How can I figure out measurements/distances and hyperspace jump time in my universe that is simple enough for readers to understand?

Question

I'm using an alternate version of the Milky Way as my setting. I need to know how far it is from one planet/area to another, and know how long it takes to jump via hyperspace -- Yes, I realize hyperspace is hand-waving. I still need some rules to tell a story. :)

In my world, jumping via hyperspace looks like this:

• You jump from one gravity well to another (anchors)
• Ship does a chemical burn to escape the origin well influence, makes calculations and then jumps.
• Hyperspace/jump time is of course less than "realtime" due to time dilation (like to have a way to figure out that based on distance)
• Ship emerges outside the target gravity well and decelerates.

I'd love to have a working map similar to this star wars map. Looking at that map, I'd know how long it would take to jump star to star from the Core Worlds to the Inner Rim.

Below was where I started, found the grid over the galaxy with the light year distances. I looked at galactic coordinates, but found it confusing and probably not necessary for the readers (or myself). Again here, just need a way to figure out basic stuff - how long does it take a ship to jump from Sagittarius to Orion, for example. What's the distance, and how long in hyperspace vs. realtime. It doesn't really matter how "real" it is, as long as it's consistent. I'm just stuck trying to work it out.

Answer 1

Light-years per hour

What's to stop you from using real-space distances themselves by, say, multiplying by a common scale factor?

For example, hyperspace speeds might be measured in units of real-space ly/hr. A ship at Earth with a "top speed" of 200 ly/hr would take ~125 hours or ~5 days to reach Sagittarius a* (galactic center) 25,000 ly away, for example.

It's perfectly consistent and the units make intuitive sense to the reader.

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If you desire different travel times measured from different observers, say, one observer in real-space and another in hyperspace, a common scale factor that describes the "rate of time" of hyperspace can be added while keeping things simple.

Travelers would likely use the "real-space velocity" that outsiders observe, to show up on-time for deliveries and such. If, by their clocks, it takes 20 hours to travel 1,000 ly, then their speed will be, by their perspective, 50 ly/hr. However, if an outsider in real-space observes that 40 hours elapses from trip start to end, then they will measure the travelers' speed as 25 ly/hr (and so, the ship's top speed may instead by listed as "25 ly/hr"). The scale factor in this instance is $\frac{1}{2}$, which describes how much slower (or possibly faster) the travelers are from the outsider's perspective.

In all cases of different top-speeds & distances, a common scale factor of

$$\frac{\text{traveler-measured time}}{\text{outsider-measured time}}$$

can be multiplied to the travelers' top-speed to find their outside "real-space" velocity.

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This math is done behind the scenes by you. What you would relay to the reader is the result of your artistic decision, the scale factor itself (hopefully a nice, round number). Ex.: "Ships age 10x slower in hyperspace than real-space" (a 20 hour trip at 50 ly/hr for the travelers is a 200 hour trip at 5 ly/hr for an outsider).

Answer 2

This is something of a Frame Challenge

And something not of a frame challenge. I think the reason you're stuck is because you're married to your map.

You see, sometimes we get way too caught up in the desire to be "realistic." I know you didn't specifically say that, but you're hanging on to a realistic map of the Galaxy. Good worldbuilding is knowing when to hold out for "realism" and when to let go and let imagination take over — especially when it's one of the small things, like travel time.

Since humanity knows absolutely squat about FTL travel, you're free to declare what your travel times will be. This is really, really important! Because when you start thinking about interstellar travel you need to realize...

• The gravity well representing your planet is moving.

• So is the gravity wells for any moons orbiting your planet.

• The gravity wells of other planets are moving.

• The gravity well(s) of your star(s) is/are moving (eeek!).

• The gravity wells of each galactic arm are moving.

• The gravity well (which isn't uniform) of the galaxy is moving.

• And finally, the gravity well represented by the center of the galaxy is non-trivial.

And that list is an awful simplification that makes angels weep and demons laugh.¹.

But the point I'm making is, you're flying from one moving target to another moving target through a medium that is, itself, moving. Worrying about how to calculate time of travel is, when you start staring the specifics in the face, pretty much a waste of time. (Every possible pun intended!)

What should you do?

• Resource: Massive Impact Design in the World's Subway Maps (image below courtesy this link and you really should read this article, the very last image is great.)

In the basic need, the complexity of subway travel is very little different from the complexity of interstellar travel. Humanity has wavered back and forth between geographically-related maps (the subway map of lower Manhattan on the right, above) and abstract but much simpler to understand maps (the subway map of lower Manhattan on the left, above) since the beginning of Subways.

Some people care about their geographical location.

Most people don't.²

What they really care about is getting from where they are to where they're going as quickly and as easily as possible. Because the details of travel are far below their radar when it comes to the important things in life — like where to get the latte you're desperate for. Think about it. Whether you think of the days before flight, the days before rail travel, or the days before sea travel, all most people wanted to know was "how long will I be on this contraption?" Otherwise, the simpler the map, the simpler the process of levering the money for the ticket out of their wallets. Therefore...

Calculation of time traveled is a function of Narrative Necessity

In other words, how fast do you want to get from Sol to Rigel? Pick a number. It's relevance to reality is irrelevant. Its relevance to your story, is relevant. If you need people to get from Sol to Rigel in a week, there's your number. You now know the distance between two points and the time you need to get between them. Distance divided by time equals velocity. You're done. Your shipboard computers will be doing all the heavy lifting anyway, right? Your readers don't really need (and many times, don't really want) to know how you calculated the transit times. They don't even particularly care if they're consistent. This is because travel times (unless a critical part of the plot of the story) are really just window dressing.

Now build an abstract map of the galaxy that shows major transit/trade paths very similar to what you see with subways, mark the time between the various "stops," then pop a cream soda and enjoy looking at a map that every reader of your story will easily understand and appreciate.

And remember that, from the perspective of characters in your story, most people will step up to a computer and say, "I want a one-way ticket from Wolf 357 to Coruscant." Plug in credit card, get robbed by everyone from tourist agents to insurance brokers to the Teamster's union, and out comes the proverbial piece of paper that says:

BOARDING TICKET XH9S779WKLZFL3260SJ1 departing Wolf 357 from orbital station A-227 on February 5, 2957 and Arriving Coruscant via orbital station V-002 on March 14, 2957. Experienced travel time: 13 days. Elapsed travel time: 37 days. PADDS enhanced with the CROSSTIME protocol will automatically update to local time and adjust your medical records to reflect your experienced age. All others must visit the courtesy desk for assistance. Have a nice trip and thank you for flying with Fontain Aerospace Routine Travel!

A computer labeled "Magic Happens Here" did all the work and unless you really think you readers will be impressed, no one needs to know how sausage is made.³

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_{¹ I get the idea that gravity falls off very quickly, but someone would need to prove that a small speed bump not noticed at sublight wouldn't ruin your suspension at FTL speeds.}

_{² That's somewhat of an unfair simplification. People care about their geographic location. Or, more precisely, their cartographic location. What they don't care about is the time required to figure out what the geography is between where they are and where they're going. The reason abstract maps are popular (whether or not they're more popular depends on a lot of variables) is because they simplify the process of choosing a destination. They're easy to read and don't look confusing. However, the purpose of this post is not to enter the "which is better?" debate. I'm just suggesting that if you step away from a "geologically accurate" map and start looking at this from the perspective of "how do people want to figure out where they're going?" most of your problem is, IMO, solved.}

_{³ And a good thing, too, because figuring out the distance between any two arbitrary stars is no small thing. If you really want to get lost down that rabbit hole, head over to The Astronomy Nexus, download their database, and start working through how to convert Earth-to-Everything measurements to SomethingElse-to-SomethingElse. I suspect you'll quickly discover it's more work than it's worth. Although if someone wanted to earn the gratitude of every worldbuilder on Earth, building a free online interface that returned the distance between any two arbitrary stars would probably do it. If that already exists, for the love of Glarnak, update the worldbuilding resources page with it.}

Answer 3

The original Traveller role playing game had limited jump distance (most advanced drives could reach six parsecs) and all jumps took the same time -- a week (as I recall, it was a few minutes more or less than 168 hours, but call it a week). They had fusion drives, and antigravity, of course, but same basic thing -- space had to be flat enough to allow a jump.

This isn't a "speed" as such -- a jump of 6 parsecs took the same time as one of one parsec.

In the end, you're handwaving the drive anyway -- you can handwave any speed or pseudospeed or jump time you like to make your world work the way you want it to.

Answer 4

Draw a Picture

Put a picture of the galactic disk in the book. Draw circles for the worlds where the action takes place.

To see how long it takes to get from Earth II to the Ugly Baby Nebula just measure the distance on the map. Use a ruler for a paper map. For a digital map use the measuring tool. For GIMP it is the compass-looking one.

Compare the distance to the red segment. The red segment is 5,000 Light years long. Once you have the distance, just divide by the speed of the spaceship, to see how long it takes to get there

In this example the distance is about 8 red segments or 40,000 light years. If the ship goes 300 light years per hour then it takes about 133 hours or five and a half days to get from Earth II to the Ugly Baby Nebula.

Answer 5

To the observer, jump time is random.

Ship does a chemical burn to escape the origin well influence, makes calculations and then jumps.

A fine discussion of these calculations here How long can it really take to calculate a hyperspace jump?

Jump time varies. A lot. It is not a straight line though sometimes it can be. At worst it is a circuitous route through higher dimensions. It can be the straight line one time and the circuitous route a minute later, for the same jump. There are a lot of things going on in multidimensional space.

The time for a jump follows a normal distribution and is unrelated to origin and destination. Most jumps take several hours. Some jumps take no time, or very occasionally less than no time. Some jumps take a long time. Very occasionally it is a very, very long time.

Answer 6

jump time is based on energy needed to transit systems

In our universe energy is neither created nor destroyed. It should be the same in fiction. I'm thinking

• Once a ship enters hyperspace the ship part of the ship (ship minus exhaust matter) must gain enough kinetic energy so that it would have gained or lost enough energy to get where it's going.

That is, if we only where considering 1 star of mass $M$ to get from $R_1$ to $R_2$ with a would require a burn of

$$\frac{M G}{R_2} - \frac{M G}{R_1} = \frac{1}{2} \Delta V^2$$

• The space ship can only travel along the direction of it's center of mass (minus the burned fuel) in hyperspace. This direction is the direction that light would have taken if nothing moved. Gravitational lensing on hyperspace travel can be a major issue if near a massive object.
• The fuel expended during hyperspace travel also exits somewhere extremely random when the space ship does.
• The velocity when exiting hyperspace is based on wherever we started from.
• Due to how the hyperspace shield opens we want to ensure that the differences in acceleration between different parts of the space ship are tiny to prevent some sort of catastrophic failure. Hence needing to be far from any center of mass. This goes as $\displaystyle \frac{1}{r^3}$
• If we were to gain energy going to $R_2$ we would counter intuitively need to thrust in the opposite direction of where we wanted to go while in hyperspace.

To specifically answer the question:

• A hyperspace jump is just based on how long it takes to thrust in hyperspace to achieve the appropriate delta V that corresponds to the energy it takes to traverse the distance. This means hyperspace travel is very fast when traversing equipotent surfaces.