Ballistic Flight PDF

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Summary

Lab report of ballistic flight practical. Using measurements from Magnum and Hobby pellets and using SUVAT equations to identify penetration abilities, rates of deceleration and projectile force....

Description

Mikail Hafeez (mh610)

Ballistic Flight

PS324 – Introduction to Ballistics

Abstract The experiment carried out was to find the different effects that muzzle velocity would have on drop distance data. The experiment also showed the difference between actual and theoretical flight paths. Two pellet types were shot from pistols to obtain the muzzle velocity, kinetic energy and acceleration data. The results that were collected were: distance from pistol to target; mass of the pellets; velocity of the pellets; and drop distance of the pellets. The data collected was used in SUVAT equations to calculate the muzzle energy, kinetic energy and acceleration to compare the different pellet types. Methodology Two groups were made and each group assigned to one of the two different pistols. Safety glasses and latex gloves were put on. Ten pellets were weighed out and a mean average was calculated. A sheet of paper was clipped onto a stop box on the other side of the room facing opposite to the pistol. A laser attached to the pistol was activated showing where the pistol was aiming onto the sheet of paper; the laser dot was marked with a pen. One member of the group loaded the pistol by removing the breech flag, cocking the pistol and placing one pellet into the barrel of the pistol. Once set up the trigger was then pulled. The breech flag was inserted back into the pistol. The velocity measurement was taken down and the area where the pellet impacted the paper was circled and numbered. The paper was moved about 2 cm to the left and the experiment was repeated four more times making the overall amount of pellets fired five. The results were then shared between the two groups so both groups had both sets of data. Results Distance from pistols to paper (m):

5.21

Pellet: Hobby Mass of all 10 pellets (kg):

8.29x10⁻³

Mean mass of 1 pellet (kg):

8.29x10⁻⁴

Pellet number 1 2 3 4 5

Velocity (ms⁻¹) 106.7 111.6 109.0 111.1 112.4

Mean velocity (ms⁻¹):

110.34

Mean drop distance (m):

0.021

Actual kinetic energy (J):

5.04

Actual acceleration (ms⁻²):

18.85

Theoretical muzzle velocity (ms⁻¹):

79.584

Theoretical kinetic energy (J):

2.625

Theoretical acceleration (ms⁻²):

9.79

Drop distance (cm) 2.3 1.9 2.5 1.9 1.9

Mikail Hafeez (mh610)

Ballistic Flight

PS324 – Introduction to Ballistics

Pellet: Magnum Mass of all 10 pellets (kg):

1.23x10⁻²

Mean mass of 1 pellet (kg):

1.23x10⁻³

Pellet number 1 2 3 4 5

Velocity (ms⁻¹) 71.17 70.37 71.27 71.53 72.67

Mean velocity (ms⁻¹):

71.402

Mean drop distance (m):

0.014

Actual kinetic energy (J):

3.135

Actual acceleration (ms⁻²):

5.25

Theoretical muzzle velocity (ms⁻¹):

97.383

Theoretical kinetic energy (J):

5.832

Theoretical acceleration (ms⁻²):

9.78

Drop distance (cm) 1.5 1.0 1.4 1.7 1.4

Analysis The experiment was carried out to observe the differences between the theoretical and actual flight paths. Two different pistol pellets were also used to show how different muzzle velocities affect the drop distance data.

1 2

The muzzle velocity was calculated by first using equation 2 ( s=ut + a t

√

2

) by rearranging to find

2s ). This would give the time from the trigger being pressed to the pellet impacting the a distance paper on the other side of the room. Then using the equation Muzzle velocity= using time t ( t=

the distance in the x-axis the muzzle velocity was calculated. The muzzle velocity for the Hobby was 79.584ms⁻¹ (see appendices 1) and for the Magnum 97.383ms⁻¹ (see appendices 2). Using the muzzle velocity the kinetic energy was calculated using

1 Kinetic energy= m v 2 2

where m = mass of

pellet and v = muzzle velocity. The kinetic energy for the Hobby was 2.625J (see appendices 3) and for the Magnum it was 5.832J (see appendices 4). To calculate the acceleration first the equation

Time=

distance velocity

was used to find time to be used in the equation

a=

2s t2

where s = drop

distance and t = time. The acceleration for the Hobby was 9.79ms⁻² (see appendices 5) and for the Magnum it was 9.78ms⁻² (see appendices 6).

Mikail Hafeez (mh610)

Ballistic Flight

PS324 – Introduction to Ballistics

As the muzzle velocity was lower for the Hobby than for the Magnum the kinetic energy should also be lower for the Hobby, which my data proves is correct. The acceleration is also a lot greater for the Magnum which correlates to the increased muzzle velocity. The actual muzzle velocities for the Hobby and Magnum were 110.34ms¯¹ and 71.402ms¯¹ respectively, making the percentage differences for the muzzle velocity of the Hobby 27.9% (see appendices 7) and for the Magnum 36.4% (see appendices 8). The actual kinetic energy for the Hobby and Magnum were 5.04J and 3.135J respectively (see appendices 9 and 10). This made the percentage differences for the kinetic energy 47.9% for the Hobby (see appendices 11) and 86.0% for the Magnum (see appendices 12). The actual acceleration for the Hobby and Magnum was 18.85ms¯² and 5.25ms¯² respectively, making the percentage difference for the Hobby acceleration 48.1% (see appendices 13) and for the Magnum 86.3% (see appendices 14). The percentage differences for the Magnum are greater than those for the Hobby. This suggests that the Magnum pellet was more susceptible to conditions that the SUVAT equations do not consider which is discussed in the conclusion. Conclusion The actual and theoretical data does not match. This is due to factors that the SUVAT equations do not consider. The SUVAT equations do not consider air resistance. Even though the pistol was fired over a short distance air resistance can still affect the velocity at which the pellet travels. The SUVAT equations do not account for the influence of gravity either. Gravity will affect the flight path of the pellet as the pellet was shot as a low velocity. The actual velocity of the Hobby was higher than the theoretical velocity. The drop distance is also greater for the Hobby. This shows that gravity had a higher influence on the Hobby pellet and therefore increased the velocity. The data may also have been affected by human error. When marking the laser point with a pen the point may have not been exactly aligned with the laser. Also when measuring the drop distance or the distance between pistol and paper, the reading may have been read wrongly which would be a human error that would affect the results. The pellets may have also been a contributing factor to the difference in actual and theoretical results and also in the difference between the two muzzle velocities. The two pellets were different shapes. This would mean that the effect of air resistance would have been different on the two pellets. The mass of the pellets were different also which affects the results. The mass of the pellets may have also been inaccurate as the mean mass of one pellet was obtained by weighing ten pellets. If more pellets had been weighed then a mean mass would have been more accurate. The percentage differences of the Magnum suggest that the Magnum pellet was more affected by these conditions....