Warp Factor scale

[Falconer]

The Writer's Guide has it that warp factor is cubed and multiplied by the speed of light. So WF2 = 8c. At WF6 it would take 10 days to travel 6ly. This is generally accepted as the TOS scale, but it's problematic IMO.

Early TNG materials state it was changed to ^5.

S&S uses WF = ly/day . WF6 means you can travel 6ly in one day (or is it parsecs?).

A bit of a non-sequitur, but, Timothy Zahn devised a logarithmic scale where 0 was a dead stop and 1 was infinite speed. (This was based on the ".5 past lightspeed" quote from ANH.) Maybe this can be adapted to the 0-10 scale (is this what TNG did per some sources?).

[Falconer]

I’ve been mulling this around in my head. I want to use the S&S base of WF1 = 1 ly/day for gamist reasons, but I wanted that exponential growth.

WF1 - 1 ly/day
WF2 - 2 ly/day
WF3 - 3 ly/day
WF4 - 5 ly/day
WF5 - 8 ly/day
WF6 - 13 ly/day
WF7 - 21 ly/day
WF8 - 36 ly/day
WF9 - 60 ly/day
WF10 - 100 ly/day

The formula itself is a little inelegant: 1.6675^(WF-1). But the results are pleasing. Earth to Rigel is a two months’ journey at WF6.

[blackbat242]

If that was the case, then there was a lot of travel time edited out of those historical tapes accidentally released on Sol3 in the past.

And that "5-year mission" was not timed according to the standard calender (or it was a much longer year).

[Falconer]

There are a number of articles by Tim Farley which were published in Stardate magazine in the early 80s in which he analyzes the speeds actually used in the show. They are archived here. He concludes the following (I converted his numbers to ly/day):

From ‘Bread and Circuses,’ we can calculate that a warp factor of between 2 and 5 corresponds to a velocity of about 301 ly/day or greater. From ‘Obsession,’ warp 6 works out to 1176 ly/day. From ‘That Which Survives,’ warp 8.4 is calculated as 2096 ly/day.

Star Trek Maps multiplies the classic WF^3 formula by a “Cochrane Factor” with an average value of 1292.7238. (Technobabble explanation: mass curves space, but a vessel traveling in subspace can take a linear “short cut”.) This works out to…

WF4.4 - 301 ly/day
WF6 - 1,052 ly/day
WF8.4 - 2,098 ly/day

Well, that lines up with the speeds given in the show.

But I’m not super interested in reconciling the show, I’m more interested in something that works well for a game. So the jury’s still out.

[Traveller]

In one of my previous attempts at merging Star Trek and Traveller, I had roughly set out speeds as follows, using the "traditional" TOS formula.


Jump     Warp
1        4
2        5
3        5.5
4        6
5        6.5
6        7


Keep in mind, jump numbers are in parsecs per week, so this highlights how slow the traditional formula actually is. Without the "Cochrane Factor" constant in play it would take over 1000 years just to get to the edge of the galaxy. So if you're looking to model something that works well for a game, you don't want to pin down specific numbers at all, because the ship travels at the speed of plot.

Remember, the ship is really just a means of getting the characters to their destination, and as such you don't really need to go into significant detail regarding warp factors. It's enough to know that Warp 6 is faster than Warp 5. However, if you absolutely have to have hard numbers...


Warp Factor   xC
1                 1,292.7238
2                10,341.7904
3                34,903.5426
4                82,734.3232
5               161,590.475
6               279,228.3408
7               443,404.2634
8               661,874.5856
9               942,395.6502
10             1,292,723.8
11             1,720,615.3778
12             2,233,826.7264
13             2,840,114.1886
14             3,547,234.1072
15             4,362,942.825
30            34,903,542.6


Using those numbers and C itself (299,792.458 km/s) it's possible to work out the distance and time needed to visit any star system at a given warp factor. I'll edit this post a little later and post the number of light years per day for completeness, but realistically, if you want something that works well for a game, don't pin down the numbers.

[Falconer]

“Speed of plot” works fine for a scripted TV show, but for a game? I’ve always felt there is no plot in a RPG, that the plot only takes shape when you recap the session. In the meantime, for the scenario to work, the participants need to agree on how things work and what things mean in order for play to be meaningful. Why does the captain sometimes order Warp Factor 2 and sometimes Warp Factor 6 and sometimes (despite Scotty’s protestations) Warp Factor 8? It’s much less satisfying if the players have no reason to be anxious about the speed or the power drain or the danger to the ship. Unless you are of the school that the RPG IS scripted by the GM, and the players just need to “ham up” their parts. To me it’s much better if they know the stakes and the risks and they make the hard decisions and a new story emerges from that mix of wills and creative agencies.

[Traveller]

"Speed of plot" works perfectly well in games and all the Star Trek adventures I have seen have a plot and an expected course of events. In fact, the printed adventures in most games have a plot of some sort, but some are more detailed than others. It's really only the quick pick-up game where you tend to have something happen without any rhyme or reason behind it.

Remember, the ship is just a means of getting to the planet, unless you're having a shipboard adventure. Regardless of whether you're traveling to a planet or are zipping about the cosmos on the ship, the actual warp factor is more an element of flavor than anything else. That is why "traveling at the speed of plot" is appropriate here.

It would be much less satisfying if the characters weren't anxious about why the captain ordered Warp Factor X, as they would know about the risks involved. Having the players be anxious over such things is a bit much, as the players are only acting out the parts of their characters. At this point, I could come up with a comparison between a film script and a game adventure, but I don't need to. Adventures are scripted, and the players get the latitude to ad-lib their responses to events.

[Falconer]

Yeah. I mean, I assume you‘re familiar with the idea that some people have more of a narrativistic goal with their RPG vs. gamist or simulationist. I’m not as anti-narrativistic as I might come across, but, I’m enough of a gamist that I want a little more detail and not to just handwave this all the time. Of course, there are plenty of times where the adventure opens with just arriving at a planet, and it doesn't matter where it is or how fast the ship went to get there. But there are other times where it would be handy to have distances and energy expenditure rules of thumb to help create tension. And immersion! I’m thinking of doing a whole session soon, of just flying through space mapping (like in “The Corbomite Maneuver“) and encountering potentially unexciting space anomalies and planets, just to create the backdrop.

[finarvyn]

I've had this discussion in my brain for 40+ years now, ever since I got the Franz Joseph Technical Manual and saw the cube rule. I think that the problem you get is that warp factors get waaaay too fast to quickly using that scale.

Instead, think of Mach numbers. Mach 1 is the speed of sound, Mach 2 is twice that speed. The board game FEDERATION SPACE basically does something like this, where Warp-4 ships move four hexes per turn, Warp-5 ships move five hexes, and so on. While this doesn't totally explain how we can travel from one star to another so quickly (Alpha Centauri is 4 light years away, so it would become one year at Warp-4) I think that the concept still works and I love the FED SPACE map so that becomes the go-to for most of my ST campaigns.

Think of D&D, where most matters of time and distance are somewhat abstracted. I don't see why a Star Trek universe couldn't work that way. Perhaps we assume that a starship moving into Warp suddenly jumps into a faster mode, maybe 10x the speed of light instead of just 1x. So after the initial jump warp space could be linear such that Warp-1 might be 10x and Warp-6 might be 60x. I just made this up so the numbers might not work well for a campaign, but I did a quick Excel spreadsheet to come up with some results of the Marv W/F Model(TM).

Alpha Centauri is 4 light years away, so somewhere around 1461 days at light speed c.
If W/F 1 was 10c, then Alpha Centauri would be 146 days travel.
If W/F 2 was 20c, then Alpha Centauri would be 73 days travel.
If W/F 3 was 30c, then Alpha Centauri would be 49 days travel.
If W/F 4 was 40c, then Alpha Centauri would be 37 days travel.
If W/F 5 was 50c, then Alpha Centauri would be 29 days travel.
If W/F 6 was 60c, then Alpha Centauri would be 24 days travel.

Not even remotely "canon" and doesn't follow any of the stuff I've seen on how W/F is "supposed" to work, but it might be a start for a reasonable system for a ST campaign.

[Falconer]

I appreciate everyone’s thoughts and insight. I’ve looked at this from every angle, and, personally, I’m sticking to my scale from post #2 in this thread. “EU” is “Energy Units” (a Starships & Spacemen mechanic). Since I’m giving the Scout only 50 EU/day, and since the Scout blueprints suggest it gets faster speeds than most ships, I decided to give it a boost.

EU expenditure	WF	LY/day	SC WF	SC LY/day
5	1	1	1	1
10	2	2	2	2
15	3	3	3.5	4
20	4	5	4.5	6
25	5	8	5.5	10
30	6	13	6.5	17	Max. Safe Cruising Speed
35	7	21	7.5	28
40	8	36	9	60	Emergency Speed
45	9	60	10	100
50	10	100	11	166

Tested this out on Friday night, it worked great!

[Falconer]

How does S&S WF scale compare with the “strict” TOS scale used by FASA?

LY/Day	TOS WF
1	7.1
2	9
3	10.3
4	11.3
5	12.2
6	13
7	13.7
8	14.3
9	14.9
10	15.4

[Stan]

Here’s the draft of the warp mechanics I plan to use in my upcoming home-brew D6 based Star Trek RPG.

First off, I’ll use a sector map that works much like the Traveller RPG, using hexes (although you could just as easily use squares if you prefer). Each hex (or square) is one parsec across and would have at most one star system (although most hexes are empty space).

A Constitution class starship traveling at its standard cruising speed of warp 6 will travel one parsec (or one hex) in 24 hours. This makes for easy math: a Constitution class ship could travel to a star system that is 8 hexes away in 8 days.

Warp speeds run from about 0.5 at the low end (from the early days of warp technology), to a theoretical maximum of 10 (see memory-alpha.fandom.com/wiki/Warp_factor). In the Original Series era, I’ll assume warp speeds for Federation ships have about six levels, with normal cruising speeds running from warp 3.6 to warp 8.

To calculate travel times for ships running at warp speeds higher or lower than warp 6, I’ll use a warp multiplier, inspired by the hyperdrive multiplier in West End Games D6 Star Wars. To determine travel times from one hex to another, simply multiply the warp multiplier of a given warp speed times the number of hexes (or parsecs).

Warp Speed	Warp Multiplier	Time (in Hours) to Travel 1 Parsec
0.5	6.5	156
1	6	144
2	5	120
3	4	96
3.6	3.4	81.6
4	3	72
5	2	48
6	1	24
7	0.75	18
8	0.5	12
9	0.25	6
9.9	0.025	0.6

I will also create a mechanic similar to West End Games D6 Star Wars to adjudicate the risk levels of going at faster warp levels for prolonged periods of time than your ship’s standard warp rating.

I’d love to hear your feedback on the above! I hope to eventually create a robust map of the Taurus Reach and publish it publicly using the above mechanics as a great sandbox-style adventuring sector, similar to FASA’s Triangle area of space.

(Side note: I plan to use the most excellent travellermap.com/make/poster map maker at TravellerMap.com to create the Taurus Reach map. Stay tuned!)

[Falconer]

I made a glorious, huge hex map of the Triangle and am using the S&S scale with it. WF = ly/day is about as complicated as I want to get, these days. Thanks for the link to the Traveller Map site, I can’t wait to test it out!

[Falconer]

Posted this elsewhere. Figured I might as well put it here, even though it is slightly redundant.

According to the TOS Writer’s Guide (and FASA followed this), you get speeds which look like this:



However, fandom painstakingly analyzed the TOS episodes and calculated that travel in the show is faster by a factor of 1292.7238 (this is the average Cochrane Factor or χ value, and is explained as having to do with the curvature of space caused by the presence of mass; see Star Trek Maps 1980). This yields, of course, MUCH faster speeds:



For my own game, I have adopted a compromise which prioritizes gamist and narrativist concerns over simulationist concerns. The goal is to give the players meaningful choices regarding what speeds they might choose. Since they are traveling on a hex map where 1 hex = 1 ly across, speeds below WF7 in FASA terms, or above WF2 in χ terms, are basically incomprehensible.

Hence, after much experimentation, here is the table I came up with. It passes the smell test. It makes every speed a reasonable and meaningful option in the game.



Now, if you want a simulationist justification, just say that Starfleet (or maybe the AFOW) recalibrated the scale. The engine is still “doing” whatever it used to do to achieve WF7.1, but we are just “calling” that WF1 now. Or when a player says “Warp 4” we can just pretend he really said 11.3.

[ThrorII]

I'm prepping Far Trek for my group when we have our next break in campaigns. I'm wanting to do a more 'cinematic' and less 'technical' game, which Far Trek exceeds at. I accept speed = wf^3 *c of the writers guide and early publications.

For warp speeds, I'm planning on doing the following:

Warp........................ Travel time between nearby systems...
1..............................1-6 years
2..............................4 months
3..............................2 months
4..............................1 month
5..............................2 weeks
6..............................1 week
7..............................3 days
8..............................1 day
9............................. 12 hours
10............................6 hours
................................3 hours
................................1 hour

Using the Sector model (20 ly on a side cube), you can move up or down the 'Travel Time' scale based on distance. Move up (longer) by 1 slot to reach a distant planet in the sector. Move up (longer) 2 slots to cross a sector. For Example: it is 1 week to reach a nearby system at warp 6, but 2 weeks to reach a far system, and 1 month to cross the sector.

Conversely, if you know the travel time for a warp speed, you can figure out the new time if you increase or decrease warp. For example: The ship is 1 week out from Outpost 4 on the Neutral Zone at warp 4, if they kick up to warp 8 (4 slots down the table), they'll be there in 6 hours.

This allows for a cinematic flow, close to the actual wf formula, without worrying about math or geometry during a game.