Introduction and such Our Procedure and such Graphs and such
Concerning
S.U.V.A.T.
Our
approach to the problem of determining the muzzle velocity of our BB gun turned
out to be a crude one. My personality as well as that of my partner led us to
attempt taking the simplest approach to gathering data, which is evident in our
procedure and use of formulas, specifically SUVAT. Nevertheless we entered our
experimentation phase confident that we would find swift results and that our
no-brainer hypothesis would be immedietly supported. While we would eventually
collect data in support of our hypothesis it would certainly not be as
“simple” as we had projected.
Our method of experimentation relied observing how far a BB dropped over
a certain distance, and through the formulas v = u + at, and s = ((u + v)/2) *t
we could calculate the velocity of each BB fired.
In both formulas the variable “v”, stands for the final velocity of
the object, in this case a BB, while the variable “u” stands for the initial
velocity of the object. The
variable “a” stands for the acceleration of the object in a downward
direction due to gravity. The variable “t” stands for the time it took for the
object to reach its final destination while “s” stands for the horizontal
and or vertical distance which the BB traveled.
These formulas prove exactly what the BB was doing from the time it left
the barrel to the time it hit our target. The
slower the velocity, the farther the object will fall and the longer it will
take for the object to reach its goal. All velocities and distances were
measured in terms of feet and inches then converted into meters while time was
measured in seconds.
Our formula was straightforward enough, but it was the observation of
this formula as it affected each shot that would prove difficult. We were
challenged with the task of setting up an apparatus in which we could observe
the BB fall. First off, we knew that the BB would have to travel a considerable
distance before falling substantially, assuming it had a muzzle velocity
anywhere near that which the manufacturer had described. Secondly this distance
would have to be near level so as to easily mark the BBs fall. Unfortunately for
us though, such spaces are hard to come by less they come in the form of public
parks or school grounds, and we were cautious of the ever watchful eye of the
law. Finally such an area would almost certainly be subject to the forces of
nature (wind in particular). We were able to find a reasonably level stretch of
125 feet in our neighborhood so we chose this as our location.
In order to measure the path of the BB over this distance, we set up a
cardboard backdrop in our garage which at least protected the target from rain.
By holding the gun level at forty-two inches in the air we would be able to see,
based on where the BB hit the backdrop, how far the BB fell during its flight.
By using a laser level we were able to assure that the gun was at a level and
that the gun was appropriately targeted at the forty-two inch mark on the
target. Honestly, the finding of the one laser sight of power was probably the
best thing to happen to our experiment. The flat line it projected also
compensated for any change in level due to the terrain. While the laser level
was certainly sophisticated, our marriage of laser level and BB gun was not. We
simply duct taped the laser level onto the barrel of the gun, interestingly; the
laser level had an almost perfect groove running along the bottom which
encompassed the barrel like a glove. We tried firing the gun from up close to
see how the BB hit in relation to the laser projected on the box and found it to
hit approximately 2 cm below the projected line as the projector is located
approximately that distance above the barrel. Knowing this, we drew two parallel
lines across the target each 2 cm apart. By aiming at the top line we were able
to measure the difference between the BBs point of impact and the bottom line
and thus correct for this error.
To assure that the gun remained steady we set up a pair of saw horses
each with a vice on each end to keep the gun in place while firing.
Unfortunately
we did not develop this idea initially and endured much hardship as a result.
Not only were our shots scattered across the seven seas but it was impossible to
judge which direction the gun was pointing. The laser projected a flat line on
the box which allowed the shooter to judge trajectory but not horizontal
accuracy. This inaccuracy resulted in the only casualty of the experiment when
my partner shot me in the arm, forcing a hospital visit. But by using a point
laser pen we were able to train the gun onto the center of the target and thus
achieve accuracy.
The method by which we recorded the impact of the BBs evolved along with
the shooting apparatus. In the preliminary trials each shot was measured in its
relation to the laser line by a spotter. While one partner shot the second
partner would record the drop in the BBs while making sure the laser was on
target. The original tests recorded the impacts on the cardboard backdrop
itself. We soon realized that such recording was far too time consuming and thus
we came up with the color coding system. When a shot connected the spotter would
simply outline the impact in a color that corresponded to that number of pumps.
Paper sheets were placed over the target and the shots were instead recorded on
them. By doing so we were able to alleviate the confusion caused by trying to
identify non-descript holes in the already cratered cardboard backdrop. This
method also allowed us to set up individual trials. We would fire 15 shots at
each pump setting from two pumps to ten, into each sheet of paper, so,
theoretically, there should have been 150 data points on each sheet of paper.
What we noticed in the trials was a pleasing trend, on all four sheets
the Red dots representing two pumps would fall in the 27 inch range while the
shots with ten pumps would drop an average of five inches. Furthermore, the
various lines of impacts would register exponentially lower then the test before
them. As all four data collections were done in slightly different weather
conditions we can assume that the results were influenced very little by the
weather. While the data points as a whole were consistent with our hypothesis,
there were certainly some exceptions. Despite having the gun firmly locked in
place and frequent checks of the laser level, there would be the occasional BB
that would hit above the test line or in an entirely different test group. These
were obvious in the lower pump ranges but somewhat more subtle in the upper
ranges. The extremely close proximity of the ten pump range and the eleven pump
range led to a number of eleven pump shots actually landing lower than those
with ten pumps. We attributed this phenomenon to the fact that we were firing
from a smoothbore low quality barrel and on the elements (although we tried to
fire when it was least windy using the wet finger method). We also speculated
that the tenth pump may have nearly or entirely maxed out the guns air pressure
and that the eleventh pump was adding a negligible amount of pressure. By
testing the drop in the BBs with an eleventh pump, we were able to determine
that any pumps past the tenth yielded no increase in velocity but rather produce
results typically poorer than those of ten pumps. We concluded from this that
the maximum power is achieved at ten pumps (a fact that the manufacturer does
not disclose).
Using
our formula we were able to determine that at ten pumps the BB gun fired at a
velocity of approximately seven hundred and forty nine feet per second which is
notably over the Manufacturers rating. However, in the course of our study we
discovered that we were not, in fact, testing muzzle velocity but rather average
velocity over a distance of one hundred and twenty five feet. Clearly a BB
moving at over six hundred feet per second would be subject to wind resistance.
Supporting the idea that a BB slows down over time was our attempt to shoot
through the target with a single pump from the middle of the street. While the
BB would simply leave a dent from that range, it would penetrate the box from
point blank range. My partner and I decided to settle on average velocity rather
than try to calculate wind resistance and thereby determine muzzle velocity as
wind resistance can get a little sticky. In any event we confirmed that each
pump does in fact increase the BBs velocity by a diminishing amount until the
gun achieves maximum velocity at approximately ten pumps. Whether this increase
is measured in terms of muzzle velocity or average flight velocity is truly
irrelevant to our thesis. Happy huntin’.