![]() ![]() A tidy space contributes to a visually larger room. Use storage solutions like under-bed storage or floating shelves to maintain an organized environment. Remove unnecessary furniture and decor, leaving only essential items. Use vertical storage solutions like tall bookshelves to draw the eye upward and create the illusion of height.ĭeclutter and organize: Keep the room clutter-free by embracing minimalism. Place furniture against walls to open up the center of the room. Opt for streamlined, space-saving furniture with legs to create an airy feel. Adequate lighting is crucial consider multiple light sources, including wall sconces and floor lamps, to eliminate shadows and brighten the room.įurniture selection and placement: Choose furniture that serves multiple purposes to maximize functionality without overcrowding. Use mirrors strategically to bounce light around the room and create the illusion of more space. Light colors reflect natural light, making the space feel larger. The height of the garage door and the ceiling are also important considerations.Ĭolors and lighting: Opt for light, neutral colors on walls and bedding to create a sense of openness. ![]() Larger garages for three or more cars can exceed 600 square feet. A small one-car garage typically ranges from 200 to 250 square feet, while a standard two-car garage may be around 400 to 500 square feet. Garage: Garage sizes vary widely based on the number of vehicles intended to be housed. Master bathrooms can be 100 square feet and above allowing for features like separate shower and bathtub areas. Small bathrooms typically range from 35 to 50 square feet, while standard bathrooms may be between 50 and 100 square feet. Master bedrooms often include additional features such as ensuite bathrooms and walk-in closets, contributing to their larger size.īathroom: Bathroom sizes vary based on their purpose. Small bedrooms are typically 100 to 150 square feet, standard bedrooms range from 150 to 250 square feet, and master bedrooms are 250 square feet and above. Larger homes may have living rooms exceeding 550 square feet, providing ample space for seating, entertainment centers, and other furnishings.īedroom: Bedroom sizes depend on their function and the size of the house. Small living rooms typically range from 200 to 350 square feet, while standard living rooms may be between 350 and 550 square feet. Living room: Living room sizes can vary based on the overall layout of the house. Ultimately, floor plans play a critical role in visualizing and realizing the design and construction of buildings and spaces. They facilitate discussions, decision-making, and problem-solving regarding the layout, functionality, and aesthetics of a space. ![]() Floor plans are also valuable for communication and collaboration between architects, designers, builders, and clients. They assist in space planning, enabling efficient utilization of the available area. Additional details such as furniture placement, fixtures, and other features may also be included to provide a comprehensive understanding of the space.įloor plans serve as essential tools in architecture, interior design, construction, and real estate. Walls, doors, and windows are represented by lines and symbols, showcasing their location and dimensions. In a floor plan, each room and area is depicted with accurate measurements and proportions. Floor plans provide a bird's-eye view of the property, allowing individuals to visualize the spatial organization and flow of the space. It showcases the layout and arrangement of rooms, walls, windows, doors, and other architectural elements. A floor plan is a scaled, two-dimensional representation of a building or space, viewed from above. ![]()
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3/16/2024 0 Comments Free ebay listing tools 2019![]() ![]() PriceĪnd finally, but most importantly – price. It’s the only way to truly know if this eBay listing tool is the best eBay listing tool for you and your business. Ideally, you want somewhere that offers your preferred communication channel – whether that’s support guides and videos, live demos, live chat, email or phone support.Īlways pick a tool that offers you the chance to try it out first. But, if you do run into difficulties, it’s useful to have adequate support to fall back on – especially in the busy world of eCommerce. ![]() Listing tools should be fairly self-explanatory. Picking a multi-channel listing tool that integrates with these channels means that you don’t need to change software at a later date. While selling on eBay may be enough for now, in the future you might have ambitions to expand to Amazon, Etsy, Wish or even your own eCommerce platform. This is perfect if you plan to sell on multiple sales channel(s), or if you need a helping hand updating bundle, kit and variation quantities. Inventory management software helps you better manage your stock by automatically updating stock levels upon sale. Particularly useful additions include: Inventory management Some of the best eBay listing tools come with additional functionality to streamline your eBay business further. Kits, bundles and variationsĪnd, if you’re looking to sell kits, bundles and variations, you’ll want to look for a tool that enables you to list these products individually and together. This is particularly great for sellers who plan to list large volumes of products. The ability to import existing listings (either your own or another’s) is a handy feature that cuts down the time it takes to list. A quick-edit feature is really useful, especially if you’re looking to expand to other sales channel(s) in the future. ![]() While no one intends to make mistakes on their listings – they happen. If you want to avoid eBay’s scheduling fee too, then you want a listing tool that holds the listing until the scheduled time – pushing it in real-time. If you want to schedule your eBay listings to target certain starting and finishing times, then you want a listing tool with scheduling functionality. Scheduling listingsĭidn’t we mention something about avoiding eBay’s scheduling fees? We definitely did. But, you might also want additional functionality such as bulk listing, quick listing and saved templates to help make the listing process even smoother. ![]() Common listing features include: Adding listingsĪll listing software will allow you to create listings and push them to eBay in the correct format. The most important feature of a listing tool is its ability to list your products to eBay. In fact, eBay listing tools are such a handy piece of kit, that there are plenty out there to choose from (including Expandly!) So how do you find the best eBay listing tool for your business? Let’s take a look at some of the key considerations to help you decide: Listing functionality ? The ability to expand to other marketplaces in the future. ? Additional tools and features, such as inventory management. ? Being able to avoid eBay’s scheduling fee. ? Quick access to saved templates, variations and product bundles. eBay listing tools are ideal for multi-channel sellers because they avoid the duplication involved in posting the same listing to multiple marketplaces.Īn eBay listing tool also has significant benefits for single-channel eBay sellers too, including: What is an eBay listing tool?Īn eBay listing tool is a piece of software used to post listings to eBay and other sales channel(s). ![]() ![]() It is important for parents to keep in mind that children are expected to be able to instantly recognize sight words they have learned previously. Teachers will generally pull from one or both of these lists to create the sight words that children should learn. Like the Dolch Word list, the Fry Sight Word List is made up of both sight words and high-frequency words and is divided by grade level. Fry updated the Fry Sight Word List in 1980, which is comprised of the most commonly used words in books, newspapers, and other publications. Edward Fry expanded the Dolch Word List to include 1,000 commonly used words in the English language. In addition to the 220 sight words, the Dolch Word List also includes 95 high-frequency nouns. The list is divided by grade level from Pre-K through third grade, but many educators believe that these words should be mastered by first grade. The list contains 220 of the most commonly used words that should be recognized by first sight. ![]() One list is called the Dolch Word List, created by E.W. There are several sight word lists for emerging readers. Children who are able to instantly recognize sight words are more likely to be confident readers because over 50-70 percent of the general English text is made up of sight words. When children recognize sight words within three seconds, they are also more likely to comprehend what they are reading. Children who are able to quickly and instantly recognize sight words are more likely to become more fluent readers who read at a good speed because they are not stopping to try to decode every word. As a result, children must learn to recognize these words automatically, or at first sight. Most sight words cannot be decoded or sounded out, and they are also difficult to represent with a picture. These sounds usually follow basic spelling rules or phonetic principles, but there are some words that did not follow rules. When we teach children to read, we are basically helping them to crack a code. Children learn to hear and say the sounds of the alphabet and then how to blend those sounds to make words. One critical skill that children need in order to build solid foundational reading skills is sight word recognition. It takes about 5 minutes a day, but once you get in the routine it becomes part of their day.No matter whether kindergarten children will be learning in person, online, or a hybrid of the two, parents and teachers are still focused on ensuring their emerging readers develop a love for reading while learning to read effectively and efficiently. That way they always had new words to work on and words they were starting to recognize. When they knew a word for a couple days in a row I took it out and put in a new word. In the end I know my kids saw five words 6 times a day. We flashed through the same five words 2 more times just before we brushed our teeth. Then we flashed through the same five words 2 more times just before dinner. With my own kids we flashed through five words 2 times every day when we got home from school. I would suggest you put all the words on flash cards and take 4 or 5 a day and work on just those words. Help too has play where look good who come does The sooner your student can learn these the sooner they can learn how to read.įor have of they said want here me this what Please remember these words are a year-long focus. One way you can help your child learn these words is by pointing them out as you read to him/her. In the classroom, we work on recognizing these words in stories we read and write, along with practicing them in isolation, such as with flash cards. ![]() The emphasis of our program is placed on exposure to and recognition of these words in a variety of contexts. There are 40 expert words that kindergarteners are responsible to learn. Our expert words are commonly used two to four letter words. The major goal of the kindergarten spelling program is to focus on what we call expert or high frequency sight words. ![]() ![]() ![]() (2019) used a distributional model to assess differences in memory retrieval performance across tens of thousands of participants spanning the aging spectrum. (2018b) used a distributional model to analyze the changes that were occurring in patients who were developing a cognitive impairment, while Taler et al. Taking a different applied approach, Johns et al. For example, Johns and Jamieson (2018) analyzed a large sample of fiction books to understand individual variance in language usage. Furthermore, they have begun to be used not just as theories of human behavior, but as analysis tools to quantify linguistic data. The representations derived from distributional models have been used to examine behavior across a number of domains, including lexical organization ( Jones et al., 2012 Hoffman et al., 2013 Hsiao and Nation, 2018 for a review, see Jones et al., 2017), episodic memory ( Johns et al., 2012b, 2014 Mewhort et al., 2017), morphological processing ( Marelli and Baroni, 2015 Marelli et al., 2017 Westbury and Hollis, 2018), lexical-perceptual integration ( Andrews et al., 2009 Johns and Jones, 2012 Lazaridou et al., 2017), prediction ( Frank and Willems, 2017), decision ( Bhatia and Stewart, 2018), and sentence processing ( Johns and Jones, 2015). The insight that these models exploit is that lexical semantic behavior seems to be systematically related to the co-occurrence of words within the natural language environment. The original, and best known, model of this class is Latent Semantic Analysis (LSA Landauer and Dumais, 1997), which spurred the development of many new approaches (e.g., Lund and Burgess, 1996 Griffiths et al., 2007 Jones and Mewhort, 2007 Shaoul and Westbury, 2010 Mikolov et al., 2013 Jamieson et al., 2018). ![]() One of the key developments in big data approaches to cognition is the emergence of distributional models of semantics, which learn the meaning of words from statistical patterns contained in very large sources of texts (see Jones et al., 2015 for a review). The results of this article provides insights into the cultural evolution of word meanings, and sheds light on alternative methodologies that can be used to understand lexical behavior.Īn emerging area within the psychological and cognitive sciences is the use of big data to develop and analyze theories of cognition ( Jones, 2017 Johns et al., in press). Additionally, it was demonstrated that users of a language have strong preferences for word meanings, such that definitions to words that do not conform to people’s conceptions are rejected by a community of language users. Overall, it was found that even for words that are not an active part of the language environment, there is a large amount of consistency in the word meanings that different people have. This was accomplished by mining a large amount of data from an online, crowdsourced dictionary and analyzing this data with a distributional model. The current article combines these two approaches, with the goal being to understand the consistency and preference that people have for word meanings. Two of the main developments of this line of research is the advent of distributional models of semantics (e.g., Landauer and Dumais, 1997), which learn the meaning of words from large text corpora, and the collection of mega datasets of human behavior (e.g., The English lexicon project Balota et al., 2007). Department of Communicative Disorders and Sciences, University at Buffalo, Buffalo, NY, United Statesīig data approaches to psychology have become increasing popular ( Jones, 2017). ![]() 3/16/2024 0 Comments Chucky movie killed my buddy![]() ![]()
3/16/2024 0 Comments Failed to authenticate with google![]() Give Unrestricted Data UsageĪre you on a Data saver mode on Android and trying to access the Play Store? The default Data saver mode can be aggressive sometimes and blocks apps like Play Store from accessing the internet.įrom the Play Store app info menu, you can give the Play Store unrestricted data usage to function normally even with Data Saver mode on. Reboot your phone and open the Play Store again. Step 4: Tap on Clear storage and Clear cache from the following menu. Step 2: Go to Apps & notifications > See all apps and select Google Play Store. Sometimes, an overburden of cache data or a bad cache can interfere with the Play Store functions, and you might end up with authentication is required error. Google Play Store collects cache data in the background to load your frequently visited app pages quickly. Step 2: Tap on the three-dot menu at the top and select Uninstall updates.Īndroid OS will revert to the factory version of Google Play Store on your phone, which will be functional. Step 1: Long-press on the Play Store app icon and go to the app info menu. You can uninstall it and revert to an earlier build. Uninstall Google Play Store UpdatesĪ recent Play Store update on your Android phone might have messed up the app function for your Google account. Step 3: Tap on Force stop from the App info menu.Įxit the screen and try to open the Play Store again. ![]() Step 2: Long-tap on the app icon and select the info button. ![]() Step 1: Identify Google Play Store on your home screen or app drawer. You can use it and fix authentication is required error in Google Play Store. Force Stop Google Play StoreĪndroid offers a handy force stop function that allows users to stop any app that’s acting weirdly. Step 5: Tap on the three-dot menu at the top and select Sync now option.Ĭlose the Settings app and open the Play Store again to see if it has resolved the issue or not. Step 3: Select the Google account that you want to sync with the Play Store. Step 1: Open the Settings app on your Android phone. This trick worked when we faced a similar issue Google Play Store. You can tap on the Retry button or close the app and open it again to see if the issue is resolved or not. Sometimes, when Google Play Store fails to establish a connection with your Google account, you might face an Authentication is required error in the app. You need to sign in to your Google Account’ message. Instead, it shows ‘Authentication is required. When you open the Play Store, it won’t load the home screen content for you. If you are facing the same, read along to learn how to fix Google Play Store’s authentication is required error on Android. Sometimes, Google Play Store fails to download apps, gets stuck at completing setup, or throws the ‘authentication is required’ error. Unfortunately, it still carries issues leaving users with a scratching head. Google Play Store continuous to be the prime source for Android users to download apps and games on the phone. ![]() 3/15/2024 0 Comments Srs root v 6.1 download![]() ![]() ![]() Launch the app from your home screen icon and select the install superuser option present on the app’s screen.Install the framaroot app (after enabling unknown sources for your device).Send it to your phone or device (if downloaded with a PC) and make sure that the apk is in your phone’s memory.Download the latest version of framaroot apk from here.To use the framaroot app to root any android phone or device directly without using a computer, you will need to complete the following steps carefully. Since the framaroot apk uses different exploits depending on the processor type, device type, and device technology, we are going to have a longer tutorial for it. But then, it very easy to use and gets updated more often than other competing root without PC applications. Rooting with framaroot apk is a little bit more technical than the iRoot and kingoapp discussed above. Use the root checker app ( linked above) to confirm that your phone is now rooted.įramaroot is another useful app to root android phone and devices without a PC, it supports a wide range of devices and has proven to be able to root MTK devices.Launch from the home screen icon and click on root to get root access.Ensure that your phone is connected to the internet.Download the latest version of Kingoapp from here or from the mirror website at.To root any android without the PC using the Kingoapp method, you will need to run through the following steps:. Personally, I did root marshmallow android devices with it and It works best for devices with internet access. One good thing about the Kingoapp is the highly improved exploits it uses to root even newer devices. It is popular and works well with many brands of Android phones and tablet devices. Kingoapp works as flawlessly as the iRoot apk and is usually my second choice for rooting without the computer. Launch the root checker app to confirm rooting as the final step.Hit the root button and watch the app perform its magic (Your device may restart at this step).Launch the root app from the icon on your phone’s home screen.Install the root apk (after enabling unknown sources for your device).Send to your phone or mobile device (if downloaded with a PC).Get the latest version of it from here.It simply lets you root android without computer, and in just a few clicks. There aren’t many options or configurations needed for this root app to work. I have had tremendous success with it on different brands of phones including Tecno, Samsung, Gionee, Itel, Infinix, Sony, Mercury, Xiaomi, and several others. IRoot apk (formerly vroot apk) is usually my first choice when it comes to rooting with or without a computer. Remember to use the navigation buttons at the end of this post to get future updates on the best root apps, and other necessary tips on effective root apk files or best rooting methods. They were listed in such a way that – it answers the question of best root android apk, root tablet apps, how to root android phone manually and/or how to root android 4.4.2, 6.0.1, etc. Here are the best root without PC apps (apk) for rooting all kinds of android phones, tablets, and PDA(s). The 12 Rooting APK to Root Android Without a Computer Install the root checker app to confirm your device is now completely rooted.Select the appropriate options (Install SuperSU for Framaroot app) to completely root your device.Install the root without PC app of your choice and launch it from your phone’s home icon.Download the Root APK from the root apps list below.Enable unknown sources in your device by => Navigating to “Security settings” on newer devices or “Application settings” for older devices.They’re all you really need to be able to root any Android without a computer. To root Android phones without computers, you’d need to complete the few steps below. It is as simple as using the “ how to root without a computer” guide below. Trust me, there isn’t much technical know-how needed to use these root apps apk. If you don’t know about rooting or need tips on how to root Android with these rooting apps, please do visit one of the links above or ask us questions about how to root android without pc using the comment box below. We started by listing the best 1-Click root android software and will continue today with the best root without PC android apps that are really flawless when it comes to rooting various brands of android smartphones and tablet devices. ![]() ![]() ![]() ![]() The Radical 8 Chakra and Soul tuning forks are the weighted tuning forks meant for the sound therapy through the vibration mode.Radical 8 Chakra & Soul Purpose Cosmic Colored Weighted Healing Tuning Forks with Activator & Pouch It may be used to trace meridian lines, balance energy centers and draw Reiki symbols.It provides relaxation and helps meditate by harmonizing your energy and creating Sacred Spaces.It relieves joint pains and inflammation.It is used for the reduction of stress.It has a frequency of 528Hz for providing balance and musical healing.The QIYUN tuning fork, made up of high-grade aluminum comes along with cleaning cloth and a silicone hammer.QIYUN Tuning Fork, 528 Hz Tuning Fork with Silicone Hammer and Cleaning Cloth Solfeggio Tuning Fork for DNA Repair Healing Uses: They facilitate change and support, liberating guilt and fear and DNA repair at different frequencies.They have a frequency of 528Hz and are considered runner up after the OM tuning forks. The Solfeggio tuning forks come in a set of 9 in a convenient carrying pouch.The product includes a carry case, activator mallet, and a Buddha bead for a smoother application and deeper relaxation.It balances the right and left hemispheres of the brain to help focus and prevent the mindless chatter and ego.Alternative treatments like massage, meditation, acupuncture are enhanced with the technique.Improvement of the physical and mental performance : It helps to focus, relax and connect dots and concentrate.The Om tuning fork with 136.1Hz frequency is the ultimate healing and relaxing solution.OM Tuning Fork 136.1 HZ Weighted – with Buddha Bead Base Green for Heart Chakra Diaphony : It is the use of tuning forks in the subtle bodies, energy fields and energy centers (aura and chakras ).The bones transmit the vibrations better than any other medium of the body. Osteophony : It uses the tuning forks on the articulations and any part of the skeleton.Son puncture : It utilizes the tuning forks on the acupuncture points, hand, and feet reflexology points, median points, Shiatsu points, spinal reflex points of the body.Nonweighted tuning forks: These do not have the weights attached and are to be listened to for comfort by adjusting fork to the patient’s ear.Weighted tuning forks: These forks have a weight connected to the end of the arm of the fork that gives more vibration to the body.The technique applies sound to the physical and subtle body to open the energetic pathways where the natural life force flows, facilitating homeostasis through which healing begins. Tuning fork for healing utilizes the calibrated tuning forks to apply pressure or vibration by point stimulation in order to release tension and promote emotional stability. Sound healing therapy is the practice of using various aspects of music for the physical and mental health restoration and well being of the patient with the help of trained healing practitioners. ![]() 3/15/2024 0 Comments Fl studio free no demo![]() ![]() You can then report bugs, make feature requests and access free downloadable content: Īs you’ve probably seen, this app has mixed reviews, now let me clarify something about some of the 1-2 star comments, to those complaining about the in app purchases: you’re really complaining about the sound packs? If you were going Desktop you’d get the synths you want, yes, but you need at minimum Producer edition to actually use audio recording in FL Studio, meaning you’d have to pay $200, meanwhile here we have an app that, including microtransactions, doesn’t even hit 25% of that yet. Please help us to help you! In the App, tap 'Help > Users & Support Forums' to register FL Studio Mobile to your Image-Line account and gain access to the forum. This is identical to the App, as a plugin inside FL Studio. Install FL STUDIO 20 for macOS / Windows and you can use the FL Studio Mobile Plugin. * We use Firebase, with your permission, to receive information about how you use FL Studio Mobile to help us improve the user experience. * In app purchases - There is an in-App shop (content and additional synths). Included SuperSaw Presets: Arps, Bass, Bells, SFX, Leads, Pads, Sequences, Synths Included MiniSynth Presets: Bass, Keys, Leads, Pads, SFX, Synths Included DirectWave Instruments: Guitars, Keyboards, Orchestral, Synth, Bass, Synth Keyboards, Synth Leads, Synth Pads, Sliced, Drums, Drum Kits and Effects. Included Drum Samples: Cymbals, Hats, Kicks, Snares, Toms, Percussion, Risers, SFX ![]() You can install your own samples and don’t need to buy content.Īll Instrument modules are included: Drum Sampler, DirectWave Sample Player, GMS (Groove Machine Synth), Transistor Bass, MiniSynth & SuperSaw.Īll Effect modules are included: Analyzer (visual), Auto Ducker, Auto-Pitch (pitch correction), Chorus, Compressor, Limiter, Distortion, Parametric Equalizer, Graphic Equalizer, Flanger, Reverb, Tuner (Guitar/Vocal/Inst), High-Pass/Low-Pass/Band-Pass/Formant (Vox) Filters, Delays, Phaser and Stereoizer. * Load your projects in the FL STUDIO* FREE 'Plugin' Version of this App#įL Studio Mobile includes in-app purchases for the DirectWave sample player. * Share your songs via Sync to other Mobile 3 devices / installations * Audio recording (external and internal sources) * IAA App support (In/Out), Audiobus support (In/Out) * User interface configurable with all screen resolutions and sizes. ![]() * Share your songs via Wi-Fi or Cloud to other Mobile 3 installations * Save and load WAV, MP3, AAC*, FLAC, MIDI Edit notes or capture recorded performances. * Mixer: Per-track mute, solo, effect bus, pan and volume adjustment * MIDI file import and Export (Single-track or Multi-track) * MIDI controller support (class compliant). * Load projects in the FL STUDIO** FREE Plugin version of this App * Instrument modules (see Included Content) * High quality synthesizers, sampler, drum kits & sliced-loop beats * Full-screen MacBook and iMac Trackpad and Mouse support. * Audio recording, track-length stem/wav import Record, sequence, edit, mix and render complete songs. Create and save complete multi-track music projects on your iPad, iPhone or Mac. ![]() 3/15/2024 0 Comments Browse airfoil database![]() ![]() 29 The LSB can be classified into several types (Owen and Klanfer 30), and “short” and “long” LSBs depend on the length of the bubble in comparison with the thickness of the displacement in it during separation. The classical semi-empirical model of the LSB is not perfect for example, there is not simply one type of structure of the LSB at a low Reynolds number. This region is usually called the “dead air region.” In the latter part of the bubble, the stronger circulation velocity and an abrupt reattachment of the shear layer lead to a rapid increase in surface pressure. As a result, the gradient of streamwise pressure is nearly zero and results in the plateau pressure being distributed. 24–26 Near the separation point, the recirculation region is characterized by slow-moving reverse flow. This pressure distribution is clearly different from that of inviscid flow. 3), the distribution of plateau pressure from the separation point to the transition point can be observed, and the pressure rapidly recovers from the transition point to the reattachment point. Combined with the pressure distribution (see Fig. The region of recirculation flow can be divided into two sub-regions relative to the average position of transition. 23 The transition in the separated shear layer is reduced to a point rather than a region. It is described by the mean dividing streamline, which intersects the surface at the separation and the reattachment points. The classic two-dimensional (2D) schematic diagram of the laminar separation bubble is shown in Fig. ![]() However, because such flows involve many problems, such as the mechanism of the triggering effect of laminar flow separation, the transition mechanism, and complex nonlinear aerodynamic characteristics, few systematic reviews of the issue are available. Some excellent reviews 18,19 of flows over an airfoil at low Reynolds numbers have been published. Mueller 17 noted in a review that laminar separation bubbles have a significant influence on the aerodynamic performance of airfoils at low Reynolds numbers and it is necessary to accurately predict the occurrence and evolution of the separation bubbles when designing highly efficient low-speed airfoils. Lissaman 5 subsequently summarized the problems of an airfoil at a low Reynolds number based on mechanical theory, experimental research, and theoretical design and concluded that flow over the airfoil in this case is closely related to separation and transition. 16 It describes the separation, transition, reattachment, and other physical phenomena in the laminar separation bubble (LSB). The theoretical basis for the aerodynamics at a low Reynolds number is the laminar separation bubble (LSB) theory proposed by Horton et al. Furthermore, it enables the cruise performance and drag divergence Mach number to be predicted with only one simulation of the cruise point, which will greatly save the computational cost of optimizations.Flow at a low Reynolds number has been widely researched as a branch of aerodynamics. It indicates that the drag divergence Mach number can be increased by obtaining a shock wave that is further upstream in the detailed design. Compared with Korn's equation, the discovered correlation reduces the maximum prediction error by approximately 40%. ![]() A new linear correlation is discovered and validated by existed airfoil databases. Correlation screening and multivariate regression are carried out to discover knowledge about the airfoil drag divergence Mach number and pressure distribution features. This paper designs a supercritical airfoil database that covers the typical free stream Mach number, angle of attack, lift coefficient, and geometry of modern transonic commercial aircraft. However, it neither reveals the key factors of fluid features on the drag divergence nor contributes to the detailed design. It is very helpful in the aircraft initial design. For example, Korn's equation predicts the airfoil drag divergence Mach number using the airfoil maximum thickness and the lift coefficient. Aerodynamic rules and knowledge are often obtained through theoretical research and experiments, which have contributed greatly to aircraft design. ![]() |
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