User:Ar8rn/sandbox

Article Evaluation

• Is everything in the article relevant to the article topic? Is there anything that distracted you?
• Is the article neutral? Are there any claims, or frames, that appear heavily biased toward a particular position?
• Are there viewpoints that are overrepresented, or underrepresented?
• Check a few citations. Do the links work? Does the source support the claims in the article?
• Is each fact referenced with an appropriate, reliable reference? Where does the information come from? Are these neutral sources? If biased, is that bias noted?
• Is any information out of date? Is anything missing that could be added?
• Check out the Talk page of the article. What kinds of conversations, if any, are going on behind the scenes about how to represent this topic?
• How is the article rated? Is it a part of any WikiProjects?
• How does the way Wikipedia discusses this topic differ from the way we've talked about it in class?

Transonic Evaluation

• Everything seems relevant, but there are several pieces of uncited information and misinformation, and the article as a whole is very short
• No obvious biases that I can see, but the lack of citations is discouraging
• Despite the brevity of the article, almost a third of it is dedicated to “transonic flows” in astrophysics, as in around stars and black holes. Very little on relevance to aircraft
• The one link is a good, recent, relevant link, yes, the other two sources are books with relevant titles
• Very little citation throughout the article, pretty much the whole article needs to be written (and some of it rewritten with appropriate citations). There are no mentions of analytical approaches to transonic flow or historical examples of the study of transonic flow over aircraft. I’ve browsed around articles of the same topic (Mach number, supercritical airfoils) and while those articles incidentally cover some of this, the dedicated page for transonic flow does not
• There is only one conversation about astrophysics, and none on aerodynamics
• Start class; physics and aviation wikiprojects
• There just... aren’t any citations. 3 sources, 2 of which are for astrophysics when “transonic” is generally regarded as a topic in aerodynamics and aircraft (it’s a flow regime between a range of Mach numbers around 1, specifically the range of flight Mach numbers where there are regions of both subsonic and supersonic flow around the object/aircraft, and has been a challenge and limitation on many aircraft for decades)

Transonic Drafts

Introduction

Transonic (or transsonic) flow is air flowing around an object at a speed that generates regions of both subsonic and supersonic airflow around that object. The exact range of speeds depends on the object's critical Mach number, but transonic flow is seen at flight speeds close to the speed of sound (343 m/s at sea level), typically between Mach 0.8 and 1.2. Ar8rn (talk) 07:33, 6 March 2021 (UTC)

History of Mathematical Analysis

Streamlines for three airflow regimes (black lines) around a nondescript blunt body (blue).

Prior to the advent of powerful computers, even the simplest forms of the compressible flow equations were difficult to solve due to their nonlinearity. A common assumption used to circumvent this nonlinearity is that disturbances within the flow are relatively small, which allows mathematicians and engineers to linearize the compressible flow equations into a relatively easily solvable set of differential equations for either wholly subsonic or supersonic flows. This assumption is fundamentally untrue for transonic flows because the disturbance caused by an object is much larger than in subsonic or supersonic flows; a flow speed close to or at Mach 1 does not allow the streamtubes (3D flow paths) to contract enough around the object to minimize the disturbance, and thus the disturbance propagates. Aerodynamicists struggled during the earlier studies of transonic flow because the then-current theory implied that these disturbances– and thus drag– approached infinity as local Mach number approached 1, an obviously unrealistic result which could not be remedied using known methods.

One of the first methods used to circumvent the nonlinearity of transonic flow models was the hodograph transformation. This concept was originally explored in 1923 by an Italian mathematician named Francesco Tricomi, who used the transformation to simplify the compressible flow equations and prove that they were solvable. The hodograph transformation itself was also explored by both Ludwig Prandtl and O.G. Tietjen's textbooks in 1929 and by Adolf Busemann in 1937, though neither applied this method specifically to transonic flow.

Gottfried Guderley, a German mathematician and engineer at Braunschweig, discovered Tricomi's work in the process of applying the hodograph method to transonic flow near the end of World War II. He focused on the nonlinear thin-airfoil compressible flow equations, the same as what Tricomi derived, though his goal of using these equations to solve flow over an airfoil presented unique challenges. Guderley and Hideo Yoshihara, along with some input from Busemann, later used a singular solution of Tricomi's equations to analytically solve the behavior of transonic flow over a double wedge airfoil, the first to do so with only the assumptions of thin-airfoil theory. Ar8rn (talk) 07:15, 10 March 2021 (UTC)

Although successful, Guderley's work was still focused on the theoretical, and only resulted in a single solution for a double wedge airfoil at Mach 1. Walter Vincenti, an American engineer at Ames Laboratory, aimed to supplement Guderley's Mach 1 work with numerical solutions that would cover the range of transonic speeds between Mach 1 and wholly supersonic flow. Vincenti and his assistants drew upon the work of Howard Emmons as well as Tricomi's original equations to complete a set of four numerical solutions for the drag over a double wedge airfoil in transonic flow above Mach 1. The gap between subsonic and Mach 1 flow was later covered by both Julian Cole and Leon Trilling, completing the transonic behavior of the airfoil by the early 1950's.

Discovering Transonic Airflow

Issues with aircraft flight relating to speed first appeared during the supersonic era in 1941. Ralph Virden, a test pilot, crashed in a fatal plane accident. He lost control of the plane when a shock wave developed over the wing and caused it to stall. Virden flew well below the speed of sound at Mach 0.675, so this brought forth the issue of transonic airflow around the plane. Kelley Johnson was one of to first engineers to investigate the effect of flow compressibility on aircraft. Wind tunnels at the time did not have the capability to simulate airspeeds close to Mach 1. The term "sound barrier" was coined by British Researcher W.F. Hilton, and over the course of WWII a lot of research went into testing planes as they approached the sound barrier and the effects of transonic airflow over aircraft.

The term "transonic" was defined to mean "across the speed of sound", and was invented by NACA director Hugh Dryden and Theodore von Kármán of the California Institute of Technology. Epitz (talk) 00:29, 15 March 2021 (UTC)

Changes in Aircraft

(change section in intro about airflows)

Initially NACA designed dive flaps to help stabilize aircraft in transonic flight. This small flap on the underside of the plane slowed the plane to prevent it from reaching a speed that caused problems, but this design only delayed finding a solution to aircraft flying at higher speeds.

After World War II major changes in aircraft design were seen to improve transonic flight. The main way to stabilize aircraft was to reduce the speed of the airflow around the wing by changing the ratio between thickness and chord. One solution to prevent shock waves was swept wings, since the airflow would hit the wing at an angle and thus increase the distance it travels going over the wing, effectively decreasing the thickness/chord ratio. Airfoils were also made flatter on the top to prevent the flow from accelerating to supersonic speeds and to further reduce the distance over the wing. Later on, Richard Whitcomb designed the supercritical airfoil.

- talk more about airfoil theory Epitz (talk) 00:29, 15 March 2021 (UTC)

Peer reviewed by Barelybeard (talk) 16:51, 19 March 2021 (UTC)

1.What does the article do well? Is there anything from your review that impressed you? Any turn of phrase that described the subject in a clear way?

Epitz: you have 3 sources, which is a good start, and provides a lot of information it seems. You do a good job of explaining the different wings developed as well. The link to “chord” is very helpful, and perhaps adding more links like that would bolster the readers quick understanding, in case they don’t understand other concepts like the sound barrier, machs, maybe a link to Ralph Virden. You overall have a really good draft here, not bullet points, full paragraphs, and it makes it easy to follow.

Ar8rn: your sections are clearly representative of the content under it. You link a lot of the people you mention and some concepts like compressible flow, which is great if the reader wants to know more about these people.

2.What changes would you suggest the author apply to the article? Why would those changes be an improvement?

Epitz: Some general spelling and grammatical mishaps. “Kelley Johnson was one of to first engineers “ to->the. “over the course of WWII a lot of research went into testing…” seems too vague for an encyclopedia article. How much is “a lot”? Do we have data like “on X amount of money went into research in the next 10 years” etc.? The section “discovering transonic airflow” also talks a bit more than just the discovery (ralph Virden crashing), but also about the coining of terms, transonic, and sound barrier, and a bit about research done. Perhaps breaking these up into their own sections (given you can get a few more sources, and expand a bit more) would probably help the reader stay focused on what the section is meant to focus on. It also seems like you are about to dive into the idea of airfoil wings more specifically- If those are a major innovation, it may be useful to make that a section, to dedicate a lot of information on them.

Ar8rn: The introduction should have a reference or two, but none is found. The first paragraph of the history of mathematical analysis is very heavy in jargon (which may be unavoidable, but maybe changing a few words here and there could help the reader).

“One of the first methods used to circumvent the nonlinearity of transonic flow models was the hodograph transformation. This concept was originally explored in 1923 by an Italian mathematician named Francesco Tricomi, who used the transformation to simplify the compressible flow equations and prove that they were solvable. The hodograph transformation itself was also explored by both Ludwig Prandtl and O.G. Tietjen's textbooks in 1929 and by Adolf Busemann in 1937, though neither applied this method specifically to transonic flow.[1]” This could use more references, after each sentence, even if its all for the [1] citation. The reader, reading along will see no citation until the end, which could as far as the reader knows, be for the last sentence, and not the whole paragraph.

3. What's the most important thing the author could do to improve the article?

Epitz: organizing and providing new sections if necessary (if say the original article has more information on the topics of development, or airfoil wings), or broadening the header to make more sense with all the information under it. General spelling and grammatical changes would help a bit.

Ar8rn: trying to simplify the reading would help the reader tremendously. Eliminating jargon as best you can into concepts that the average person could understand would be the most important change.

Personal takeaways

Epitz: from looking at your draft, it shows me how much easier it is to follow being in paragraph form than bullet points. I currently have a series of bullet points under headings, but have yet to integrate them all together to provide a full narrative/explanation.

Ar8rn: When thinking about the history of my topic (alkahest), I should focus on how one alchemist led to the innovation and influence of others

Response to Peer Review

Thank you for the honest review Barelybeard! For your first comment, the introduction does have a citation, it’s just only shown in the main article since that’s the addition I made early on. I’ve added it to the sandbox as well for clarity.

For the second point: yeah, jargon is a huge problem. Like you mention some things can’t be removed, such as the more common (if technical) terms—e.g. “differential equations”, probably even “linearize”—but I definitely need to go back and expand and link where I can. I’ve been planning to draw from a couple other sources to supplement what’s there with more descriptive explanations (the first paragraph of “History of Mathematical Analysis” actually has this, seen from the explanation of disturbances), but it needs more work in this regard. Ar8rn (talk) 16:28, 2 April 2021 (UTC)

(This response is also from the peer review in my sandbox (epitz) from Bayerite)

Both peer reviewers talked about the need to improve my grammar so I will work on improving that along with my wording to make sure it is as clear as possible.

As I continue to do more research I will include more sources and make sure all sentences end with a cited source. On terms not explained I'll add links to other Wikipedia articles if there are pages. Specially responding to Bayerite comments they mentioned that terms like “swept wings” and “airfoils” were not explained I will add more details about the aircraft design developments and want to connect those advancements to how they impacted aircraft designs used more recently. However, some of the people mentioned do not necessarily add value to explaining the topic but are helpful in explaining the history and progression of how transonic airflow was discovered and dealt with. I do not want the article to stray too much into other topics. Above they also mentioned making more board heading and I think that will help me organize the paragraphs in my section better. I'm glad that overall my organization makes sense going from defining the problem to solutions implemented. I will stick to that formatting when I add more details into this section. Overall, as I continue to do more research, I want to include more sources and make sure all my sentences are cited. Epitz (talk) 16:39, 2 April 2021 (UTC)

Transonic Notes

Things to add/edit:

• Citations to introduction
• History of study
• Modern analytical approaches
• Effects on design of aircraft and propellers (mostly summary & links to supercritical airfoil, critical mach)
• Airshows / demonstrations? Seems like a good lead in to talking about condensation clouds too

Sources (citations):

1. Fundamentals of Aerodynamics, 6e (ISBN: 1259129918)
2. Boundaries, Contingencies, and Rigor (https://www.jstor.org/stable/3182966)
3. Fluid Dynamics for the Study of Transonic Flow (ISBN: 9780195362954)
4. Introduction to Transonic Aerodynamics (ISBN: 9789401797474)
5. Aerodynamic Principles of Flight Vehicles (ISBN: 9781600869174) - Good source for uncited stuff in intro

Source 2 goes through the history of the math with some explanations, while source 3 goes through the ACTUAL math (very nasty) with some more in-depth conceptual explanations but no historical facts.

Picture: p. 32, source 3

Intro

Transonic (or transsonic) flow is air flowing around an object at a speed that generates regions of both subsonic and supersonic airflow around that object. The exact range of speeds depends on the object's critical Mach number, but transonic flow is seen at flight speeds close to the speed of sound (343 m/s at sea level), typically between Mach 0.8 and 1.2. (Source 1, p 757)

Most modern jet powered aircraft are engineered to operate at transonic air speeds. Transonic airspeeds see a rapid increase in wave drag due to pockets of supersonic flow ending in shock waves, and it is the fuel costs of the drag that typically limits the airspeed. Attempts to reduce wave drag can be seen on all high-speed aircraft. Most notable is the use of swept wings, but another common form is a wasp-waist fuselage as a side effect of the Whitcomb area rule.

Math

- Being in the transonic regime strips away some important normal assumptions used in both wholly subsonic and supersonic flow analysis, mainly that the object being studied is small or thin enough that its disturbance within the flow is correspondingly small. These assumptions turn a nasty nonlinear set of diff eq's into a neater (if still somewhat nasty) set of linear diff eq's. As seen in the diagram, these assumptions are fundamentally untrue for transonic flow because the disturbance is much larger than in subsonic or supersonic flow; a flow speed close to or at Mach 1 does not allow the flow streamtubes (3D flow paths) to contract enough to minimize the disturbance, and thus the disturbance propagates. (p 32-33) Mathematically what happens is the thin-airfoil compressible flow equations used to describe airflow are no longer linear (even assuming small perturbation), i.e. superposition no longer applies, and everything becomes messy again. (p 38)

- WWII era mathematicians and engineers initially wanted to just use the simplified linear compressible flow equations/solutions with a nonlinear term subbed in to make the math work for transonic flow, but that was too big of a shortcut to take. (page 38 source 3?)

- Their next guess was to do a hodograph transformation (of rate of climb and climb angle fame-- it's a tool still used today!). Where normally the motion of an object is described by its path in the x-y plane with a specified time at each point (and therefore velocity), the hodograph plane describes motion graphically in terms of x and y velocity components, u and v. This concept was originally explored in 1923 by an Italian mathematician named Francesco Tricomi, who used the transformation to simplify the nonlinear compressible flow equations as much as possible. His equations were supposedly very interesting from a mathematical perspective (the dude was a stereotype of 'enlightened mathematician divorced from reality'), which was why he worked with them-- he wasn't actually interested in the physics, just the math. He proved that these equations were solvable, though.

- The hodograph transformation was explored by both Ludwig Prandtl and O.G. Tietjen's textbooks in 1929 and by Adolf Busemann in 1937, though neither applied this method specifically to transonic flow. (textbooks are "fundamentals of hydro and aeromechanics" and "applied hydro and aeromechanics")

- Gottfried Guderley, a German mathematician and engineer at Braunschweig, discovered Tricomi's work in the process of applying the hodograph method to transonic flow near the end of World War II. He focused on the nonlinear thin-airfoil compressible flow equations (only thin-airfoil, not the general nonlinear compressible flow equations), which is what Tricomi derived. Guderley and Hideo Yoshihara later used a singular solution of Tricomi's equations to analytically solve the behavior of transonic flow over a double wedge airfoil, the first to do so with only the assumptions of thin-airfoil theory.

[insert actual equations? needs some more textbook/reference love]

- Although successful, Guderley's work was still focused on the theoretical, and only resulted in a single solution for a double wedge airfoil at Mach 1. Walter Vincenti aimed to supplement Guderley's Mach 1 work with numerical solutions that would cover the range of transonic speeds between Mach 1 and wholly supersonic flow. Vincenti drew upon the work of Howard Emmons as well as Tricomi's original equations to complete a set of four numerical solutions for the drag over a double wedge airfoil in transonic flow above Mach 1. The gap between subsonic and Mach 1 flow was later covered by both Julian Cole and Leon Trilling, completing the transonic behavior of the airfoil by the early 1950's.

- Theodore von Kármán, Klaus Oswatitsch and K. Wieghart