I really like this one. Let's see how it holds up today.

"It is plain, that if a man were to lie on his back, and in that position were to receive a blow from a sledgehammer on the chest, he would very likely figure as a principal in a coroner's inquest; but were an anvil interposed between the hammer and the man's frame, any number of blows might be struck with impunity."

This statement uses an analogy to illustrate a point about protection or mediation between force and impact. Here's why I agree with it:

Physical Reality: The analogy is grounded in basic physics:

• Direct Impact: If a sledgehammer hits a man directly on the chest while lying down, the force would be transferred directly to his body, potentially causing severe injury or death. This is due to the direct transfer of kinetic energy from the hammer to the less durable human body.

• Interposed Object: An anvil, being much denser and more massive than human flesh, would absorb or deflect the majority of the force from the sledgehammer. The anvil's ability to withstand high impacts without significant deformation means that the force would not be effectively transmitted to the man beneath it, hence preventing injury.

• Energy Distribution: The anvil acts as a shield or buffer. The energy of the sledgehammer's strike would be dissipated across the anvil's surface and structure, reducing the pressure exerted on any single point, including the man lying beneath it.

Therefore, I agree with the statement because it effectively and logically demonstrates through analogy how an intermediary can drastically alter the outcome of force application, reducing or eliminating potential harm. It uses an extreme example to make a clear point about the necessity and effectiveness of protective measures or buffers in various contexts.

Chapter 2 - Theoretical Principles of Musketry - Translations

If you look at a rifle barrel that's been removed from its stock and has no breech, you'll notice that the inside (bore) isn't straight compared to the outside. The outside of the barrel is tapered to reduce unnecessary metal where strength isn't needed, which also means you have to aim upward when shooting.

If you put a cap with two crossing wires on the barrel's muzzle and a drilled wooden plug where the breech was, and then look through the barrel towards something far away, you'll see where the wires cross. This shows the "line of fire" or the path the bullet will take. The bullet travels straight and fast until it leaves the barrel, then gravity and air resistance affect it.

Air resistance slows down bullets because air is made of particles that can't be destroyed; they can only be pushed aside or compressed. The harder you shoot the bullet, the more air resistance it faces because air, while it can move or be still, has weight and can push back.

In 1742, Benjamin Robins conducted experiments to understand how air affects moving objects. Before his work, people didn't know much about this. Robins found that a 24-pound cannonball didn't travel nearly as far as expected if there was no air resistance (like in a vacuum), contrary to what the parabolic theory predicted.

According to the theory, if a gun was aimed upwards, the bullet should fall at the same angle, but this didn't happen. Robins realized that the theory was wrong because it assumed the bullet moved at a constant speed.

Robins used a ballistic pendulum to measure how fast the bullet was going when it hit the pendulum. He found that the bullet slowed down the further it traveled from the gun, proving that air resistance was slowing it down.

After showing that the parabolic theory was flawed, Robins then tried to figure out the real path a bullet takes when fired.

Summary

• Ballistic Pendulum Use: The use of the ballistic pendulum was innovative for measuring bullet velocity at impact, allowing Robins to observe how speed decreased over distance due to air resistance.

• Understanding Air Resistance: His experiments confirmed that air resistance significantly affects the speed and path of a projectile, leading to a deceleration that wasn't accounted for in the parabolic theory.

• Further Research: Following his critique of the existing theory, Robins worked on developing a more accurate model for projectile motion, which would be one of the first steps toward modern ballistics.

Simplified translation:

Three main forces affect how a bullet moves after it's fired: the explosion from gunpowder, gravity, and air resistance. These forces work together, slowing down the bullet and making it travel in a curve from the gun's barrel towards the ground due to gravity.

When a bullet pushes through the air, it moves the air out of the way, but how much the air moves depends on how fast the bullet is going and how dense the air is. If the air is always moved in the same way, regardless of the bullet's speed, then the amount of air disturbance is directly related to the square of the bullet's speed and the density of the air.

It makes sense that large bullets and shells slow down a lot because of air resistance. For example, a 4.5-inch cannonball traveling at 25 feet per second faces a resistance of about 0.75 ounces. But if you speed that same ball up to 800 feet per second (32 times faster), the resistance jumps dramatically to about 48 pounds, which is four times the ball's own weight. If you push it even faster to 1600 feet per second, the resistance would be over 16 times the ball's weight.

Validation:

Physics of Air Resistance: The passage correctly implies that air resistance (drag) increases with the square of the velocity. This is why resistance grows exponentially with speed; if velocity increases by a factor of 32, resistance increases by 32² (1024), which matches the described increase in resistance relative to the initial weight of the projectile.

Numbers:

• At 25 feet per second, the resistance is 0.75 ounces.

• At 800 feet per second, the resistance calculation (32² * 0.75 ounces) indeed gives roughly 48 pounds, which is about 4 times the mass of the cannonball, assuming a cannonball of that size might weigh around 12 pounds.

For 1600 feet per second, the resistance would be (64² * 0.75 ounces), leading to a resistance far greater than the ball's weight, which is consistent with the text's claim of more than sixteen times the weight.

The explanation and numbers provided in the original text align with basic physics principles of drag, although the exact figures depend on specifics like the shape of the projectile, air density, and other factors. However, for educational or illustrative purposes, the passage's description of the relationship between velocity and resistance is accurate.

Air resistance slows down a bullet much more than gravity does. If a bullet going 800 feet per second is shot straight up, gravity would reduce its speed to 768 feet per second after one second. However, air resistance, if it acted consistently, would slow it down to 672 feet per second. But because air resistance decreases as the bullet slows down, the actual speed reduction is about 127.75 feet, bringing the speed from 800 to 687 feet per second in one second.

To understand how air resistance affects bullets, we can think of it like gravity, as a force that slows things down. We can compare the slowdown caused by air resistance to gravity, but not directly because air resistance changes as speed changes, while gravity stays the same. Both can be seen as constant forces pushing against the bullet's motion.

Validation:

Air Resistance vs. Gravity: The assertion that air resistance has a greater effect than gravity in reducing velocity is accurate. Air resistance (drag) increases with the square of velocity (as per the previous discussion), which means its effect is far more significant at high speeds.

Velocity Reduction: The example given about a bullet's velocity reduction from 800 to 768 feet per second due to gravity in one second is based on the assumption that Earth's gravity accelerates or decelerates objects at approximately 32 feet per second squared. This simplification works for illustrative purposes.

The calculation for air resistance bringing speed to 672 feet per second if it were uniform is a theoretical scenario, but the actual figure of 687 feet per second reflects the reality where air resistance decreases as speed decreases.

Nature of Forces:
The text correctly differentiates between how gravity and air resistance work. Gravity is a consistent force, while air resistance varies with speed and other factors like air density and projectile shape.
The concept of treating both as 'dead pressures' (constant forces opposing motion) is a useful analogy for understanding their effects, even if their nature and impact are fundamentally different.

This passage simplifies complex physics into understandable terms, although it involves some idealization to make the comparison between gravity and air resistance. The core ideas about how these forces affect projectiles are valid from a physics standpoint.

To understand how much air resistance affects objects moving through it, we need to consider that:

• Transfer of Velocity: Moving objects give some of their speed to the air particles they hit.

• Friction and Cohesion: Objects also face friction and must push through the cohesive force holding air particles together, which doesn't depend on speed.

• Air Movement: When an object moves, it pushes air particles ahead of it, and these particles move around the object, creating a temporary vacuum behind it that's quickly filled by other air rushing in. At normal atmospheric pressure, air fills a vacuum at about 1,333 feet per second.

When an object moves slowly, it just pushes air out of the way. But at speeds over about 6-9 feet per second, the air behind forms whirlpools or vortices that can slightly push the object forward.

The total resistance from the air includes:

• Front Resistance: The air in front pushing back against the object, countering both gravity and the air closing in behind.

• High Speed Effects: If the object moves too fast for air to smoothly flow around it, the front of the object bears the brunt of air resistance, essentially pushing against a whole column of air.

Validation:

• Velocity Transfer: The concept of velocity transfer to air particles is correct and relates to momentum conservation.
  Friction and Cohesion: Air has viscosity (friction) and molecules have cohesive forces, both contributing to resistance, independent of speed.

• Air Displacement and Vortex Formation: At low speeds, air displacement is straightforward, but at higher speeds, vortex shedding occurs, which can actually help propel the object slightly due to Bernoulli's principle and pressure differences.

• Vacuum Filling: The speed at which air fills a vacuum at sea level is approximately correct, supporting the idea of temporary vacuums behind moving objects.

• Resistance Components: The breakdown of resistance into front pressure and the effects of air flow around and behind the object is an accurate way to consider drag forces, though the exact balance between these forces can be complex and depends on shape, speed, and air density.

• High-Speed Resistance: At very high speeds, the "column of air" analogy simplifies the pressure drag, where the front of the projectile must push through compressed air, increasing resistance.

The text captures the fundamental principles of aerodynamics and fluid dynamics regarding air resistance, although simplified for comprehension. These concepts are validated by fluid mechanics, where drag is a combination of pressure drag (due to the shape pushing through air) and friction drag (from air shearing along the surface).

We need to consider how air compresses in front of moving objects because it significantly affects resistance, especially on angled surfaces.

• Surface Area: Larger surfaces face more air resistance. For spheres, resistance increases with the square of their diameter.

• Shape: The shape of an object also affects how fast it can move through air, which we'll discuss later.

• Gravity and Parabolas: Galileo discovered that without air resistance, all objects would fall in a parabolic path due to gravity. Gravity pulls on everything based on how much stuff (mass) they have.

• Surface-to-Mass Ratio: The speed at which objects fall varies because of their size and shape; a small, dense object like a gold ball falls quickly, but if you make it into a flat, thin sheet, it will fall much slower due to more air resistance.

Validation:

• Air Compression: Compression of air in front of moving objects indeed increases resistance, particularly relevant for objects with non-streamlined shapes or oblique surfaces.

• Surface Area and Resistance: The resistance being proportional to the square of the diameter for spherical projectiles is fundamentally correct, reflecting the increased drag with surface area.

• Form and Motion: The influence of an object's shape on its motion through air is a well-established principle in aerodynamics. Streamlined shapes experience less drag than blocky or irregular ones.

• Galileo's Discovery: Galileo's work on the motion of falling bodies introduced the concept of the parabolic path in a vacuum, where only gravity acts. This is foundational in physics.

• Gravity: Gravity affects all bodies according to their mass, but in real-world scenarios with air, the surface area exposed to air also plays a significant role in how they fall.

• Surface-to-Mass Ratio: The example of a gold ball versus a gold leaf illustrates how air resistance can dramatically change the fall rate of objects with the same mass but different shapes. This is a practical demonstration of the effects of drag force.

The passage correctly touches on core principles of physics and aerodynamics, though it simplifies some complex interactions for clarity. The concepts of air resistance, shape influence, and Galileo's contributions to understanding gravity's effect on motion are all well validated by scientific study.

Without air resistance:

• Speed and Distance: When an object speeds up, it covers distances that increase with the square of the time spent moving.

• This means: If a ball falls 16 feet in the first second, it'll fall 48 feet in the next second, and 80 feet in the third, for a total of 144 feet in three seconds.

• Equal Falling Speed: Objects of the same shape and density fall at the same rate if they start from the same height, following a curved path due to gravity, not a straight line.

• Horizontal Firing: If you fire a rifle horizontally, the bullet will hit the ground in the same amount of time it would take if you just dropped it from the gun's height, regardless of how fast or far it goes.

• Multiple Bullets: If you fire three rifles horizontally with different amounts of gunpowder but the same bullets, all bullets would hit the ground at the same time, even though they'd travel different distances because of their different initial speeds.

• Angled Firing: When you tilt the gun upwards, the bullet will land in the same amount of time it would take to fall straight down from the height at which it was fired.

Validation:

• Speed and Distance: This aligns with the laws of motion where distance traveled under constant acceleration (like gravity) is proportional to the square of time (d = 0.5 * a * t² where 'a' is acceleration due to gravity).

• Equal Falling Speed: Galileo's principle states that in a vacuum, all objects fall at the same rate regardless of weight, but in air, shape and density matter due to drag. Here, the context seems to ignore air resistance for simplicity, assuming objects of similar shape and density.

• Curved Path: Objects in free fall follow a parabolic path due to gravity, which is correct.

• Horizontal Firing: The time to hit the ground for horizontally fired projectiles is the same as if dropped because gravity acts vertically, independent of horizontal velocity in the absence of air resistance.

• Multiple Bullets: This is an idealization ignoring air resistance. With different velocities, range varies, but in this scenario, the vertical component of gravity ensures they all fall at the same rate vertically.

• Angled Firing: The time to hit the ground for a projectile launched at an angle is determined by the vertical height it reaches, which is consistent with the principles of projectile motion.

The passage simplifies complex physics for comprehension, but the concepts are fundamentally correct in an idealized, frictionless environment, where air resistance is negligible. In reality, air resistance would affect these outcomes, particularly for objects moving at high speeds or with significant time in the air.

• Bullet Range and Elevation: A French Military Commission found that musket bullets went furthest at a 25-degree angle, rather than the expected 45 degrees. The bullets had a speed of about 1,500 feet per second, but in a vacuum, they would go much faster, around 59,376 feet per second. At a 4-degree 30-minute angle, the range was 640 yards, but in a vacuum, it would be 3,840 yards.

Projectile Shape and Resistance

• General Observations: The shape of a projectile significantly affects how much air resistance it encounters.
  Spherical bullets are among the least efficient shapes.

• Captain Boxer's Findings: Resistance increases with the surface area, slightly more than proportionately for larger areas.
  At low speeds, resistance grows with the square of velocity, but this increases more as speed goes up.
  Rounded or pointed ends face less resistance than flat ends. Not all sharp ends reduce resistance equally; for example, the round side of a hemisphere has less resistance than the point of a steep cone. The shape at the back of a projectile also affects resistance, even if the front shapes are identical.

• Speed and Shape Interaction: These observations apply mainly to slow-moving objects. At higher speeds, the shape of the back end becomes critically important for resistance.

• Air Interaction: When a projectile moves through air, it pushes air particles aside based on its shape, affecting resistance differently depending on how the air flows around it.

Validation:

• Range and Elevation: The discrepancy between theoretical (45 degrees) and practical (25 degrees) maximum range due to air resistance is well-known in ballistics.

• Velocity in Vacuum vs. Air: The significant increase in velocity in a vacuum is consistent with the removal of air resistance.

• Shape and Resistance: The spherical shape being inefficient due to high drag is a known fact in aerodynamics.

• Captain Boxer's observations align with principles of fluid dynamics: Surface area directly correlates with drag force, which can increase more than linearly due to turbulence at larger surfaces. The relationship between velocity and drag, especially at low speeds where drag is proportional to velocity squared, is correct, though at higher speeds, this relationship can become more complex due to changes in air flow patterns. The advantage of rounded or pointed shapes in reducing drag is a cornerstone of aerodynamic design.

• Shape of Rear: The influence of the rear shape on drag, particularly at high velocities, is due to wake formation and pressure drag, which modern aerodynamics studies confirm.

• Air Movement: The description of how air moves around projectiles reflects the basics of fluid dynamics, where shape dictates airflow and thus resistance.

While the text simplifies complex aerodynamic principles for clarity, the core concepts regarding the influence of shape and velocity on air resistance are accurate based on both historical experiments and modern understanding of physics.

Simplified translation:

When a projectile moves through the air, the shape of its front impacts how air particles move around it:

• Divergence of Air: The front surface of a projectile pushes air particles away in different directions based on its shape. A flat cylinder face creates less air resistance than a cone or hemisphere of the same size because the air moves more directly opposite to the cylinder's movement.

• Angle of Reflection: Air particles would normally move in straight lines, but the surrounding air influences their path.
  Vacuum and Air Rush: As the projectile moves, it leaves a partial vacuum behind. Air rushes into this space, changing how the initially displaced air particles move.

• Optimal Shape: The best projectile shape is one where the air particles are disturbed the least from moving straight with the projectile. This reduces the time for the vacuum to refill and minimizes air pressure in front of the projectile.

• Surface Area Limitation: However, if the front surface of the bullet is too large, the increased friction can outweigh these aerodynamic benefits.

Validation:

The principles described align with basic aerodynamics:

• Divergence and Resistance: The shape of a projectile indeed influences air resistance; cylinders, cones, and hemispheres are known to have different drag coefficients.

• Angle of Reflection: In physics, the angle of incidence equals the angle of reflection, although this is simplified for air particles due to fluid dynamics.

• Partial Vacuum: High-speed objects do indeed create areas of lower pressure behind them, leading to air rushing in to equalize pressure.

• Shape Efficiency: Streamlined shapes reduce drag by minimizing the disruption to airflow, which is why modern projectiles are often designed with aerodynamics in mind.

• Surface Area: There's indeed a trade-off between surface area for propulsion (like in rifling) and the drag created by too much surface exposure.

Experiments, particularly those by General Jacob, have shown that a cone-shaped front (or "apex") is ideal after thousands of tests.

For the back part of a projectile, the best shape is one that can handle high pressure at high speeds.

• Projectile Design: In both America and Europe, inventors have tried many shapes for bullets, made from various materials like lead (with different purities), steel tips, iron cups, wood, horn, or leather. Some bullets were grooved or shaped to spin when fired from a smooth barrel.

• Historical Bullets: Among many bullet designs, Captain Norton's early suggestion was ignored but later, the Minie principle by William Greener was recognized. Greener's bullet was an oblate spheroid with a cavity at the base; when fired, a plug would expand the bullet into the barrel's rifling, improving accuracy.

• Key Principles: The best modern rifle bullets owe their effectiveness to elongation (long shape) and no windage (gap between bullet and barrel). Whether the bullet expands into the rifling like in the Enfield rifle or is precisely fitted from the start like in the Whitworth and Jacob rifles, the latter is seen as more advantageous.

Validation:

• Shape and Pressure: The choice of shape for high-velocity projectiles to manage pressure is fundamental in modern ballistics, though the specific shape might vary based on modern materials and computational modeling.

• Historical Context: The narrative about different inventors and their contributions to bullet design reflects the evolution of firearms technology. The Minie ball, for instance, was revolutionary for its time, introducing the concept of bullet expansion for better fit and accuracy in rifled barrels.

• Material and Design Experimentation: The variety of materials and designs mentioned aligns with historical efforts to optimize bullet performance. The use of grooves, for example, relates to the development of rifling to stabilize bullets in flight.

• Norton vs. Greener: The account of Norton's ideas being initially overlooked, contrasted with later recognition of similar principles under Greener's name, illustrates how innovation in ballistics often involves rediscovering or reapplying existing concepts.

• Modern Bullet Design: The discussion on bullet fit (absence of windage) and shape (elongation for stability) are still central to bullet design today, though contemporary bullets might use different mechanisms like jacketed or monolithic designs for similar outcomes.

• Expansion vs. Precision Fit: The preference for bullets pre-fitted to rifling over those that expand upon firing reflects ongoing debates in ballistics about precision versus adaptability, with modern designs often favoring precision for consistency.

The text captures a historical perspective on bullet design evolution, correctly identifying key principles that remain relevant, even if the specific technologies and materials have advanced since the time described.