In naval architecture and aerospace engineering, the fineness ratio is the ratio of the length of a body to its maximum width. Shapes that are short and wide have a low fineness ratio, those that are long and narrow have high fineness ratios. Aircraft that spend time at supersonic speeds, e.g. the Concorde, generally have high fineness ratios. At speeds below critical mach, one of the primary forms of drag is skin friction. As the name implies, this is drag caused by the interaction of the airflow with the aircraft's skin. To minimize this drag, the aircraft should be designed to minimize the exposed skin area, or "wetted surface". One solution to this problem is constructing an "egg shaped" fuselage, for example as used on the home-built Questair Venture. Theoretical ideal fineness ratios in subsonic aircraft fuselages are typically found at about 6:1, however this may be compromised by other design considerations such as seating or freight size requirements. Because a higher fineness fuselage can have reduced tail surfaces, this ideal ratio can practically be increased to 8:1. Most aircraft have fineness ratios significantly greater than this, however. This is often due to the competing need to place the tail control surfaces at the end of a longer moment arm to increase their effectiveness. Reducing the length of the fuselage would require larger controls, which would offset the drag savings from using the ideal fineness ratio. An example of a high-performance design with an imperfect fineness ratio is the Lancair. In other cases, the designer is forced to use a non-ideal design due to outside factors such as seating arrangements or cargo pallet sizes. Modern airliners often have fineness ratios much higher than ideal, a side effect of their cylindrical cross-section which is selected for strength, as well as providing a single width to simplify seating layout and air cargo handling. As an aircraft approaches the speed of sound, shock waves form on areas of greater curvature. These shock waves radiate away energy that the engines must supply, energy that does not go into making the aircraft go faster. This appears to be a new form of drag—referred to as wave drag—which peaks at about three times the drag at speeds even slightly below the critical mach. In order to minimize the wave drag, the curvature of the aircraft should be kept to a minimum, which implies much higher fineness ratios. This is why high-speed aircraft have long pointed noses and tails, and cockpit canopies that are flush to the fuselage line. More technically, the best possible performance for a supersonic design is typified by two "perfect shapes", the Sears-Haack body which is pointed at both ends, or the von Kármán ogive, which has a blunt tail. Examples of the latter design include the Concorde, F-104 Starfighter and XB-70 Valkyrie, although to some degree practically every post-World War II interceptor aircraft featured such a design. Missile designers are even less interested in low-speed performance, and missiles generally have higher fineness ratios than most aircraft. The introduction of aircraft with higher fineness ratios also introduced a new form of instability, inertial coupling. As the engines and cockpit moved away from the aircraft's center of mass, the roll inertia of these masses grew to be able to overwhelm the power of the aerodynamic surfaces. A variety of methods are used to combat this effect, including oversized controls and stability augmentation systems. (Wikipedia).
This video defines a ratio and provides several examples on how to write a ratio and shows how to simplify a ratio. http://mathispower4u.wordpress.com/
From playlist Ratios and Rates
This is a short video tutorial on the basics of ratios. For interactive applets, worksheets, and more videos go to http://www.mathvillage.info
From playlist All about ratios and proportions
Introduction to Ratios (2 of 2: Equivalent Ratios)
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From playlist Basic Ratios & Rates
This video introduces the Golden ratio and provides several examples of where the Golden ratio appears. http:mathispower4u.com
From playlist Mathematics General Interest
Identifying and solving proportions
This is a short video tutorial on identifying and solving proportions. For interactive applets, worksheets, and more videos go to http://www.mathvillage.info
From playlist All about ratios and proportions
This is a short video tutorial on equivalent ratios. ✤ ✤ ✤ INTERACTIVE APPLETS AND WORKSHEETS ✤ ✤ ✤ http://fearlessmath.net ✤ ✤ ✤ FOLLOW ME ON TWITTER ✤ ✤ ✤ http://twitter.com/dhabecker
From playlist All about ratios and proportions
Ratios Introduction - what are ratios?
Ratios are used to compare different quantities. In this introduction to ratios we will look at what ratios are, how we deal with ratios of different measurement units and that ratios can be simplified. To donate to the tecmath channel:https://paypal.me/tecmath To support tecmath on Pa
From playlist Ratios
This is a short video tutorial on simplifying ratios. For interactive applets, worksheets, and more videos go to http://www.mathvillage.info
From playlist All about ratios and proportions
Modeling ticket fines with exponential function | Algebra II | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:exponential-growth-decay/x2f8bb11595b61c86:exponential-functions-from-tables-graphs/v/modeling-ticket-fines-with-exponential-function Pra
From playlist Mathematics I | High School Math | Khan Academy
Janet Scheel: "High Rayleigh Number Convection in a Slender Cylinder for Prandtl Number of 1"
Transport and Mixing in Complex and Turbulent Flows 2021 "High Rayleigh Number Convection in a Slender Cylinder for Prandtl Number of 1" Janet Scheel - Occidental College Abstract: We report results from direct numerical simulations of turbulent Rayleigh-Benard convection for a Prandtl n
From playlist Transport and Mixing in Complex and Turbulent Flows 2021
Power series are functions -- Calculus II
This lecture is on Calculus II. It follows Part II of the book Calculus Illustrated by Peter Saveliev. The text of the book can be found at http://calculus123.com.
From playlist Calculus II
The Golden Ratio: Is It Myth or Math?
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From playlist Be Smart - LATEST EPISODES!
What's Fine-Tuning in Cosmology? | Episode 1902 | Closer To Truth
What is fine-tuning in cosmology? Here’s the claim: cosmic conditions that allow complex structures — galaxies, stars, planets, people — depend on a few “constants of nature” lying within tight ranges of values. But is fine-tuning valid? Featuring interviews with Geraint Lewis, Luke Barnes
From playlist Closer To Truth | Season 19
ChatGPT and Reinforcement Learning
ChatGPT + Reinforcement Learning. We're also going to talk about the method ChatGPT learns to be so factual + non-toxic: Proximal Policy Optimization ABOUT ME ⭕ Subscribe: https://www.youtube.com/c/CodeEmporium?sub_confirmation=1 📚 Medium Blog: https://medium.com/@dataemporium 💻 Github: h
From playlist ChatGPT
GCSE Science Revision Chemistry "Nanoparticles" (Triple)
Find my revision workbooks here: https://www.freesciencelessons.co.uk/workbooks In this video, we look at nanoparticles. First we explore the relative sizes of particles including nanoparticles. We then look at the surface area : volume ratio of particles and link this to the use of nanop
From playlist 9-1 GCSE Chemistry Paper 1 Structure and Bonding
Advanced Hydraulics by Dr. Suresh A Kartha,Department of Civil Engineering,IIT Guwahati.For more details on NPTEL visit http://nptel.iitm.ac.in
From playlist IIT Guwahati: Advanced Hydraulics | CosmoLearning.org Civil Engineering
Three ways to solve a proportion
This is a short video tutorial on three ways to solve a proportion. For interactive applets, worksheets, and more videos go to http://www.mathvillage.info
From playlist All about ratios and proportions
99 Problems #7 - GCSE Edexcel Maths - Q73-80 - exam style questions & revision
Q73-80 of 99 problems of exam style questions for the edexcel higher tier. paper - http://bit.ly/34leFM2 mark scheme - http://bit.ly/2OguJsZ full playlist with walkthrough of the whole paper: https://www.youtube.com/watch?v=yVUZhPyZexY&list=PLm4auYJQkF_oWOza0GJGTjbccZpxrNKyr Topics co
From playlist 99 problems - GCSE Higher revision