Leonhard Euler's Critical Analysis of Jacob Bernoulli's Proposal for Ship Propulsion Using Internal Motion

المفاهيم الأساسية

Internal forces within a closed system, such as a ship, cannot generate net motion, as the action and reaction forces cancel out. External interactions are required to propel a ship forward.

الملخص

The content presents Leonhard Euler's critical examination of a proposal by Jacob Bernoulli for propelling a ship using internal motion. Euler systematically analyzes the forces involved in Bernoulli's proposed mechanism, which utilizes a pendulum striking an elastic platform within the ship.

Euler first establishes the fundamental principle that internal forces within a closed system, such as a ship, cannot generate net motion, as the action and reaction forces cancel out. He then proceeds to calculate the specific forces involved in the pendulum's descent, impact, and ascent, demonstrating that the backward forces during the pendulum's swing exactly cancel out the forward force from the impact.

Euler also considers the effect of water resistance and friction, showing that even in the presence of these external factors, the internal forces still cannot produce net forward motion for the ship. He highlights a remarkable mechanical paradox where friction can actually enable motion that would not occur without it.

Through rigorous analysis, Euler concludes that any mechanism relying solely on internal forces, whether pressures or impacts, cannot propel a ship forward. External interactions are required to generate net motion, as the center of mass of the closed system remains stationary under the influence of internal forces alone.

الإحصائيات

The weight of the pendulum is assumed to be one-hundredth of the total weight of the ship.
Bernoulli calculated that the ship could be propelled a distance of 82.5 feet per minute without considering the reduction in water resistance due to a beaked prow.
With a beaked prow, Bernoulli estimated the ship's speed could exceed 260 feet per minute, or 15,649 feet per hour.

اقتباسات

"For no matter how much men or other machines placed in the ship strive to propel it, since the reaction is always equal to the action and both are sustained equally by the ship, no motion is thereby achieved."
"Just as in pressures (or so-called dead forces) the reaction is always equal and opposite to the action, so too in collisions a similar equality holds—which is all the less surprising since any collision can quickly be reduced to pressures."
"Hence, all efforts by those aboard the ship to propel it are in vain, unless they are able to apply themselves to the shore or another body situated outside the ship."

الرؤى الأساسية المستخلصة من

A translation of L. Euler's " Examination of an artifice for propelling a ship by the principle of internal motion"

by Sylvio R. Bi... في arxiv.org 10-02-2024

https://arxiv.org/pdf/2410.00283.pdf

استفسارات أعمق

What other historical examples or contemporary applications demonstrate the fundamental principles of conservation of momentum and the necessity of external interactions for generating net motion in mechanical systems?

The principle of conservation of momentum is a cornerstone of classical mechanics, and its implications can be observed in various historical and contemporary contexts. One notable historical example is the development of the steam engine during the Industrial Revolution. The steam engine operates on the principle of converting thermal energy into mechanical work, where the steam exerts pressure on the pistons, creating motion. However, the effective propulsion of a steam-powered vessel relies on the interaction between the engine's output and the external water, which provides the necessary resistance and reaction forces to generate forward motion.
In contemporary applications, the design of rockets exemplifies the necessity of external interactions for propulsion. Rockets operate on Newton's third law of motion, where the expulsion of gas at high velocity in one direction results in the rocket moving in the opposite direction. The effectiveness of this propulsion system is contingent upon the rocket's ability to expel mass (the exhaust gases) into the external environment, demonstrating that internal mechanisms alone cannot achieve motion without external interactions.
Another modern example is the use of propellers in marine vessels. Propellers convert rotational motion into thrust by interacting with the water. The water acts as an external medium that allows the vessel to move forward. This interaction is crucial, as the thrust generated by the propeller must overcome the resistance of the water to achieve net motion, reinforcing the principle that internal forces alone cannot propel a ship.

How might Bernoulli's proposed mechanism be modified or combined with external forces to potentially achieve effective ship propulsion, while still adhering to the principles of classical mechanics?

To modify Bernoulli's proposed mechanism for effective ship propulsion, one could integrate external forces into the design. For instance, rather than relying solely on the internal motion of a pendulum, a hybrid system could be developed that utilizes the pendulum's motion to drive an external mechanism, such as a propeller or paddle wheel.
One potential modification could involve using the pendulum to generate mechanical energy that is then transferred to an external propulsion system. For example, the pendulum could be connected to a gear system that, when the pendulum swings, turns a propeller or paddle wheel submerged in water. This would allow the ship to harness the internal motion of the pendulum while simultaneously interacting with the external environment, thus adhering to the principles of classical mechanics.
Additionally, incorporating sails or other wind-driven mechanisms could further enhance propulsion. By combining the pendulum's mechanical energy with wind energy, the ship could achieve greater speeds and efficiency. This dual approach would ensure that the propulsion system benefits from both internal and external forces, maximizing the potential for effective ship movement while remaining consistent with the laws of motion.

Given the insights from this analysis, how might the design of modern ships and propulsion systems be influenced to maximize efficiency and performance in a manner consistent with the laws of motion?

The insights from Euler's examination of Bernoulli's mechanism highlight the importance of external interactions in achieving effective propulsion. Modern ship design and propulsion systems can be influenced by these principles in several ways to maximize efficiency and performance.

Hybrid Propulsion Systems: Modern vessels can benefit from hybrid propulsion systems that combine traditional methods (like diesel engines) with renewable energy sources (like wind or solar power). By utilizing sails or solar panels alongside conventional engines, ships can reduce fuel consumption and increase efficiency, leveraging both internal and external forces.

Streamlined Hull Design: The principles of fluid dynamics and resistance can be applied to the design of ship hulls. By creating streamlined shapes that minimize drag, ships can move more efficiently through water. This design consideration aligns with the understanding that external forces (like water resistance) significantly impact motion.

Active Control Systems: Implementing active control systems that adjust the ship's orientation and propulsion based on real-time environmental conditions can enhance performance. For example, using sensors to optimize sail angles or propeller pitch in response to wind and water currents can maximize thrust and minimize resistance.

Energy Recovery Systems: Incorporating systems that capture and reuse energy from the ship's motion can improve overall efficiency. For instance, regenerative braking systems can harness energy during deceleration, which can then be used to assist in propulsion, aligning with the conservation of momentum principles.

Research and Development of New Materials: Utilizing advanced materials that reduce weight and increase strength can lead to more efficient designs. Lighter ships require less energy to propel, allowing for better performance while adhering to the laws of motion.

By integrating these considerations into modern ship design and propulsion systems, engineers can create vessels that operate efficiently and effectively, harnessing both internal mechanisms and external interactions to achieve optimal performance in accordance with classical mechanics.