# Modeling Methods for SpaceTethers.com simulator

Current list of what we can model:
• Gravity, momentum, orbits, projectiles
• Atmosphere, drag, supersonic heating
• Rocket (single stage so far - could easily do more but with SSTT only need one)
• Moon (in this case Earth is not at center of coordinate system)
• Heat flow through thermal protection system (TPS)

## Modeling Methods for SpaceTethers.com simulator

The simulator models the tether as a number of masses (maybe 100 or 1000, whatever slices is in input) connected by weightless springs. These masses and springs have the mass and strength right for that section of the tether. These values are calculated from the density and tensileGpa in the input and diameter at that section of the tether. The diameter is a linear function from the diameter at the 2 ends given by bigEndDiameter and smallEndDiameter.

Each time step (deltaT) we calculate the forces on the springs. Next we calculate the forces on the masses from the springs and gravity. Next we calculate the acceleration, new velocity, and new position of the masses.

If you set a massCd (drag co-efficient) and massA (area for modeling) we do drag calculations as explained in nasa drag page.

When simulating drag we model the atmosphere using the nasa atmosphere model. There is a nice illustration of the atmosphere showing the different parts and that this model is valid to LEO altitudes.

For a rocket the thrust is the mass flow rate times the exhaust velocity. The rocket engine part of the acceleration then comes from the F=MA equation using the current mass of the rocket. Other than this a rocket is modeled like a simple mass.

If you put in a massNoseAngle the simulator will model the shockwave and calculate mach number, shock angle, pressure, and temperature on front of the vehicle. The basic idea is that the shockwave is compressing the air and this makes it hot.

If there is a Cd greater than 0 we will output a stagnation temperature and a black body temperature. This black body temperature only takes into account radiation and not conduction. For high temperatures it should be a reasonable approximation but for low speed and low velocities it is not.

For heat absorbtion through the Thermal Protection System (TPS) the model is an insulation layer that passes heat linearly based on the temperature difference, thermal conductivity, and insulation area divided by the thickness.

We use Java double (double precision floating point number) for all simulation floating point. This has a 53 bit signed mantissa. This means there are about 15 decimal digits of precision. When we are modeling something going past the moon (about 3.8E8 meters from Earth) using a coordinate system that is centered inside the Earth, we don't have that much precision relative to the moon. It is as if we used up 8 digits or so. However, still have much better than milimeter precision, so there should not be any real problem.

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