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Wait Calculation
The Wait Calculation was introduced by Andrew Kennedy in his paper "Interstellar Travel: The Wait Calculation and the Incentive Trap of Progress",[1] published in the Journal of the British Interplanetary Society (JBIS).
Kennedy refutes the notion that continued growth will inhibit setting out for the stars because travelers expect to be overtaken by later travelers who have faster speeds at their disposal. He points out that, assuming technology develops in such a way that there is exponential growth in the velocity of travel, there is an optimal departure time for arriving earliest.
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 (now, Tnow, or after waiting, \( T_t \), ) and growth in velocity of travel can be formed at its simplest by
\( \frac{T_{now}} {T_{t}} = {(1+r)}^\tfrac{t} {2} \)
where r is the mean annual increase in world power production.
Taking a journey to Barnard's Star, six light years away, as an example, Kennedy shows that with a world mean annual economic growth rate of 1.4% and a corresponding growth in the velocity of travel, the quickest human civilization might get to the star is in 1,110 years from the year 2007.
Kennedy's paper also states that a sudden discovery — like faster-than-light travel — will not nullify earlier velocities of travel and voyaging efforts. 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.
References
Kennedy, Andrew (July 2006). "Interstellar Travel: The Wait Calculation and the Incentive Trap of Progress". Journal of the British Interplanetary Society (JBIS) 59 (7): 239–246.
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