Crossbow firing range: what affects the characteristics of the shot. How far and how accurately archery shoot: World records for range and accuracy of archery

Arrow weight, its speed and flight energy

Many archers like to argue which is more important - the speed or the weight of the arrow. My personal opinion is: I'd rather be hit by a feather flying at a speed of 67 m/s than a log at a speed of 53 m/s.

Another favorite topic of debate is the balance of an arrow, or center-to-center distance (FOC - front-or-center). Here the debate is as to what percentage of the total weight of the arrow should be on the front of the arrow. Some shooters, mainly those who compete in archery tournaments, really attach great importance to this, while the rest are indifferent to this problem. Below I will describe how to calculate the balance of an arrow, and then it's up to you to decide how important this is.

To determine the FOC of an arrow, you need to find its center of gravity and mark it.

Theorists say that for a perfectly fitted arrow, the front part (from the geometric center of the arrow to the tip) should have only 10-15% of the total weight of the shaft. In order to calculate the percentage balance of an aluminum or carbon arrow, you need to do the following: take an arrow already equipped (with a tip and plumage) and determine the point on it at which the arrow is in balance. Mark this point with a marker. Then find the geometric middle of the arrow by measuring with a ruler from the bottom of the shank to the end of the tube (while excluding the insert and tip, whether training or hunting), and divide the resulting length by 2. Mark this point on the tube. Now measure the distance between the two marks and divide it by the distance from one end of the tube to the geometric midpoint. This will be the balance of the arrow in percentage terms. This process is similar for wooden poles with one exception: to find the geometric center of the pole, simply measure the distance from the bottom of the shank to the edge of the glued tip and divide the resulting value by 2. Further operations are the same.

Consider the following example: Let's say the measured distance from the bottom of the shank to the end of the tube is 70 cm, so the geometric midpoint is 35 cm. The equilibrium point is shifted 5 cm closer to the tip. 5 divided by 35 is 0.143, or 14%. This means that only 14% of the total weight of the boom is on the front of the boom, which is quite acceptable by the standards. FOC.

What does it mean? Usually an arrow with FOC more than 15% in flight earlier tilts down with the tip, while at the arrow with FOC from 10 to 15% the flight path will be flatter. If, like me, you're using 145-175 grain practice or blade-tipped aluminum arrows, you simply won't be able to achieve a balance of 10-15%. Usually, FOC my arrows is 20-25%. Do you think I care? No. But it's me. I don't want to spend a lot of time and money trying to balance my arrows to this standard, especially since they all fit perfectly on my bow and fly on an ideal trajectory. And besides, none of the animals I shot cared about the balance of my arrows.

You may want to know how much energy your arrow transfers to the target at the moment of contact. This energy, known as kinetic energy ( E k), measured in joules (J). To calculate the energy of an arrow flying at maximum speed, you need to know its total weight in kilograms (m) and its speed ( V) in meters per second.

Arrow speed is best measured with an accurate chronograph. To do this, release a few arrows and calculate their average speed. Here is the formula for calculating the kinetic energy of an arrow:

For example, let's say your arrows have an average speed of 55 m/s and their total weight is 500 grains. 55 squared is 3025; We multiply 3025 by 0.0324 kg (1 grain = 0.0648 g, hence 500 grains = 32.4 g, or 0.0324 kg) and we get 98.01. Divide 98.01 by 2 to get approximately 49 J.

This figure shows how much energy in joules your arrow has when flying at maximum speed. And the further the arrow flies, the less its speed and, accordingly, the less its kinetic energy.

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Very often, poorly informed sellers talk about the crossbow as a superweapon with some kind of transcendental capabilities. According to them, crossbows, or can shoot very far. Yes, a modern crossbow shoots an arrow at 800 meters, but this is far from the effective range of a crossbow.

Arrow trajectory when fired

The crossbow has far from the highest arrow flight speed. However, the crossbow does its job quite well. The fastest crossbow shoots an arrow at a speed of 120 meters per second. The arrow weighs 420 grains - this is a troy measure of weight (approximately in grams, this is equal to 27 grams). If we compare a crossbow arrow and a bullet, we will notice that the arrow is 3-5 times heavier than a bullet, and the length of the arrow varies between 20-22 inches (or 50-55 cm). During the flight, the arrow is influenced by various natural factors (wind, gravity, etc.). Already after 25 meters this is felt: every subsequent 5 meters the arrow flies 3-7 cm lower, 1-3 m / s of speed is also lost (depending on the technical characteristics, the firing range of the crossbow also changes).

Crossbow firing range

Ten Point Pro Slider (tested crossbow) with a force of 79.5 and an arrow speed of 93 m / s showed all the advantages of a crossbow over a bow. Testing was conducted at three distances of 20, 40 and 60 yards (or 18.29m, 36.58m and 54.86m). I note that the performance of the bow and crossbow is almost the same. According to the test results, we can say that the similarity is maintained only at a distance of 20 yards - the arrows fall right on target. At a distance of 40 yards, the crossbow arrow lost height - about 30 cm. At a distance of 60 yards, the loss doubled (60 cm). At all distances, the depth of entry of the crossbow arrow is the same, that is, hunting with a crossbow is possible even at 50 meters, but you need to aim with an adjustment for loss of height. Even to choose a distance twice as large - 100 meters - the arrow will enter with the same force, but hitting such a target is a difficult task that a trained shooter can handle. Of course, the tested crossbow is far from the most powerful, and its speed is average, but such a test made it possible to evaluate the firing range of a crossbow.

Summary

Experienced hunters say that a wild boar can be killed from 75 meters (if you have a Phantom CLS crossbow in your hands). To do this, you must be able to calculate the trajectory of the arrow flight, taking into account the loss of height and taking into account the direction and strength of the wind. Such lucky shots are rare and are the pride of a hunter's resume. According to the recommendations of the manufacturers, the optimal distance for hunting is 40 yards, no more, this is the aiming range of a crossbow. It should be remembered that, unlike firearms, hunting with a crossbow requires even more skill and skill. In fact, hunting with a crossbow is suitable for those who are not afraid of difficulties and really appreciate vivid sensations.

Arrows

The ammunition of an archer on a campaign usually ranged from 20 to 100 or 200 arrows. The Scythians, Arabs or Mongols carried them all with them, the archers of other nations more often kept arrows in the convoy, in this case the portable ammunition ranged from 10 to 40 arrows.

The tip was made of bone (among the barbarian peoples and in Europe until the 11th-13th century), hard wood (in ancient Egypt), bronze or solid steel. Often it was flat and leaf-shaped, repeating the shape of flint tips, but even the Scythians invented a more perfect faceted tip, which became the standard first in Asia and then in Europe. The plumage of the arrow was not necessarily present. In general, a good arrow, suitable for long-range and accurate shooting, was a fairly technological product, its manufacture required little material, but a lot of labor. Manual labor was not valued in the Middle Ages, but an archer could not make a good arrow on a campaign on his own.

To withstand the acceleration under the influence of a bowstring stretched with such force, the arrow had to have a certain flexibility. As modern studies show, when fired, an arrow placed on a bow bends somewhat under the influence of a bowstring, and then, in the first seconds of flight, straightens up and makes oscillatory movements. Simply put, it trembles, deviating from the axial trajectory to the side of firing. The shooter must take this factor into account when aiming. The stability of the properties of the wood from which the arrow was made was prerequisite accurate shot.

Crossbow arrows experienced much greater loads when fired. So, even the ancient Greek crossbows, used since the 4th century BC. BC e. in the Greek army and referred to as "gastrafet" they fired arrows 40-60 cm long with faceted metal tips and had a bowstring tension force of up to 90 kg. They pulled the gastrafet, resting its butt against their stomach, which explains the name. A flexible arrow for a bow simply broke with such a blow, which forced the crossbow arrows to be made thicker, stiffer and shorter.

In order to conserve the energy of an arrow at ranges common in warfare of the time, exceeding at least 100 yards under combat conditions, heavy and slow-flying arrows must be used. A heavy, slow-moving arrow loses less energy over a given distance than a faster-moving arrow for the same initial kinetic energies. Remember the sports bow at the beginning of our article. Will a 20 gram arrow fired from it at a speed of 300 meters per second (that's about 1000 km / h !!!) be able to pierce the armor? At point-blank range, perhaps, but not at a combat shot distance. The force of air resistance to the movement of the arrow is proportional to the square of the speed. Of course, this aerodynamic law is not true for all speeds. But, starting from a speed of 10 meters per second and up to 100 meters per second, it is correct with very high accuracy.

It was found that at very low speeds, like the speeds of the pendulum of a clock, the air resistance increases in proportion to the first power of the speed. With an increase in the speed of movement, the air resistance begins to increase in proportion to a higher degree of speed, and at a speed of movement of the body equal to 10 m / s, it reaches exactly the square of this speed. This ratio of air resistance and speed remains constant with very high accuracy up to a speed of 100 m/sec. Only after that does it begin to grow noticeably faster than the square of the speed, especially when approaching the speed of sound, equal to 333 m/sec. Slightly above it, namely at 425 m/s, the deviation of the increase in air resistance from the point of the square of the velocity reaches its greatest value.

This means that a light and fast modern sports arrow will very soon be stopped by air resistance and at the end of the trajectory will have a speed not much higher than the speed of a heavy arrow, since it will experience more air resistance. But that's not all. The ability of a bow to give energy to an arrow, as we have already seen, depends on the weight of the arrow. A light arrow will break off, almost without slowing down the contractions of the bowstring and the body of the bow. Heavy, on the contrary, will take away a lot of energy from the same bow. So, for a given bow strength, there is some optimal weight arrows and this weight should be high enough. We must consider here another important point - the trajectory of the arrow. To fire a bow with a heavy arrow at the maximum distance, you need to shoot along a ballistic trajectory. The arrow will fly in a parabola with a significant climb. At the initial moment of time, the energy of an arrow fired at an angle can be represented as the sum of two components: vertical and horizontal. As the trajectory rises, the vertical component of the velocity decreases due to the counteraction of the earth's gravity and air resistance and, at the top of the flight, becomes zero. Then the arrow "pecks" down and moves further with a decrease - picking up speed! And than more weight arrows, the greater the speed it will pick up due to gravity. A heavy arrow thrown from a height of several kilometers would gain some final speed due to the equalization of the force of attraction and the force of air resistance, as happens, for example, with a parachutist. This means that the technique of throwing an arrow depends significantly on its weight. A light, modern sports arrow, fired from a bow with a huge initial speed, flies like a bullet at a slight angle to the horizon along a flat trajectory and is significantly slowed down by air resistance, which limits the range of the shot to about 100 - 150 meters. A heavy medieval arrow with a forged tip soars into the clouds, and, turning, hits the target almost from above. Have you ever wondered why some medieval helmets look like sun hats? The effectiveness of the bow increases as the arrow becomes heavier and enhances the features mentioned above. Therefore, in the Middle Ages, they did not particularly care about reducing the weight of the arrow, except for recreational purposes. By modern standards, the tips were extremely massive and the shafts were made more often from heavy woods. The weight of the shaft of arrows that have come down to us is 30-80 grams. To them you need to add the weight of the spike - a forged sharp tip. A good arrow weighed over 150 grams. As already mentioned, the development of more powerful bows led to the use of heavier arrows, allowing full use of the increased recoil energy of these bows. This process started long before the Middle Ages. Archery equipment found in cemeteries helps archaeologists understand the requirements of the people who used it. For example, the Scythians made arrowheads from bronze; The arrowheads shown here, 25–50 mm long (top row), were made in the 3rd century BC. BC e. With the advent of armor, there was a need for heavier and larger iron tips that could pierce them. Such tips appeared among the Huns (bottom row). To the right of each tip is shown its profile when viewed from the sharp end.

An arrow is not a bullet, it is much heavier. This means that the energy stored by it is higher. And if a bullet (weighing 9 grams) at the end of a ballistic trajectory sometimes cannot penetrate a padded jacket (it falls on your boots after flying two or three kilometers), then an arrow, with its steeper trajectory, even picks up speed on the descent with an ultra-long shot. Just throw a 9 gram bullet and a 200 gram sharp arrow from the balcony - the bullet will not even stick into the ground, and the arrow will pierce someone's head. What if there is no helmet? Or is the hand not covered with a shoulder pad? There were even such special steel arrows in the First World War for dropping them in whole heaps from an aircraft over clusters of infantry and, especially, cavalry.

Enemy warriors dressed in armor. Arrows with a "dry leaf" tip, known since the Stone Age, ceased to be effective against plate infantry and forged cavalry. With the improvement of military armor, hunting arrows - "shear", with a wide and sharp flat tip, were replaced by more massive faceted, and then spike-like tips, designed to pierce metal armor. The drawings show arrowheads known to archaeologists, mined on the territory of the Russian state.

One can clearly see the difference between hunting arrows with a tip in the form of a leaf, often a forked or flat "blade" from narrow, long, awl-shaped or faceted armor-piercing tips. The former were used against unprotected horses or against weakly armored warriors, the latter could penetrate the most serious shell from a short distance.

The most famous and well-documented in medieval Europe are battles with the massive participation of English archers. The English archer carried with him a bunch of 24-30 arrows (bunch). The rest were transported in a convoy. Unlike modern sporting and even hunting arrows, English combat arrows of that time were much more utilitarian in nature. The shaft of the arrow was a fairly thick (up to 12 mm at the widest) part of a stick of variable cross section, 75-90 cm long. (Can you imagine how much such an arrow weighs, even without a tip?) plumage went on. The plumage consisted of 3 feathers. The length of the plumage reached 25 cm, which was necessary to stabilize the heavy tip. For the manufacture of plumage, goose feathers were mainly used. they were not lacking. A tip was attached to the other end of the arrow shaft. Although there were many varieties of tips, two were mainly used in military operations: wide with a bent mustache (broadhead) and narrow, needle-shaped (bodkin). The broadhead was used to fire at unprotected infantry and horses. Bodkin had a trihedral needle-shaped tip and was used to defeat heavily armed soldiers, including at long distances. Sometimes, to improve the penetrating effect, archers waxed arrowheads. By the way, the tips for combat arrows were of the socket type - i.e. the shaft was inserted into the tip. This was done for several reasons. Firstly, when the arrow hit the armor, the socketed tip protected the arrow shaft from splitting and the arrow could be reused. And the arrows, as we have already said, could not simply be cut off in a nearby forest. Arrows required specially selected and seasoned wood. Archer and arrow maker were professions of comparable difficulty. Secondly, the tip was not fixed rigidly, and when the arrow was pulled out, it could remain in the wound. Thirdly, the removable tip greatly facilitated the transportation of bundles of arrows by archers. By the way, English archers never wore quivers with arrows on their backs. Arrows were carried either in special bags or behind a belt. In battle, archers most often stuck arrows into the ground in front of them, which facilitated the shooting process and increased the rate of fire. An additional "effect" of this handling of arrows was the serious (often lethal) complications caused by the ingress of earth into the wounds, which served as a pretext for accusing the British of using poisoned arrows.

Arrow tests

We are aware of a number of tests carried out by modern authors in order to clarify the combat characteristics of the medieval bow.

So, for example, a group of American researchers tested the penetrating ability of arrows using modern bow designs. Arrows were also used for sports, only the tips were replaced. When testing a 1 mm steel plate against a 60 Ft Lb arrow, the following results were obtained:

* the wide tip did not pierce the plate, although the tip came out the other side by about 0.25 inches,

* the short spiked tip dampened the energy considerably, but the arrow fumbled 6 inches (the torn edges of the punched hole encircled the arrow shaft),

* the middle spiked tip completely pierced the plate, and would have nailed its owner.

It turned out to be important to lubricate the tips with wax or oil. this greatly improved the penetrating power. (Remembered the waxed arrowheads of English archers.) The used arrow weighed 30 grams. (very light by medieval standards and common today for hunting) and fired from a bow at 255 fps. from a distance of 14 yards. The arrow left the bow with an energy of 65 Ft Lbs and 59 Ft Lbs per hit. (Initial loss of speed is somewhat greater due to the "jitter" of the arrow.) At 100 yards this energy would be reduced to 45 Ft Lbs and at 200 yards probably to 40 Ft Lbs. At such long distances, the energy loss is determined mainly by the weight of the arrow and the type of fletching used. The arrowhead was made of steel with a small carbon content, but heated and then cooled. While strong enough for mild steel, it was clearly worse than a medieval tip. Another tip was tested with a very strong steel end insert. This measure greatly improved performance, reducing the energy needed to break through the plate by perhaps 25%.

The results of these experiments are close to those published in Peter N. Jones' book Metallography and the Relative Efficiency of Tips and Protective Armor in the Middle Ages. This study attempted to recreate medieval armor work and used carefully crafted replica arrows and a 70 pound yew bow. It was found that spiked tips pierced 2 mm of raw iron when hit at a right angle, at an angle of 20 degrees, such tips could no longer pierce metal with a thickness of 2 mm, but they pierced it with a thickness of 1 mm. These arrows had an energy equal to 34 Ft Lbs at the time of impact, but weighed twice as much as modern arrows for a 60 pound bow. These replica medieval arrows had better tips than those used for the first tests.

So, there was always the risk that an arrow could penetrate plate armor. Depending on the distance and angle of impact, the defender could count on the level of shell protection only up to certain limits. Still, the spiked tip is much less lethal than the wide-edged one, and the unfortunate knight had a higher chance of surviving. Of course, the arrows did not fly one at a time, but simply being knocked off a horse and unable to fight proved fatal in the context of war. Moreover, small wounds could be fatal in the absence of antibiotics.

In 1918, the Englishman S.T. Pope (book "Archaelogy by experiment") investigated the range and penetration power of bows from various sources. Apache hickory bows, ash chehen, African ironwood, composite Tatar and Turkish (horn, metal, wood, sinew) and English yew longbows were used. The range of the bow and the force of its tension were studied, which was measured with weights (pulling the bowstring 71 cm from the bow). Several hundred arrows were fired with different points, using the English method (three fingers on a bowstring) and the Sioux hunters, when the bowstring is pulled with four fingers, and the arrow is held between the thumb and forefinger. The bowstrings were different - made from linen and silk fibers, mutton intestines and cotton yarn. The strongest was the Irish bowstring with a diameter of 3 cm from 60 twisted linen threads.

* A 1.04 m long Apache bow made of hickory, stretched 56 cm with a force of 12.7 kg, threw an arrow 110 m.

* Cheen ash bow 1.14 m, stretched 51 cm with a force of 30.5 kg - 150 m

* Tatar 1.88 m, bent 71 cm with a force of 13.7 kg - 91 m

* Polynesian hardwood 2 m, 71 cm 22 kg - 149 m

* Turkish 1.22 m, 74 cm force 38.5 kg - 229 m

* English yew 2 m, 71 cm 24.7 kg - 169m

* English yew 1.83 m by 91 cm 28.1 kg - 208 meters.

These are not all the tests carried out, because a Tatar bow is also described, 1.88 m long, with a string made of rawhide, which was pulled by two people. One, sitting, rested his feet on the bow, pulling the string with both hands no further than 30 cm, because he could no longer, and the other laid the arrow. It's funny that he shot only at 82 m, although they said that his first owner (the bow was about 100 years old) shot himself, sending an arrow at 400 m. The Turkish bow was made from ox horns, hickory wood, mutton intestines and skin. Among the arrows used by Pope were California Indian bamboo arrows with a birch front and turkey plumage. They were 63 and 64 cm long, and flew 10% further than the English arrows. The average speed of the arrow flight turned out to be about 36 m / s.

At short distances, the power of a bow shot surpasses the fighting power of modern hunting weapons. Tests made by other researchers showed that a steel-tipped pine arrow fired from a bow with a draw force of 29.5 kg at a distance of 7 meters pierced 140 paper targets, while a 14-gauge hunting shotgun pierced only 35 targets with a round bullet. (I wonder how much he would have pierced with a sharp sub-caliber bullet.) To determine the quality of the tips, pine boards 22 cm thick and an imitation of an animal body were used - a box without side walls, filled with raw liver and covered with deer skin. Arrows with obsidian tips pierced the box, with metal ones they pierced or pierced right through. The following experiment was carried out with a mannequin dressed in sixteenth-century chain mail from Damascus. They shot from a distance of 75 m with a bow with a pull force of 34 kg, steel tips. The arrow tore through the chain mail, causing a rain of sparks, and entered 20 cm deep into the dummy, resting on back chain mail. Then they checked the ability of arrows to kill. From 75 meters they killed a running deer - an arrow pierced its chest right through. They also killed eight deer, three adults and two young bears. Two adult bears were killed by hits to the chest and heart from a distance of 60 and 40 meters. Five arrows were fired at the attacking bear, four of which stuck in the body, and the fifth pierced the stomach and flew another 10 meters. (Well, the flayers are these American researchers J. Seriously speaking, I don’t trust the origin of the “sixteen-century chain mail from Damascus.” Not a single museum worker or collector, being in his right mind, would agree to give a rarity for testing in such a barbaric way Most likely, there was a late reconstruction in the image and likeness of ancient chain mail, inferior to it in terms of characteristics.)

Of course, all these experiments were carried out by people who did not make it their goal to learn how to shoot and hit the enemy with a bow. They are as far from the real characteristics of a medieval warrior as the results of modern professional athletes are from the results of a team of street boys. At the same time, they clearly reveal the combat characteristics and features of the use of bows.