102 lines
3.2 KiB
Markdown
102 lines
3.2 KiB
Markdown
---
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title: Lecture 5 Homework
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author: Aidan Sharpe
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date: February 24th, 2025
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geometry: margin=1in
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---
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### 1.1 What are the individual principles used to create a balanced weapon system?
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The weapon system should be robust, simple, and predictable.
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### 1.2 Name three of the measures of weapon effectiveness.
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Weapon systems may be measured in terms of circular error probability ($\text{CEP}_\text{XX}$), probability of mission kill ($P_\text{MK}$), probability of guidance ($P_G$), and probability of hit, damage, or kill ($P_H$, $P_D$, $P_K$).
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### 1.3 Is the ENU coordinate system in invariant?
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No, because all three directions (East, North, and up) are dependent on where on the surface you are.
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### 1.4 Assume only one illuminator and one launcher in the combat system, what two limitations of the combat system determine the depth of fire?
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With only one illuminator, only one semi-active missle can be supported at a time. With only one launcher, the time between firings is limited by the the launchers minimum time between missile launches ($\Delta T_{L_\text{min}}$).
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### 1.5 What are the two main philosophies in weapon scheduling? How are they different?
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#### Quickdraw
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Shoot early and often to maximize the number of shot opportunities.
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#### Sharpshooter
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Maximize the performance of every shot by trading firing rate for shot quality.
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### 2.1 Delay between missile launches ($\Delta T_L$)
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$$\Delta T_L = T_H \left(1 + \frac{v_t}{v_m}\right)$$
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```python
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import numpy as np
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import matplotlib.pyplot as plt
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MIN_DELAY = 5
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T_HOMING = 8
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V_MISSILE = 700
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def launch_delay(t_homing, v_missile, v_target):
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return t_homing*(1 + v_target/v_missile)
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def main():
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# Range of target speeds from 0 to 1200 (inclusive)
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v_target = np.arange(1200+1)
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# Delta T_L for each target speed
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delays = launch_delay(T_HOMING, V_MISSILE, v_target)
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plt.plot(v_target, delays, label=r"$\Delta T_L$")
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plt.hlines(0, v_target[-1], MIN_DELAY,
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label=r"$\Delta T_{L_\text{min}}$", color='r')
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plt.legend()
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plt.savefig("launch-delay.png")
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plt.show()
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```
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Since the homing time is longer than the minimum time between missile launches, there is no such target speed where $\Delta T_{L_\text{Min}} = \Delta T_L$.
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### 2.2 Depth of Fire
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$$\text{TET} = \frac{\text{ROF} - R_\text{min}}{V_T}$$
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$$\text{TOF}_1 = \frac{\text{ROF}}{V_M + V_T}$$
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$$\text{DOF} = \frac{\text{TET} + \text{TOF}_1}{T_H} + 1$$
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```python
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import numpy as np
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import matplotlib.pyplot as plt
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TARGET_RANGE = 20E3
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MIN_RANGE = 2E3
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MIN_DELAY = 5
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T_HOMING = 8
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V_MISSILE = 700
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def depth_of_fire(target_range, min_range, t_homing, v_target, v_missile):
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t_engagement = (target_range - min_range) / v_target
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t_flight = target_range / (v_missile + v_target)
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return (t_engagement + t_flight)/t_homing
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def main():
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# Range of target speeds from 0 to 1200 (inclusive)
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v_target = np.arange(1200+1)
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dof = depth_of_fire(TARGET_RANGE, MIN_RANGE, T_HOMING, v_target, V_MISSILE)
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print("DOF for V_T=200:", depth_of_fire(TARGET_RANGE, \
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MIN_RANGE, T_HOMING, 200, V_MISSILE))
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plt.plot(v_target, dof, label="Depth of Fire")
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plt.savefig("depth-of-fire.png")
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plt.show()
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```
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DOF, where $V_T = 200$[m/s] is 14.0278 shots.
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