Richard Feynman as soon as quipped that "Time is what occurs while not anything else does. For time is not anything yet swap. The Quantum Story: A history in 40 moments. The 20th century was once outlined via physics. From the minds of the world's prime physicists there flowed a river of rules that might delivery mankind to the head of wonderment and to the very depths of human depression. This used to be a century that started with the certainties of absolute wisdom and ended with the information of absolute uncertainty.
Show sample text content. The cock used to be then pulled again absolutely sooner than the set off liberating it and inflicting the flint to spark, hence igniting the primer. The caplock method needed to look forward to advancements in chemistry. The explosive salts referred to as fulminates have been built within the 19th century. This spring-loaded cock will be published by means of the set off and strike a skinny steel cap containing fulminate, which might then detonate, sending scorching gasoline down the touch-hole to ignite the cost.
It was once a less complicated approach than any earlier approach, requiring much less education for the musketeer and allowing extra quick firing. It was once additionally extra powerful and was once much less vulnerable to rainy climate. They have been invented in , possibly through the good Swedish army chief, King Gustavus Adolphus.
Common parlance refers to bullet velocity when, to a physicist, it should sometimes be speed. I will generally try to distinguish between these terms. Part I Internal Ballistics Before gunpowder, weapons began and ended with the rock; Stone Age man would throw a small one by hand, whereas medieval man would launch a large one from a sophisticated counterpoise siege engine such as a trebuchet. Between these two extremes, other projectiles appeared: sling stones, arrows, throwing spears, and crossbow bolts.
Ballistics enters into the trajectories of all these projectiles— and of musket balls, bullets, and shells—even before they leave the weapon that launched them. A projectile weapon, be it a bow, a trebuchet, or a Winchester rifle, is a machine designed to supply energy to its projectile. More specifically, it is designed to send the projectile at high speed in a very particular direction. Internal ballistics describes the process of generating the desired velocity;1 external ballistics describes how a projectile flies through the air.
In these first three chapters I will be describing internal ballistics and will begin here with the internal ballistics of pre-gunpowder weapons. The throwing arm is not a simple stiff lever that rotates to generate hand speed—though we will model it as such here.
If we observe the throwing arm with more care, we see that it moves more like a whiplash, generating great speed at the thin end. Also, when you throw a rock carefully chosen for shape and weight , you add speed by arching your body forward at just the right moment, and add force by pushing with your trailing leg.
We will learn later how maximum range relates to launch velocity: that is the subject of external ballistics. Suppose we were to approximate the action of a throwing arm by the rotation We know that this is only a rough model the more sophisticated model of Cross models the arm as a hinged rod , but it will suffice for my purposes.
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A stiff arm that is 2 feet long needs to rotate at a rate of five cycles per second 5 Hertz, or 5 Hz to achieve such a range. In technical note 1, I show that a real arm hinged at the elbow can do better than this stiff arm. A hinged arm creates a whiplash effect that increases launch speed by about a third for the simple model of technical note 1—and probably by more for a real arm. This is why we throw rocks or baseballs with elbow initially bent. However, he gets some of this speed back because, unlike a baseball pitcher, he is allowed to run up to where he throws the ball, instead of standing still.
Throwing a Javelin Olympic javelin throwers also run up to the launch point, to increase their distance.
In this action, modern javelin throwers are imitating historical antecedents fig. A javelin is heavier than a sling stone, and so the point can cause damage to an enemy even if he is armored. Javelin throwers of classical history were often skirmishers who peppered the ranks of enemy heavy infantry, softening them up just before their own heavy infantry attacked.
The Roman javelin the pilum had a characteristically long tip made of soft metal, with a barbed end. The metal would bend when it struck an enemy shield, so that the pilum could not be thrown back. If it penetrated the shield, it could not be easily removed, so the enemy soldier would be obliged to throw his shield away just as the Romans were about to attack. Figure 1. Ancient Greek infantryman, or peltast, with three javelins.
Illustration courtesy of Johnny Shumate. How much does running up to the launch point increase range? In figure 1. The graphs of figure 1. For low-speed projectiles of limited range, such as the javelin, this assumption is reasonable, but when we come to examine bullet trajectories, we will most certainly need to take drag into account. The Sling Our first projectile weapon, the sling, is an ancient and nearly universal tool, found all across classical Eurasia and also in Mesoamerica.
Biblical peoples and ancient Greeks and Romans all used the sling as a military weapon. It dates from the Stone Age and was inexpensive and simple to make, though using a sling effectively takes a lot of training. In Roman times, Ballearic Islanders in the western Mediterranean were famous for their skills with the sling. More than one Roman historian records the story that boys on these islands were trained by withholding their food until they could hit it with a sling stone. The sling consists of two cords, traditionally made of wool or hemp, with a pouch in the middle to hold the sling stone.
One cord end was fashioned into a loop, through which the middle finger of the throwing hand was placed see fig.
Their Arrows Will Darken the Sun: The Evolution and Science of Ballistics
The other loose cord end was knotted, so that it could be easily gripped between thumb and forefinger. The projectile is released by letting go of this knotted cord—at just the right moment. Skilled slingers were recruited for They could send a projectile to a quite considerable distance—exceeding the range of ancient bows. The most common sling projectile was a rounded stone, but military use often led to specially manufactured clay or lead projectiles of biconical shape like a pointed football ; these flew farther than stone projectiles and did more damage.
A projectile in a sling pouch can be launched in one of several different ways. The simplest and most accurate, though with the shortest range, is the underarm shot. This is like a golf swing, with the sling replacing a club. A golf shot can send a ball — yards, but an underarm sling slot is shorter: the wrists cannot be used to power the sling through the bottom of a swing the way they do for a golf club. Also, the length of a sling that is used in underarm mode is quite short.
A Ballearic slinger, in Roman times. There is a sidearm delivery in which the sling is swung sideways—the An overhead delivery is similar except that the sling can be rotated several times, like a lasso; here the sling length can be increased to perhaps 4 feet say 1. Experienced slingers can do better than this, by taking advantage of the whiplash lever-arm effect that we saw in technical note 1 for the throw. The current world record for a stone shot from a sling is over yards.
Longer ranges were claimed for slingers of the Old World classical civilizations. One problem with the sidearm or overhead delivery is that aiming is more difficult. Another problem for the military use of slings was that the sidearm and overhead deliveries require a lot more room, and so the number of slingers that can be brought into action at any one place is limited. Fewer readers, I wager, will appreciate the role that ballistic weapons played in ancient warfare.
So, here I will provide a broad outline of some of the features that ballistic weapons brought to the battlefields of ancient Greece and Rome—indeed to all battlefields of antiquity from prehistory to the dawn of firearms. From a purely tactical point of view, the important factors that determined the outcome of battles were quality and nature of arms, troop density on the ground, and mobility.
Thus, heavy infantry such as Roman legionaries and Greek hoplites wore armor and carried close-quarter weapons such as swords as their main armament; they fought in densely packed formations that could maintain order while turning, or moving over rough ground. Light infantry wore no armor and carried projectile weapons such as javelins, slings, and bows.
They were much more loosely organized, and because they carried less and were not in formation, they could move much faster, over rougher terrain. Obviously, in close combat the light infantry would get pulverized by the Light infantry acted as skirmishers, spread out in front of the advancing enemy heavies, sending showers of projectiles at them from a safe distance, trying to break up their formation and soften them up so that friendly heavy infantry would prevail against them.
As the enemy advanced, the skirmishers would withdraw behind their own heavy infantry units and let the opposing heavy infantry formations slug it out. Cavalry was initially used to increase mobility about a battlefield. It was only gradually, over the course of centuries, that heavy cavalry was developed, taking up the role that tanks would adopt in modern warfare— rolling over the opposition, plowing through lighter units like bulls in a china shop.
Light cavalry were often just light infantry on horseback: they could move faster but otherwise were no match for the foot soldiers. Light infantry skirmishers would beat light cavalry skirmishers most of the time—it was simply a matter of logistics. Foot soldiers could fire arrows farther than horse archers because until powerful composite bows discussed below became common, horse archer bows were weaker. Horse archers fired from a moving platform and needed to control their mounts, and so were usually less accurate.
They carried less ammunition, and they presented bigger targets. Heavy cavalry in dense formation were vulnerable to well-organized archers, as we will see, while skirmishing archers or slingers were easy prey for lighter cavalry units, who could run them down. Densely packed units of heavy infantry were similarly vulnerable to javelins, arrows, and sling stones but not to heavy cavalry the horses had more sense than their riders and would refuse to charge into massed ranks of armored soldiers bristling with long spears.
So this is the mix of military units common throughout the battlefields of the ancient world: heavy and light cavalry and infantry; dense units equipped to fight in close order and diffuse units equipped to fight at a distance. Advancing technology advancing more slowly in past centuries, to be sure, but advancing inexorably influenced these battles by changing the delicate balance between different units. Chariots fell out of use, and then slings. Archery upgraded. Cavalry adapted.
Firearms appeared and changed everything—but only slowly, as we will see in chapter 2. Staff Sling A staff sling is a sling on a stick. As a weapon it lasted longer than the simple sling—well into the Middle Ages. It threw a heavier projectile than the simple sling could do, and farther. It also required two hands to operate.
Imagine casting a heavy fishing pole; this is the action of a staff slinger. Why is the range greater than for a simple sling? It is because the lever distance— from shoulder to projectile—is increased. The arms hold a staff which could exceed 6 feet in length to one end of which a sling is attached. Note the progression of increasing lever distance.
Their Arrows Will Darken the Sun: The Evolution and Science of Ballistics
An arm with an effective length of perhaps 2 feet can throw a rock 60 yards; an arm-plus-sling of 4 or 5 feet effective length can throw upwards of yards; an arm-plus-staff-plus-sling of perhaps 10 feet effective length can throw farther—how much farther we determine in technical note 3. This increases the whiplash effect. And with two hands swinging the staff, more power goes into the swing. The result is shown in figure 1. This is true whatever acceleration the slinger applies to the staff.
This makes sense: it takes more energy to move a heavy staff than a light one. When the projectile is released, it takes away some of the energy that the slinger provided to the staff, but not all. Energy remaining in the staff for example, kinetic energy due to staff movement is not available to the projectile and so is wasted. Staff sling launch speed and efficiency for a staff of length 6. So what is the range of a staff sling? The angular accelerations of figure 1. Ignoring drag, such a launch speed would send the projectile yards m over level ground.
However, we are now entering the region of high projectile speeds, and so we really cannot ignore drag. I will discuss drag in the chapters on external ballistics; for now, let us just say that a staff sling is capable of sending a projectile several hundred yards. Longbow and Crossbow The bow is almost as old and ubiquitous as the sling. The crossbow was known to the ancient Greeks and Chinese and was widely used in the Old World until well after the development of gunpowder weapons, as we will see.
The simplest type of bow is the self bow, which was made from a single piece of wood. A famous example of this type of bow is the English longbow fig. This type of bow was mass-produced in the fourteenth and fifteenth centuries as a military weapon: self bows are inexpensive, compared with the composite bows we will consider next, and are relatively easy to manufacture.
Despite the simplicity of the longbow, considerable skill went into the construction. Wood was cut carefully from yew trees in winter, before the sap rose. The back of the bow farthest away from the archer consisted of elastic sapwood, which is strong under tension, while the belly nearest the archer consisted of heartwood, which is stronger under compression. The bow cross section was approximately D-shaped, with the back being flat and carefully cut along the grain. The wood was worked in slow stages over three or four years. Self bows do not have particularly long ranges.
Even the powerful English longbows which were over 6 ft long attained ranges of only — yards — m. Their main tactical advantage was their high rate of fire—up to 12 arrows per minute. The main surprise that emerges from all studies of bow dynamics is the efficiency of these machines. Indeed, an idealized bow one which has a massless, inelastic bowstring and is not subject to friction or drag forces is perfectly efficient. My model of internal ballistics for this idealized bow shows how energy is transferred entirely to the arrow just before it is released from the bowstring see fig.
Real bowstrings have mass, and this mass reduces efficiency. A second feature that emerges from my model and others is the rapidity with which the arrow accelerates see fig. For the English longbow of figure 1. English longbow. A simple self bow—one made from a single piece of wood—this example is 6. Photo by James Cram. Composite bows were more sophisticated than self bows. Composite bows were made of wood, horn, and sinew, glued into place. The wood was cut along the grain for tensile strength.
The horn, on the belly side of the bow, was elastic but very strong in compression. Sinew, from the leg or neck tendons of cattle, was attached to the back side of the bow because it is strong in tension. Such bows were the result of a great deal of historical trial and error, presumably over a considerable period they evolved surprisingly early Many cultures developed composite bows independently.
Thus, Inuit peoples in the Canadian Arctic developed bows with sinew strung under tension, rather than glued, along the back side of the bow. More southerly American Indians also made use of sinew to prestress their short bows, either by the Inuit method or using glue. The composite bow offered two advantages over the self bow: it was more powerful than a self bow of the same size, and it was short enough to be used by cavalry. Most of the nomadic tribes that periodically swept across Asia— wreaking havoc in China and Europe over a thousand years from the fourth century AD—were armed principally with short composite bows.
The main disadvantage of this bow was its complex and expensive construction. Internal ballistics for an idealized longbow. The bow gives up its energy entirely to the arrow. The high point of ancient bow construction is often considered to be epitomized by the Persian and Turkish composite bows. These bows became strongly recurved during the construction process. An unstrung recurved bow curves away from the archer, sometimes to the extent that the bow tips meet or cross. This means that the braced strung bow is under significant tension, increasing the draw weight and hence the power of the bow.
The range of composite recurved bows is surprising—but that is a topic for another chapter. As the arrow is released, the bowstring straightens.
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Because part of the string is now in contact with the bow, the string cannot vibrate when the arrow flies off, so the amount of energy that is wasted by string vibration is reduced. Recurve bows are more efficient than other bows because the effective bowstring length of the braced bow is reduced. A bow is braced when it is strung but not drawn.
Crossbows are extremely powerful short bows attached to a stock—in some ways the forerunner of muskets, as we will see. The bow itself is very stiff and difficult to span to draw because it is thick and made of composite Crossbows from classical antiquity could be spanned by hand. The bowman could pull on the string with both hands, while the stock was held against his belly.
More powerful bows required a windlass device consisting of a ratchet and pulleys. All this power released a bolt as crossbow arrows are known that could travel perhaps — yards — m. As you can see from figure 1.
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A crossbow, with a lever device for spanning. Note the trigger mechanism. The bolt is placed along a longitudinal groove in the stock. The advantage of crossbows over longbows was that the bowman needed relatively little training and strength. The disadvantage was the slow rate of fire—perhaps one or two bolts per minute. The internal ballistics of crossbows is the same as that of longbows, though the parameters are different.
From the perspective of the ballistics historian, crossbows are significant because they are closely analogous to—and indeed in many ways anticipated the early use of—gunpowder weapons. Crossbows overlapped with early hand-held gunpowder weapons and provided the standard against which these new weapons were measured. I wrote about it a few years ago, but since then some impressive high-speed photographic evidence has been released that dramatically confirms the technical explanation. Picture a longbow viewed from above. It is drawn and the arrow is about to be released.
Hit the pause button; picture the arrow geometry in your mind. The back end of the arrow has a groove the nock that holds the bowstring in place. The arrow shaft lies alongside the bow handle. Because of bow handle thickness, the arrow is not pointing exactly at the target but instead is offset, pointing a little to the left if the arrow shaft passes to the left of the handle. Now resume the motion, as our archer releases the bowstring.
The string rapidly approaches the bow handle, and so the arrow accelerates but also think about it increases the offset angle. Surely, then, at release the arrow will move away to the left of the target direction, due to deflection by the bow handle? This makes sense, but it does not happen—real arrows are released in the target direction. Hence the paradox. The explanation is strange. A perfectly stiff longbow arrow may indeed follow a trajectory that deflects from the target direction, but real arrow shafts are far from being stiff.
What happens is this: rapid acceleration by the bowstring causes a wooden arrow shaft to buckle. That is, the shaft bends longitudinally under pressure from the string, and the arrow head realigns with the line of sight direction due to this bending. Once past the handle, the arrow then bends back the other way: it vibrates in a horizontal plane. The vibration is initiated by the sudden impulse provided by the bowstring; its frequency depends upon arrow shaft characteristics.
You can see that it is important, if the arrow is not to be deflected by the bow handle, that the vibration must not be too fast or too slow, because then the arrow fletching the feathers would strike the handle. At just the right frequency, the arrow bends around the handle, barely touching it after the initial release. This is why it is important for archers to match the bow and arrow: as with firearms, the ammunition and the weapon must be designed for each other.
In one video, the camera is positioned behind the Both show quite clearly how the arrow vibrates horizontally in flight—it more resembles a swimming eel than a rigid rod—and how it bends around the bow handle and follows the line of sight direction. Varied in form and size, these machines dominated siege warfare for two thousand years.
I will consider two very different examples here. The onager was a throwing weapon of classical antiquity, familiar to both the Greeks and Romans, that was powered by the torsion of twisted rope or sinew. The trebuchet was a much larger siege engine of the medieval period, widely used across Europe and the Middle East, that was powered by gravity. In a way that was analogous to the competition between crossbows and early hand guns, the trebuchet was an important competitor of fourteenth- and fifteenth-century European cannon and set the standard for these early artillery weapons.
Onager The onager was powered by twisted sinew or rope or even human hair. See fig. The throwing arm was ratcheted back into a cocked position, a projectile usually a round stone was placed in position, and the arm was released by a trigger mechanism. The arm would then fly forward, to be stopped abruptly by a padded beam or post, at which point the projectile was launched. The abrupt stopping of the throwing arm would cause the rear end of the engine to kick upwards—hence the name an onager is a type of wild ass.
A Roman onager. Here, the projectile is placed in a short sling; in other designs the sling is replaced by a spoon-shaped depression at the end of the throwing arm. This reduced accuracy especially important in that siege engines were often required to aim at the same section of wall or tower with many consecutive shots and also reduced the rate of fire.
Trebuchet All four of these problems were solved in the Middle Ages with the trebuchet illustrated in fig. The trebuchet belongs to a class of siege engines known as counterpoise engines because the power comes from a heavy counterweight at the short end of a hinged throwing arm, as shown in the figure. The throwing arm acted like a lever; the throwing end of the arm moved four or five times faster than the counterweight end because the hinge was four or five times closer to the counterweight.
In addition, there was a long sling attached to the throwing arm, which effectively increased the arm length and provided the whiplash effect that we encountered earlier. The mechanism was smooth; this staff sling on steroids gently released its projectile and then continued its swing, like a golf club swinging through the hit. Trebuchets could be built big, and were: an early version of the arms race in medieval Europe and the Middle East led to the growth of these engines. Castle walls were built stronger and higher, so trebuchets were made bigger to throw larger rocks to knock them down, so castle walls were made stronger to resist these projectiles, and so on.
By the time cannons were well enough developed to put a stop to the proceedings by forcing a radical redesign of castles, as we will see in the next chapter , both castles and trebuchets were very large. The largest trebuchets launched heavy projectiles usually rocks, though sometimes rotting corpses to spread disease among the besieged and were powered by counterweights of up to 20 tons. A trebuchet—the heavy artillery of the Middle Ages. The throwing arm has a sling at one end, containing the projectile, and a counterweight at the other, providing power.
Some of these machines were massive, with counterweights up to 20 tons. The internal ballistics of trebuchets are quite complicated, so here I will simply summarize the results of my analysis. Lighter projectiles can be sent farther; heavier projectiles less far. Historical records claim some large trebuchets could fire projectiles that weighed over a ton. Modern reconstructions are able to group their shots closely—within a few yards at ranges of a couple of hundred yards.
The whiplash effect works well only for certain geometries; crucial parameters include the ratio of short to long lever arm lengths i. Medieval siege engineers did not have the theoretical understanding that we have, of course, and yet they managed by empirical means to produce near-optimum engine designs. Pre-gunpowder mechanical projectile weapons made use of the lever principle and of the whiplash effect to maximize the launch speed of projectiles.
Their power came from human muscles as in the case of thrown rocks or slings , from the release of stored elastic energy bows, onagers , or from stored gravitational energy trebuchets. Crossbows and trebuchets provided the performance levels against which early gunpowder weapons would be measured. Following the hugely successful The Science Book and The Math Book comes a richly illustrated chronology of physics, containing short, entertaining, and thought-provoking entries.
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At first, this hefty new tome from Oxford physicist Penrose The Emperor's New Mind looks suspiciously like a textbook, complete with hundreds of diagrams and pages full of mathematical notation. On a closer reading, however, one discovers that the book is something entirely different and far more remarkable.
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His fun and factual explanations are free of complicated equations; notes cover the key aspects of ballistics physics for the more technically inclined. Denny has perfected this engaging balance of science and story. For study or hobby, Their Arrows Will Darken the Sun is an entertaining guide to the world of ballistics.
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