Consider a Pursuer(missile) P and Evader E according to the interception geometry according to the following diagram:

{oA = a fixed point at sea level}
Altitude(w.r.t. oA) Pursuer P = h_P
Altitude(w.r.t. oA) Evader E = hh_E
downrange distance P = dh_P
downrange distance E = dh_E

Let the pursuer be an AIM120C5 beyond-visual-range (BVR) air-to-air missile, also knownas the advanced medium-range air-to-air missile (AMRAAM).

Assumptions :

AMRAAM has a constant mass mP= 130 kg, which corresponding to its mass with half of itsrocket fuel.

We assume that AMRAAM is equipped with a boost-sustain rocket motor whose thrust profile is given by

The drag coefficient is given as follows:

C_d,P (M_P) = pchip(M_P,i,C_d,P,i,M_P)

We get this data from the model specifications

M_P,i = [0 0.6 0.8 1 1.2 2 3 4 5], C_d,P,i = [0.016 0.016 0.0195 0.045 0.039 0.0285 0.024 0.0215 0.020].

S_P (ref. area) = 2.3 m²

Let the evader be an F-16 fighter jet.

Assumptions :

F-16 has a constant mass m_E = 10000 kg.

Thrust profile for the F-16 be given by

T_E (hE) = (ρ(h_E ))/(ρ(0)) x 76310 N {approximation of the maximum dry thrust at the altitude h_E}.

The drag coefficientis given as follows:

C_{d,E(ME) = pchip(ME,i,Cd,E,i,ME)}

We get this data from the model specifications

M_E,i = [0 0.9 1 1.2 1.6 2], C_d,E,i = [0.0175 0.019 0.05 0.045 0.043 0.038].

S_E (ref. area) = 28 m²

Usually for random initial conditions or the specific initial conditions prescribed in MATLAB Driver Code, would indicate a high altitude BVR engagement scenario. So, in order to curtail it here for the sake of representation we terminate the engagement if any one of the following "fuzing" conditions are satisfied:

1. t > 500 s
2. R(t) < 10 m ; either R(t) crosses 0 or ̇R(t) > 0
3. h_P (t) < 0 ; h_E (t) < 0
4. V_P (t) < 0 ; V_E(t) < 0

Guidance Law for Pursuer: n_z,P = −3(|R(dot)|) ̇β(dot) subject to: |n_z,P|< 40 g.

Conditions at the start of the engagement simulation:

γ_P(0) = 0 rad, γ_E(0) = π rad; h_P(0) = 10000 m, h_E(0) = 10000 m; d_P(0) = 0 m, d_E(0) = 30000 m.

V_P (t)= 900 m/s; V_E (t)= 450 m/s

   Result: Detonation = 1;

           Miss Distance = 0.8077 m

Gravity Corrected Guidance Law for Pursuer: n_z,P = −3(|R(dot)|) ̇β(dot) – gcos(γ_p) subject to: |n_z,P|< 40 g.

 Result: Detonation = 0;

         Miss Distance = 1.0872e+05 m

Conditions at the start of the engagement simulation:

γ_P(0) = 0 rad, γ_E(0) = π rad; h_P(0) = 10000 m, h_E(0) = 10000 m; d_P(0) = 0 m, d_E(0) = 30000 m.

V_P (0)= 450 m/s; V_E (0)= 450 m/s

To further test the validity of dynamic engagement, in order to justify its interception capability, we take another set of assumptions:

{ Conditions at the start of the engagement simulation: γ_P(0) = 0 rad, γ_E(0) = π rad; h_P(0) = 10000 m, h_E(0) = 10000 m; d_P(0) = 0 m, d_E(0) = 30000 m, V_P (0)= 450 m/s; V_E (0)= 450 m/s}

• When we take the gravity corrected guidance law (as described above) and evader maneuver as:

    Result: Detonation = 1; (No interception/wide-impact detonation{data imperative})

            Miss Distance = 3.0126e+04 m

• When we take the gravity corrected guidance law (as described above) and evader maneuver as:

     Result: Detonation = 1;

             Miss Distance = 9.3248e-04 m