Notice the distance increases until after 45
degrees, than
it starts to decrease even though the time
in flight is longer.
Trajectory with Air Resistance If
we
convert our values and plug them into a
trajectory calculator, we can get a more
accurate distance. From the calculator, if
we convert back to metric, we end up with
822.96 meters as
the distance traveled by the dart at a
10-degree angle.
www.shooterscalculator.com/
Barrels
Barrels
can have a huge impact on the forces of
the projectile. A gun’s range can be
increased with a longer barrel because
the rapidly escaping pressure behind the
projectile can accelerate the projectile
for a longer duration of time. However,
there comes a point where a too long of
barrel can induce more friction to the
projectile and limit the capabilities.
This simple phenomenon can be calculated
by the impulse momentum theorem. The
theorem states that the change in
momentum is equivalent to the force
times the change in time.
∆p=F*∆T
The
change in momentum starting from rest is
the mass of the projectile times the
muzzle velocity. The units cancel on the
right since force is mass times meter
divided by second times second. After
exiting the barrel, the force of the
pressure difference cannot accelerate
the dart. To maximize the change in
momentum, either the force could
increase or increase the time of the
force on the projectile. The latter can
easily be modified to most guns by
increasing the barrel length.
A
barrel in a typical real firearm has
fluting which are channels in the inside
surface of the barrel in a spiral to
induce a rotational force on the bullet
as it leaves the barrel. This spin on
the bullet provides stability in the air
and can increase the range. However,
this would be very difficult to
reproduce in already molded PVC pipe, so
it is not on the air rifle.
There
are
multiple barrels for different
applications which can screw onto the
rifle. The first three in the image at
right are each a step up in size of
standard PVC pipe, and the last is a
tri-barrel which are three PVC pipes
attached to a 3D printed model. The
different barrel sizes can better fit
projectiles so there is the least amount
of wasted compressed air.
