The "Tau factor" is the relationship of speed/velocity to the relative slowing of time. The closer one gets to the speed of light, the smaller the Tau factor, and the slower time seems to move. Theoretically, though one can reach immense velocities in the space of space, one can only ever approach Tau Zero. It remains unattainable. Cf. on the one hand, the old science fiction novel by Poul Anderson, Tau Zero, and on the other hand, Speed , a recent film which seems to be all motion, all movement, all lines of velocity.

An extract from "Some Thoughts on Science Fiction":

The Tau factor reflects the relativistic effects of velocity. The dimension of velocity is lengthened by the factor, time is shortened, and mass increases.

The mass increase can be used to denote the least amount of fuel possible to gain that speed. Note that in reactions, propellant must be accelerated as well.

Tau = [1 - (velocity2/light speed2)]1/2

or

Tau = [1 - (% light speed)2]1/2

mass due to acceleration = 1/tau -1

mass = [1 - (% light speed)2]-1/2 - 1

At 86.6% light speed, mass = 1 (mass of ship is doubled)

Note that, given instantaneous acceleration (best case) in a ship using propellant, 3/4 of the ship must be fuel or propellant (1/4 propellant, going 86.6% light speed in the opposite direction, 1/2 fuel to accelerate both ship and propellant)