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Abstract:
A nomogram (or nomograph) is a graphical representation of three or more pieces of data; knowledge of two of those values visually leads to the other(s). Typically, a sharp pencil and keen eye will produce results within 5% of an exact numerical solution. Nomograms predate personal computing devices and hand-held electronic calculators by almost 100 years. It wasn’t until the mid-1980s that operators and engineers had access to personal computers; prior to this time mainframe computations or hand calculations were the only means to arrive at precise answers. Such calculations were used to produce nomograms for those that did not have access to such computational devices. Thus, prior to the mid-1980s many operators and engineers relied on nomograms to perform what would now be considered back-of-the-envelope computations. Presented here is the construction of some useful nomograms regarding minimum-time, continuous low-thrust, circle-to-circle, orbit transfers in addition to nomograms relating miss distance to off-cycle thrust time as well as to maximum probability. The nomogram relating miss distance to maximum probability and its associated standard deviation is not limited to low-thrust transfers and can be used for any collision avoidance maneuver planning. The nomograms are useful for pre-mission planning and determining if further numerical processing is even worth the bother. Their main advantages are that no software or licenses are required, nor even understanding of the underlying fundamentals. All that is needed is a straight edge, a sharp pencil, and good eyesight. In a matter of seconds one can arrive at proximate answers, making them very convenient for initial assessments.
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Citation:
Alfano, S., “Low-Thrust Transfer Nomograms,”2018 AAS/AIAA Astrodynamics Specialist Conference, Snowbird Utah USA, 18 August 2018.
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Comparing the effectiveness of positional accuracy improvements
