Interstellar travel and the Wait Calculation

The Wait Calculation was introduced by Andrew Kennedy in his paper, Interstellar Travel: The Wait Calculation and the Incentive Trap of Progress, published in the British Interplanetary Society's technical journal JBIS [Interstellar Travel: The Wait Calculation and the Incentive Trap of Progress, JBIS V 59 no 7 July 2006]

In this paper, Kennedy lays to rest the fear that continued growth will put off travellers setting out for the stars because they expect to be overtaken by later travellers who have faster speeds at their disposal. This disincentive to depart may even inhibit investment in interstellar travel. Kennedy shows that from any point in time to a given destination, there is a minimum to the total time to destination even with continuing exponential growth in the velocity of travel, and that voyagers can have the reasonable expectation of arriving without being overtaken by later voyagers by waiting a time, t, before leaving, where the relation between the time it takes to get to a destination and growth in velocity of travel can be formed at its simplest by,

(journey time now) / (journey time at time t) = (1 + r) exp (t / 2)

and r = mean annual increase in world power production

Taking a journey to Barnard's Star as an example, Kennedy shows that with a world mean annual economic growth rate of 1.4%, the quickest human civilisation might get to the 6 light year destination is in 1,110 years from now (2007).

Kennedy's paper also makes the point that a sudden discovery - like faster than light travel - that will nullify earlier velocities of travel and voyaging efforts, will not happen. Long term growth rates necessarily include all extraordinary discoveries and inventions, making the wait calculation a fair depiction of the facts facing interstellar voyagers. Thus, the minimum time to a given destination is an important consideration for competing colonisers of the stars. And the minimum wait time for any reasonable destination occurs long before relativistic velocities are reached.