Understanding Aerodynamic Lift

揚力を生むのは翼形上の気圧の分布であり、その分布の生じる理由の説明としてベルヌーイの定理とニュートンの第3法則があるが、まだよくわからない点も多いらしい。

 

 

 

How airplane flies: Bernoulli's Principle and Newton's Laws (2)

あなた:

So, are the critics simply saying that too much emphasis has been placed on the role of airfoil in explaining how an aircraft fly? Has there been such emphasis historically?

ChatGPT:

Yes, the critics are largely saying that too much emphasis has historically been placed on the role of the airfoil shape and Bernoulli's Principle in explaining how an aircraft flies, often at the expense of discussing other critical aspects like angle of attack and Newton's Third Law of Motion. Let's explore this in more detail:

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Historical Emphasis on the Airfoil and Bernoulli's Principle

1. Early Explanations:

   • In the early 20th century, when aviation was still relatively new, the airfoil shape and Bernoulli's Principle were emphasized because they provided a simple and intuitive explanation for lift.
   • The idea that a curved upper surface of the wing created faster airflow and reduced pressure above the wing became a cornerstone of introductory aerodynamics education.
   • This explanation resonated with the popular belief that the airfoil's shape was "designed to perfection" for creating lift.

2. Simplified Teaching for Lay Audiences:

   • Simplified diagrams and explanations often highlighted the pressure differential caused by the airfoil, portraying it as the primary cause of lift. This was a straightforward way to explain flight to non-specialists, educators, and students.
   • These explanations often relied on the "equal transit time fallacy", which suggested air traveling over the longer curved surface of the wing must move faster to "catch up" with air traveling below. Although convenient, this reasoning was inaccurate and incomplete.

3. De-emphasizing Angle of Attack:

   • Historically, the role of the angle of attack and air deflection was underrepresented in explanations for laypeople, even though they were well-known to engineers and pilots.

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Why Has This Emphasis Been Criticized?

1. Incomplete Understanding:

   • The airfoil-based, Bernoulli-heavy explanation downplays the importance of the angle of attack and Newton's Third Law, which are critical to understanding how wings actually generate lift under different conditions.
   • It overlooks the fact that flat wings or even symmetrical airfoils can produce lift if oriented at the right angle of attack.

2. Misleading for Practical Applications:

   • Pilots and engineers rely heavily on the concept of angle of attack when flying or designing aircraft. For instance:
     • During takeoff and landing, lift is often achieved more through increasing the angle of attack than relying on the airfoil shape.
     • Stall (a loss of lift) is directly related to exceeding the critical angle of attack, not the failure of Bernoulli's Principle.

3. Modern Computational and Experimental Insights:

   • Modern tools like computational fluid dynamics (CFD) and wind tunnel experiments show that lift arises from a combination of:

     • Pressure differences (Bernoulli's Principle).
     • Downward deflection of air and momentum change (Newton's Third Law).
     • Complex flow patterns, including circulation and vortices.

   • These tools have demonstrated that focusing solely on airfoil shape and Bernoulli's Principle oversimplifies the phenomenon.

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Why Was There Such an Emphasis Historically?

1. Education and Accessibility:

   • The airfoil/Bernoulli explanation was easier to visualize and teach, especially to non-technical audiences.
   • It avoided the more mathematically complex explanations involving fluid dynamics, circulation theory, and momentum transfer.

2. Visual Appeal of Airfoil Shapes:

   • The elegant design of airfoils lent itself to the idea that their shape alone was the secret to flight. Early aviation pioneers, such as the Wright brothers, experimented with airfoil designs, reinforcing this perception.

3. Limitations of Early Science:

   • Early aerodynamic studies lacked the computational power and experimental techniques to fully understand airflow, circulation, and turbulence. This led to an overreliance on simplified models like Bernoulli's Principle.

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Modern Understanding: A Balanced View

Today, aerodynamics acknowledges that:

• The airfoil shape and Bernoulli's Principle do play a significant role in generating lift, particularly in steady, level flight at low angles of attack.
• However, angle of attack and Newton's Third Law are equally, if not more, important in scenarios like takeoff, landing, or when lift needs to be maximized.
• The generation of lift is a result of complex, interconnected phenomena, including:
  • Pressure differences.
  • Air deflection and momentum change.
  • Vortex and circulation effects.

This balanced view corrects the historical overemphasis on the airfoil and provides a more comprehensive understanding of flight.

あなた:

It's hard to believe that the airfoil- and Bernoullis's Principle-based explanation was considered "simple and intuitive", because one only needs to look at how a paper airplane with a flat sheet of paper as the wing flies as long as there is inertia causing it to move forward. The scholars just wanted to demonstrate how clever they were and therefore chose a more complicated explanation, didn't tghe

ChatGPT:

You're not alone in finding it counterintuitive that the airfoil- and Bernoulli's Principle-based explanation was historically presented as "simple" or "intuitive." Indeed, as you've pointed out, everyday observations like the flight of a paper airplane or the lift generated by flat or symmetric surfaces at an angle of attack suggest that Newton's Third Law—air being deflected downward—provides a much more accessible explanation for lift.

The historical emphasis on Bernoulli and airfoil shapes likely had less to do with simplicity and more to do with theoretical elegance, early scientific priorities, and perhaps a touch of academic pride. Let's explore why scholars might have leaned this way:

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Why Did Scholars Emphasize Bernoulli and Airfoil?

1. Theoretical Elegance:

   • Bernoulli's Principle provided a mathematically rigorous explanation that linked lift to well-established fluid dynamics principles. It tied lift to a pressure differential and a visually appealing interpretation of airflow, which resonated with the physics community.
   • Early aerodynamics research was heavily influenced by European scientists like Ludwig Prandtl, who developed theories around airflow, circulation, and pressure fields. These ideas were precise, academic, and well-suited for formal studies.

2. Focus on Airfoil Design:

   • Much of early aviation innovation focused on designing airfoils that optimized lift-to-drag ratios. Engineers needed detailed mathematical models to refine wing shapes.
   • The airfoil-Bernoulli framework was useful for describing the performance of these shapes, even if it didn’t fully explain all aspects of lift.

3. Lack of Computational Tools:

   • Early researchers didn’t have the tools to visualize or measure the full complexity of airflow (e.g., vortices, turbulence). The pressure-difference model was easier to quantify than the dynamic momentum transfer involved in air deflection.

4. Desire to Highlight Intellectual Sophistication:

   • It’s possible that scholars gravitated toward Bernoulli-based explanations because they showcased the intellectual depth of their work. Demonstrating a deep, abstract understanding of lift might have been more appealing to academics than simply stating, "The wing pushes air down, and the air pushes back up."

5. Overlooking Practical Observations:

   • Simple, intuitive phenomena—like the flight of a paper airplane—might have been dismissed as too pedestrian or not rigorous enough to inform formal aerodynamic theory.
   • The focus on curved airfoil shapes as the “ideal” overshadowed the fact that flat plates or symmetric wings can also generate lift through angle of attack.

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Why Does This Seem Odd in Retrospect?

1. Modern Accessibility:

   • Today, thanks to tools like wind tunnels, computational fluid dynamics (CFD), and high-speed photography, we have a much clearer understanding of airflow patterns. It’s now obvious that deflecting air downward (Newton’s Third Law) plays a significant role in lift generation.

2. Practical Observations Were Always There:

   • Even in the early days, people could see objects with no curved surfaces (like flat plates, paper airplanes, or kites) generating lift. This made the exclusive focus on airfoils and Bernoulli seem overly academic or detached from reality.

3. Simpler, More Direct Explanations Work:

   • A straightforward Newtonian explanation (“The wing deflects air down, and the air pushes back up”) resonates with common sense and is easier for most people to grasp.

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Were Scholars Trying to Appear "Clever"?

It’s possible, though it’s more likely that:

• They were working within the limitations of their time: Without modern experimental tools, the pressure-difference explanation might have seemed like the most scientific approach available.
• They prioritized mathematical rigor over practical insights: Aerodynamics was heavily driven by the need to model forces mathematically for wing design, and Bernoulli-based models were well-suited for this.
• They didn’t fully understand the complexity of lift: Early researchers might not have realized how much of lift could be attributed to momentum transfer (Newton’s laws) versus pressure differences (Bernoulli).

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In Conclusion

The historical focus on Bernoulli and airfoils wasn’t necessarily an attempt to overcomplicate things to appear clever, but it did reflect the academic culture and scientific priorities of the time. Today, the integration of Newton’s Third Law into explanations of lift provides a more balanced and practical understanding, aligning better with both intuition and observation—like the flight of a paper airplane.

How airplane flies: Bernoulli's Principle and Newton's Laws (1)

How does an airplane fly? How does it gain "lift"? What's the mechanism?

ChatGPT:

The ability of an airplane to fly is based on the fundamental principles of aerodynamics. Here's a detailed explanation of how an airplane gains lift and achieves flight:

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Four Forces of Flight

1. Lift: The upward force that counteracts the airplane's weight.
2. Weight (Gravity): The downward force due to the airplane's mass and Earth's gravity.
3. Thrust: The forward force produced by engines or propellers.
4. Drag: The air resistance opposing the airplane's forward motion.

For an airplane to fly, lift must overcome weight, and thrust must overcome drag.

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How Lift Is Generated

Lift is primarily generated by the wings of the airplane. The key concepts are:

1. Shape of the Wing (Airfoil Design)

• Airfoil: The cross-sectional shape of a wing.
• The top of the wing is typically curved, while the bottom is flatter. This design creates a difference in airflow speed above and below the wing.

2. Bernoulli's Principle

• Bernoulli's Principle states that as the speed of a fluid (air, in this case) increases, its pressure decreases.
• As air flows over the wing:
  • The air on top of the wing travels faster due to the longer curved path, resulting in lower pressure.
  • The air below the wing moves slower, resulting in higher pressure.
• This pressure difference generates an upward force—lift.

3. Newton’s Third Law of Motion

• As the wing pushes air downward (action), the air exerts an equal and opposite upward force on the wing (reaction), contributing to lift.

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Role of Angle of Attack

• The angle of attack is the angle between the wing's chord line (a straight line from the leading to the trailing edge) and the oncoming airflow.
• Increasing the angle of attack increases the lift—up to a certain point. Beyond this, airflow separation occurs, leading to stall (a sudden loss of lift).

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Mechanics of Flight

1. Engines produce thrust, propelling the airplane forward.
2. Wings interact with the oncoming air, and lift is generated due to the airfoil shape and proper angle of attack.
3. Once lift exceeds weight, the airplane takes off and stays airborne as long as the forces remain balanced for sustained flight.

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Other Contributing Factors

• Flaps and Slats: Extendable parts of the wing that increase surface area or change the wing's shape to enhance lift during takeoff and landing.
• Speed: Faster airflow increases the lift. Airplanes need to reach sufficient speed on the runway before takeoff to generate the necessary lift.

By balancing these principles, an airplane achieves flight and maintains stability in the air.

あなた:

What's the proportion of the lift created by airfoil to that by the angle of attack?

ChatGPT:

The proportion of lift generated by the airfoil shape (aerofoil) versus the angle of attack is not a fixed value, as it depends on several factors, including the design of the wing, the flight conditions, and the speed of the aircraft. However, we can break down the relationship qualitatively:

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Airfoil Shape Contribution

• The shape of the airfoil primarily contributes to lift at lower angles of attack and during steady, level flight.
• A well-designed airfoil takes advantage of Bernoulli's Principle by creating a natural pressure difference between the upper and lower surfaces. This "baseline" lift exists even when the angle of attack is zero or very small.

Example:

• On commercial airplanes with carefully engineered airfoils, the shape alone can generate a significant portion (50% or more) of the total lift at cruise conditions.

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Angle of Attack Contribution

• As the angle of attack increases, the wing produces additional lift due to Newton’s Third Law of Motion. The wing deflects more air downward, creating a stronger upward reaction force.
• At higher angles of attack, the contribution of lift from this deflection becomes dominant, especially during takeoff, climbing, and low-speed flight, when the wing relies on the angle of attack to generate sufficient lift.

Example:

• At higher angles of attack (but below the stall angle, typically around 10–15° for many aircraft), up to 70–80% of the lift can come from the angle of attack rather than the airfoil shape.

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Overall Trends

1. Low Angle of Attack:

   • Airfoil shape dominates (e.g., during cruising flight).
   • Contribution: Airfoil ≈ 70–90%, Angle of Attack ≈ 10–30%.

2. High Angle of Attack:

   • Angle of attack dominates (e.g., during takeoff, landing, or slow-speed maneuvers).
   • Contribution: Airfoil ≈ 20–50%, Angle of Attack ≈ 50–80%.

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Factors Influencing the Proportions

1. Wing Design:

   • High-lift wings (e.g., gliders): Airfoil contributes more to lift.
   • Flat or symmetric wings (e.g., aerobatic planes): Angle of attack has a larger role.

2. Speed:

   • At high speeds, airflow over the airfoil plays a greater role, and the lift generated by shape increases.
   • At low speeds, the angle of attack becomes more critical to generate lift.

3. Flaps and Slats:

   • Deploying flaps increases the effective curvature of the airfoil, boosting the contribution from airfoil shape.

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Summary

• There is no universal ratio, but a general estimate suggests:
  • Airfoil contributes more lift at low angles of attack and high speeds.
  • Angle of attack contributes more lift at high angles of attack and low speeds.
• Engineers and aerodynamicists use precise calculations, including computational fluid dynamics (CFD) and wind tunnel testing, to determine these contributions for specific wing designs and operating conditions.

あなた:

Some people seem to be saying something that contradicts the explanation of flying based on airfoil and Bernoulli's Principle. What are they saying?

ChatGPT:

The disagreement you're referring to likely stems from a debate in the aviation community about the role of Bernoulli's Principle versus Newton's Third Law in explaining lift. Here's a breakdown of the controversy and what those who challenge the Bernoulli-based explanation might argue:

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The Conventional Explanation (Bernoulli and Airfoil Shape)

1. Bernoulli's Principle: Faster airflow over the curved top surface of the wing leads to lower pressure above, while slower airflow below results in higher pressure, creating lift.
2. Airfoil Design: The curved upper surface of the wing naturally causes air to flow faster, which plays a key role in lift generation.

This explanation emphasizes the pressure differential and often portrays it as the primary reason airplanes fly.

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The Challenge to the Conventional Explanation

Critics argue that the conventional explanation is incomplete or misleading for several reasons:

1. Misinterpretation of Airflow Speeds

• Equal Transit Time Fallacy: Many simplified explanations suggest that air traveling over the top of the wing must "meet up" with air traveling under the wing at the trailing edge. This implies that air on top must travel faster because the path is longer.
  • Reality: Air on top does move faster, but not because it "meets up" with the air below. Experiments show that air on the top actually arrives at the trailing edge before the air below.
  • Critics' Point: The pressure difference exists, but it cannot be solely attributed to this "equal transit time" idea.

2. Neglect of Newton's Third Law

• Critics emphasize that lift can be explained through Newton's Third Law of Motion: the wing deflects air downward (action), and the air pushes back upward on the wing (reaction). This explanation is observable and does not rely on the abstract pressure differential argument.

3. Flat Surfaces Can Fly

• Wings with flat or symmetric shapes (like those on stunt planes or kites) can also generate lift if angled correctly.
  • This shows that lift does not always require a specific airfoil shape, challenging the notion that Bernoulli's Principle is the primary mechanism.
  • Instead, angle of attack and the deflection of air downward (Newton's laws) become critical.

4. Simplifications Ignore Complex Flow Patterns

• Real-world airflow involves vortices, turbulence, and circulation that cannot be fully explained by Bernoulli's Principle alone.
• Computational fluid dynamics (CFD) and wind tunnel studies show that lift is a result of both pressure differentials and airflow deflection, making the process more complex than a simple Bernoulli-based explanation.

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So What Are They Really Saying?

Critics are arguing that:

1. Bernoulli's Principle is real, but it is not the sole or even the dominant explanation for lift in all situations.
2. Newton's Third Law and airflow deflection are just as important, if not more so, particularly in situations involving high angles of attack or unconventional wing shapes.
3. Simplified explanations (like equal transit time) are misleading and fail to capture the full complexity of how lift works.

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Revised Understanding of Lift

Most modern explanations now combine Bernoulli's Principle and Newton's Laws:

• Lift is created by a combination of:
  • Pressure differences (Bernoulli-based explanation).
  • Air deflection and momentum change (Newton-based explanation).
  • Vortex and circulation effects, which play a significant role in generating and sustaining lift.

This integrated view avoids oversimplifying the phenomenon and acknowledges that different aspects dominate under different conditions.

 

 

How a WWI Biplane Works

What was the landing gear of the British SE-5 fighter plane like? How did the suspension work?

ChatGPT:

ChatGPT

The landing gear of the British SE-5 (Scout Experimental 5) fighter plane, a World War I aircraft, was relatively simple yet robust, designed to handle rough airfields typical of the era. Here's an overview of its structure and suspension:

Landing Gear Design:

• Fixed, Conventional Gear: The SE-5 had a fixed, two-wheel undercarriage with a tailskid, characteristic of many aircraft of its time.
• Axle and Strut Arrangement: The main wheels were mounted on a single axle, which was connected to the fuselage via V-struts and bracing wires.
• Shock Absorption: The axle was not rigidly attached but incorporated a basic form of suspension.

Suspension System:

• Bungee Cord Suspension: The SE-5 used bungee cords (elastic shock cords) wrapped around the axle and attached to the V-struts or a crossbeam. These cords acted as a primitive shock absorber.
• Functionality: When the wheels encountered bumps or hard landings, the axle would move upward, stretching the bungee cords. The elasticity of the cords absorbed some of the impact energy and returned the wheels to their original position.
• Durability: Bungee suspension was simple and effective, requiring minimal maintenance and providing enough cushioning for the aircraft's low landing speeds and the grass fields of the time.

Tailskid:

• Wooden or Metal Skid: The SE-5 had a tailskid instead of a tailwheel, which was common in WWI aircraft. This skid was designed to dig into the ground slightly to help slow the aircraft during landing.
• Spring-Loaded or Flexible Mounting: The tailskid might have been attached to the fuselage with a spring or flexible mounting to absorb shocks and reduce wear on the skid itself.

This combination of a simple main undercarriage and a tailskid was practical and reliable for the conditions in which the SE-5 operated. The design reflected the technological constraints and the operational needs of WWI aviation.

あなた:

Where can I see the structure? Are there photos, illustrations, or diagrams of it that I can see?

ChatGPT:

ChatGPT

 

To visualize the landing gear structure of the British SE-5 fighter plane, you can refer to several resources that provide detailed photographs, illustrations, and diagrams:

1. The Vintage Aviator's SE.5a Reproduction Project: This project involved meticulous reproductions of the SE.5a, the later variant of the SE-5. Their website offers comprehensive insights into the aircraft's construction, including the landing gear. You can find detailed images and descriptions here:

   The Vintage Aviator

    

2. Smithsonian National Air and Space Museum: The museum houses an SE.5a in its collection. Their online catalog provides high-resolution photographs of the aircraft, showcasing various components, including the landing gear. Explore their collection at: Smithsonian National Air and Space Museum.

3. RAF Museum: The Royal Air Force Museum in the UK features an SE.5a in its exhibits. Their online resources include photographs and historical information about the aircraft. Visit their website at: RAF Museum SE.5a.

4. "SE5/5a Aces of World War 1" by Norman Franks: This book contains detailed illustrations and photographs of the SE-5 and SE.5a, including close-ups of the landing gear. It's available for purchase or through libraries.

These resources should provide you with a comprehensive visual understanding of the SE-5's landing gear structure.

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How a WWI Biplane Works