The traditional Sci-Fi nebula is thick as ketchup (I'm lookin' at you Star Trek!) but the reality of nebulae we know about is that a pilot wouldn't even notice that they're in one due to particle sparsity unless the computer told them (which means the closer you get to a nebula, the more it vanishes... that's really cool if you think about it). I suspect most people don't realize that the seemingly opaque and beautifully colored nebulae we look at are that way because one is looking through lightyears' worth of volume.
So here's the question. Can someone provide a graph of particle density vs. maximum ship velocity so worldbuilders have an idea of what they can do with a nebula?
- The ship is a sphere measuring 1 km in diameter.
- The Y axis is particle density. Non-relativistic particle density. The kind of solid dust that makes up nebulae in the first place. Energy passing through the nebulic space is not a part of this question. (We're starting to strain at gnats, folks.)
- The X axis is maximum ship velocity.
- The ship has no active shields. The leading hemisphere of the ship is 10-meter-thick titanium.
- The fact that real nebulae have variable particle densities is to be ignored.
One assumes that there comes a time where either particle impact damage or heat from the passage will prohibit greater velocity. Based on this chart, worldbuilders should be capable of deriving nebula opacity at various distances. (Think "visibility" from an airplane pilot's perspective.) However, providing that kind of reference is not part of this question.