Possible Superluminal Speed Scales

Exponential

S^x = C c

x: Exponent (constant)
S: Scale
C: Speed in multiples of the speed of light

An existing example of this is Star Trek's Warp Scale, as used in TOS and ENT. In this system, x is three.

• Warp 1: 1³ = 1 c
• Warp 1.5: 1.5³ = 3.375 c
• Warp 2: 2³ = 8 c
• Warp 3: 3³ = 27 c
• Warp 4: 4³ = 64 c
• Warp 5: 5³ = 125 c
• Warp 6: 6³ = 216 c
• Warp 7: 7³ = 343 c
• Warp 8: 8³ = 512 c
• Warp 9: 9³ = 729 c
• Warp 10: 10³ = 1 Kc

Logarithmic

log_b C = S
b^S = C c

b: Base
S: Scale
C: Speed in multiples of the speed of light

An inversion of the Exponential system, with a constant base and the Scale as the exponent.

Example: Base-10

• Scale 1: 10¹ = 10 c
• Scale 1.5: 10^1.5 = 31.62 c
• Scale 2: 10² = 100 c
• Scale 3: 10³ = 1 Kc
• Scale 4: 10⁴ = 10 Kc
• Scale 5: 10⁵ = 100 Kc
• Scale 6: 10⁶ = 1 Mc
• Scale 7: 10⁷ = 10 Mc
• Scale 8: 10⁸ = 100 Mc
• Scale 9: 10⁹ = 1 Gc

Factorial

S! = C c

S: Scale
C: Speed in multiples of the speed of light

Only integer speed scales are possible. Advancement would occur in generational steps, rather than continuous, gradual increase.

• Generation 1: 1! = 1 c
• Generation 2: 2! = 2 c
• Generation 3: 3! = 6 c
• Generation 4: 4! = 24 c
• Generation 5: 5! = 120 c
• Generation 6: 6! = 720 c
• Generation 7: 7! = 5.04 Kc
• Generation 8: 8! = 40.32 Kc
• Generation 9: 9! = 362.88 Kc