Greetings (And help formulating an equation)

[Anthony23]

Hello Physics Forums members! My name is Anthony, first time user of the boards, and wanting to send a friendly hello to everybody! While not a Math wizard, I have a strong grasp on most mathematical and physics concepts and I have a deep fascination of all things Space and Sci-Fi.

Without further ado, I come to you with a mathematical dilemma I'm having for a computer game I'm working on, called Warspace. In this universe, interstellar travel is achieved through a Fold Drive, which of course warps or "folds" space for the ship, reducing linear movement to 0.

The game itself is pretty in-depth with its mechanics, and of course I could completely oversimplify the entirety of the fold drive system and use something like "if you have X drive, then you can move Y light years," but I'd rather formulate an equation that I can use to plug in certain values and calculate a relativistic distance folded based on certain criteria.

The equation itself would solve for fold distance in light years based on several variables, including the mass of the starship in metric tons, the number of wave guides the ship uses, the maximum power rating of each of those wave guides measured in watts, and the percentage of hull that the fold drive occupies, which includes the weight of the wave guides. There are also some rules within the universe that dictate fold distance, including:

• A ship must dedicate at least 20% of its hull (or its displacement in metric tons) to the fold device, which includes wave guides
• A fold drive occupying a larger percentage of the hull can move the ship a greater distance with the same amount of power
• Wave guide configurations work in prime number configurations, but are prone to increasing margins of error beyond seven wave guides
• Gravity wells from nearby stars can cause the fold drive to behave erratically, making a minimum safe distance at least half of the distance of the system's furthest planet (This info doesn't really contribute to a final solution, but it might be relevant)
• A ship that dedicates more hull space to the wave guides and fold device can fold a greater distance with the same amount of power
• While a ship with a larger fold device can move greater distances on the same power, the margin for error also increases, decreasing the accuracy of the fold.

So that about covers it for some of the conditions. I don't know if real-world physics might come into play to help generate a realistic model (probably just a hypothetical model for sanity's sake), and I know this is a tall order, but if I can get a working equation in some spreadsheet models I'm working on, we will have a strong base for our fold-capable ships in the game universe!

If you guys have any questions, comments, concerns, or want to grill me for any noobish things I've done in this post that I'm not aware of, please send those thoughts my way, all input is appreciated!

(If anyone is interested, here are some screenshots from an early prototype of the game. Everything is at a 1:1 scale, meaning you are seeing full-size Earth and stars in this pic.)

(Here's a pic of a star up close and personal, to get a feel. That one is the scale of our sun.)

 

[Khashishi]

That looks really cool!
It sounds like the physical size of the ship is more important than mass, since the idea of waveguide elicits a certain geometric shape of wormhole. It sounds like you are describing movement in terms of instant jumps followed by a refractory period rather than a constant fast movement.

Well here's a made up equation...

$d = k \frac{E}{m} \phi(n)$

k is a fudge constant.
E is energy consumption.
m is mass.
$\phi(n)$ is the Euler totient function, because you wanted a reason to enforce prime numbers
n is the number of waveguides. n must be greater than 1
The length of the waveguide must be the length of the ship, since that's the size of the fold.
A waveguide takes up 10% of the volume of a ship. Since you need >2 waveguides, you need at least 20% of hull.

Commentary:
A group of ships can act like a larger ship by focusing their waveguides together, but with increasing margin of error for n>7, which could mean scatter in final destination.

$\Delta d = x d \phi(n)^2$
$\Delta d$ is some scatter in the final destination. It scales with d and $\phi(n)^2$. Adjust constant x so scatter is large for n > 7.

 

[Anthony23]

Ah, thank you for the input! This is a great starting point, I'm going to play around with the equations tonight!

As for some of the great commentary, I haven't actually decided on any set idea for size or length of a waveguide, considering that some of the models we've created each look a little different. For instance, I have a 2 waveguide trade ship (the ship in the screenshots) that runs on a 100MW fusion reactor, while I have a 2-3 kilometer long space station with a 5 waveguide that might be outputting somewhere in the 2-3 terrawatt range. I'm still playing around with numbers, of course, and I'm going off of a lot of real-world data of what today's naval ships and current nuclear generators produce in power, and guessing what we might be producing 150 years from now.

This is the station in the game from 13 Kilometers away, standing next to the world's largest building.(whether this is even theoretically or architecturally possible is completely out of the question, but still freaking crazy cool to look at.) The waveguides are the spheres located on the sides and bottom of the station.

Here is a size pic of the ship in the previous screen shots (if you look by the landing gear, you can see a person wireframe for size comparison):

The trader houses the fold drive and Electrogravitic Induction engines (works somewhat like the theoretical warp drive that has been making its rounds in the news) in the two large cylinders on each side of the hull.

As for how I envisioned the jumps to work, it would take some amount of time, perhaps a few minutes, maybe longer depending, to actually initiate the fold. A threshold would need to be reached by the waveguides, and the fold would more or less be instantaneous to observers outside while strange time fluctuations would occur to those within the ship/field as they transition from point A to B. If anybody has ever been stoned out of their gourd, it would be a more exaggerated feeling of one who thinks it took forever to get up from the couch and walk to the fridge, lol. I do like the idea of a combined effort to make more distant fold!