretation of Lorentz transformations with a relativistic measuring process based on both, stretched time and length units, whereby the measurements as a consequence measure a shortened distance and time lines as variables due to used units. The space shuttles are getting longer instead of shorter and a barn-pole paradox does not occur. The spatial locations remain in their locations and space is not contracted and not changed. The failure is that by contracting both units and distance the Lorentz factor is eliminated and relativity was vanished. This leads to a discovered invariance of speed of light contradicting 2-d postulate. The elementary particles have their own measuring devices for time and length in the form of wavelengths and frequencies and they read distances and durations of different lengths from space using their own relativistically different units. The new interpretation is covered by the two postulates of Einstein. This is a sensational result too in view of all dramatic and romantic history as there is really a failure discovered. The Lorentz transformations remain being in use with another method. The new theory and the discovered problems of logical failures are explained vividly in the same manner as Special Relativity was using easy be thought samples. Reader do not need a high level of mathematics to be fit for as it is a more qualitatively thematic for every one who is interested in relativity matters.

We developed an automated system for navigating photonic chips through layout for automatic testing as well as assisted troubleshooting. The system was built to allow, in addition to standard grating-coupling measurements, top-scattering measurement along the waveguide structures for characterization of the devices/materials for each platform layout and estimate the optical loss per unit of length, making it to improve the next generation of devices. Micrometer resolution mapping along the digitized path of the waveguide was achieved, enabling video monitoring of scattering events and changes in the intensity map.

Mixing is one of the most commonly used processes in food, animal feed, chemical, cosmetic, etc., industries. It is supposed to provide high-quality homogenous, nutritious mixtures. To provide appropriate mixing of materials while maintaining the process high efficiency and low energy consumption it is crucial to explore and describe the material flow caused by the movement of mixing elements and the contact between particles. The process of mixing is also affected by structural features of the machine components and the mixing chamber, speed of mixing, and properties of the mixed materials, such as the size of particles, moisture, friction coefficients. Thus, modeling of the phenomena that accompany the process of mixing using the above-listed parameters is indispensable for appropriate implementation of the process. The paper provides theoretical power calculations that take into account the material speed change, the impact of the material friction coefficient on the screw steel surface and the impact of the friction coefficient on the material, taking into account the loading height of the mixing chamber and the chamber loading value. Dependencies between the mixer power and the product degree of fineness, rotational speed of screw friction coefficients, the number of windings per length unit, and width of the screw tape have been presented on the basis of a developed model. It has been found that power increases along with an increase in the value of these parameters. Verification of the theoretical model indicated consistence of the predicted power demand with the power demand determined in tests performed on a real object for values of the assumed, effective loading, which was 65–75%.

This study aimed to propose a new forecast combination method for landslide displacement based on the monitoring dataset. Considering the existence of outlier data, the 3σ method was used to eliminate them firstly. In order to diminish the effect of different length units, Z-score normalization was employed in this paper. Space reconstruction was performed to calculate the Lyapunov exponent, which was to verify whether the time series were chaotic. Three models were further studied here, namely, adding-weight one-rank local-region prediction method, adding-weight zero-rank local-region prediction method, and the largest Lyapunov exponent method. Furthermore, they are compared with respect to accuracy with each other and measured data so as to establish a forecast combination method. In order to check its validity, this method was applied to the analysis of the dataset of a 434-day displacement monitoring project performed on 12 monitoring points distributed on 4 profile maps on Qinghuasi Landslide Treatment Project in Yan’an, China. This model, which was not only implemented on a single point but also extended some results to a profile map, effectively, predicted the slope deformation in Qinghuasi landslide site. Prediction results indicate that the displacement of A-A profile map is relatively minimal, while slope deformation has been significant on the whole profile map of C-C. Situations at B-B and D-D are better than C-C profile map, though local failures have occurred at these two profile maps. This new model achieved a higher accuracy. Engineering measures based on these predicting results work effectively, which shows that it would be helpful in practical applications. This paper provides new idea and calculating method that can be used to develop deep data-mining approaches for landslide displacement prediction.

The paper deals with geodetic and metrological activities in the field of length parameter, on the basis of which the uniformity and accuracy of measurements and gauges are ensured also in international extent. The historical role of surveyors in determining the basic unit of length is briefly described. Furthermore, the impact of the application of the laser tracker on the accuracy of determination of the characteristics of the geodetic length standard Koštice (Czech Republic) is evaluated. Based on laboratory tests performed in VUGTK and interlaboratory comparative tests with a leading laboratory in the length parameter in Veisala (Finland), the declared uncertainties of measurement of the VUGTK laboratory were confirmed. These are applied in the metrological traceability of the geodetic length base in Javoriv (Ukraine).

For media with periodic changes in Young's modulus and yield strength, the problems of stress, strain and displacement distribution around single excavation of spherical and cylindrical shape are solved. The density of the medium is determined by the difference between the elastic modules and the yield strength in the blocks and interblock space. In each case analytical solutions are obtained. Influence of blocks quantity on length unit and differences in properties of blocks and interlayers on the nature of changes in stress, strains and displacements was studied. It is noted that blockness is one of the factors that form zonal disintegration around excavations.

We investigate the structure of the gravity-induced Generalized Uncertainty Principle in three dimensions. The subtleties of lower dimensional gravity, and its important differences with respect to four and higher dimensions, are duly taken into account, by considering different possible candidates for the gravitational radius, $R_g$, that is the minimal length/maximal resolution of the quantum mechanical localization process. We find that the event horizon of the $M \neq 0$ Ba\~{n}ados-Teitelboim-Zanelli micro black hole furnishes the most consistent $R_g$. This allows us to obtain a suitable formula for the Generalized Uncertainty Principle in three dimensions, and also to estimate the corrections induced by the latter on the Hawking temperature and Bekenstein entropy. We also point to the extremal $M=0$ case, and its natural unit of length introduced by the cosmological constant, $\ell = 1 / \sqrt{-\Lambda}$, as a possible alternative to $R_g$, and present a condensed matter analog realization of this scenario., Comment: v2: 26 pages, 4 figures, accepted for publication in Phys.Rev.D

On the one hand, it is correct that we can choose our units of measure arbitrarily. A yard as a unit of length and a pile of sand running through an egg timer as a unit of time are completely sufficient to formulate our physical laws. However, we will not find this too pleasurable, because randomly chosen units or units specifically chosen for a certain problem can lead to tedious parameters. The largest problem is however its constancy and reproducibility.

Results of joint investigations of the State Primary Standard of the unit of length, the meter (GET 2–2010), State Primary Special Standard of the unit of length (GET 199–2018), and State Primary Special Standard of the unit of length in the field of measurements of the geometric parameters of surfaces of complex form (GET 192–2017) are presented. The objective of the study is to confirm the metrological characteristics of the standards. As a result of the investigations, assurance of the uniformity of measurements of the unit of length in the Russian Federation is confirmed.

A network is given whose edges need to be constructed (or restored after a disaster). The lengths of edges represent the required construction/restoration times given available resources, and one unit of length of the network can be constructed per unit of time. All points of the network are accessible for construction at any time. For each pair of vertices, a due date is given. It is required to find a construction schedule that minimizes the maximum lateness of all pairs of vertices, where the lateness of a pair is the difference between the time when the pair becomes connected by an already constructed path and the pair’s due date. We introduce the problem and analyze its structural properties, present a mixed-integer linear programming formulation, develop a number of lower bounds that are integrated in a branch-and-bound algorithm, and discuss results of computational experiments both for instances based on randomly generated networks and for instances based on 2010 Chilean earthquake data. The online appendix is available at https://doi.org/10.1287/ijoc.2017.0796 .

The most important data on the thermal regime of the Earth’s interior come from temperature measurements in deep boreholes. The drilling process greatly alters the temperature field of formations surrounding the wellbore. In permafrost regions, due to thawing of the formation surrounding the wellbore during drilling, representative data can be obtained only by repeated observations over a long period of time (up to 10 years). Usually a number of temperature logs (3–10) are taken after the well's shut-in. Significant expenses are required to monitor the temperature regime of deep wells. In this paper, we introduce a new approach in predicting the undisturbed formations temperatures from shut-in temperature logs in deep wells. The main features of the suggested method are following: the refreezing of the thawed formations (around the wellbore) is completed, the temperature logs are taken after refreezing, the starting point in the well thermal recovery is moved from the end of well completion to the moment of time when the first shut-in temperature log was conducted. It is shown that after refreezing the further cooling of a well can be approximated by a constant (per unit of length) linear heat source. Hence, the Horner equation can be used for predicting the temperature of frozen formations for estimation of the formation temperature. A simple method to process field temperature data is presented. To demonstrate this approach, temperature shut-in time data for four depths from four wells in Alaska were successfully used.

The residual vibration of steel rail is rich in the mechanical properties, which include the constraint, that was, the degree of tightness of the fastener. The aim of this research is to characterize the tightness of rail fastener. A fractal analysis procedure based on 1-D curve length calculation is proposed, which applies a length unit to cover fastening the behavior of fasteners. Using the rail vibration data under periodic pulse excitation measured by a track fastener inspection vehicle, this method can derive the fractal dimension of fastener tightness directly (D∈ [1, 2)). Furthermore, 1-D curve length method is also introduced into multi-fractal spectrum analysis for investigating fine scale information. The statistical analysis demonstrates that, fractal dimension Dl, Dr, and multi-fractal parameters αfmax, ∆α can reflect the change process of the tightness of rail fasteners effectively. Therefore, it shows potential to use the fractal parameters of the rail vibration signal to characterize the tightness of the fastener.

Until now, the question of geometrical construction (or: reconstruction) of the violin form has been the subject of numerous hypotheses. Without doubt, instruments were designed using the tools of that period, namely, a ruler and a compass and applying the ideas of Pythagoras or Vitruv, to achieve a perfectly balanced instrument. In particular, the question of a “standard unit” is of importance. Previous research mostly dealt in geometrical construction and not in a “standard unit”. Based on our recent discoveries of tools and drawings, we suggest that instruments of the Brescian and Cremonese schools might have used a standard length unit that could have been the Roman oncia. This unit was applied to the Stradivari instruments, later to all Cremonese violins. But initially, the relationship between the proportions did not emerge, until a completely, new construction system, using concentrical circles, was applied. Consequently, all necessary markers for the construction and the radii of the outline can now easily be detected. The construction might be also applicable to violas, violoncellos and even the smaller violins, too. Also the violin scrolls were successfully analyzed.

The tolerances for the alignment of the magnets on the girders of the proposed particle accelerator of the Brazilian Synchrotron Light Laboratory (LNLS), Sirius, are as small as 40 μm for translations and 0.3 mrad for rotations. The functional axis of the magnets is measured by the vibrating wire technique, which employs conductive wires of diameters of approx. 0.1 mm. Since the alignment has to be performed targeting these magnetic axes, rather than their geometric centrelines, non-contact measuring sensors mounted on a coordinate measuring machine have been chosen to measure the relative deviations between magnets. To better the measurement accuracy for that specific measuring task, to allow interim checks on multiple coordinate measuring systems, and to provide effective traceability to the SI unit of length, a multipurpose geometrical artefact has been devised. The reasoning behind this development and the first measurement results are described in this paper.

Achieving a uniform welding seam with minimum overheating is crucial to obtain high quality joints in laser welding. The classical formula of the overlapping factor for laser pulsed welding was modified by the introduction of empirical corrections from the application of static pulses involving constant energy combinations of laser power and pulse duration. The energy re-allocation in the case of dynamic pulses was studied as a function of the laser displacement speed. Energy optimization criteria aiming the minimization of the energy per length unit or surface unit were introduced. An optimized uniform welding seam with minimum thermal affectation was obtained by means of dynamic pulses.

The use of the thermal imaging method for active nondestructive evaluation of subsurface defects of articles is examined. The scale factors for converting the values of defect size from pixels to length units are estimated. The effect of size and depth of a defect on the distribution of heat along the surface is analyzed.

Suppose that a destroyed network needs to be restored by a number of servers (construction crews) that are initially located at some nodes of the network (depots). Each server can restore one unit of length of the network per unit of time. When several servers are simultaneously working at the same point, their restoration speeds combine additively. The servers can travel within the already restored part of the network with infinite speed, which means that travel times are negligible with respect to construction times. It is required to minimize the time when each node becomes connected to at least one of the depots. We show that the problem is strongly NP-hard on general networks, and present fast polynomial algorithms for trees and cactus networks which are connected networks where each node and each edge belong to at most one cycle. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(1), 60–68 2017

The certified reference material BAM-L200, a nanoscale stripe pattern for length calibration and specification of lateral resolution, is described. BAM-L200 is prepared from a cross-sectioned epitaxially grown layer stack of AlxGa1-xAs and InxGa1 xAs on a GaAs substrate. The surface of BAM-L200 provides a flat pattern with stripe widths ranging down to 1 nm. Calibration distances, grating periods and stripe widths have been certified by TEM with traceability to the length unit. The combination of gratings, isolated narrow stripes and sharp edges of wide stripes offers a plenty of options for the determination of lateral resolution, sharpness and calibration of length scale at selected settings of imaging surface analytical instruments. The feasibility of the reference material for an analysis of the lateral resolution is demonstrated in detail by evaluation of ToF-SIMS, AES and EDX images. Other applications developed in the community are summarized, too. BAM-L200 fully supports the implementation of the revised International Standard ISO 18516 (in preparation) which is based on knowledge outlined in the Technical Report ISO/TR 19319:2013.

Firstly, the direction finding solution at the midpoint of a single base array is given for the purpose of this paper and the several functions relation between phase and frequency is also described. Then, the expression of phase difference rate is described based on the multichannel phase difference measurement. With stripping time difference item correspond to the baseline length from phase difference rate, a function is extracted which signifies the differential characteristics of wavelength integer and phase difference in a unit of length. Simulation calculation found that the variation of differential function of path difference in a unit of length is very regular. The corresponding corrected value can is determine directly by distinguishing the range of differential item of phase difference obtained by actual measurement. Thus, the function expression can be obtained that is equivalence with the quondam differential function of path difference and that is nothing to do with the difference item of wavelength integer. On this basic, several parameters are analyzed by using the method of phase difference measurement without phase ambiguity. The research results in this paper may provide a powerful technical support for engineering practical design related to the phase measuring.

Background: The redefinition of a unit of length - a meter - through a unit of time and a fundamental constant - the speed of light in vacuum - has opened up the fundamental possibility of a significant reduction in the uncertainty of its reproduction. Now progress in areas such as absolute ballistic gravimetry, control of large-sized aspherical optics, laser interferometry, and the production of electronic components in the semiconductor industry have made this feature extremely relevant. It is known that the measuring scale of laser interferometers used for precision distance measurement is non-linear, since the common-mode surfaces of any real radiation beam are located irregularly in space. To compensate for the effect of this irregularity on the measurement result, it is necessary to know the precision phase structure of real laser beams. Objectives of the work is comparing existing methods for studying the phase structure of optical radiation beams and estimating the distribution of the topological phase shift of a relatively uniform plane wave. Materials and methods:. The well-known theoretical methods for calculating the topological phase shift of in-phase surfaces of an optical beam are considered and compared - the Lommel-Debye method based on the Fresnel-Kirchhoff integral, the modified method based on the Rayleigh-Sommerfeld integral and the Gaussian beam method based on a parabolic equation. Results: Each method performed calculations of the accumulated phase lag of the focused radiation beam when moving the observation plane relative to the focal point. The distribution of the relative change in the distance between the in-phase surfaces in the range of displacements from λ to 106•λ was also calculated. The most adequate physical picture of the phenomenon was obtained by the Gaussian beam method based on a parabolic equation. Conclusion: The results will be used to reduce the systematic error of laser interferometers.

The actual status of metrology infrastructure of B&H on the state level and possibilities for improvement in future was discussed in this paper. The Institute of Metrology of Bosnia and Herzegovina (IMBiH) is a Government authority on the state level performing the functions of conformity assessment. Institute also has a role in harmonization of B&H legislation with the EC Directives. Since 2009. IMBiH has been full member of the European Association of National Metrology Institutes (EURAMET). Basic adopted laws in force on metrology in B&H are Law of metrology as well as Law on Measurement Units. The metrology system in B&H is highly decentralized, with a lack of correspondence between different levels of authorities. Accredited laboratories and other laboratories occupied with length measurement make their own traceability chain using laboratories in region and without inclusion of IMBiH. Laboratory for length in IMBiH is responsible for the realization and maintenance of the National Standard for Length and transferring unit of the length to lower rank standards and calibration of measuring instruments. Unit of length, in the Laboratory for length is realized through Iodine stabilized He-Ne laser of wavelength 633 nm. The laser is realized according to the definition of meter, i.e. according to the requirements of the International Recommendation for Practical Realization of the meter (CIMP 1997/2001 ‘Mise en pratique’). This laser can be used for calibration of other lasers with wavelength of 633 nm including laser interferometers for length measurements.

The following pages explore the traces of a way of thinking of areas and lengths that seems strange to us but which in a number of mathematical cultures was so familiar that there was no need to explain it: so strange and so familiar, indeed, that modern historians have declared passages in the sources that reflect this conceptual structure to be erroneous, confused or meaningless. I refer to the habit to imagine lines as carriers of a virtual breadth equal to one length unit, and areas as composed of such unit strips. This habit was widely spread in many environments of practical mensuration. In these it was easy to agree on using the basic unit of length as standardized breadth: land was, so to speak, measured as cloth is still sold nowadays, with its physically determined breadth. But it is also reflected in texts which are more theoretical in origin though still inspired or coloured by practical mensuration and its language.

In antiquity, the radius of the Earth was a basic unit of length for attempts to infer distances to the Moon and the Sun. Measurement of the distance to the Sun was attempted by Aristarchus, Hipparchus, and Ptolemy, but they failed, since the Sun is so far away. Copernicus’ heliocentric system gave the Earth–Sun distance special importance; it could be used as a measuring ruler within the Solar System. Kepler’s third law emphasized the same thing: the times of revolution around the Sun, obtained from observations, determine the relative sizes of the planetary orbits in Earth–Sun distance units. When astronomers started determining distances (parallaxes) of stars, the Earth–Sun distance finally replaced our planet’s radius as the natural unit. However, the actual measurement of this basic distance uniti, the distance to the Sun, turned out to be quite a demanding endeavour.

Two iterative, after school design experiments with small groups of middle school students were conducted to investigate how students constructed quantitative unknowns, conceived of as values of fixed quantities that are not known but can be determined. Students solved problems about an unknown height or length measured in two different units. Of 13 students who participated, 6 structured quantities into three levels of units. These students constructed an unknown as a height consisting of an indeterminate number of length units, each of which consisted of smaller length units, and they symbolized these relationships in their equations. The other 7 students structured quantities into two levels of units. Five of these students symbolized only the relationships between the measurement units, with two students demonstrating more basic and advanced solutions. The study shows that grappling with unknowns as measured and indeterminate is beneficial for students’ construction of variable.

The article presents the results of an experimental study of coaxial and orthogonal methods for comparing laser measuring interferometric systems using a standard measuring complex of length from the State Primary Special Standard of a Unit of Length in the range from 2 to 60 m. transmission errors of the unit of length up to 0.5 microns.

The ship domain is a concept commonly proposed as a safety assessment criterion in planning collision avoidance manoeuvres of a ship or its safe route. The work presents authors’ methods for determining an effective ship domain based on tests using Electronic Chart Display and Information System (ECDIS) simulator. The tests were conducted on non-autonomous real time models of ships steered by expert navigators. Domains were determined for ships of different sizes and speeds. The ship domain was approximated to an ellipse. The study covered absolute and relative domains, the latter defined in ship length units. The dependence of the domain shape and size on ship size and speed has been analysed and described. The formulated analytical relationships enable us to determine the domain of a ship varying in size and speed.

This paper proposes a novel non-circular parametric curve interpolation algorithm based on the unit arc length increment method (UALI). In this method, axial coordinates are taken as functions of arc length. The reference point moves by 1 basic length unit (BLU) along a curve in each interpolation period, and the corresponding projections on each coordinate are added into accumulators of each axis respectively. An axis will then move by 1 BLU when its accumulator exceeds 1 BLU. Theoretically, based on the UALI method, an interpolation algorithm is derived for parametric curves such as involutes, Archimedes spirals, cycloids, and parabolas. This interpolation algorithm is applicable for ruled surfaces of a workpiece with different parametric curves in the upper and lower planes. Tool compensation is considered for both non-tapered workpieces as well as tapered workpieces. Simulation results and experiment results demonstrate the advantages of this interpolation algorithm, and the accuracy of this interpolation algorithm is analyzed.