74 lines
2.0 KiB
Markdown
74 lines
2.0 KiB
Markdown
---
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title: Weapon Systems Homework 3
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author: Aidan Sharpe
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date: February 17th, 2025
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geometry: margin=1in
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---
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# 1. Rocket Motor Equation
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```python
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def specific_impulse(v_burnout, w_launch, w_burnout):
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return v_burnout / (g*np.log(w_launch/w_burnout))
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def main():
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v_burnout = 1000
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w_rocket = 300
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w_propellant_0 = 800
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w_lauch = w_rocket + w_propellant_0
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I_sp = specific_impulse(v_burnout, w_lauch, w_rocket)
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v_exit = I_sp * g
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print("I_sp:", I_sp)
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print("V_e:", v_exit)
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# Assume constant weight flow rate
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a_burnout = 18*g
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weight_flow_rate = a_burnout*w_rocket/v_exit
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dt = 0.1
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t = np.arange(0, 12, dt)
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w_propellant = w_propellant_0 - weight_flow_rate*t
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w_propellant = np.maximum(w_propellant, 0)
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thrust = weight_flow_rate*v_exit/g
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w_total = w_rocket + w_propellant
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# Acceleration in g is force/weight
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acceleration_g = thrust/w_total
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v_no_gravity = np.cumsum(acceleration_g*g)
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v_gravity_45_x = v_no_gravity*np.cos(np.pi/4)
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v_gravity_45_y = v_no_gravity*np.sin(np.pi/4) - np.cumsum(g*np.ones_like(acceleration_g))
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v_gravity_45 = np.sqrt(v_gravity_45_x**2 + v_gravity_45_y**2)
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```
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$I_{SP} = 78.46$
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$V_e = 769.66$
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# 2. Projectile with Attack Angle
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I have been re-writing the math from the cannonball exercise to make it easier to expand in the future. For this reason, I am still working on my simulation routine:
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```python
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def simulate(mass, position, velocity, acceleration, attack_angle):
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altitude = position[1]
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speed = np.linalg.norm(velocity, 2)
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Mach = atmosphere.Mach(altitude, speed)
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axial_drag = np.array([-axial_drag.CA(Mach), 0])
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dynamic_pressure = atmosphere.dynamic_pressure(altitude, velocity)
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elevation = np.atan(velocity[1]/velocity[0]) + attack_angle
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gravity = mass*g*np.array([np.cos(-angle-np.pi/2), np.sin(-angle-np.pi/2)])
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normal_force = np.zeros(2)
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normal_force[1] = TARGET_ACCEL - np.linalg.norm(axial_drag + gravity, 2)
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```
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