Version 0.9
The model is designed for numerical simulation of atmospheric reentry of the aerodynamically-enabled bodies. The model is implemented in Microsoft Excel.
Normally, the aerodynamic forces are expressed in the following form:
D = Cx(.)qS
L = K(.)D = Cy(.)qS
where:
D - drag force
L - lift force
q = ½ rV2 - dynamic pressure
S - characteristic area of the body
Cx - drag coefficient
Cy - lift coefficient
K = L/D - aerodynamic quality
In reality, the aerodynamic coefficients (Cx, Cy) depend upon many factors among which the most important is the velocity (more precisely – Mach number). This dependence is complex and in some cases is not completely known.
In this version, the spreadsheet uses the most primitive model of the aerodynamics. The aerodynamic coefficients are considered to be constant in entire velocity range – from subsonic to hypersonic. However far from reality, this model still demonstrates the typical features of the trajectory including repeated reentry. Besides, for high speed reentry, the velocity is hypersonic for the most of the trajectory – in this range the aerodynamic coefficients do not change significantly.
The spreadsheet consists of several worksheets:
Main - The main page. Contains the input and output data
Simulation - Discrete simulation. Each line contains the system state at a certain time
The user provides the following input data:
Craft parameters:
m - mass of the reentering body (kg)
S - aerodynamic area of the body (m2)
Cx - aerodynamic drag coefficient (D = qCxS)
K - aerodynamic quality (K = L/D)
Initial conditions:
H - initial height (km)
V - initial velocity (m/s)
a - velocity angle to the horizon (degrees)
Simulation parameters:
Dt - simulation time step (s)
On the Main page there are charts of trajectory, velocity and acceleration during the reentry. Also the range (km) and total time (s) of the flight (until landing) are provided. More system parameters can be taken as needed from Simulation worksheet.