ammunition dynamics
TRANSCRIPT
PS556 Ammunition Dynamics Dimitra Riga (dr280) 27 Mar 2015 ABSTRACT Ballistic Flight concerns the science of observing differences between theoretical flight paths and
those observed in reality. A number of different measurements were taken so as to evaluate the
effect of elevation angle on flight characteristics. Thus if different pellets; with different muzzle
velocities; different angles; and different dynamics; affect the drop data. In this report it is
established by close analysis of the data collected, what actions took place after the pellets exited
the barrel and before they hit the target. Furthermore work has been placed towards the
aerodynamic drag and gravity of ammunition illustrated during this experiment and the way
different pellets act towards these forces. The analysis linked to this report associates the factor of
a higher pellet muzzle velocity, with a more accurate shoot. It also illustrates that the heavier the
ammunition type; the better itโs ballistics performance. Furthermore the lower the pellet drag
observed; the lower the drop allowing for greater ballistic coefficient.
PS556 Ammunition Dynamics Dimitra Riga (dr280) 27 Mar 2015 METHODOLOGY
The effect of elevation angle in ballistic flight
One framed mounted air pistol was used to fire two different ammunition types; Bisley Magnum .22
Pellets (5.5mm) and Umarex Hobby- Sport Pellets (0.77g 11.9gr; Kal 5.5mm Cal .22). Firstly 10 of
each type of lead pellets were weighted by using the supplied balance, so as to calculate a mean
mass value. Then a check was undertone to ascertain that the pistol barrel was horizontal and the
distance between the pistol muzzle and the paper clipped on the box was taken. After the laser
attached to the barrel gave a marked position on the graph paper and the pistol was fired, so as to
take the velocity measurements from the chronographs and note the position of any holes in the
target papers. The same procedure was repeated five time a -3ยฐ, 0ยฐ and +3ยฐ angles.
Aerodynamics
On the second part of the experiment the ammunition dynamics were measured in a chamber
model that housed the different ammunition used during the flight and held a rail system connected
to a fan. By an anemometer adjacent to the cone in the test chamber a measurement of the
airflow velocity that the pellet model experienced during different fan speeds was recorded. Then
the drag force was linked to a computer using Cassy software, that calculated the average drag
force for a fixed duration of time. Five reading were recorded for each pellet as well as the
diameters of these models used, so as to be accessed during further data analysis.
PS556 Ammunition Dynamics Dimitra Riga (dr280) 27 Mar 2015 RESULTS Important numerical values collected during the practical class. First Part : The effect of elevation angle in ballistic flight
โข Range distance 5.2 m
โข Weight of lead pellets (weight of 10 units/pellets)
10 Hobby - Sport Line Pellets +7.81 g (0.781g mean)
10 Bisley Magnum .22 Pellets + 13. 65 g (1.365 mean)
โข Measured Muzzle Velocity and Average Muzzle Velocity at 0ยฐ elevation
Hobby-Sport Line Pellets measure muzzle velocity (m/s)
Bisley Magnum .22 Pellets measured muzzle velocity (m/s)
1 99.18 74.78
2 100.4 73.60
3 102.8 74.99
4 101.3 76.46
5 101.4 76.46
Average muzzle velocity (m/s) 101.016 75.258
โข Drop Distance (measuring the distance between the laser mark and the actual mark produced by
the pellet on the graph paper), measurements that will help ascertain the accuracy and damage caused by different type of ammunition. Elevation Hobby-Sport Line
Pellets (cm) Bisley Magnum .22 Pellets(cm)
0ยฐ 1 0.3 1.4 2 0.5 1.2 3 0.5 1.8 4 0.9 1.4 5 0.4 1.2 +3ยฐ 1 31.6 32.1 2 31.8 32.0 3 31.9 31.9 4 31.5 31.4 5 31.1 31.6 -3ยฐ 1 27.8 27.3 2 27.5 27.5 3 28.0 27.0 4 28.2 27.5
PS556 Ammunition Dynamics Dimitra Riga (dr280) 27 Mar 2015 5 28.0 27.3 Mean drop distance 0ยฐ 0.52 1.4 Mean drop distance +3ยฐ
31.58 31.8
Mean drop distance -3ยฐ
27.9 27.32
Second Part : Aerodynamics
โข Diameter of hobby โflat headโ projectile model : 55.25mm
`Cross sectional area: 3.06916x10-3m
โข Diameter of magnum โround headโ projectile model : 56.48mm
Cross sectional area: 3.1787044x10-3m
โข Diameter of actual hobby/magnum pellets : 5.5mm
Drag Force (N) Flow Velocity (m/s)
Hobby projectile model
1 0.05325ยฑ0.00010 8.3
2 0.1178 ยฑ0.0017 10.8
3 0.2024ยฑ0.0010 16.9
4 0.3113ยฑ0.0018 19.4
5 0.3835ยฑ0.011 23.9
Magnum projectile model
1 0.0630ยฑ0.0003 10.9
2 0.0722ยฑ0.0003 14.4
3 0.1154ยฑ0.0010 16.4
4 0.1343ยฑ0.0007 20.9
5 0.1537ยฑ0.0008 22.6
PS556 Ammunition Dynamics Dimitra Riga (dr280) 27 Mar 2015 ANALYSIS
First Part :The effect of elevation angle on flight characteristics
โข Using the mean mass, measured range, and measured drop data calculate the theoretical muzzle velocity of the pellets using Newtonian mechanics (SUVATs). Used to give us more data about the ballistic flight mechanisms observed in the experiment as well as to bring perspective towards the realistic expectations that one can have when using different ammunition types.
s = ๐๐ +๐
๐a๐๐ ๐ซ๐๐๐ซ๐ซ๐๐ง๐ ๐๐ ๐๐จ๐ซ ๐ญ = โ
๐๐ฌ
๐
s = distance (M)
u= initial velocity (m/s)
a=acceleration (m/sยฒ)
t=time (s)
Hobby โ Sport Line Bisley Magnum .22
t = โ2s
a t = โ
2s
a
๐ก = โ2 ร(5.2 ร10โ3)
9.81 ๐ก = โ
2 ร( 0.0140)
9.81
๐ก = โ0.0104
9.81 ๐ก = โ
0.028
9.81
๐ก = 0.033๐ ๐๐ ๐ก = 0.053๐ ๐๐
PS556 Ammunition Dynamics Dimitra Riga (dr280) 27 Mar 2015 โข Calculation for speed, used to evaluate the impact of different pellet muzzle velocity to the efficiency of a weapon (due to the fact that audience background knowledge in ballistics would effectively observe the importance of the difference in speed). Thus the higher the speed; the more accurate the ammunition (the more damage observed).
๐๐๐๐๐ =๐๐ข๐ฌ๐ญ๐๐ง๐๐
๐๐๐๐
s= speed (m/s)
d=distance (M)
t= time (s)
Hobby โ Sport Line Bisley Magnum .22
๐ ๐๐๐๐ =distance
๐ก๐๐๐ ๐ ๐๐๐๐ =
distance
๐ก๐๐๐
๐ ๐๐๐๐ = 5.2๐
0.033๐ ๐ ๐๐๐๐ =
5.2๐
0.053๐
๐ ๐๐๐๐ = 157.57๐/๐ 2 ๐ ๐๐๐๐ = 98.11๐/๐ 2
โข Acceleration due to gravity (hobby, 0ยฐ)
Using the measured range and drop data gathered, a theoretical value was calculated for acceleration due to gravity using Newtonian mechanisms. The reason for that would be that the gravity is of major importance to our report, since gravity is a concept that differs between different geographical locations ( i.e. earth vs. moon, the University of Kent vs. the highest point of Everest mountain).
๐ =๐๐ฌ
๐ญยฒ
a= acceleration (m/sยฒ)
s= distance (M)
t= time (s)
PS556 Ammunition Dynamics Dimitra Riga (dr280) 27 Mar 2015 Hobby โ Sport Line Bisley Magnum .22
๐ =2s
tยฒ ๐ =
2s
tยฒ
๐ = 2 ร(5.2ร10โ3)
0.033 ๐ =
2 ร0.0140
0.053
๐ = 0.0104
0.0332 ๐ = 0.028
0.0532
๐ = 9.56m/๐ 2 ๐ = 9.97m/๐ 2
โข Acceleration due to gravity (hobby, +3ยฐ)
๐ =๐๐
๐(๐๐๐๐๐๐๐๐๐๐๐) ๐๐จ๐ฌ๐
t= time (s)
s= distance (M) in the x direction
v= final velocity (m/s)
Hobby- Sport Line Bisley Magnum . 22
๐ก =๐ ๐ฅ
๐ฃ(๐โ๐๐๐๐๐๐๐๐โ) cos3 ๐ก =
๐ ๐ฅ
๐ฃ(๐โ๐๐๐๐๐๐๐๐โ) cos3
๐ก = 5.2๐
101.016๐๐๐ (+3) ๐ก = 5.2๐
75.258๐๐๐ (+3)
๐ก = 0.05154763799๐ ๐๐ ๐ก = 0.06919046745๐ ๐๐
PS556 Ammunition Dynamics Dimitra Riga (dr280) 27 Mar 2015
๐ = ๐(๐๐ก๐ซ๐จ๐ง๐จ๐ ๐ซ๐๐ฉ๐ก) ๐ฌ๐ข๐ง ๐
u= initial velocity (m/s)
v= final velocity (m/s)
Hobby- Sport Line Bisley Magnum .22
๐ข = 101.061sin (+3) ๐ข = 75.258 sin(+3)
๐ข = 5.289124074๐/๐ ๐ข = 3.938699395๐/๐
๐ =๐(๐ฌ โ ๐ฎ๐ญ)
๐ญยฒ
a= acceleration (m/sยฒ)
s= distance (M)
u= initial velocity (m/s)
t= time (s)
Hobby- Sport Line Bisley Magnum .22
๐ =2(sโut)
tยฒ ๐ =
2(sโut)
tยฒ
๐ =2(0.3158โ5.289124074 ร0.05154763799)
0.05154763799ยฒ ๐ =
2(0.3180โ3.938699395 ร0.06919046745)
0.06919046745ยฒ
๐ = 0.0863162939
2.657158982 ร 10โ3 ๐ =
0.09095909543
0.06919046745ยฒ
๐ = 32.4844296 ๐/๐ 2 ๐ = 19.0000001๐/๐ 2
โข Acceleration due to gravity (hobby, - 3ยฐ)
PS556 Ammunition Dynamics Dimitra Riga (dr280) 27 Mar 2015
๐ =๐๐
๐(๐๐๐๐๐๐๐๐๐๐๐) ๐๐จ๐ฌ๐
t= time (s) s= distance (M) in the x direction v= final velocity (m/s) Hobby- Sport Line Bisley Magnum . 22
๐ก =๐ ๐ฅ
๐ฃ(๐โ๐๐๐๐๐๐๐๐โ) cos3 ๐ก =
๐ ๐ฅ
๐ฃ(๐โ๐๐๐๐๐๐๐๐โ) cos3
๐ก = 5.2๐
101.016๐๐๐ (โ3) ๐ก = 5.2๐
75.258๐๐๐ (โ3)
๐ก = 0.05154763799๐ ๐๐ ๐ก = 0.06919046745๐ ๐๐
๐ = ๐(๐๐ก๐ซ๐จ๐ง๐จ๐ ๐ซ๐๐ฉ๐ก) ๐ฌ๐ข๐ง ๐
u= initial velocity (m/s) v= final velocity (m/s) Hobby- Sport Line Bisley Magnum .22
๐ข = 101.061sin (โ3) ๐ข = 75.258 sin(โ3)
๐ข = โ5.289124074๐/๐ ๐ข = โ3.938699395๐/๐
PS556 Ammunition Dynamics Dimitra Riga (dr280) 27 Mar 2015
๐ =๐(๐ฌ โ ๐ฎ๐ญ)
๐ญยฒ
a= acceleration (m/sยฒ) s= distance (M) u= initial velocity (m/s) t= time (s) Hobby- Sport Line Bisley Magnum .22
๐ =2(sโut)
tยฒ ๐ =
2(sโut)
tยฒ
๐ =2(0.3158โ(โ5.289124074 ร0.05154763799)
0.05154763799ยฒ ๐ =
2(0.3180โ(โ3.938699395 ร0.06919046745)
0.06919046745ยฒ
๐ = 1.176883706
2.657158982 ร 10โ3 ๐ =
1.181040905
0.06919046745ยฒ
๐ = 442.9105348 ๐/๐ 2 ๐ = 246.7018521๐/๐ 2
PS556 Ammunition Dynamics Dimitra Riga (dr280) 27 Mar 2015 Second Part : Aerodynamics
๐ ๐ =๐๐๐๐๐๐
๐ ๐ซ๐๐๐ซ๐ซ๐๐ง๐ ๐๐ ๐๐จ๐ซ ๐๐ =
๐๐ ๐
๐๐ยฒ๐
Fd = drag force (N)
Cd = drag coefficient
๐ = density of medium (Kgm-3) , which is 1.2 Kgm-3
V = flow velocity (m/s)
A = cross sectional area (m2)
โข Drag coefficients for hobby pellet
1. Cd =2Fd
AVยฒฯ =
2 ร0.053225
3.06916๐ฅ10โ3๐ ร8.32ร1.2 =2.517328866
2. Cd =2Fd
AVยฒฯ =
2 ร0.1178
3.06916๐ฅ10โ3๐ ร10.82ร1.2 =0.5484373196
3. Cd =2Fd
AVยฒฯ =
2 ร0.2024
3.06916๐ฅ10โ3๐ ร16.92ร1.2 =0.3848276947
4. Cd =2Fd
AVยฒฯ =
2 ร0.3113
3.06916๐ฅ10โ3๐ ร19.42ร1.2 =0.4491639382
5. Cd =2Fd
AVยฒฯ =
2 ร0.3835
3.06916๐ฅ10โ3๐ ร23.92ร1.2 =0.3645849915
PS556 Ammunition Dynamics Dimitra Riga (dr280) 27 Mar 2015 โข Drag coefficients for magnum pellet
1. Cd =2Fd
AVยฒฯ =
2 ร0.0630
3.06916๐ฅ10โ3๐ ร10.92ร1.2 =0.287949795
๐. Cd =2Fd
AVยฒฯ =
2 ร0.0722
3.06916๐ฅ10โ3๐ ร14.42ร1.2 =0.1890781888
๐. Cd =2Fd
AVยฒฯ =
2 ร0.1154
3.06916๐ฅ10โ3๐ ร16.42ร1.2 =0.2329953925
4. Cd =2Fd
AVยฒฯ =
2 ร0.1343
3.06916๐ฅ10โ3๐ ร20.92ร1.2 =0.1669600863
6. Cd =2Fd
AVยฒฯ =
2 ร0.1537
3.06916๐ฅ10โ3๐ ร22.62ร1.2 =0.1634128519
PS556 Ammunition Dynamics Dimitra Riga (dr280) 27 Mar 2015
๐ช๐ =๐ฆ
๐ช๐ ๐ช๐ฎ๐
ร ๐ ๐
Cb = ballistic coefficient (kgm-2)
m = mass (Kg)
Cd = drag coefficient
CG1= drag coefficient of G1 bullet, 0.5191
โข Ballistic Coefficient for hobby pellet
1. ๐ถ๐ =m
๐ถ๐๐ถ๐บ1
ร๐2 =
0.0007812.517328866
0.5191ร0.00552
= 5.323983832
2. ๐ถ๐ =m
๐ถ๐๐ถ๐บ1
ร๐2 =
0.0007810.5484373196
0.5191ร0.00552
= 24.43710102
3. ๐ถ๐ =m
๐ถ๐๐ถ๐บ1
ร๐2 =
0.0007810.3848276947
0.5191ร0.00552
= 34.8265428
4. ๐ถ๐ =m
๐ถ๐๐ถ๐บ1
ร๐2 =
0.0007810.4491639382
0.5191ร0.00552
= 29.83814381
5. ๐ถ๐ =m
๐ถ๐๐ถ๐บ1
ร๐2 =
0.0007810.3645849915
0.5191ร0.00552
= 36.76021039
PS556 Ammunition Dynamics Dimitra Riga (dr280) 27 Mar 2015
โข Ballistic Coefficient for magnum pellet
1. ๐ถ๐ =m
๐ถ๐๐ถ๐บ1
ร๐2 =
0.0013650.287949795
0.5191ร0.00552
= 81.34699745
2. ๐ถ๐ =m
๐ถ๐๐ถ๐บ1
ร๐2 =
0.0013650.1890781888
0.5191ร0.00552
= 123.8844702
3. ๐ถ๐ =m
๐ถ๐๐ถ๐บ1
ร๐2 =
0.0013650.2329953925
0.5191ร0.00552
= 100.5514341
4. ๐ถ๐ =m
๐ถ๐๐ถ๐บ1
ร๐2 =
0.0013650.1669600863
0.5191ร0.00552
= 138.1116276
5. ๐ถ๐ =m
๐ถ๐๐ถ๐บ1
ร๐2 =
0.0013650.1634128519
0.5191ร0.00552
= 143.3415485
One can observe certain discrepancies between the theoretical and observed muzzle velocitiy as
well as the acceleration (take into account gravity). The muzzle velocity for the magnum was
90.144m/s, but the calculated velocity was 157.55m/s. Also the observed velocity for hobby was
114.1m/s, but the calculated one was 98.11m/s. This can be accounted for by looking at the air
resistance as well as the pressure and humidity.
Furthermore the elevation observed affected more the hobby pallet, rather than the magnum pallet
that was heavier in weight, even though it should be considered that we had a range of 5.2m.
PS556 Ammunition Dynamics Dimitra Riga (dr280) 27 Mar 2015
The change in flow velocityโs effect on drag coefficient
From the graphs one can see that the relationship between drag force generated and flow velocity differ a lot from the hobby pellet that is a lot more unsteady than the magnum pellet. With the magnum pellet demonstrating a steadier trend of results.
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0 5 10 15 20 25 30
Flo
w v
elo
city
(m
/s)
Drag Force (N)
Relationship between drag force generated and flow velocity for the hobby pellet
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0 5 10 15 20 25
Flo
w v
elo
city
(m
/s)
Drag Force (N)
Relationship between drag force generated and flow velocity for the magnum pellet
PS556 Ammunition Dynamics Dimitra Riga (dr280) 27 Mar 2015
Relationship between drag coefficient and flow velocity
One can clearly see that the projectile design can affect the ballistic coefficient. Thus the projectile design is directly linked with its aerodynamic ability, the heavier a projectile; the larger the surface area that drags the projectile and makes it slower.
Furthermore it is obvious that the hobby pellets have significantly worst values, with the highest of
them being 36.7 Kgm-2 whilst the magnumโs was 143.3 Kgm-2 . The magnumโs smoother head
makes it easier to go against the drag force and that makes this pelletโs design more aerodynamic.
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 5 10 15 20 25
Dra
g co
eff
icie
nt
Flow Velocity (m/s)
Relationship between drag coefficient and flow velocity for the hobby pellet
0
0.5
1
1.5
2
2.5
3
0 5 10 15 20 25 30
Dra
g C
oe
ffic
ien
t
Flow Velocity (m/s_
Relationship between drag coefficient and flow velocity for the hobby pellet
PS556 Ammunition Dynamics Dimitra Riga (dr280) 27 Mar 2015
CONCLUSION
One can observe that on the first part of the experiment concerning the effect of the elevation angle on ballistic flight, it is obvious that the heavier pellet (magnum) does travel slower on an +3 angle, but far more accurately than the lighter pellet (hobby) that experience a faster travel but is affected more by the gravity and loses the ability to maintain its velocity. Furthermore gravity can be accounted for by looking at how long the pellets stay on air, since the longer they are between our range distance; the more the values will be effected. The magnum thus is a heavier projectile, that travels slowly and accurately. At the same time the hobby is lighter, faster and achieves better data.
Furthermore as far as the second part of the experiment is concerned the magnum has a better coefficient, since it can be affected less from the drag since it is a lot heavier than the hobby. Also the different between the height observed while air drop was not really drastic keeping both pellets.