In the world of airsoft we are used to handling terms, units and expressions of the world of physics without knowing or understanding them very well.
By The Night Horseman, 2001.
In this article we are going to look at certain basic concepts that help us better understand this relationship between airsoft and the physical sciences and clarify the meaning of some terms.
This ancient branch of Physics began to be studied, without being aware of it, by the first humanoids who dedicated themselves to throwing stones and sticks. They realized that the trajectory of the projectile is affected by various physical aspects common to all, these natural and universal physical aspects are the physical laws. These laws govern the trajectory of any projectile, including the bbs used in airsoft.
Basically ballistics studies the movement of a body in one, two or three dimensions, based on a velocity, a trajectory, an effect and a morphology of the initial projectile that is modified by air resistance and gravity under ideal conditions, that is , without turbulence, winds or birds that deflect the projectile.
The most developed ballistics is the one that studies the projectiles fired by firearms where the resistance factor of the air is tried to minimize by the morphology, the gyroscopic effect that is imprinted on it, the mass and the speed of exit of the projectile. But since the ballistics of our bbs are affected by air resistance due to their spherical morphology, low weight and speed of exit in different ways, classical ballistics cannot be applied directly. That is why the trajectory of a bb is more similar to that of an arrow than that of a bullet (hence, many times we are forced to use the parabolic shot instead of the most effective tense shot).
To move in the world of physics we must know how its parameters are measured and how to convert those parameters into other similar ones. To measure these parameters we use the metric units that vary depending on the parameter to be measured. At airsoft we are interested in the output speed of the bb and the weight of it.
With these two parameters we will be able to obtain others such as the kinetic energy that we will talk about later.
To measure the output speed of the bb we use two types of units:
- Units of the international metric system: “m / s”; meters per second (the meters the bb travels in one second).
- Units of the Anglo-Saxon pagan-medieval system: "fps"; feet per second (that is, the feet that the bb travels in one second).
Because the unit of time is the same (seconds) we only need to know the equivalence between feet and meters to go from one unit to another:
one foot is 0´3048 meters
one meter is 3 feet.
To go from "m / s" to "fps" we must multiply by 3'2808 and to go from "fps" to "m / s" we must multiply by 0´3048.
Example: my fusco shoots at 330 fps then 330 x 0´3048 we can say that my fusco shoots at 100´584 m / s
Fortunately, they do not give us the weight of the bb in grains or in pagan pounds, but they offer it to us in international units, that is, in "grams". Usually a bb weighs 0.2 grams, that is a fifth of a gram (that is, with 5 bbs we would have 1 gram of weight). But to use this value in physics we must do it in kilograms.
To go from grams to kilograms we divide by 1000, so 0'2 grams will be 0'0002 kilograms.
The correct way to measure the power of an AEG is determined by means of this value, since, although we are used to resembling output speed (““ fps ”) to power, it is completely incorrect, although it has some relation.
The kinetic energy could be equated to the damage done by the projectile since both the muzzle velocity and the mass of the projectile are involved in this parameter (an impact at 300 fps of a 0'20 bb is not the same as that of a bb that weigh 0'40).
Kinetic energy, by definition, is the ability to do the “work” of a moving body on another system. Thus exposed is gibberish, especially the concept of "work", I will try to explain it plainly; Let's say that when there is an impact on us, the bb (the body) transmits an energy (performs a "job") at the point of impact that results in deformation of our tissues dissipating that energy (the kinetic energy of the bb is transmitted from the bb to our body). Thus this kinetic energy depends on the speed and weight of the bb.
That “work” that I have commented previously may seem to some of you a strange concept but it is not like that, you are very used to using it, how many times have you said something about springs of a July?
The unit of the international system for measuring work and energy is the famous “July”. Thus the kinetic energy is measured in joules, which is a correct measure for calculating the power or damage that an AEG can do. This is his equation:
Ec = ½ mvv
Ec = kinetic energy
m = mass of bb in kilograms
v = speed of the bb in m / s
Example: my fusco shoots ammunition of 0´20 grams at a speed of 350 fps, what power does it have ?:
We pass the speed am / s; 350 fps x 0´3048 = 106´68 m / s.
We pass the weight of the bb to kilograms; 0´20 grams = 0´0002 kilograms
We substitute in the formula the elements:
Ec = ½ x 0´0002 x 106´68 x 106´68 = 1.138 Joules of power.
As I mentioned earlier, the factors that affect the trajectory of a projectile under ideal conditions are, mainly, air resistance and gravity (others such as variations in gravity and the rotation of the earth are neglected for simplicity).
Assuming that we are able to regulate the hop-up so that the bb has a trajectory as straight as possible (which is a lot to suppose) we could apply a series of formulas to know its effective scope.
The part of physics that studies the movement of a body in two dimensions (or three, but we only care about two) is the "mechanics".
The mechanics do not take into account the air resistance since in principle it is very low for bodies that are not very light. Thus, if we shoot horizontally, the bb would be attracted to the ground by gravity (in a vacuum it would keep its trajectory straight and would not slow down, ideal for our games, but if it is difficult to get a field here imagine up there).
In these terms we could calculate the "fall" of the bb, that is, how far away from us the ground would touch.
We study the movement of the projectile in two dimensions (height and length) because it matters very little to us if it deviates sideways when calculating the range. Thus we can describe the movement of a bb using two interrelated formulas that describe the movement of said bb for each of the two dimensions. The first measures the distance (length) that the bb would reach in a time if gravity did not exist and the second measures the distance that the bb travels in the vertical (height) for a given time without taking into account the horizontal component (length):
- For the length, and neglecting the air resistance, we have: X = VTT
Where X is the distance the projectile travels (range), V is the speed of the projectile and T is the time the projectile is in the air.
- For the height we have: Y = VT - ½ gTT
Y being the height of the shot, V the vertical velocity of the projectile, T the time the projectile is in the air and g the gravity.
If we assume that we shoot our AEG from the shoulder (about 1 meters high) at a speed of 5 m / s. The velocity of the projectile has a horizontal but not vertical component, in that direction it undergoes acceleration towards the ground by gravity, so the vertical speed of the projectile is zero. The acceleration of gravity is, on average, 100´9.
We substitute in the second formula such that:
1´5 = 0 - ½ 9´8 TT
We clear the time (T) to find how many seconds it would take for the projectile to reach the ground: o:
TT = 0´3
T = 0'54 seconds
We substitute in the first formula:
X = 100 x 0´54 = 54 meters
Thus we would have obtained a theoretical maximum range of 54 meters on the horizontal. This assuming that we shot parallel to the ground and had no air resistance. If we wanted to increase the parabola and reach a greater distance, we would achieve the maximum range shooting at an angle of 45º with the horizontal if the objective is at our same height.
Why do we discard air resistance in these calculations? Air resistance depends largely on the velocity of the projectile and its shape, so if a ball is thrown at 20 m / s the air resistance will be negligible for movement of said ball, but if a shotgun pellet is launched at 900 m / s the range is reduced up to 20 times because at higher speeds the air resistance is much greater. So we would need a function that would calculate the air resistance for velocity at each point in the projectile's trajectory, which is very complex. If we take into account air resistance, these mechanical formulas would not be valid.
There are ballistic programs capable of calculating trajectories based on ammunition caliber, muzzle velocity, and bullet morphology, but only for fire ammunition.
DIFFERENCES BETWEEN DIFFERENT WEIGHT AMMUNITION
Chronograph measurements of the exit speeds of our AEG must be done with ammunition of the same weight since only speed is measured, not power. .
If with the same AEG we shoot ammunition of 0´20 and 0´30 we will obtain two different exit speeds, the second lower than the first.
This is because the air that pushes the gear box piston has to move more weight.
Despite the lower exit velocity, the projectile's trajectory is straighter because, as we mentioned before, having more weight is less affected by passing through the air layers.
We see that the exit velocity varies, but does the kinetic energy of the projectile vary?
As we have seen before, when calculating the range of a projectile the weight of the projectile does not intervene at all, only the speed. Therefore two projectiles of different weight at the same speed will have the same range, what differentiates them then ?; kinetic energy.
Example: If my AEG shoots at 350 fps ammunition of 0´20 grams, the projectiles have an Ec of 1´138 J
If I shoot 0'30 gram ammunition the speed drops dramatically to 285 fps but the kinetic energy remains.
So if we measure two AEG firing 0´20 and 0´30 each and give us the same speed of, for example, 350 fps, the kinetic energy would be 1'138 J and 1'7 J; the second would do a lot more damage than the first giving the same chronograph speed.
With which if we use more heavy ammunition in the same AEG we will improve the precision, we will do the same damage but we will lose range.
I hope it was mild if you read this brick in its entirety.