Bulletin of Mathematical Biology

, Volume 81, Issue 10, pp 3803–3822 | Cite as

Lift and Drag Acting on the Shell of the American Horseshoe Crab (Limulus polyphemus)

  • Alexander L. DavisEmail author
  • Alexander P. Hoover
  • Laura A. Miller
Original Article


The intertidal zone is a turbulent landscape where organisms face numerous mechanical challenges from powerful waves. A model for understanding the solutions to these physical problems, the American horseshoe crab (Limulus polyphemus), is a marine arthropod that mates in the intertidal zone, where it must contend with strong ambient flows to maintain its orientation during locomotion and reproduction. Possible strategies to maintain position include either negative lift generation or the minimization of positive lift in flow. To quantify flow over the shell and the forces generated, we laser-scanned the 3D shape of a horseshoe crab, and the resulting digital reconstruction was used to 3D-print a physical model. We then recorded the movement of tracking particles around the shell model with high-speed video and analyzed the time-lapse series using particle image velocimetry (PIV). The velocity vector fields from PIV were used to validate numerical simulations performed with the immersed boundary (IB) method. IB simulations allowed us to resolve the forces acting on the shell, as well as the local three-dimensional flow velocities and pressures. Both IB simulations and PIV analysis of vorticity and velocity at a flow speed of 13 cm/s show negative lift for negative and zero angles of attack, and positive lift for positive angles of attack in a free-stream environment. In shear flow simulations, we found near-zero lift for all orientations tested. Because horseshoe crabs are likely to be found primarily at near-zero angles of attack, we suggest that this negative lift helps maintain the orientation of the crab during locomotion and mating. This study provides a preliminary foundation for assessing the relationship between documented morphological variation and potential environmental variation for distinct populations of horseshoe crabs along the Atlantic Coast. It also motivates future studies which could consider the stability of the horseshoe crab in unsteady, oscillating flows.


Immersed boundary method Computational fluid dynamics Pedestrian aquatic locomotion 



We would like to thank Brad Erickson and Jonathan Rader for help with laser scanning and 3D-reconstruction, and Miles Hackett for help with experiments. Additionally, we would like to thank the UNC Office of Undergraduate Research and the William W. and Ida W. Taylor Foundation for funding. This work was also supported by NSF DMS Grant #1151478 (to L.A.M.).


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Copyright information

© Society for Mathematical Biology 2019

Authors and Affiliations

  • Alexander L. Davis
    • 1
    • 4
    Email author
  • Alexander P. Hoover
    • 2
  • Laura A. Miller
    • 3
    • 4
  1. 1.Duke UniversityDurhamUSA
  2. 2.Department of Mathematics, Buchtel College of Arts and SciencesUniversity of AkronAkronUSA
  3. 3.Department of MathematicsUniversity of North CarolinaChapel HillUSA
  4. 4.Department of Biology, Coker Hall, CB 3280University of North CarolinaChapel HillUSA

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