Abstract The paper describes a spreadsheet-based analysis of the motion of a climber ascending an Earth space elevator tether. The tether is represented by elements of varying lengths, each of mean cross-sectional area based on a taper ratio equation from earlier studies. The tether tension force is calculated in each element based on gravity and centrifugal forces plus the tension force in the element below. A climber is defined by mass, drive power and maximum speed: no consideration is given to design details, the analysis assumes a tractive force simply defined by the traction power. These details derive the mean climber speed on each tether segment and hence the time to ascend each segment. Spreadsheet logic then allocates multiple climber masses on elements at variable travel time spacings, for example 24 h spacings for climbers despatched from the Earth Port once per day. The effective weight of each climber yields an additional tether tension force, giving the total tension in the tether at any altitude. Spreadsheet enhancements include an algorithm for daylight duration at varying altitudes, variable with the time of year: this permits an option for climber spacing to be calculated for solar-powered climbing. The impact of input parameters (climber mass, power and maximum speed, departure intervals, continuous or daylight-only climbing, etc.) yield outputs such as maximum tether tension and climb time. The value of this technique becomes apparent when inputs are adjusted to yield similar tether tensions, representing a scenario with a maximum tether stress limit. It is possible to find, for example, how the maximum climber gross mass varies with maximum speed or drive power. Examples of findings include (1) the benefits of higher power and maximum speed are complex, and highly dependent on the climber power/weight ratio (2) 24-h climbing might allow 20% more payload (for any given tether strength and climber design) compared with daylight-only climbing (3) two smaller climbers launched daily might enable 15% more payload to be raised compared with a single daily launch. Such deeper understanding of climber dynamics highlights the complexity of climber design optimisation: key parameters are the net climber power/mass ratio and the maximum climber speed.

Highlights • Method described to maximise payload • Smaller climbers with 24-hr power are best