Warp Speed calculations using Fibonacci numbers

[Sgt_G]

I had a oddball idea and played around with some numbers to see if it would work. What if the Warp Speed calculation are misunderstood? What if instead of W being linear, it actually follows a spiral as described by the Fibonacci Sequence?

Under the current method Warp Speed cubed equals Light Speed:

1 = 1 = one LY takes a year
2 = 8 = one LY takes 45 days
3 = 27 = one LY takes 13 days
4 = 64 = one LY takes 6 days
5 = 125 = one LY takes 3 days
6 = 216 = one LY takes 40 hours
7 = 343 = one LY takes 25 hours
8 = 512 = one LY takes 17 hours
9 = 729 = one LY takes 12 hours
10 = 1000 = one LY takes 9 hours


However, if we go by the Fibonacci Sequence, the first two numbers, 0 & 1, are sub-light. The third number, also 1, would be Warp 1. Same as above. Warp 2 = 1+1, and Warp 3 = 1+2. So far so good. But the next Fibonacci number means Warp 4 becomes 2+3 = 5, and then Warp 5 becomes 3+5=8. The chart then becomes:

1 (0+1) = 1^3= 1 = one LY takes a year
2 (1+1) = 2^3 = 8 = one LY takes 45 days
3 (1+2) = 3^3 = 27 = one LY takes 13 days
4 (2+3) = 5^3 = 125 = one LY takes 3 days
5 (3+5) = 8^3 = 512 = one LY takes 17 hours
6 (5+8) = 13^3 = 2,197 = one LY takes 4 hours
7 (8+13) = 21^3 = 9,261 = one LY takes 56 minutes
8 (13+21) = 34^3 = 39,304 = one LY takes 13 minutes
9 (21+34) = 55^3 = 166,375 = one LY takes 3 minutes
10 (34+55) = 89^3 = 704,969 = one LY takes 45 seconds

[All times are rounded off.]

Under this chart, you can actually get someplace in a reasonable amount of time.

Thought???

 

[Mytran]

That's an intriguingly original (yet mathematic) way to get the ever increasing speeds required for higher warp factors.

It'll be interesting to see how it compares to TOS's usual suspects

 

[CRM-114]

I had a oddball idea and played around with some numbers to see if it would work. What if the Warp Speed calculation are misunderstood? What if instead of W being linear, it actually follows a spiral as described by the Fibonacci Sequence?

Under the current method Warp Speed cubed equals Light Speed:

1 = 1 = one LY takes a year
2 = 8 = one LY takes 45 days
3 = 27 = one LY takes 13 days
4 = 64 = one LY takes 6 days
5 = 125 = one LY takes 3 days
6 = 216 = one LY takes 40 hours
7 = 343 = one LY takes 25 hours
8 = 512 = one LY takes 17 hours
9 = 729 = one LY takes 12 hours
10 = 1000 = one LY takes 9 hours


However, if we go by the Fibonacci Sequence, the first two numbers, 0 & 1, are sub-light. The third number, also 1, would be Warp 1. Same as above. Warp 2 = 1+1, and Warp 3 = 1+2. So far so good. But the next Fibonacci number means Warp 4 becomes 2+3 = 5, and then Warp 5 becomes 3+5=8. The chart then becomes:

1 (0+1) = 1^3= 1 = one LY takes a year
2 (1+1) = 2^3 = 8 = one LY takes 45 days
3 (1+2) = 3^3 = 27 = one LY takes 13 days
4 (2+3) = 5^3 = 125 = one LY takes 3 days
5 (3+5) = 8^3 = 512 = one LY takes 17 hours
6 (5+8) = 13^3 = 2,197 = one LY takes 4 hours
7 (8+13) = 21^3 = 9,261 = one LY takes 56 minutes
8 (13+21) = 34^3 = 39,304 = one LY takes 13 minutes
9 (21+34) = 55^3 = 166,375 = one LY takes 3 minutes
10 (34+55) = 89^3 = 704,969 = one LY takes 45 seconds

[All times are rounded off.]

Under this chart, you can actually get someplace in a reasonable amount of time.

Thought???

Out of curiosity, where was it established the warp scale was based on Light Speed cubed?

 

[Mytran]

The season 2 writers' guide, then popularised in Whitfield's book

 

[uniderth]

Voyager. 'Nuff said.

 

[Sgt_G]

Voyager. 'Nuff said.

Meaning?

 

[thribs]

There is a memory Alpha Page about warp speeds and goes into the differences between the TOS and next gen scales.
There are even equations.

 

[uniderth]

Meaning?

In Star Trek the Enterprise went fast over long distances on a few occasions. Yet in Voyager it was to take 75 years to make it home.

 

[Sgt_G]

There is a memory Alpha Page about warp speeds and goes into the differences between the TOS and next gen scales.
There are even equations.

I'm aware. I was just suggesting another option....

Voyager was to take 75 years to make it home.

Ah. Okay. I was afraid you were referring to that stupid "Warp Ten" episode.

 

[uniderth]

Ah. Okay. I was afraid you were referring to that stupid "Warp Ten" episode.

You mean that bad dream Tom had after watching too many Captain Proton episodes.

Though, to address your OP. It's interesting to see a Fibonacci warp scale. I've never heard of one before.

 

[Mytran]

How would you go about calculation partial warp factors with a Fibonacci sequence?

 

[Sgt_G]

It should probably be some sort of log scale, but for simple math, I would just on a linear scale based on the difference between the two whole number values. 3 --> 5 = 0.2 each, 5 -- > 8 = 0.3 each, etc, etc.

 

[Mark_Nguyen]

I like it as a sci-fi concept. The thing is, the Fibonacci sequence is an abstract mathematical concept... It doesn't REALLY mean anything or have consequences in the physical world; it's really just a "neat thing" some Italian nerd came up with and published. You can argue that cubing the warp factor is equally as abstract when applied to velocities, but at least as a concept it does get applied to other real-world maths.

In TNG they tried applying it roughly to some mysterious universal constant of lightspeed travel as it relates to power required to travel a certain warp factor. The power/speed line that they came up with was completely arbitrary, but at least it was an attempt at relating actual physics to sci-fi concepts.

Mark

 

[Sgt_G]

Actually, the Fibonacci sequence is found all over nature, such as in the arrangment of petals on a flower.

Why would it work for Warp Drive? My explantion is each Warp level creates a "shell" of warped space/time, nesting the previous level(s). The size of each shell increases (or perhaps reduces) in a ratio following the sequence, which also happens to be close to the Golden Ratio = 1.618

 

[CorporalCaptain]

How would you go about calculation partial warp factors with a Fibonacci sequence?

There's a closed form expression for Fibonacci numbers that continuously fills it in at all fractional values.

https://en.wikipedia.org/wiki/Fibonacci_number#Closed-form_expression

 

[Sgt_G]

I used to be really good at math, but that looks Greek to me.

 

[Mytran]

There's a closed form expression for Fibonacci numbers that continuously fills it in at all fractional values.

https://en.wikipedia.org/wiki/Fibonacci_number#Closed-form_expression

Thanks for this. It's nice to know that there is an answer, even if I don't understand it!

 

[Jedi Marso]

Neat idea.

 

[JasonJ]

I'm on board with this as a possibility... it makes sense to me. On this scale, Earth to Vulcan 16LY away at warp 6 would take just a touch under 3 days, which fits with what Scotty tells Spock in one of the films (I forget which- it was when he offered Spock a ride back home).

Of course, if Voyager could sustain it without too many long breaks/cool downs, they could have reached the AQ in 166 days at Warp 9. Even at slower warp speeds on this scale, and accounting for the odd nebula or alien first contact and warp core cool down... still a far cry from the 80 years they say on screen. But then again, the show wouldn't be able to go on for as long if that were the case.

 

[Matthew Raymond]

Call me old-fashioned, but I feel like it's a mistake to use a Warp scale where you need a copy of MATLAB to calculate a decimal Warp factor.