Remote interactive density measurement method for college physics experiment
By building a hardware measurement unit and a remote interaction system, the problems of operational complexity and low data processing efficiency in university physics density measurement experiments were solved. Cross-platform remote control and automation of experimental reports were realized, thereby improving teaching quality and efficiency.
Patent Information
- Application Number
- CN202610051381.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-01-15
- Publication Date
- 2026-03-03
Smart Images
Figure CN121600759A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of physical experiment measurement technology, specifically a remote interactive density measurement method for university physics experiments. Background Technology
[0002] Density measurement is one of the core fundamental experiments in university physics lab courses. Its purpose is to help students understand the physical nature of matter density, master the measurement methods and data processing logic for physical quantities such as mass and volume, and cultivate their experimental operation and scientific inquiry abilities. Currently, universities mainly rely on traditional offline operation modes and some digital improvements for density measurement experiments, but many technical problems still need to be solved in practical applications.
[0003] Traditional density measurement experiments require students to perform the operation in a physical laboratory, relying primarily on manual instruments such as physical balances. Students must manually weigh the object to be measured using the hydrostatic weighing method; based on Archimedes' principle of buoyancy, the volume of the object can be calculated by immersing it in water and observing its apparent mass; and then manually record the data, substitute it into formulas to calculate the density value and uncertainty. This model has significant limitations: firstly, the experimental methods are outdated, the operation process is cumbersome, and the requirements for operational standardization are extremely high. Human errors can easily occur in aspects such as the selection of measurement locations, the accuracy of instrument readings, and the avoidance of environmental interference, affecting the accuracy of experimental data; secondly, the experiment is completely limited by space and time. Students must rely entirely on laboratory equipment to complete the operation within a designated laboratory time period, which cannot meet the diverse teaching needs of laboratory equipment integration with the Internet of Things, digital acquisition of real-world experimental data, intelligent experimental data analysis and processing, and automated experimental report output.
[0004] To overcome the time and space limitations of offline experiments, some solutions employ virtual simulation technology to construct simulated experimental environments, allowing students to perform virtual operations via computer terminals. While this approach solves the time and space constraints, it is essentially a simulation based on pre-programmed deductions, lacking interaction with real experimental hardware. Students cannot access actual experimental equipment or experience real physical phenomena, making it difficult to cultivate real instrument operation skills and problem-solving abilities. Furthermore, the development and maintenance costs of virtual simulation systems are high, and the consistency between the simulation scenario and the real experiment is difficult to guarantee, easily leading to a disconnect between theory and practice and failing to achieve the teaching effects of real experiments.
[0005] Some digital improvement solutions involve installing electronic measuring equipment in the laboratory to achieve automatic data acquisition and preliminary processing. However, these solutions are mostly local operation modes, requiring wired connections between experimental equipment and digital display panels or computers, and lack an effective remote interaction mechanism. Students still need to rely on existing laboratory equipment for debugging, parameter setting, operation execution, and data acquisition, and cannot use their own mobile phones, tablets, or laptops to wirelessly connect to the experimental equipment for control and real-time monitoring. Furthermore, existing solutions are mostly only for measuring single types of substances (such as conventional solids or liquids), lacking adaptability to substances with different density characteristics (such as solids less dense than water), resulting in limited functionality. In addition, the recording, calculation, and reporting of experimental data still require manual intervention, leading to low data processing efficiency. Moreover, the archiving, sharing, and teaching evaluation of experimental results lack systematic support, making it difficult to meet the needs of large-scale experimental teaching and management in universities.
[0006] In summary, existing technologies for density measurement experiments in university physics have significant shortcomings in terms of ease of operation, spatial and temporal flexibility, pedagogical adaptability, and data processing efficiency, failing to fully meet the demands of diverse teaching scenarios and high-quality experimental teaching in universities today. Therefore, developing a technology that combines real-world hardware interaction with IoT-enabled experimental equipment, allowing students to wirelessly connect to the equipment using their mobile phones (any platform), tablets, or laptops after entering the laboratory, is crucial for addressing the pain points of existing technologies. This approach cultivates hands-on experimental skills while meeting the needs of university physics inquiry-based experimental teaching for process visualization, real-time data processing, and automated reporting. Summary of the Invention
[0007] To address the shortcomings of existing technologies, this invention provides a remote interactive density measurement method for university physics experiments, solving the problems mentioned in the background section.
[0008] To achieve the above objectives, the present invention provides the following technical solution: a remote interactive density measurement method for university physics experiments, comprising the following steps: constructing a hardware measurement unit including an ESP32-S3 main control module, an HX711 high-precision force sensor module, an LCD1602 local display module, and a mechanical structure. The ESP32-S3 main control module has a built-in web server and generates a graphical web interface. Under the same Wi-Fi network, students' mobile phones, tablets, or laptops can access the interface through a browser to achieve remote control and connect to the density measurement device.
[0009] Preferably, the method provides calibration functions through a web interface, guiding users to complete the tare and standard weight calibration operations of the sensor. The calibration operation data is transmitted in real time to the ESP32-S3 main control module for storage and processing.
[0010] Preferably, the method provides step-by-step guidance and corresponding data acquisition buttons on the web interface for different modes such as solid mass measurement in air, solid apparent mass measurement in water, and liquid density measurement. Users can follow the steps and click the buttons to lock and record the real-time data to the system data queue.
[0011] Preferably, the method incorporates a density calculation algorithm and uncertainty assessment model based on the GUM method. After data acquisition is completed, the user triggers a calculation command, and the system calls the corresponding formula to calculate the density and relative uncertainty of the analyte and displays the results.
[0012] Preferably, the method includes an automatic report generation step. After the user triggers the report generation command, the system integrates the experimental step records, raw collected data, calculation results, uncertainty analysis, and timestamp information to generate a structured experimental report on the web page. The experimental report can be saved or shared on students' mobile phones, tablets, or laptops.
[0013] Preferably, during the construction of the hardware measurement unit of the method, the DT pin and SCK pin of the HX711 module are respectively connected to two GPIO pins of the ESP32-S3 main control module, the LCD1602 is connected to the ESP32-S3 main control module through the I2C interface, the hardware measurement unit is connected to a 3.3V stable power supply and fixed on the experimental platform, and the object to be measured is suspended below the force sensor.
[0014] Preferably, in the method, after the ESP32-S3 main control module is powered on, it automatically connects to the preset Wi-Fi router. After the connection is successful, the built-in web server is started, and the device IP address is displayed on the LCD1602. The terminal device accesses the web interface by entering the IP address.
[0015] Preferably, when measuring solids with a density greater than water, the method includes the following specific steps: after completing sensor calibration, suspend the solid below the force sensor, and after stabilization, trigger the air weight acquisition command and record the value. F 1 and convert it to mass m 1. Completely immerse the solid in a water-filled beaker without touching the container. Once stable, trigger the apparent weight acquisition command in the water and record the value. F 2 and convert to mass m 2; System call formula r =( m 1 / ( m 1- m 2))× r 水 Calculate the density of the solid and simultaneously synthesize and display the relative uncertainty. U ρ .
[0016] Preferably, when measuring solids less dense than water, the method adds a sediment-related measurement step to the conventional collection steps, and the web interface guides the user to complete the measurement of the solid mass in air. m 3. The sedimentation aid is immersed in water while the solid being tested is suspended in air by its apparent mass. m 4. The solid to be tested and the sedimentation aid combination are completely submerged in water, and the mass is considered as follows: m 5. After data acquisition, the system switches to the corresponding calculation formula to complete the calculation of density and relative uncertainty.
[0017] Preferably, when measuring an unknown liquid, the method guides the user to complete the data acquisition of the mass of a standard solid in air, the apparent mass of a standard solid in water, and the apparent mass of a standard solid in the liquid to be tested, and the system calls the formula. r 液体 =(( m 6- m 8) / ( m 6- m 7))× r 水 Calculate the density of the liquid, where m 6 represents the mass of a standard solid in air. m 7 represents the apparent mass of a standard solid in water. m 8 represents the apparent mass of the standard solid in the liquid to be tested, and the relative uncertainty is evaluated and displayed.
[0018] This invention provides a remote interactive density measurement method for university physics experiments. It has the following advantages: 1. By integrating hardware measurement units, remote interaction units, and software intelligent processing units, and with the help of step-by-step guidance and automated data processing functions provided by the web interface, this remote interactive density measurement method greatly simplifies the operation process of traditional density measurement experiments, reduces human error, and allows experimenters to focus more on understanding physical principles and observing the experimental process, effectively improving the teaching quality and learning experience of university physics experiments.
[0019] 2. By building a cross-platform access channel through the built-in Web server of the main control module, this method does not require the installation of a dedicated application. It enables various terminal devices to remotely control experimental equipment, view measurement data in real time, and trigger key operation commands in the same Wi-Fi network environment. This breaks the limitations of physical experiments on site and time, enhances the flexibility and convenience of experimental teaching, and provides reliable support for diverse teaching scenarios such as remote teaching and self-directed inquiry experiments.
[0020] 3. By realizing the informatization and automation of the entire process of experimental calibration, data acquisition, density calculation, uncertainty assessment and experimental report generation, this method eliminates the tedious steps of manually recording data, manually calculating and compiling reports in traditional experiments, thereby improving experimental efficiency and the accuracy of data processing. At the same time, with the help of the automatic generation, saving and sharing functions of structured experimental reports, it is convenient to archive and manage experimental data and exchange and display teaching results. Moreover, the overall modular design makes the cost controllable and easy to promote on a large scale in university laboratories. Attached Figure Description
[0021] Figure 1 This is the overall flowchart of the present invention. Detailed Implementation
[0022] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0023] Please see the appendix Figure 1 This invention provides a remote interactive density measurement method for university physics experiments, comprising the following steps: constructing a hardware measurement unit including an ESP32-S3 main control module, an HX711 high-precision force sensor module, an LCD1602 local display module, and a mechanical structure. The ESP32-S3 main control module has a built-in web server and generates a graphical web interface. Terminal devices on the same Wi-Fi network access the interface through a browser to achieve remote control. The method provides calibration functions through the web interface, guiding users to complete the tare and standard weight calibration operations of the sensor. The calibration operation data is transmitted in real time to the ESP32-S3 main control module for storage and processing.
[0024] Specifically, by constructing a hardware measurement unit with the ESP32-S3 main control module as its core, integrating the physical quantity sensing capabilities of the HX711 high-precision force sensor module and the real-time feedback function of the LCD1602 local display module, and leveraging the web server built into the ESP32-S3 main control module to build a network communication bridge, a visual graphical web interface is generated as a remote interaction carrier. This allows terminal devices within the same Wi-Fi network coverage area to directly establish a connection with the hardware measurement unit via a browser, enabling remote control without additional dedicated software. Simultaneously, utilizing the guided calibration logic designed in the web interface, operations such as sensor tare and standard weight calibration are transformed into intuitive interactive commands. After the user triggers the relevant operation, the corresponding calibration data is transmitted to the ESP32-S3 main control module in real time via the network. The module then receives, stores, and processes the data, ensuring the accuracy of the sensor measurement benchmark and laying the foundation for the precision of subsequent density measurements. This achieves efficient collaboration between hardware devices and remote terminals, real-time data interaction, and convenient operation.
[0025] The method provides step-by-step guidance and corresponding data acquisition buttons on the web interface for different modes such as solid mass measurement in air, apparent mass measurement of solid in water, and liquid density measurement. Users can follow the steps and click the buttons to lock and record the real-time data to the system data queue.
[0026] Specifically, based on the physical logic differences in density measurement of different substances, specific operation procedures are designed for measuring the mass of solids in air, the apparent mass of solids in water, and the density of liquids. By constructing a step-by-step guidance mechanism with corresponding data acquisition interaction buttons in the web interface, complex experimental operations are broken down into standardized and visualized step instructions. After completing operations such as physical placement and environmental preparation according to the interface guidance, users can click the corresponding acquisition button to trigger the system's real-time data locking function. With the real-time sensing capability of the sensors in the hardware measurement unit, the current physical quantity data is acquired and recorded in an orderly manner in the system's preset data queue. This achieves accurate, streamlined, and orderly data acquisition in different measurement scenarios, providing standardized and complete raw data support for subsequent density calculations, while reducing the complexity of user operations and ensuring the standardization of experimental operations and data accuracy.
[0027] The method incorporates a density calculation algorithm and uncertainty assessment model based on the GUM method. After data acquisition, the user triggers a calculation command, and the system calls the corresponding formula to calculate the density and relative uncertainty of the analyte and displays the results. The method includes an automatic report generation step. After the user triggers a report generation command, the system integrates experimental procedure records, raw data acquisition, calculation results, uncertainty analysis, and timestamp information to generate a structured experimental report on a web page. The experimental report can be saved or shared.
[0028] Specifically, a density calculation algorithm and uncertainty assessment model based on the GUM method are pre-embedded in the system. When the user completes data acquisition and triggers the calculation command, the system can match the corresponding calculation logic according to the selected measurement mode, call the preset algorithm to automatically calculate the raw data stored in the data queue, accurately derive the density and relative uncertainty of the analyte, and present the results in real time. At the same time, through the preset structured report generation logic, after the user triggers the report generation command, the system automatically extracts key information such as step records, raw data acquisition, calculation results, uncertainty analysis results, and timestamps from the entire experimental process, integrates them into a structured experimental report on the web page in a standardized format, and supports users to directly save or share the report through the web page. This realizes full automation and standardization from data processing to experimental result output, ensuring the scientific accuracy of data processing and improving the convenience of experimental result organization and circulation.
[0029] During the construction of the hardware measurement unit, the DT and SCK pins of the HX711 module are connected to the two GPIO pins of the ESP32-S3 main control module, respectively. The LCD1602 is connected to the ESP32-S3 main control module through the I2C interface. The hardware measurement unit is connected to a 3.3V stable power supply and fixed on the experimental platform. The object to be measured is suspended below the force sensor.
[0030] Specifically, standardized pin and interface connections enable collaborative operation of various functional modules. The DT and SCK pins of the HX711 module are connected to the two GPIO pins of the ESP32-S3 main control module, respectively, establishing a transmission channel for force sensor measurement data. This allows the physical quantity signals sensed by the sensor to be accurately transmitted to the main control module. An I2C interface is used to establish communication between the LCD1602 and the ESP32-S3 main control module, ensuring that key information processed by the main control module can be displayed locally in real time. A stable 3.3V power supply is provided to the hardware measurement unit to ensure stable operation of each module and avoid the impact of voltage fluctuations on measurement accuracy. Fixing the entire hardware to the experimental platform reduces external vibration interference. Suspending the object under test below the force sensor allows the gravity or buoyancy of the object to directly act on the sensor, providing a stable and accurate physical quantity input foundation for subsequent data acquisition. This achieves hardware-level functional integration and measurement condition optimization.
[0031] In this method, the ESP32-S3 main control module automatically connects to the preset Wi-Fi router after power-on. After successful connection, the built-in web server is started, and the device IP address is displayed on the LCD1602. The terminal device can access the web interface by entering the IP address.
[0032] Specifically, utilizing the network communication and server building capabilities of the ESP32-S3 main control module, it automatically triggers a preset Wi-Fi connection program upon power-up, establishing a network connection with the designated router to open a data transmission channel. Upon successful connection, the built-in web server is immediately started, and a graphical web interface is loaded and published. Simultaneously, the main control module transmits the acquired device IP address to the LCD1602 local display module via the I2C communication protocol for visual presentation, providing users with an access identifier. Terminal devices within the same Wi-Fi network environment can establish a communication link with the web server via a browser by entering this IP address, enabling remote access and interaction with the experimental equipment and laying the network foundation for subsequent remote operation and data transmission.
[0033] When measuring solids denser than water, the method includes the following specific steps: After completing sensor calibration, suspend the solid below the force sensor. Once stable, trigger the air weight acquisition command and record the value. F 1 and convert it to mass m 1. Completely immerse the solid in a water-filled beaker without touching the container. Once stable, trigger the apparent weight acquisition command in the water and record the value. F 2 and convert to mass m 2; System call formula r =( m 1 / ( m 1- m 2))× r 水 Calculate the density of the solid and simultaneously synthesize and display the relative uncertainty. U ρ .
[0034] Specifically, based on Archimedes' principle of buoyancy, the system first eliminates system errors through sensor calibration to ensure accurate measurement. The solid is suspended below the force sensor to collect airborne values, which are then converted into mass to obtain the mass data corresponding to the solid's true weight. The solid is then completely immersed in water without contacting the container. The buoyancy of the water on the solid causes a change in the sensor's detected value, which is collected and converted into apparent mass. The difference between the actual mass and the apparent mass is used to deduce the volume of water displaced by the solid (i.e., the solid volume). Using pre-defined calculation logic and the density of water, the system calculates the solid density by the ratio of the actual mass to the displaced water volume. Simultaneously, it integrates error factors from each stage of the measurement process, synthesizes relative uncertainty through an uncertainty assessment model, and displays it synchronously, achieving accurate measurement of the density of this type of solid and characterizing the reliability of the results.
[0035] When measuring solids less dense than water, the method adds sediment-related measurement steps to the conventional collection process, and the web interface guides the user to complete the measurement of the solid mass in air.m 3. The sedimentation aid is immersed in water while the solid being tested is suspended in air by its apparent mass. m 4. The solid to be tested and the sedimentation aid combination are completely submerged in water, and the mass is considered as follows: m 5. After data acquisition, the system switches to the corresponding calculation formula to complete the calculation of density and relative uncertainty.
[0036] Specifically, based on Archimedes' principle of buoyancy, and considering the characteristic that such solids cannot be completely submerged in water on their own, a sinking aid is introduced to assist in volume measurement on top of conventional measurement logic. Guided by a web interface, the system sequentially collects the actual mass of the solid in air, the apparent mass of the solid above the water surface when the sinking aid is submerged alone, and the apparent mass of the solid and sinking aid combined and completely submerged. The difference between the apparent mass of the solid and sinking aid combined and completely submerged, and the apparent mass of the solid above the water surface when the sinking aid is submerged alone, is used to deduce the volume of water displaced by the solid (i.e., the solid's own volume). Combined with the solid's actual mass, the system automatically switches to the appropriate calculation logic for the measurement scenario, accurately calculating the solid's density. Simultaneously, it integrates the error components from each data acquisition stage and uses a pre-set uncertainty assessment model to synthesize and display the relative uncertainty, achieving accurate measurement of the solid's density and verifying the reliability of the results.
[0037] When measuring an unknown liquid, the method guides the user to collect data on the mass of a standard solid in air, the apparent mass of a standard solid in water, and the apparent mass of a standard solid in the liquid to be tested. The system then calls the formula. r 液体 =(( m 6- m 8) / ( m 6- m 7))× r 水 Calculate the density of the liquid, where m 6 represents the mass of a standard solid in air. m 7 represents the apparent mass of a standard solid in water. m 8 represents the apparent mass of the standard solid in the liquid to be tested, and the relative uncertainty is evaluated and displayed.
[0038] Specifically, based on Archimedes' law of buoyancy and density comparison logic, using a standard solid with known density characteristics as the measurement medium, the system guides users through a web interface to sequentially collect the actual mass data of the standard solid in air, its apparent mass data in water, and its apparent mass data in the liquid to be tested. The volume of water displaced by the standard solid (i.e., the volume of the standard solid) is derived using the difference between its mass in air and its apparent mass in water. Similarly, the volume of liquid displaced by the standard solid (equal to the solid volume) is derived using the difference between its mass in air and its apparent weight in the liquid to be tested. The system then calls upon calculation logic adapted to this measurement scenario, combining it with the density of water, and accurately calculates the density of the liquid to be tested by the correlation between the mass difference and volume of the two displaced liquids. Simultaneously, it integrates error factors from the three data acquisition stages, and uses a pre-set uncertainty assessment model to synthesize and display the relative uncertainty, thus achieving accurate measurement of the density of unknown liquids and characterizing the reliability of the results.
[0039] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.
Claims
1. A remote interactive density measurement method for university physics experiments, characterized in that, Includes the following steps: A hardware measurement unit is constructed, comprising an ESP32-S3 main control module, an HX711 high-precision force sensor module, an LCD1602 local display module, and a mechanical structure. The ESP32-S3 main control module has a built-in web server that generates a graphical web interface. Terminal devices on the same Wi-Fi network can access the interface through a browser to remotely control the density measurement device. Students can connect to the experimental equipment from any platform, such as a mobile phone, tablet, or computer, to achieve intelligent data acquisition, processing, and report generation.
2. The remote interactive density measurement method for university physics experiments according to claim 1, characterized in that, The method provides calibration functions through a web interface, guiding users to complete the tare and standard weight calibration operations of the sensor. The calibration operation data is transmitted in real time to the ESP32-S3 main control module for storage and processing.
3. The remote interactive density measurement method for university physics experiments according to claim 1, characterized in that, The method provides step-by-step guidance and corresponding data acquisition buttons on a web interface for different modes such as solid mass measurement in air, apparent mass measurement of solid in water, and liquid density measurement. Users can follow the steps and click the buttons to lock and record real-time data to the system data queue.
4. The remote interactive density measurement method for university physics experiments according to claim 1, characterized in that, The method incorporates a density calculation algorithm and uncertainty assessment model based on the GUM (Guide to the Expression of Uncertainty in Measurement) method. After data acquisition is completed, the user triggers a calculation command, and the system calls the corresponding formula to calculate the density and relative uncertainty of the analyte and displays the results.
5. The remote interactive density measurement method for university physics experiments according to claim 1, characterized in that, The method includes an automatic report generation step. After the user triggers the report generation command, the system integrates the experimental step records, raw collected data, calculation results, uncertainty analysis, and timestamp information to generate a structured experimental report on the web page. The experimental report supports saving or sharing.
6. The remote interactive density measurement method for university physics experiments according to claim 1, characterized in that, During the construction of the hardware measurement unit of the method, the DT pin and SCK pin of the HX711 module are connected to the two GPIO pins of the ESP32-S3 main control module, respectively. The LCD1602 is connected to the ESP32-S3 main control module through the I2C interface. The hardware measurement unit is connected to a 3.3V stable power supply and fixed on the experimental platform. The object to be measured is suspended below the force sensor.
7. The remote interactive density measurement method for university physics experiments according to claim 1, characterized in that, In the method described, the ESP32-S3 main control module automatically connects to the preset Wi-Fi router after power-on. After successful connection, the built-in web server is started, and the device IP address is displayed on the LCD1602. The terminal device accesses the web interface by entering the IP address, thereby realizing the data connection between the terminal device and the experimental equipment.
8. The remote interactive density measurement method for university physics experiments according to claim 3, characterized in that, When measuring solids denser than water, the method includes the following specific steps: After completing sensor calibration, suspend the solid below the force sensor; once stable, trigger the air weight acquisition command and record the value. F 1 and convert it to mass m 1. Completely immerse the solid in a water-filled beaker without touching the container. Once stable, trigger the apparent weight acquisition command in the water and record the value. F 2 and convert to mass m 2; System call formula ρ =( m 1 / ( m 1- m 2))× ρ 水 Calculate the density of the solid and simultaneously synthesize and display the relative uncertainty. U ρ .
9. The remote interactive density measurement method for university physics experiments according to claim 3, characterized in that, When measuring solids less dense than water, the method adds a sediment-related measurement step to the conventional collection steps, and the web interface guides the user to complete the measurement of the solid mass in air. m 3. The sedimentation aid is immersed in water while the solid being tested is suspended in air by its apparent mass. m 4. The solid to be tested and the sedimentation aid combination are completely submerged in water, and the mass is considered as follows: m 5. After data acquisition, the system switches to the corresponding calculation formula to complete the calculation of density and relative uncertainty.
10. The remote interactive density measurement method for university physics experiments according to claim 3, characterized in that, When measuring an unknown liquid, the method guides the user to collect data on the mass of a standard solid in air, the apparent mass of a standard solid in water, and the apparent mass of a standard solid in the liquid to be tested. The system then calls the formula. ρ 液体 =(( m 6- m 8) / ( m 6- m 7))× ρ 水 Calculate the density of the liquid, where m 6 represents the mass of a standard solid in air. m 7 represents the apparent mass of a standard solid in water. m 8 represents the apparent mass of the standard solid in the liquid to be tested, and the relative uncertainty is evaluated and displayed.