import numpy as np
import matplotlib.pyplot as plt

TARGET_RANGE = 20E3
MIN_RANGE = 2E3
MIN_DELAY = 5
T_HOMING = 8
V_MISSILE = 700

def depth_of_fire(target_range, min_range, t_homing, v_target, v_missile):
    t_engagement = (target_range - min_range) / v_target
    t_flight = target_range / (v_missile + v_target)
    return (t_engagement + t_flight)/t_homing


def launch_delay(t_homing, v_missile, v_target):
    return t_homing*(1 + v_target/v_missile)


def main():
    # Range of target speeds from 0 to 1200 (inclusive)
    v_target = np.arange(1200+1)

    # Delta T_L for each target speed
    t_L = launch_delay(T_HOMING, V_MISSILE, v_target)

    plt.plot(v_target, t_L, label=r"$\Delta T_L$")
    plt.hlines(0, v_target[-1], MIN_DELAY, label=r"$\Delta T_{L_\text{min}}$", color='r')
    plt.legend()
    plt.savefig("launch-delay.png")
    plt.show()

    dof = depth_of_fire(TARGET_RANGE, MIN_RANGE, T_HOMING, v_target, V_MISSILE)
    print("DOF for V_T=200:", depth_of_fire(TARGET_RANGE, MIN_RANGE, T_HOMING, 200, V_MISSILE))

    plt.plot(v_target, dof, label="Depth of Fire")
    plt.savefig("depth-of-fire.png")
    plt.show()


if __name__ == "__main__":
    main()