Snake Locomotion

choi

(1) This posting discusses only two modes of sane locomotion: serpentine and sidewinding (more is understood about the former; at the budding stage for the latter). No discussion about other modes of locomotion, snake swimming, or climbing a tree, because nothing is known.
(2) Locomotion. (under "Snake") Encyclopaedia Britannica, undated
https://www.britannica.com/animal/snake/Locomotion
("paragraph 1" The snake has overcome the handicap of absence of limbs by developing several different methods of locomotion, some of which are seen in other limbless animals, others being unique. The first method, called serpentine locomotion, is shared with almost all legless animals, such as some lizards, the caecilians, earthworms, and others. This is the way most snakes move and has been seen by any zoo visitor. The body assumes a series of S-shaped horizontal loops, and each loop pushes against any resistance it can find in the environment, such as rocks, branches, twigs, dust, sand, or pebbles. The environment almost always provides sufficient resistance to make movement possible, and many snake species never use any other method of locomotion. Such species, when placed on a surface providing no resistance, such as smooth glass, are unable to move, whipping and thrashing around without progress. Snakes, like fishes and eels, swim by lateral undulation, which is essentially identical to serpentine locomotion. The sea snakes, however, possess a distinct anatomy in the form of a flattened, oarlike tail")

(3) serpentine locomotion
(a) The Secret of a Snake's Slither. uploaded by National Science Foundation on June 9, 2009
https://www.youtube.com/watch?v=5CchyctRFrQ

Note: This is a recap, with anime, of the next.
(b) Hu DL et al, The Mechanics of Slithering Locomotion. PNAS, 106: 10081 (2006).
https://www.pnas.org/content/106/25/10081
(paragraph 1 of Discussion: "Our simple theoretical model based on snake friction coefficients captures the general trends found in our experiments, although predicted speeds tend be somewhat lower than those measured. We offer several possible sources of discrepancy between observed and predicted speeds. We believe that the largest contributor to these disparities is given by the dynamic load-balancing we have observed in snake locomotion. Previous investigators have observed that at high speeds, snakes lift the curved parts of their bodies off of the ground as they travel in lateral undulation and in sidewinding. This can be seen clearly in Fig 3A, which shows a corn snake slithering on a mirrored surface. Through the lens of our model, we interpret this behavior as the snake dynamically distributing its weight so that its belly is periodically loaded (pressed) and unloaded (lifted), concentrating its weight on specific points of contact. We have observed that these points of contact correspond approximately to points of zero body curvature. By incorporating into the frictional force of our model a nonuniform weight distribution that concentrates weight on points of zero body curvature [ie, load; while others segments of the snake, in curves, are lifted], we provide a mechanical rationale for body-lifting. * * *  These calculations show that unloading of the model snakes' body leads to augmentation of forward speed Ūavg from 0.17 to 0.23, an increase of 35% that is in greater accordance the observed speeds")

Note:
(i) Comprehend authors' terminology:
"loaded (pressed)" -- meaning contacting the ground.
"unloaded (lifted)"
"We have observed that these points of contact correspond approximately to points of zero body curvature. * * * inflection points in shape (marked by black dots) where the load is greatest"
(ii) inflection (n): "mathematics   a change of curvature from convex to concave at a particular point on a curve  <the point of inflection of the bell-shaped curve>"
https://www.lexico.com/definition/inflection
(iii) Now look at Fig 3C, whose caption reads in part: "Red lines indicate sections of the body with a normal force <1; the red dot indicates the center of mass. Inflection points of body shape, shown in black, show where the load is greatest."

Take notice that the two black dots of a simulated snake usually are similarly situated in the snake body, though at one point, there is only one black dot. I view the anime (1:33 to 2:06 in the YouTube video clip) frame by frame, and stick to my conclusion.

choi

(4) sidewinding locomotion
(a) Creepy But Cool: How Snakes Can Move Without Legs. Board of Conservation, Dickinson County, Iowa, undated
https://dickinsoncountyconservat ... -move-without-legs/

Note:
(i) Here is a pirated copy of Encyclopaedia Britannica copyrighted 2012, which does not show up in the free version of Encyclopaedia Britannica. (I assume the blue parts of snake body are those in contact with the ground.
(ii) The illustration on sidewinding shows that two points of a sidewinder touch the sand -- it appears the same two points; I do not know these two points are anatomically different from other parts of snake body. This illustration on sidewinding is WRONG. See the slow motion at (4)(c).

(b) Asher Elbein, Starting to Unpeel the Skin-Deep Physics if Sidewinder Snakes. New York Times, Mar 2, 2021, at page D2 (in ScienceTimes section).
https://www.nytimes.com/2021/02/ ... snakes-physics.html
(the lead author of a paper is "Jennifer Rieser, a professor of physics at Emory University in Atlanta. That's [lower friction on sand compared to hard ground is] why sidewinders slither sideway. * * * The sidewinding rattlesnakes [those in southwestern US and northwestern Mexico; they are rattlesnakes, the sidewinders in Africa or Middle East are not rattlesnakes], for example, can travel at the speed of 18 miles per hour, making it the world's fastest snake")

Note: There is no need to read it, as it merely showed two photos, WHICH MAY BE FOUND NEXT.

(c) Carol Clark, Press release: Physics of snakeskin Sheds Light on Sidewinding; Discovery may aid robot locomotion. Emory University, Feb 1, 2021.
https://news.emory.edu/features/ ... nakeskin/index.html

Quote:

(i) the first 2 1/2 paragraphs: "Most snakes get from A to B by bending their bodies into S-shapes [laterally; that is, when the observer is watching from above] and slithering forward headfirst. A few species, however — found in the deserts of North America, Africa and the Middle East — have an odder way of getting around. Known as 'sidewinders' * * * ")

(ii) "Rieser notes that American sandy deserts are much younger than those in Africa. The Mojave of North America accumulated sand about 20,000 years ago while sandy conditions appeared in the Sahara region at least seven million years ago.

" 'That may explain why the sidewinder rattlesnake still has a few micro spikes left on its belly,” she says. “It has not had as much time to evolve specialized locomotion for a sandy environment as the two African species, that have already lost all of their spikes.'

Note:
(i) Please view
(A) the slower-motion video of the sidewinding (at the top of the Web page), and
(B) the two photos (which the paper in (4)(b) does not show, displaying Abstract only unless a reader pays for the content).
(ii) The press release, quoting Rieser, is PARTIALLY wrong to says that in slithering, a snake press all points of its body on the ground. The statement is true only when the snake leisurely. In urgency (to move faster), this kind of snake lifts parts (note the plural form) of its body, too.
(iii) The Name Mojave, Mojave Desert Heritage & Cultural Association, undated
https://mdhca.org/the-name-mojave
(beside the water)
The water alludes to Colorado River.

(d) Both (4)(a) and (b) point to the research paper:
Rieser JM et al, Functional Consequences of Convergently Evolved Microscopic Skin Features on Snake Locomotion. PNAS _: _ (online publication Feb 9, 2021).
https://www.pnas.org/content/118/6/e2018264118
(part of Abstract: "While previous studies have characterized ventral surface features of some snake species, the functional consequences of these textures are not fully understood. Here, we perform a comparative study, combining atomic force microscopy measurements with mathematical modeling to generate predictions that link microscopic textures to locomotor performance. We discover an evolutionary convergence in the ventral skin structures of a few sidewinding specialist vipers that inhabit sandy deserts—an isotropic texture that is distinct from the head-to-tail-oriented, micrometer-sized spikes observed on a phylogenetically broad sampling of nonsidewinding vipers and other snakes from diverse habitats and wide geographic range. A mathematical model that relates structural directionality to frictional anisotropy reveals that isotropy enhances movement during sidewinding, whereas anisotropy improves movement during slithering via lateral undulation of the body")

My comment:
(i) We can not read the paper. Thus we can not make an independent judgment whether the pits account for the sidewinding. But I doubt such a microscopic change will have such a great impact on the gross locomotion.
(ii) The convergent evolution in the title means that the three snakes, in three continents, independently evolved the same sidewinding.