### Sub-space Equations: Drift and Pointing

This post is continued from the previous one, talking more about depth and a bit about velocities.

Generally a well pointed ship will come out tangential to the orbit of a gravity well, and fall into the correct orbit with only minor modifications. Of course if it comes in perpendicular it could cause the ship to quickly fall to its destruction, or be at an escape velocity on the other side of the gravity-well pointed away from the mass.

But there are a few problems with traveling in subspace, other than getting your heading just right. There is drift. Drift causes a ship to essentially lose depth in subspace, meaning that potential energy in our universe is lost.

Where po is the starting depth and 256 is a conversion variable related to a light year and deltaD is the distance traveled in light years. This equation hits about 0 depth in 32 light years, this causes ships to pop out of subspace with 0 potential energy, essentially an energy vacuum. If not deeply inside of a gravity well this can cause a catastrophic energy re-balance that can overwhelm a ship's shields.

The dimensionality of this equation might seem suspect. Shouldn't entering into subspace deeper in a gravity well mean that the entity is deeper in subspace if it is so tied to our gravity wells? This equation is more of an approximation. It is much more of a logarithmic curve, however, in order to go "deeper" it would probably be inside the event horizon of a small black-hole, which brings up an interesting point. If a ship were able to survive the tidal forces could it escape a black-hole via sub-space?

The other end is much more enigmatic, what happens if the ship dodges the near certainty of exiting subspace? It might continue to build up further and further debt, but would the probability of exiting subspace further approach 1? Or would it hit a peak and then taper off causing a very small percentage of ships to be trapped until reaction mass was exhausted and the shielding failed?

The largest problem for day-to-day travel is getting orbits correct because velocity is conserved throughout the process, and you would rather be in the same orbital position relative to a gravity well as the one you left, meaning that your potential energy in orbit would be conserved, except for drift.

To get an idea of the distances and tiny angles involved, and the real limiting factor to navigation apparent: precision.

Where e_r is the acceptable error in radians, d_a is the acceptable error in distance from target, and delta D is the distance to travel. Delta D and d_a are the same units so let's take travelling 1 light-year.

Going through this we find that it is about 1.5x10^-5 radians, somewhat simple for computers to handle. In fact being off by the whole distance of the Earth to the Sun is definitely not something you want to risk, at least not toward the sun. The real limiting factor is the control dynamics of the craft itself. Most small craft will have large reaction wheels, able to spin a craft with high accuracy and maintain pointing during minor shifts of mass. Milliseconds before entry into subspace a smaller more accurate set can get the error down to around 10^-10 or 10^-11. On the other end this translates to 1500 km. Still not great for a tight orbit on a planet.

The smallest consistent error was set by a crew on a small commercial packet ship averaging 350 km off of set targets. The captain of the ship went on to found his own company for delivering extremely sensitive information very quickly, because normal space still takes time to maneuver if you aren't in the right orbits even with powerful engines. He did very well for himself up until a small adjustment made while maintaining the reaction wheels deviated his craft by 1000 km causing a spectacular splash in the target planet's ocean, and disintegrating the craft. The resulting tsunami was quite small as most of the energy dissipated in different frequencies.

Larger ships use maneuvering thrusters to get a general alignment and then use several large sets of reaction wheels to precisely align, though generally their accuracy is 10^-9 or slightly better meaning they need to give themselves more than 150,000 km error.

I mentioned shield failure, I will discuss consequences next time.

Generally a well pointed ship will come out tangential to the orbit of a gravity well, and fall into the correct orbit with only minor modifications. Of course if it comes in perpendicular it could cause the ship to quickly fall to its destruction, or be at an escape velocity on the other side of the gravity-well pointed away from the mass.

But there are a few problems with traveling in subspace, other than getting your heading just right. There is drift. Drift causes a ship to essentially lose depth in subspace, meaning that potential energy in our universe is lost.

The dimensionality of this equation might seem suspect. Shouldn't entering into subspace deeper in a gravity well mean that the entity is deeper in subspace if it is so tied to our gravity wells? This equation is more of an approximation. It is much more of a logarithmic curve, however, in order to go "deeper" it would probably be inside the event horizon of a small black-hole, which brings up an interesting point. If a ship were able to survive the tidal forces could it escape a black-hole via sub-space?

The other end is much more enigmatic, what happens if the ship dodges the near certainty of exiting subspace? It might continue to build up further and further debt, but would the probability of exiting subspace further approach 1? Or would it hit a peak and then taper off causing a very small percentage of ships to be trapped until reaction mass was exhausted and the shielding failed?

The largest problem for day-to-day travel is getting orbits correct because velocity is conserved throughout the process, and you would rather be in the same orbital position relative to a gravity well as the one you left, meaning that your potential energy in orbit would be conserved, except for drift.

To get an idea of the distances and tiny angles involved, and the real limiting factor to navigation apparent: precision.

Where e_r is the acceptable error in radians, d_a is the acceptable error in distance from target, and delta D is the distance to travel. Delta D and d_a are the same units so let's take travelling 1 light-year.

Going through this we find that it is about 1.5x10^-5 radians, somewhat simple for computers to handle. In fact being off by the whole distance of the Earth to the Sun is definitely not something you want to risk, at least not toward the sun. The real limiting factor is the control dynamics of the craft itself. Most small craft will have large reaction wheels, able to spin a craft with high accuracy and maintain pointing during minor shifts of mass. Milliseconds before entry into subspace a smaller more accurate set can get the error down to around 10^-10 or 10^-11. On the other end this translates to 1500 km. Still not great for a tight orbit on a planet.

The smallest consistent error was set by a crew on a small commercial packet ship averaging 350 km off of set targets. The captain of the ship went on to found his own company for delivering extremely sensitive information very quickly, because normal space still takes time to maneuver if you aren't in the right orbits even with powerful engines. He did very well for himself up until a small adjustment made while maintaining the reaction wheels deviated his craft by 1000 km causing a spectacular splash in the target planet's ocean, and disintegrating the craft. The resulting tsunami was quite small as most of the energy dissipated in different frequencies.

Larger ships use maneuvering thrusters to get a general alignment and then use several large sets of reaction wheels to precisely align, though generally their accuracy is 10^-9 or slightly better meaning they need to give themselves more than 150,000 km error.

I mentioned shield failure, I will discuss consequences next time.

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