Current division is the principle that determines how electric current splits between parallel branches according to their resistance. This guide explains how to calculate the exact current in each branch using Ohm's law and Kirchhoff's current law, with practical examples and limitations.

Current Divider Rule: Formula, Derivation, and Worked Example

Active high-pass filters remove unwanted low-frequency signals while preserving useful higher frequencies. This article covers first- and second-order filter design, Sallen-Key and multiple-feedback topologies, and practical applications in audio electronics, instrumentation, and signal processing.

Active High Pass Filter: Theory, Design, and Applications

Active low-pass filters use op-amps, resistors, and capacitors to pass low-frequency signals while attenuating higher frequencies. This article covers first-order and second-order filter design, Sallen-Key and MFB topologies, cutoff frequency, Q factor, and applications.

Active Low Pass Filter Design and Implementation

A bandpass filter is a circuit that allows a selected range of frequencies to pass while reducing low and high frequencies. This article covers the design of active bandpass filters using op-amps, resistors, and capacitors, including cutoff and center frequencies,, Sallen-Key and MFB topologies.

Active Bandpass Filter Design Guide

A comprehensive technical comparison of low-pass and high-pass filters, covering how each works, practical circuit implementations, and when to use them in electronics and signal processing.

Low Pass Filter vs High Pass Filter – Theory, Design, and Applications

Learn how source transformation simplifies complex circuit analysis by converting between Thévenin voltage sources and Norton current sources – complete with definitions, derivations, step-by-step examples (including dependent and AC sources), common pitfalls, and advanced applications.

Source Transformation in Electrical Circuit Analysis: Thevenin–Norton Equivalence & Circuit Simplification

Kirchhoff's Current Law applies to simple and complex nodes for smooth analysis

aster KCL circuit analysis with our comprehensive engineering guide covering nodal analysis, modern simulation tools, and industry applications. Learn advanced techniques used by leading engineers. Start optimizing your circuit designs today.

KCL Circuit Analysis: Advanced Engineering Methods & Best Practices 2025

As digital workflows, simulation, and automation reshape how products and systems are designed and built, architecture continues to serve as both a testing ground and a source of innovation. At <a href="https://cdfam.com/amsterdam-2025/" target="_blank" rel="noopener noreferrer">CDFAM Amsterdam 2025</a>, the architectural scale takes center stage—highlighting how computational methods developed for buildings are now informing work across manufacturing, infrastructure, and robotics.This year’s program features architects and engineers applying advanced design logic, performance simulation, and fabrication-aware modeling to large-scale structures. But it also shows how these same methods are being translated to smaller scales—from 3D-printed metal components to adaptive building skins and modular city infrastructure.<h3>Architectural Engineering in Practice</h3>A keynote from Mathew Vola, Director and Arup Fellow, anchors this year’s architectural track. With more than two decades of experience leading large-scale, computationally intensive building projects across Europe, Asia, and Australia, Vola has played a key role in embedding digital workflows into Arup’s global design practice.<img src="https://s3-us-west-1.amazonaws.com/wevolver-project-images/froala%2F1747312664466-Keynote+Presentation++Mathew+Vola++Arup+Fellow+%26+Director.jpg" style="width:100%px" class="fr-fic fr-dib" />Through the development of inForm, Arup’s internal computational design platform, Vola has helped standardize and scale digital tools for geometry, simulation, and performance analysis. His efforts have supported a network of hundreds of engineers applying these tools to complex problems—ranging from façade optimization to sustainability metrics.One example is the Santiago Bernabéu Stadium renovation, presented at CDFAM Berlin 2024 by Arup’s Rick Titulaer. In that case, parametric simulation and sun-path analysis were used to rationalize thousands of façade panels and reduce glare impacts—demonstrating how architectural computation can address performance and buildability at massive scale.<iframe width="640" height="360" src="https://www.youtube.com/embed/ywqg6xSjQ8M?&amp;wmode=opaque&amp;enablejsapi=1&amp;origin=https://www.wevolver.com" frameborder="0" class="fr-draggable"> </iframe><h3>Selected Architectural Presentations at CDFAM Amsterdam 2025</h3><ul><li>Tiffany Cheng (Cornell University) – Bioinspired and Biobased 4D-Printing for Adaptive Building Facades Using cellulosic materials and hygromorphic structures, Cheng shows how plant-like motion can be harnessed for climate-responsive architecture.</li><li>Dr. Vittoria Laghi (University of Bologna) – Green Steel Construction with Topology Optimization and Metal AM Combining structural engineering with 3D metal printing, Laghi demonstrates how digital fabrication and performance simulation can minimize material use in steel assemblies.</li><li>Verena Vogler (McNeel Europe) – New Developments in Rhino and Grasshopper for Ecological Performance A preview of tools expanding environmental analysis within core parametric modeling workflows—including a new plugin developed through the EU-funded ECOLOPES project.</li><li>Dr. Luca Breseghello (DTU) – 3D Concrete Printing for Low-Impact Structures Exploring stress-based material placement for slabs and beams using computational concrete printing, validated with life-cycle assessment and physical testing.</li><li>Urban Futures Lab (Barashkov &amp; Drusinsky) – Strategic Foresight through Computational Urban Analysis Applying trend data and cultural indicators to adaptive urban planning frameworks—combining hard simulation with human-context design.</li></ul><h3><img src="https://s3-us-west-1.amazonaws.com/wevolver-project-images/froala%2F1747312845346-Tiffany+Cheng+Facade+CDFAM+Large.jpeg" style="width:100%px" class="fr-fic fr-dib" /></h3><h3>Architecture as a Scalable Design Framework</h3>Past CDFAM events have shown how architectural logic can scale up and down—applied to façade systems, structural elements, and increasingly to non-building products. From Ronald Rael’s robotic mud printing for housing to Keyan Rahimzadeh’s metadata-driven glass façade systems, architectural computation has repeatedly demonstrated value far beyond form-making.Presenters like Madeleine Eggers (KPF) have shown how geometric workflows once used only in large buildings can be standardized and applied to global megaprojects. Meanwhile, engineers like Sean Turner and Dauphin Flores (Henderson Engineers) are applying similar logic to mechanical systems—transforming legacy workflows into modular, reusable systems that enable automation and traceability across infrastructure projects.<iframe width="640" height="360" src="https://www.youtube.com/embed/V8fcGLjFpuU?&amp;wmode=opaque&amp;enablejsapi=1&amp;origin=https://www.wevolver.com" frameborder="0" class="fr-draggable"></iframe> <h3>Cross-Pollination Across Industries</h3>Importantly, many of the architectural tools and mindsets showcased at CDFAM are now being applied outside the built environment. Architects trained in spatial reasoning, simulation, and fabrication-aware design are now contributing to product design, footwear development, medical technology, and advanced manufacturing.One such example is Onur Yüce Gün at New Balance, who has applied generative design and performance modeling to athletic footwear—translating architectural methods to human-scale products.Whether designing complex buildings or embedded components, these practitioners share a common approach: combining parametric logic, physical constraints, and simulation in real-time feedback loops that drive innovation across sectors.<iframe width="640" height="360" src="https://www.youtube.com/embed/zC26STEM8zA?&amp;wmode=opaque&amp;enablejsapi=1&amp;origin=https://www.wevolver.com" frameborder="0" class="fr-draggable"></iframe> <h3>Join the Conversation at CDFAM Amsterdam 2025</h3>CDFAM Amsterdam 2025 offers a single-track, interdisciplinary program focused on computational design across scales—from architectural systems to microstructures, from generative tooling to machine learning in simulation.Whether you work in architecture, product design, energy, aerospace, robotics, or advanced manufacturing, the event provides a rare opportunity to engage with experts building the next generation of digital workflows.Register at <a rel="noopener" target="_new" href="https://cdfam.com">cdfam.com</a> to join a global community pushing computational design forward—across domains, industries, and scales.

As seen at CDFAM Computational Design Symposium

Computational Design at Architectural Scale

This is the fourth article in a 6-part series featuring articles on &quot;Bringing Intelligence to the Edge&quot;. The series looks at the transformative power of AI in embedded systems, with special emphasis on how advancements in AI, embedded vision, and microcontroller units are shaping the way we interact with technology in a myriad of applications. This series is sponsored by <a href="https://www.wevolver.com/profile/mouser.electronics" target="_blank">Mouser Electronics</a>. Through their sponsorship, Mouser Electronics shares its passion and support for engineering advancements that enable a smarter, cleaner, safer manufacturing future.Most modern consumer-driven industries accumulate large volumes of data, but without a filtering mechanism that maps, charts, and trends data models, the raw data has little to no utility. Traditional analytical mechanisms are no longer up to the task&mdash;the sheer amount of data and the speed at which it&rsquo;s being accumulated has made it economically and operationally necessary to scale up analytical capacity using data science.&nbsp;The Internet of Things (IoT) is constantly collecting data, and the organization, distribution, and analysis of all this data is the new frontier of artificial Intelligence (AI). While conventional data analysis methods are still being implemented, AI is proving to be a more precise and time-efficient tool in processing the big data crunch. AI can recognize patterns and notice inconsistencies in real-time. AI algorithms can save significant time and energy by compiling data from multiple sources and presenting it with a uniform, consistent approach. AI and machine learning can substantially improve secure and predictive analytics operations in the data center and beyond, anticipating and even preventing potential issues before they become problems. AI can restructure data collection and analysis operations in real-time and reduce unanticipated network interruptions. The marriage of AI and data science can improve data set structuring, help reach conclusions and significantly enhance IoT operations.&nbsp;<h1 dir="ltr">Data Science and Machine Learning</h1>Data science is the integrated approach of extracting insights from growing volumes of data using various scientific methods, algorithms, and processes. Data science is driven by software that recognizes hidden patterns within unprocessed data and draws conclusions from those patterns. These valuable insights help facilitate corporate decision-making by interpreting problems analytically and generating viable solutions.Cross-Industry Standard Process for Data Mining (CRISP-DM) is a process model that provides an overview of the data science life cycle. It&rsquo;s essentially a framework that assists in planning, organizing, and implementing a data science project. CRISP-DM consists of the steps in Figure 1:&nbsp;<img src="https://images.wevolver.com/eyJidWNrZXQiOiJ3ZXZvbHZlci1wcm9qZWN0LWltYWdlcyIsImtleSI6ImZyb2FsYS8xNjkwODkxNDY2MjY5LWltYWdlMy5qcGciLCJlZGl0cyI6eyJyZXNpemUiOnsid2lkdGgiOjk1MCwiZml0IjoiY292ZXIifX19" style="width: 300px;" class="fr-fic fr-dib" alt="crisp-dm-steps">Fig. 1: CRISP-DM steps. Source: Renesas ElectronicsMachine learning is a branch of AI dependent on models to perform autonomous tasks without required extensive programming. It relies on statistical techniques or algorithms that allow users to make predictions and/ or decisions based on historical data. Data scientists utilize technologies like machine learning and AI to examine data and make predictions about imminent developments and potential issues, significantly reducing the need for human intervention. When critical thinking encounters machine-learning algorithms, data science can help achieve better insights, guide efficiency efforts, and inform predictions. The goal is for businesses to benefit from data science to make progressive decisions and create more innovative products and services.&nbsp;<h1 dir="ltr">What Is Data Analytics?</h1>Data analytics is the science of scrutinizing raw or unprocessed data to derive meaning so it can be applied to decision-making. Data analytics employs several modern tools and techniques that help to structure data and make it understandable.Several preliminary steps need to be applied in the process before data analytics can begin:&nbsp;<ul><li dir="ltr">Data needs to be collected from a variety of sources.&nbsp;</li><li dir="ltr">Data needs to be interpreted correctly so it may be accurately organized and grouped.&nbsp;</li><li dir="ltr">Data needs to be examined to eliminate any replications or transcription errors.&nbsp;</li><li dir="ltr">Data may be managed by tables and/or spreadsheets. Data analytics can be subdivided into four main categories (Figure 2): descriptive, diagnostic, predictive, and prescriptive.&nbsp;</li></ul><img src="https://images.wevolver.com/eyJidWNrZXQiOiJ3ZXZvbHZlci1wcm9qZWN0LWltYWdlcyIsImtleSI6ImZyb2FsYS8xNjkwODkxNTAwOTA2LWltYWdlNi5qcGciLCJlZGl0cyI6eyJyZXNpemUiOnsid2lkdGgiOjk1MCwiZml0IjoiY292ZXIifX19" style="width: 300px;" class="fr-fic fr-dib" alt="categories-data-analytics">Fig. 2: Four main categories of data analytics. Source: Renesas ElectronicsReal-time analytics is the process of preparing, assessing, and analyzing data as it becomes available. Coupling real-time analytics with AI has provided businesses with fresh and revealing insights into the consumer experience. It has provided support personnel and IT the opportunity to act preemptively rather than react, resolving potential issues before endpoint users even realize there is an issue to report. The combination of AI and real-time analytics has completely transformed consumer and consumer support experiences.<h1 dir="ltr">Endpoint Analytics of Things</h1>According to the analytics firm International Data Corporation (IDC), 45% of data collected from IoT devices needs to be analyzed nearer to the endpoint (i.e., closer to the device itself) to optimize overall efficiency rather than transmitted to the cloud.[1] Shifting away from the cloud has several potential advantages: Transferring data to the cloud can be costly, as it requires significant bandwidth and power to support large and potentially lengthy data transmissions. Potential latency issues are also a factor; as the time expended during transmission increases, so does the need for higher server capacities to handle all incoming data. Situations may also arise where IoT devices lack a stable internet connection, and decisions must be made at the endpoint. Solutions that can support the consumer experience using analytics at the endpoint are often required.&nbsp;Analytics of Things (AoT) is a term used to describe the analysis of data generated by IoT devices. AoT makes it possible to operate business intelligence within an application rather than a data warehouse. It also assists in understanding patterns, detecting anomalies, predicting potential issues, setting maintenance intervals, and optimizing processes.&nbsp;Over the years, organizations have relied on data analytics based on a centralized architecture for their data-driven planning and visions of the future. The data is increasing every second, and there is a requirement for a revolutionary approach to overcoming data transfer latency, improving privacy, and meeting customer expectations. The real-time response has especially become necessary after the convergence of AI, 5G, and IoT. Distributing intelligence across the end of the network provides an opportunity for more efficient data analytics and real-time decision-making at the endpoints with little to no latency. Performing these functions directly on endpoint devices with low processing capabilities is referred to as endpoint data analytics (Figure 3).<img src="https://images.wevolver.com/eyJidWNrZXQiOiJ3ZXZvbHZlci1wcm9qZWN0LWltYWdlcyIsImtleSI6ImZyb2FsYS8xNjkwODkxNTM3ODYwLWltYWdlMS5qcGciLCJlZGl0cyI6eyJyZXNpemUiOnsid2lkdGgiOjk1MCwiZml0IjoiY292ZXIifX19" style="width: 300px;" class="fr-fic fr-dib" alt="endpoint-data-analytics">Fig. 3 Endpoint data analytics. Source: Renesas Electronics<h1 dir="ltr">The Data Science Support System</h1>Various technologies and sensors facilitate the processing of data analytics at the endpoint. Sensors are required not only to gather and accumulate data but also to assist in assessing and understanding the surrounding environment. Commonly implemented types of sensors include GPS for determining location and thermometers and barometers for measuring temperature and pressure. Cameras, lasers, and radar/ sonar can also be used to detect people and/or objects nearby.&nbsp;Communication technologies such as Wi-Fi and 5G assist in gathering and transmitting data. The data is then fed into data science algorithms that play a central role in assessing the data and recommending potential courses of action. In certain use cases, the outcome of the analytics performed at the endpoint can even be used to make automatic adjustments to a device&rsquo;s plan of action. An autonomous vehicle, for example, may change routes depending on traffic data collected from other vehicles in the same area or on weather and/or road conditions being monitored by onboard sensors. Data analytics can help categorize potential actions and adjustments into classes to improve the overall decision-making process; for example, the autonomous vehicle can classify potential actions as operational (e.g., optimizing the route for better road and weather conditions) or tactical (e.g., optimizing the route to reduce travel time).&nbsp;Leveraging the power of predictive maintenance, intelligent sensors embedded in factory equipment can collect data on optimal operations to help manufacturers reduce downtime and avoid potential revenue loss. Anticipating and acting on potential out-of-service issues means that plants can run at peak efficiency<h1 dir="ltr">Where AI and Data Science Go from Here</h1>Traditional business intelligence tools are not structured to process vast amounts of unstructured data. Data science utilizes more advanced tools to assist in sifting, grouping, and analyzing large volumes of data from different sources across multiple interconnected fields. Take marketing, for example: Exploring essential demographic factors like a customer&rsquo;s age, orientation, location, and behavioral patterns can assist in creating highly targeted advertising campaigns. These ads provide more precise recommendations by relying on browsing and purchase history to evaluate the customer&rsquo;s inclination toward buying a specific product. In banking, monitoring unusual customer behavior can aid in detecting and exposing fraud. By scrutinizing and assessing a patient&rsquo;s medical records, data science may help predict and prevent potential medical problems.&nbsp;<h1 dir="ltr">Conclusion</h1>Developments in data analytics and AI have transformed the consumer support experience. Real-time analytics respond to the data collected immediately (when its value is at its peak), and data analytics unlock the almost unlimited potential of that data, increasing overall business value and potentially enabling enterprises to secure a high position in the marketplace. Businesses in all sectors rely on machine learning models to make more accurate predictions and effective decisions, thereby improving production efficiency and assisting in overcoming potential security issues in communications between devices and the cloud. Endpoint AI has enhanced the entire process by speeding up the work, providing better results, and improving business decision-making.This article is based on an e-magazine: <a href="https://www.mouser.com/news/renesas-ai/renesas-intelligence-edge-ebook.html" target="_blank">Bringing Intelligence to the Edge</a> by Mouser Electronics and Renesas Electronics Corporation. It has been substantially edited by the Wevolver team and Electrical Engineer <a href="https://www.wevolver.com/profile/ravi.rao" target="_blank">Ravi Y Rao</a>. It&#39;s the fourth article from Bringing Intelligence to the Edge Series. Future articles will introduce readers to some more trends and technologies shaping the future of Edge AI.<hr>This&nbsp;<a href="https://www.wevolver.com/article/bringing-intelligence-to-the-edge-series" target="_blank" rel="noopener noreferrer">introductory article</a>&nbsp;unveils the &quot;Bringing Intelligence to the Edge&quot; series, exploring the transformative potential of AI at the EdgeThe&nbsp;<a href="https://www.wevolver.com/article/implementing-ai-in-iot-endpoints-balancing-performance-feasibility-and-data-constraints" target="_blank" rel="noopener noreferrer">first article</a>&nbsp;examines the challenges and trade-offs of integrating AI into IoT devices, emphasizing the importance of balancing performance, ROI, feasibility, and data considerations for successful implementation.This&nbsp;<a href="https://www.wevolver.com/article/revolution-of-endpoint-ai-in-embedded-vision-applications/" target="_blank" rel="noopener noreferrer">second article</a>&nbsp;delves into the transformative role of Endpoint AI and embedded vision in tech applications, discussing its potential, challenges, and the advancements in processing data at the source.&nbsp;The&nbsp;<a href="https://www.wevolver.com/article/four-metrics-you-must-consider-when-developing-tinyml-systems/edit" target="_blank" rel="noopener noreferrer">third article</a>&nbsp;delves into the intricacies of TinyML, emphasizing its potential in edge computing and highlighting the four crucial metrics - accuracy, power consumption, latency, and memory requirements - that influence its development and optimization.The&nbsp;<a href="https://www.wevolver.com/article/data-science-and-ai-driven-real-time-analytics" target="_blank" rel="noopener noreferrer">fourth article</a>&nbsp;delves into the realm of data science and AI-driven real-time analytics, showcasing how AI&#39;s precision and efficiency in processing big data in real-time are transforming industries by recognizing patterns and inconsistencies.The&nbsp;<a href="https://www.wevolver.com/article/endpoint-mcu-implementation-of-voice-user-interface" target="_blank" rel="noopener noreferrer">article five</a>&nbsp;delves into the integration of voice user interface technology into microcontroller units, emphasizing its transformative potential.The&nbsp;<a href="https://www.wevolver.com/article/reality-ai-a-game-changer-in-sensor-data-analysis" target="_blank" rel="noopener noreferrer">article six</a>&nbsp;delves into the profound impact of edge AI on system optimization, maintenance, and anomaly detection across diverse industries.<hr><h1 dir="ltr">About the sponsor: Mouser Electronics</h1>Mouser Electronics is a worldwide leading authorized distributor of semiconductors and electronic components for over 1,200 manufacturer brands. They specialize in the rapid introduction of new products and technologies for design engineers and buyers. Their extensive product offering includes semiconductors, interconnects, passives, and electromechanical components.<img alt="mouser-electronics-logo" src="https://images.wevolver.com/eyJidWNrZXQiOiJ3ZXZvbHZlci1wcm9qZWN0LWltYWdlcyIsImtleSI6ImZyb2FsYS8xNjkwODkxNTQ4NTE2LTE2OTA4OTE1NDg1MTYucG5nIiwiZWRpdHMiOnsicmVzaXplIjp7IndpZHRoIjo5NTAsImZpdCI6ImNvdmVyIn19fQ==" width="720" height="91" class="fr-fic fr-dii"><h1 dir="ltr" id="isPasted">References</h1>[1] How the Edge Computing Layer Helps with Latency, IEEE Innovation at work, [Online], Available from: &nbsp;<a href="https://innovationatwork.ieee.org/how-the-edge-computing-layer-helps-with-latency/" target="_blank">https://innovationatwork.ieee.org/how-the-edge-computing-layer-helps-with-latency/</a>

Article 4 of Bringing Intelligence to the Edge Series: AI is proving to be a more precise and time-efficient tool in processing the big data crunch by recognizing patterns and noticing inconsistencies in real-time.

Data Science and AI-Driven Real-Time Analytics

<h2 id="isPasted">Some Historical Perspective</h2>The relationship between physical engineering and the programmable computer is as old as the computer itself. The reality is that, for most of us, crunching lots of numbers by hand is frustrating, time-consuming, and error-prone.The British government of the 1820s agreed, opting to fund the early development of Charles Babbage&#39;s difference engines. These were visually striking machines: large mechanical computers, some capable of solving 7th order polynomials, that were intended to dramatically reduce the cost of production of tabulated trigonometric and logarithmic functions &mdash; the kind that were incredibly useful to scientists, engineers and navigators in the immediate aftermath of the Industrial Revolution.Fast forward to 1945, and we see the first glimpse of modernity: ENIAC, the world&#39;s first programmable, electronic, general-purpose digital computer. If you&#39;re curious as to what was it designed for, the answer is the computation of artillery and mortar firing tables; a task that involves exactly the kind of Newtonian mechanics calculations that will be familiar to any undergraduate mechanical or aerospace engineering student (see: Mayevski&#39;s <a href="https://books.google.co.uk/books/about/Trait%C3%A9_de_balistique_ext%C3%A9rieure.html?id=jE_zAAAAMAAJ&redir_esc=y" target="_blank">Trait&eacute; de balistique ext&eacute;rierure&nbsp;</a>, or the US Army Ballistic Research Laboratories&#39; <a href="https://asset-pdf.scinapse.io/prod/77299953/77299953.pdf" target="_blank">The Production of Firing Tables for Cannon Artillery</a>).Just a decade or so after ENIAC, IBM drew up its first specifications for a new programming language, The IBM Mathematical Formula Translating System, familiar to many of us as FORTRAN. Developed expressly for science and engineering, FORTRAN is a true titan of the scientific computing world. If you&#39;ve ever fired up MATLAB, analysed a load-case with an <a href="https://en.wikipedia.org/wiki/Finite_element_method" target="_blank">FEA</a> package, or run some new geometry in <a href="https://en.wikipedia.org/wiki/Computational_fluid_dynamics" target="_blank">CFD</a> &mdash; then it&#39;s almost certain that FORTRAN is involved in that stack somewhere, even six or seven decades on.<hr><h2 id="isPasted">Why Software Matters For Hardware</h2>The advantages of using digital computers in the physical engineering disciplines are both marked and multifarious, and I hope somewhat obvious.At a low level, these advantages can be quite straightforward. They include things like providing engineers with the ability to perform large numbers of calculations with little to no risk of human error. Think of something like repeated matrix multiplication, perhaps as part of a kinematics problem. How confident would you be in getting every step of that calculation right, without accidentally picking up a value one row down or one column across from where you intended? Thankfully, with the help of a few lines of FORTRAN, MATLAB, or Python, the computer can perform these calculations on your behalf, perhaps billions of times, without the threat of inconsistency or human error. At least... <a href="https://en.wikipedia.org/wiki/Pentium_FDIV_bug" target="_blank">almost all of the time.</a>At a higher level, however, these advantages are even more pronounced. They are the culmination of decades of work across several disciplines; the output of engineers, scientists and mathematicians who have designed, implemented, and shared computational techniques that address a myriad of challenging problems &mdash; from solving partial differential equations at scale, enabling modern FEA and CFD, through to the development of boundary representation solid modelling techniques that enable modern CAD systems. The convergence of these technologies has revolutionised engineering; accelerating development cycles, reducing the need for physical testing, and helping the world&#39;s engineers improve the quality and performance of everything from ships to spacecraft.As an illustration, think of the draughting process. For many engineering professionals who started their careers prior to the 1990s, draughting work would have still involved a drawing board, pens, and paper, cellulose, and/or linen. In the event of a mistake, the draughtsperson would have had to break out the scalpel or Tipp-Ex to &#39;erase&#39; the error, or issue an entirely separate drawing amendment to be paired with the original documents. With modern CAD systems, minor drawing modifications completed prior to release go completely unnoticed, and subsequent amendments can be as simple as a quick tweak and a brief change order &mdash; no redrawing of anything, no folder of amendments.<img src="https://images.wevolver.com/eyJidWNrZXQiOiJ3ZXZvbHZlci1wcm9qZWN0LWltYWdlcyIsImtleSI6ImZyb2FsYS8xNjg1NTI3MDQ5MjY0LUhXRHJhd2luZ09mZmljZS5qcGciLCJlZGl0cyI6eyJyZXNpemUiOnsid2lkdGgiOjk1MCwiZml0IjoiY292ZXIifX19" style="width: 300px;" class="fr-fic fr-dib"><figcaption id="isPasted">The Harland &amp; Wolff Drawing Office, Belfast, at some point during the 1960s or 1970s. My father served part of his apprenticeship in this room a decade or two later. Maritime Belfast/National Museums Northern Ireland</figcaption>Better yet, imagine the difference in resource requirement and development cycle times for something like a turbocharger. If every minor tweak to blade or housing geometry requires an entire manufacture, assembly, and balancing routine before the new design makes it to the gas stand, every iteration will fall weeks behind and cost significantly more to explore than its simulation-driven counterpart &mdash; where a design change could make it to CFD in a matter of minutes. This is before we even consider the introduction of something like mathematical optimisation into this loop, where the responsible engineer could define their objective function, their variables, and their constraints, and conceivably let the computer play tunes with the geometry, feed that into the simulation, interrogate the results, then rinse and repeat until it reaches an optimum. Ultimately, well correlated models, <a href="https://en.wikipedia.org/wiki/All_models_are_wrong" id="isPasted" target="_blank">even if wrong</a>, are incredibly useful.<hr><h2 id="isPasted">Why Hardware Matters for Everyone</h2>So computers are wonderful tools, and so are the niche software packages we run on them, but so what? Well, I believe we now find ourselves at a critical point in both the trajectory of engineering as a discipline, and in its utility as a mechanism for improving our lives as a species. We have a lot of *very* active engineering fields right now, with a lot of important problems to address &mdash; and in the end, at some point, somebody has to actually make stuff to make things better.For example, it seems to me that we are standing but a few feet forward of the starting line in a new, privately funded space race. We have seen SpaceX engineers repeatedly achieve nothing short of a triumph of control engineering: reversing a rocket onto a barge in the ocean, opening the door to reuse, and as a result, both dramatically reduced space access costs and dramatically increased launch cadence. We have companies like SpinLaunch working to yield orbital access mechanisms that help escape <a href="https://www.nasa.gov/mission_pages/station/expeditions/expedition30/tryanny.html" target="_blank">the tyranny of the rocket equation&nbsp;</a>.We have a burgeoning paradigm shift in personal transport, with electric cars, scooters, and e-bikes encroaching further and further on the internal combustion engine&#39;s long-established territory.We have additive manufacturing evolving into a serious, cost-competitive manufacturing technique that can achieve geometries beyond the reach of traditional subtractive approaches, and we have generative design technology helping engineers produce mathematically optimised, often organic-looking solutions to pressing design problems. To see the power of these two in concert, just look at <a href="https://www.czinger.com/" target="_blank">Czinger</a> and <a href="https://www.divergent3d.com/" target="_blank">Divergent</a>.And, of course, we have ever more compelling incentives to overhaul the majority of our civilisation&#39;s energy infrastructure, pushing us to diversify the means by which we generate electricity, fostering the development of improved wind, solar, and &mdash; I hope &mdash; nuclear technologies.In short, we&#39;ve got a lot of real-world engineering to tackle, and plenty of hardware to build.<hr><h2 id="isPasted">Software is Eating the World</h2>Ultimately, it strikes me that the way in which we develop the physical systems around us is changing, and not all our tools yet accommodate this.Despite the arrival of an entire range of engineering software systems in the latter part of the last century, these were typically specialised products, often designed to form improved but effectively like-for-like replacements of an existing way of accomplishing a given task, whether that was replacing the draughtsman and his drawing board with a CAD workstation, or replacing a complex, <a href="https://twitter.com/CalumDouglas1/status/1550594001874698246" target="_blank">stiffness-altering oil pressure measurement apparatus&nbsp;</a>around a bearing with a CFD case.As a result, we find ourselves at a point where, as a profession, we&#39;re equipped with some extremely impressive tools; tools that can help us build the shorter iterative loops that are required to yield accelerated system development.However, it feels like we&#39;re still using these revolutionary tools, developing the technology that is critical to our species&#39; future, inside an operational framework that was designed for slide rules, drawing boards, and row after row of draughtsmen packing a tobacco smoke filled drawing office.Our systems are heavily siloed, our teams often fragmented. We struggle to collaborate across teams, sites, and time zones. We have vast and unstructured knowledge bases that are full of effectively undiscoverable data, put beyond the reach of those who don&#39;t know exactly where to look. And we struggle for visibility &mdash; of tasks, responsibilities, upcoming changes, and most importantly, of our data.Even the big players recognise this. Dassault push <a href="https://discover.3ds.com/reduce-non-value-added-work" target="_blank">research</a> that shows engineers spend 34% of their time performing &#39;non-value-added&#39; work; dominated by the amount of time spent just looking for stuff, trawling through network drives and cluttered inboxes. This same research shows that engineers are typically working with outdated information 20% of the time &mdash; imagine a full day a week, every week, for every member of your team, just being thrown away because of bad input data. This pattern has to change.In fact, for newer hardware companies, I think some things have *already* changed. <a href="https://a16z.com/2011/08/20/why-software-is-eating-the-world" target="_blank">Software is eating the world&nbsp;</a>applies not only to the electronic control of fuel injectors and ignition coils, but to the adoption of software-like management practices, with a focus on short design-build-test loops. I may hate the confusing, jargon-heavy nomenclature of &#39;agile&#39; methodology, but there is some method in the madness.<hr><h2 id="isPasted">Better, More Collaborative Software for Engineering Teams</h2>The future that I see is one where we not only have specialised tools for specific parts of the engineering cycle, but we have a central, engineering specific hub; an operating system that ties these things together.We want to see the world&#39;s physical engineering teams build better products faster; to achieve shorter development cycles, to iterate faster, and to better leverage their internal knowledge &mdash; so that they can achieve their goals, whether that&#39;s kinetic launch, faster cars, or greener energy.We think this will be brought about by transforming how hardware teams communicate, collaborate, and manage technical knowledge. That means better, more connected software; software that focuses on resolving the productivity-killing shortfalls in current engineering process. We think hardware teams should have technical communication mechanisms that are fast, painless, and traceable; that allow new hires to find the information they need, without requiring someone else to go rooting through their inbox for half an hour. We think engineers should be able to see what colleagues are working on, how these items are prioritised, and what&#39;s coming next. We think engineers should be able to annotate drawings, share calculations and schematics, and offer opinions on proposed solutions &mdash; all in real-time, wherever they are, with all that data stored and indexed for easy discoverability down the line.&nbsp;Above all, we think engineers should have a single source of truth to work with; a repository of version-controlled design values, simulation outputs, and performance targets &mdash; whether those are scalar values, or n-dimensional maps.In the end, what we want to see is engineering teams moving beyond the pain of e-mail ping-pong with spreadsheets and presentations, to stop scrawling performance differentiating IP over paper drawings that are destined for the shredder, and to start letting the computers handle the busywork.

Betty Jean Jennings and Fran Bilas at the main ENIAC control panel. Moore School of Electrical Engineering. U.S. Army, ARL Technical Library Archives

The recent history of our physical engineering disciplines is intertwined with computing. The future is too. 

The Future of Hardware is... Better Software

<h2 id="isPasted">Quick Wins</h2>We&#39;ll be looking at three items here that should be broadly universal across any Mechanical Engineering function, and should also be applicable to other disciplines. Our objective is to highlight some minor changes in workflow that can offer a significant benefit for your team. Taking these in order...<hr><h2 id="isPasted">1. Drawings: Datum Tables</h2>This is something I started doing several years ago to combat my own frustration with trying to read other people&#39;s drawings, and I was always surprised that it wasn&#39;t a standard practice in any of the design departments I&#39;ve worked in.Picture the scene: one of your colleagues has just finished off the drawings for a new cylinder head, and they pass them to you for peer review. If your brain works anything like mine, the first things you want to check are all the major datum features. However, when a drawing pack runs to six or seven substantial pages, this turns into a less entertaining, more time-consuming, monochrome version of Where&#39;s Wally? &mdash; which isn&#39;t really what we&#39;re after.For me, the fruit doesn&#39;t hang much lower. Work up a table&dagger; that lists datum features in alphabetical order, list their sheet, list their grid reference, then place the table somewhere easy to find on the drawing. Anyone else lifting the drawings will be able to dive right into reading the important bits, without having to scour the thing for ten minutes before they start actually thinking about the task at hand. This can as simple as Table 1.<img src="https://images.wevolver.com/eyJidWNrZXQiOiJ3ZXZvbHZlci1wcm9qZWN0LWltYWdlcyIsImtleSI6ImZyb2FsYS8xNjg0MjI1NDYxMjE1LVRhYmxlSW1hZ2UucG5nIiwiZWRpdHMiOnsicmVzaXplIjp7IndpZHRoIjo5NTAsImZpdCI6ImNvdmVyIn19fQ==" style="width: 766px;" class="fr-fic fr-dib">Table 1 &dagger;If you&#39;re so inclined, I also imagine that it should be possible to implement automatic table assembly with a little bit of code. From memory, when I last explored this with CATIA v5 macros, I couldn&#39;t find any reference to datum objects in the object model documentation.<hr><h2 id="isPasted">2. Excel: Named Ranges</h2>As the sort of engineer whose professional home lies in writing code to analyse, simulate, and control physical systems, this point is much closer to my heart. With a few notable use-case exceptions, such as its easily accessed optimisation tools, I basically hate Excel. I consider it to be like the adjustable spanner of the software world: it might work for the task at hand, but it&#39;s still the wrong tool for just about every job.I believe that Excel inadvertently pushes people to construct terribly organised models and analyses that are often borderline unintelligible, and that building a clean solution in Excel requires the adoption of some very considered practice that you would basically get by accident if you did this work in any one of MATLAB, Python, Julia, Fortran etc. &mdash; the list goes on.More specifically, when I&#39;m forced to unpick somebody else&#39;s Excel-based model or analysis, there is one overwhelmingly common piece of practice that makes me want to tear my hair out: an overflowing formula bar, brimming with unnecessary parentheses and mysterious references to <code>!Sheet2&nbsp;</code>and <code>$C$907</code>. Let&#39;s take a real-world example of how unnecessarily messy this can get, even for relatively simple cases, then we&#39;ll move onto cleaning things up.<h3>The Problem</h3>The simple example case I&#39;m going to give here will be familiar to anyone who&#39;s ever designed an engine, a gas strut, or a (hydro)pneumatic suspension system: computing gas pressure in a cylinder of known volume. We&#39;re going to use the <a href="https://en.wikipedia.org/wiki/Van_der_Waals_equation" target="_blank">Van der Waals equation of state,&nbsp;</a>owing to the fact that the ideal gas law is pretty rubbish at approximating the behaviour we&#39;d typically see in any of these systems. The Van der Waal&#39;s equation of state is given by:<img src="https://images.wevolver.com/eyJidWNrZXQiOiJ3ZXZvbHZlci1wcm9qZWN0LWltYWdlcyIsImtleSI6ImZyb2FsYS8xNjg0MTY3MzEzOTIyLUVxMS5wbmciLCJlZGl0cyI6eyJyZXNpemUiOnsid2lkdGgiOjk1MCwiZml0IjoiY292ZXIifX19" style="width: 766px;" class="fr-fic fr-dib">For simplicity, we&#39;ll take the case for n moles of gas, so this becomes:&nbsp;<img src="https://images.wevolver.com/eyJidWNrZXQiOiJ3ZXZvbHZlci1wcm9qZWN0LWltYWdlcyIsImtleSI6ImZyb2FsYS8xNjg0MTY3MzQ0NzcxLUVxMi5wbmciLCJlZGl0cyI6eyJyZXNpemUiOnsid2lkdGgiOjk1MCwiZml0IjoiY292ZXIifX19" style="width: 766px;" class="fr-fic fr-dib">Where:<ul><li>P denotes pressure.</li><li>V denotes volume.</li><li>n denotes moles of gas.</li><li>R&nbsp;denotes gas constant.</li><li>T denotes gas temperature.</li><li>a denotes Van der Waals constant for intermolecular interaction.</li><li>b denotes Van der Waals constant for real gas molecule volume.</li></ul>In our example scenario, we can pretend that we&#39;re solving for pressure, with all other values known, so we can quickly rearrange as follows:&nbsp;<img src="https://images.wevolver.com/eyJidWNrZXQiOiJ3ZXZvbHZlci1wcm9qZWN0LWltYWdlcyIsImtleSI6ImZyb2FsYS8xNjg0MTY3Mzk1NTExLUVxMzQucG5nIiwiZWRpdHMiOnsicmVzaXplIjp7IndpZHRoIjo5NTAsImZpdCI6ImNvdmVyIn19fQ==" style="width: 766px;" class="fr-fic fr-dib">Equation shuffling out of the way, let&#39;s pluck some values from the air and get these plugged into a spreadsheet to see what we&#39;re dealing with. The values we&#39;re going with assume a 10cc volume, 20&deg;C, and enough pure nitrogen fill to generate approximately 86barA.<img src="https://images.wevolver.com/eyJidWNrZXQiOiJ3ZXZvbHZlci1wcm9qZWN0LWltYWdlcyIsImtleSI6ImZyb2FsYS8xNjg0MjIxMjQ5NDg2LVNjcmVlbnNob3QgMjAyMy0wNS0xNiAxMDA5MTYucG5nIiwiZWRpdHMiOnsicmVzaXplIjp7IndpZHRoIjo5NTAsImZpdCI6ImNvdmVyIn19fQ==" style="width: 766px;" class="fr-fic fr-dib">The typical quick spreadsheet setup leaves us with something that looks like this:&nbsp;<img src="https://images.wevolver.com/eyJidWNrZXQiOiJ3ZXZvbHZlci1wcm9qZWN0LWltYWdlcyIsImtleSI6ImZyb2FsYS8xNjg0MTY3NTAxNDA0LTIyMDUxOS0zUXVpY2tXaW5zLU5vTmFtZWRSYW5nZS5wbmciLCJlZGl0cyI6eyJyZXNpemUiOnsid2lkdGgiOjk1MCwiZml0IjoiY292ZXIifX19" style="width: 730px;" class="fr-fic fr-dib">In my view, this isn&#39;t the end of the world; all the referenced cells are close by, and I can pick apart the formula quickly &mdash; but you can already see that extension of this sort of pattern to something more complex will start to cause serious headaches. By the time you&#39;re working with something which has parameters spanning sheets and substantially more complex formulas in play, this method is a nightmare.&nbsp;<h3 id="isPasted">The Solution</h3>Thankfully, a better way forward here is entirely quick and painless: <a href="https://support.microsoft.com/en-us/office/define-and-use-names-in-formulas-4d0f13ac-53b7-422e-afd2-abd7ff379c64" target="_blank">named ranges.&nbsp;</a>Named ranges effectively allow us to assign variable names of our choosing to these parameters, while also allowing us to configure the scope of the variables, i.e., whether they are visible only on a given worksheet, or whether they&#39;re global across the workbook.Setting a named range on a single value is as easy as clicking the cell in the top-left corner that currently shows cell address, overwriting it with an appropriate value, and hitting enter. There are plenty of other websites that explain how to use the &#39;Name Manager&#39; tools and get the most out of named range usage, but I&#39;ll just show you how much cleaner things look once you&#39;ve converted cell addresses to named ranges:<img src="https://images.wevolver.com/eyJidWNrZXQiOiJ3ZXZvbHZlci1wcm9qZWN0LWltYWdlcyIsImtleSI6ImZyb2FsYS8xNjg0MTY3NTI3MDI2LTIyMDUxOS0zUXVpY2tXaW5zLU5hbWVkUmFuZ2UucG5nIiwiZWRpdHMiOnsicmVzaXplIjp7IndpZHRoIjo5NTAsImZpdCI6ImNvdmVyIn19fQ==" style="width: 766px;" class="fr-fic fr-dib">At least to my mind, this is an immediate and significant improvement. Compared with how it was previously, it is now substantially more straightforward to compare the formula with our target equation above. Any misplaced brackets or indices that might otherwise cause some serious pain to review or debug can now be caught much more readily, and you can move forward with increased confidence that your spready is trustworthy.<hr><h2 id="isPasted">3. Files: Naming Convention</h2>Finally then, the best (and shortest) tip: file naming convention. As far as I&#39;m concerned, there is precisely one correct way to name the sort of files generated by most engineering operations, and that way is as follows:<ul><li><code>YYMMDD-FileName.ext</code></li></ul>For example, the file in our named range scenario might be called something like <code>220519-NamedRangeExample.xlsx</code>.By placing the date at the start of the filename, and by following the <a href="https://en.wikipedia.org/wiki/ISO_8601" target="_blank">ISO8601</a> date component order, lexicographical sorts will yield files in chronological order, irrelevant of when they were copied to the particular directory.Then, by adopting dashes instead of spaces, underscores, or whatever else you might fancy for separation of sections of the file name, you&#39;re making the decision up-front that you simply want to avoid any funnies with respect to how filenames are handled.For example, any files appearing at a web URL will have spaces substituted for <code>%20</code>, which isn&#39;t exactly readable, and underscores can cause issues with both certain platforms and certain indexing systems.&nbsp;

computational method and analysis

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