An analysis of the orientation of an orb-web spider

In nature, orb-web spinning spiders are often observed residing on the hub of their web, facing down. An explanation of this phenomenon has only recently appeared in the literature [Zschokke, S., Nakata, K., 2010. Spider orientation and hub position in orb webs. Naturwissenschaften 97, 43-52, doi:10.1007/s00114-009-0609-7], although a similar explanation is implicit in Masters and Moffat [1983. A functional explanation of top-bottom asymmetry in vertical orbwebs. Animal Behaviour 31, 351-391, doi:10.1016/S0003-3472(83)80010-4] and ap Rhisiart and Vollrath [1994. Design features of the orb web of the spider, Araneus diadematus. Behavioural Ecology 5, 280-287]. In the present article a mathematical description of the region a spider can reach in a fixed amount of time, based on the velocity, turning rate, and initial orientation of a spider, is proposed. Maximizing the amount of prey caught on the web in the long term corresponds to maximizing the area of the region. The orientation that maximizes this area is shown to be downwards. The paper concludes with a conjectured explanation for the vertical asymmetry of orb-webs.