- #1
roldy
- 237
- 2
I'm working on a project for myself in regards to atmospheric reentry. I've come across some equations that describe the reentry trajectory. I decided to derive the equations using the diagram shown in the attached picture. Are these correct? The reason why I'm asking is that I'm getting small values for [itex]\phi[/itex] which is the angular displacement (range). I'm numerically integrating these equations. I've included plots from my program for altitude vs range and altitude vs velocity.
For this test I'm using the following initial values:
α = 35°
S = 12.97 m2
g = 9.815(R/(R + alt))2 m/s2
ρ = 1.752e-alt/6700 kg/m3
m = 3855.54 kg
θ = 0°
V = 750 m/s
alt = 120000 m
[itex]\phi[/itex] = 0°
time step size dt = 0.1
[itex]C_L = 2\sin^2\alpha \cos \alpha[/itex]
[itex]C_D = 2\sin^3\alpha[/itex]
[itex]L = 1/2C_d \rho V^2 S[/itex]
[itex]D = 1/2C_d \rho V^2 S[/itex]
[itex]\dot{V} = -D/m - g\sin\theta[/itex]
[itex]\dot{\phi} = V\cos\theta/(R + alt)[/itex]
[itex]\dot{\theta} = (L/m - g\cos\theta)/V - \dot{\phi}[/itex]
[itex]\dot{alt} = -V\cos\theta[/itex]
For this test I'm using the following initial values:
α = 35°
S = 12.97 m2
g = 9.815(R/(R + alt))2 m/s2
ρ = 1.752e-alt/6700 kg/m3
m = 3855.54 kg
θ = 0°
V = 750 m/s
alt = 120000 m
[itex]\phi[/itex] = 0°
time step size dt = 0.1
[itex]C_L = 2\sin^2\alpha \cos \alpha[/itex]
[itex]C_D = 2\sin^3\alpha[/itex]
[itex]L = 1/2C_d \rho V^2 S[/itex]
[itex]D = 1/2C_d \rho V^2 S[/itex]
[itex]\dot{V} = -D/m - g\sin\theta[/itex]
[itex]\dot{\phi} = V\cos\theta/(R + alt)[/itex]
[itex]\dot{\theta} = (L/m - g\cos\theta)/V - \dot{\phi}[/itex]
[itex]\dot{alt} = -V\cos\theta[/itex]