Mechanics and energetics of medusan jet propulsion
Abstract
A theoretical model is developed to describe the mechanics and energetics of medusae which swim by jet propulsion. The model leads to four generalizations: (i) The acceleration reaction, not drag, is the dominant fluid force experienced by swimming medusae. (ii) There exist behaviors such as contraction time and relative duration of the relaxation of contraction phases which maximize the velocity and efficiency and minimize the cost of locomotion during normal swimming. Also, escape performance is maximized with certain behaviors. Existing data for medusae show that many operate near these optima. (iii) The ratio of efficiency to cost of locomotion is a reasonable measure of swimming behavior and provides a means to study the relationships between swimming behavior and size, (iv) For medusae of a particular shape exhibiting a particular swimming behavior there exists a unique size which maximizes the ratio of efficiency to cost of locomotion.
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At steady state, average swimming speed should grow as f^1/2.
“This leads to the approximation that the average swimming speed, ¯ U should grow as f 1 / 2 .”
From Measurements and modeling of swimming speed dependence on stroke frequency in scyphozoan jellyfish (2026) · cites this paper as [18]
Previous analytical descriptions of jellyfish swimming predict that swimming speed should increase with stroke frequency until constrained by the body's physical limitations.
“Previous analytical descriptions of jellyfish swimming predict that swimming speed should increase with stroke frequency until constrained by the body's physical limitations.”
From Measurements and modeling of swimming speed dependence on stroke frequency in scyphozoan jellyfish (2026) · cites this paper as [18]
Assuming frequency-independent stroke kinematics, the impulse imparted per stroke remains approximately constant.
“Assuming the kinematics of a stroke are independent of the frequency at which the stroke occurs, then the impulse imparted per stroke, I, remains approximately constant.”
From Measurements and modeling of swimming speed dependence on stroke frequency in scyphozoan jellyfish (2026) · cites this paper as [18]
The first thrust equation (T1) was adapted from a model for jet speed based on conservation of mass.
“The first thrust equation ( T 1 ) was adapted from a model for jet speed based on conservation of mass [18].”
From Measurements and modeling of swimming speed dependence on stroke frequency in scyphozoan jellyfish (2026) · cites this paper as [18]
All three analytical models calculated the jellyfish velocity by iteratively solving a force balance based on prior work on jellyfish energetics by Daniel.
“All three models calculated the jellyfish velocity by iteratively solving a force balance, based in prior work on jellyfish energetics by Daniel [18].”
From Measurements and modeling of swimming speed dependence on stroke frequency in scyphozoan jellyfish (2026) · cites this paper as [18]
Prevalent analytical models of jellyfish swimming have been based on hydrozoan jellyfish traits, which use jet propulsion, rather than scyphozoan jellyfish, which use paddling propulsion.
“prevalent analytical models of jellyfish swimming have been based on the swimming traits of hydrozoan jellyfish which utilize jet propulsion, rather than scyphozoan jellyfish which utilize paddling propulsive methods.”
From Measurements and modeling of swimming speed dependence on stroke frequency in scyphozoan jellyfish (2026) · cites this paper as [18]
At higher frequencies, the assumption of frequency-independent stroke kinematics will break down, and reduced stroke amplitudes will lead to a deviation from the f^1/2 scaling.
“At higher frequencies, it can be predicted that the assumption of frequency-independent stroke kinematics will break down. Reduced stroke amplitudes will lead to a deviation from the f 1 / 2 scaling.”
From Measurements and modeling of swimming speed dependence on stroke frequency in scyphozoan jellyfish (2026) · cites this paper as [18]
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Measurements and modeling of swimming speed dependence on stroke frequency in scyphozoan jellyfish
Yoder, N. K., & Dabiri, J. O. (2026) · arXiv · doi:10.48550/arxiv.2604.14491
“These studies utilized kinematics-based momentum models [18] and vortex wake models [17] to determine swimming speed.”
- Authors
- Daniel, T. L.
- Corresponding author
- Daniel, Thomas L.
- ORCID
- Daniel, Thomas L.
- Venue
- Canadian Journal of Zoology
- Publisher
- Canadian Science Publishing
- Published
- 1983-06-01
- Volume
- 61
- Issue
- 6
- Pages
- 1406-1420
- ISSN
- 0008-4301 (ISSN-L)
- 1480-3283
- OpenAlex
- W2016201039
- Cited by
- 135
- References
- 0
- Citations by year
- 2026: 2 · 2025: 3 · 2024: 6 · 2023: 7 · 2022: 1 · 2021: 6 · 2020: 8 · 2019: 4 · 2018: 2 · 2017: 5 · 2016: 2 · 2015: 3 · 2014: 4 · 2013: 5 · 2012: 5
- FWCI
- 2.73
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Canadian Journal of Zoology (publishedVersion)
- Topics
- Physical Sciences › Earth and Planetary Sciences › Paleontology › Marine Invertebrate Physiology and Ecology
- Physical Sciences › Engineering › Aerospace Engineering › Biomimetic flight and propulsion mechanisms
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Micro and Nano Robotics
- Keywords
- jellyfish, jet propulsion, swimming mechanics, swimming energetics, contraction time, swimming efficiency, cost of locomotion, escape performance, body size scaling
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