Many readers will by now have seen the second film in the Avatar series, 'The Way of Water' (TWOW). I felt that the story of the film resembled that of the first film a bit too much, but never mind that; this is not a blog about cinema, but about speculative biology. Luckily, TWOW offers new species to enjoy, to watch again and to think about. I used the book ‘The Art of Avatar TWOW' by Tara Bennett to write this post. There will probably be two posts on TWOW; this one will be about the
skimwing, chosen because it has a lot to offer from a biomechanical
point of view. It will be a long post and there are equations at the end, so you have been warned...
That book contains quotes and explanations that confirm a conclusion I had drawn from viewing the first film, and that is that the shapes and form of the life forms on Pandora are primarily governed by audience appeal, with biological plausibility taking a definite second place. I deplored that second place when I wrote my post about the first film, posted 13 years ago to the day. I still do, but now accept that the people in charge of making films think this is what the audience wants. They may be right; but I, and I guess many readers of this blog, are not typical in this regard. We like our science well-done, not rare. Relegating plausibility to second place is acceptable as long as film makers do not claim that the life forms they present are biologically sound. I got the impression that they did make that claim for the first film, but for TWOW the book acknowledges that the director's opinion of audience appeal came first.
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| Click to enlarge; copyright 20th century studios |
The goal: can we answer the question whether skimwings can 'taxi' as shown?
The skimwing is basically a gigantic flying fish: it has a long slender body and two fins that double as wings. Like flying fish, the skimwing is fast enough to partially leave the water, with just the tail in the water to propel it. Flying fish use this stage to accelerate and leave the water altogether, but skimwings do not do that; they just taxi along.
Could the skimwing as shown really taxi in the way flying fish do? That is not an easy question because of all the factors that are involved. Let's consider the problems.
1. While taxiing, the animal's tail provides thrust propelling the animal forwards, but the tail may also produce some upwards force. If so, the wings need to provide less lift than if all the upwards force is due to lift. In this post, I will assume that the tail only provides forward thrust, so the wings are responsible for all the upwards force. But I will get back to this matter in the end.
2. As for lift, we will use conventional equations. See this post for an introduction. We are not on Earth, so lift is altered by the higher atmospheric density on Pandora, where the story takes place (1.2 times that of Earth).
3. The animal's weight is also other than it would be on Earth because the gravity constant of Pandora is lower than the one of Earth (it is said to be 0.8 of that of Earth).
4. A more difficult effect to deal with is the 'ground effect', which means that flying objects (animals and aircraft) experience extra lift if they fly close to the ground. The literature makes it clear that flying fish use the ground effect, and the book states that skimwings do so too.
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| Click to enlarge; copyright 20th century studios |
5. Finally, there is a literally enormous difference between skimwings and flying fish: flying fish are only about 35 cm long and I estimate skimwing length to be 12.2 to 13.5 meter. I derived that estimate using the image above, in which the skimwing appears to be 4.5 times as long as an adult Na'vi. The internet tells me that Na’vi are 2.7 to 3 meters tall. I used a skimwing length of 12.5 m as a reasonable estimate.
I am not an aeronautical engineer, so what follows should be seen as nothing more than a layperson's attempt to understand how all the above factors might work together. But first, what do we know about flying fish?
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| Click to enlarge; from Wikipedia |
Flying fish can swim, 'taxi' and glide
Flying fish are often said to take to the air to escape predators (Socha 2015). That may well be true but has not been proven; other animals jump out of the water for a variety of reasons. Squid may glide above water to escape predators too but also to catch prey (Socha 2015); whales apparently breach to impress other whales, while dolphins may do so to achieve greater overall speed. As jumping out of the water must take a lot of energy this seems a strange way to save energy, but moving through air obviously offers less resistance than through water, so that gain may offset the additional energy needed to leave the water.
There is another odd effect going on here, and that is that swimming just below the surface of the water costs more than swimming in deeper water. Why? Well, all swimmers push water out of the way to make room for themselves, but in shallow water some of that displaced water moves upwards, which costs more energy than if the water only moves sideways. That additional energy cost may just tip the balance, making leaving the water more efficient than pushing all that water up (Socha 2015).
Taxiing
Flying fish accelerate under water, break though the water's surface, and then accelerate some more with only their tail underwater, from 10 to 20 meters per second (Socha 2015). That's from 36 to 72 km/h. Calculations show that they need 350 Watt to swim underwater at 10 m/s, but only 36 Watts while taxiing; taxiing is therefore quite efficient (Deng 2019). So far so good!
Flying fish then leave the water and glide, held aloft by their two or four wings (some species use both pectoral and pelvic wings, others just the pectoral wings). Although some papers describe the flight path as relatively flat (Fish 1989, Socha 2015), meaning at a constant height above the surface, this can only be an approximation. The reason is that flying fish have no propulsion while in the air, so the glide is either completely passive or else lift is helped in some way. In a true passive glide losing height is physically unavoidable (Socha 2015).
This suggests that their lift is indeed helped. Updraughts can help (Fish 1989) and so can the ground effect. In fact, the relatively flat trajectory itself suggests that the ground effect does help (Socha 2015). Wind tunnel experiments with stuffed flying fish (Really? Yes, really) showed that the ground effect reduced drag (let's say that ‘drag’ is the force impeding forwards motion) by 14%. As lift stayed the same, the so-called lift-to-drag ratio was improved, which is not bad at all (Park 2010). Remember that number of 14%, because we will need it later.
As flying fish know their physics they do come down to the water and may repeat the procedure: taxi, glide, land, etc. They may cover distances of some 400 meters in 30 seconds (Park 2010), suggesting a mean speed of 48 km/h.
Gliding
The wings proved to be like bird wings, in particular as regards wing loading. 'Wing loading' is calculated as the area of the wings divided by weight of the animal, so it tells you how much kg a square m of wing carries. A low value makes flying easier. The wings of flying fish are designed for high lift and low drag (Fish 1989). The four-winged species have lower wing loading, pointing to increased lift at low speeds, than the two-winged species.
Scaling flying animals
Now it gets more complicated. But not that much, so hang on! I have discussed scaling winged animals before, but I will repeat the main thoughts here. What we will do is to take Earth’s flying fish, scale them up, export them to Pandora to accommodate the different atmosphere and gravity, calculate their weight there, and then see whether they can produce enough lift to keep that weight aloft in Pandoran air.
Lift is proportional to just three relevant parameters (there are two more: angle of attack and a constant, but if we keep these the same throughout we can ignore them).
- density of the air (D), in kg per cubic meter
- area (A) of the wing, in square meters
- square of speed (S^2), in meter per second (I cannot use superscript, which is why I used '^2' to indicate a squared speed)
LIFT = D x A x S^2
If a flying animal flies at a stable height and does not sink, the amount of lift it generates must equal its weight. We can calculate weight W as the product of the gravity constant G and the mass of the animal M.
WEIGHT = G x M
So remember this for stable flight:
LIFT = WEIGHT
Now we need another look at scaling; (see here for flying and here and here for an introduction). Suppose we take an animal with length L and make its length, height and width all twice as large as before (that's called 'isometric scaling'). Its length becomes 2L. However, the area of the wings is the product of length and width of the wings, and as each became twice as long, the area becomes four times (2x2) as large. However, the volume of the animal has three dimensions, so that becomes eight times (2x2x2) as large. The mass corresponds to the volume and also becomes eight times as large. The lesson here is that mass increases more than area, and that is a problem.
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| Click to enlarge; copyright Gert van Dijk |
Weight becomes eight times as large, but the four times larger wing area will only get you four times the lift. To fly stably, lift must equal weight, so we must find a way to achieve eight times the original amount of lift. In the scheme, above, the first way to do so is labelled 'Enlarged flying fish 1'. In that option, squared velocity was made twice its original value. To do that, velocity itself needs to become 1.4 times larger (1.4 is about the square root of 2). Hence, the larger animal has to fly faster if its wings stay in proportion with the body. But to land and take off, the animal needs to be able to fly at low speeds too: you cannot fly fast all the time.
Is flying faster the only solution? No, we can also choose to have the enlarged animal fly at the same speed as its predecessor ('Enlarged flying fish 2'). We still need to achieve eight times the lift, so we need to make the wing area eight times larger. If we make the length and width of the wing each 2.83 times larger (2.83 is about the square root of 8) we get that. Mind you, this solution will reach a dead end at some point because the enlarged wings will also add weight, which needs to be lifted, etc. I discussed how much weight such larger wings will add to the animal in an earlier post (here); it is dramatic!
To conclude, we have a choice of achieving more lift for the larger animal by either enlarging wing area or flying faster; either solution will reach a limit at some point. On Earth, larger birds combine larger wing area as well as higher speed to achieve that higher lift. That combination can only be an evolutionary compromise between the costs of high speed (difficulty in taking off and landing) and large wings (more weight). There must be a physical limit where flight is no longer feasible for an animal. Does scaling up the skimwing tip the scales? (Sorry for that one, but I could not help myself)
The case of the skimwing
The length of a skimwing is at 12.5 meter 35.7 times larger than that of a flying fish. If we multiply the dimensions of a flying fish by 37.5, its wing area becomes 1275 times larger and its mass becomes about 45,500 times larger. Wow!
We now need to do an analysis as explained above, but the animal gets to be not twice the size, but 37.5 times. The results of this thought experiment are in the appendix, for those who want numbers. If we choose to scale the animal isometrically, meaning that the proportions of the animal stay the same, then it must taxi not at 20 m/s (72 km/h) as the flying fish manages to do, but at a staggering 351 km/h. That is wholly unrealistic; for one, the Na'vi sitting on top would be blown off…
How about the other approach, meaning making the wings larger? Well, isometric scaling made the wing length and width each 35.7 times larger. It turns out that we need to make each 174 times larger instead! I did not bother calculating how much weight that would add.
Save the skimwing!
But the animal might derive part of the upwards force from beating its tail. True, but there is a good reason why tail walking dolphins are not large. It is, once again, scaling: the force needed to push against the water depends on the cross section of the muscles, meaning area, and needs to equal the animal's weight. It is the exact same problem as before: force increases with the square of length and weight with the third power. Turning to tail walking instead of gliding trades one unsurmountable scaling effect for another.
But how about the ground effect? Well, in flying fish that reduced drag by 14%. While that is not the same as increasing lift, it may be treated that way. The appendix shows that a gratis 14% increase in lift still do not result in a viable animal, and neither did halving the mass of the skimwing: that won’t fly (sorry for that one too).
Conclusion
What a pity. It seems that the designers did not realise how much that third power puts a brake on scaling up animals. Admittedly, those effects are not immediately obvious, but it's not rocket science either. The simple conclusion is that 12.5-meter-long taxiing flying fish are too large to work, even under Pandora's favourable gravity and atmosphere.
Does it matter? The science in TWOW seems fairly typical for how Hollywood treats science, meaning with rather limited respect for plausibility or accuracy. That's not good news; actually, it's not news at all. However, there is good news: the film shows a very profound love for the natural world. If that helps make people care about nature, I'm all for it.
As far as that love for nature is concerned, consider this: the skimwing differs in only one important aspect from flying fish: its size, and it is exactly that difference that makes the skimwing impossible. But everything else that makes Pandoran skimwings fascinating was already fascinating about flying fish, right here on Earth.
Acknowledgement
Abbydon made insightful comments on a first draft of this post. He also added remarks about wave effects that would make using skimwings as public transportation rather unreliable.
Selected references
FE Fish. Wing design and scaling of flying fish with regard to flight performance. J Zool Lond 1990; 221: 391-403
Park H, Choi H. Aerodynamic characteristics of flying fish in gliding flight. J Exp Biol 2010; 213: 3269-3279
Deng J, Wang S, Zhang L. Why does a flying fish taxi on sea surface before taking off? A hydrodynamic interpretation. https://doi.org/10.1101/765560
Socha JJ, Jafari F, Munk Y, Vyrnes G. How animals glide: form trajectory to morphology. Can J Zool 93: 901–924 (2015) dx.doi.org/10.1139/cjz-2014-0013
Sullivan TN, Meyers MA, Arzt E. Scaling of bird wings and feathers for efficient flight. Sci. Adv. 2019;5: eaat4269
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Appendix
Abbreviations and parameters
FF Flying Fish
SW SkimWing
Length L
Area (wings) A
Volume V
Mass M
Weight W
Speed S
Density of air D
(local values for Pandoran SW and Earth FF)
DSW = 1.2 ∙ DFF
Gravity constant G (local values for SW and FF)
GSW = 0.8 ∙ GFF
Lift LIFT
----------------------------------------------------------------------
Take the length of the animal of the FF as base value of 1; the SW is 35.7 times longer.
LFF = 1
LSW = 35.7 ∙ LFF
This results in the following for area and volume for SW:
ASW = (35.7)2 ∙ AFF or ASW = 1275 ∙ AFF
VSW = (35.7)3 ∙ VFF or VSW = 45500 ∙ VFF
For weight we get:
WSW = VSW ∙ GSW Pandoran values
WFF = VFF ∙ GFF Earth values
For lift we get:
LIFTFF = DFF ∙ SFF2 ∙ AFF
LIFTSW = DSW ∙ SSW2 ∙ ASW
We can now start filling in values for Pandora using Earth parameters, not altering wing area A and speed S on Pandora yet:
for lift: LIFTSW = (1.2 ∙ DFF) ∙ SSW2 ∙ ASW
for weight WSW = VSW ∙ GSW
WSW = VSW ∙ (0.8 ∙ GFF)
WSW = (45500 ∙ VFF )∙ (0.8 ∙ GFF)
WSW = 36400 ∙ VFF ∙ GFF
WSW = 36400 ∙WFF
If the flight is stable, weight must equal lift, so it follows that:
LIFTSW = 36400 ∙ LIFTFF
(1.2 ∙ DFF) ∙ SSW2 ∙ ASW = 36400 ∙ DFF ∙ SFF2 ∙ AFF
SSW2 ∙ ASW = 30333 ∙ SFF2 ∙ AFF
We have SW parameters on the left and Earth FF parameters on the right and can play with this relationship.
Variant 1 assumes isometric scaling, making ASW = 1275 ∙ AFF
SSW2 ∙ 1275 ∙ AFF = 30333 ∙ SFF2 ∙ AFF
SSW2 = 23.8 ∙ SFF2
We know that the speed of FF = 20 m/s, so
SSW2 = 23.8 ∙ 400 = 9516
SSW = 97.6 m/s or 351 km/h
This is obviously a ridiculous speed and cannot work. Perhaps larger wings may do the trick if we abandon isometric scaling.
Variant 2 starts a few steps back.
SSW2 ∙ AFF = 30333 ∙ SFF2 ∙ AFF
If we assume that the skimwing has the same speed as Flying fish, then SSW2 = SFF2
AFF = 30333 ∙ AFF
This means that the width and lengtn of the wing have to increase by the square root of 30333, meaning they become 174 times larger instead of the original 35.7 times. This is ridiculous, and the real situation would be worse because the arger windg wopuld weigh a lot more, which he haven’t accounted for yet!
Are there ways out?
The ground effect seems to reduce drag by 14%. That is not the same as increasing lift by 14% but assume that lift is indeed increased by this amount.
SSW2 ∙ 1275 ∙ AFF = 0.86 ∙ 30333 ∙ SFF2 ∙ AFF
SSW2 = 20.5 ∙ SFF2
SSW2 = 20.5 ∙ 400 = 8200
SSW = 90.6 m/s or 326 km/h
or
AFF = 26086 ∙ AFF
The wing's length and width have to become 161 times larger. Ground effect does not save the skimwing, and that holds for an isometric as well as for a non-isometruc approach.
What if we make the skimwing relatively more slender than the FF, by halving the volume of its body? This results in:
SSW2 ∙ ASW = 15167 ∙ SFF2 ∙ AFF
SSW2 ∙ 1275 ∙ AFF = 15167∙ SFF2 ∙ AFF
SSW2 = 11.9 ∙ SFF2
We know that the speed of FF = 20 m/s
SSW2 = 11.9 ∙ 400 = 4758
SSW = 69.0 m/s or 248.3 km/h
If we assume that the skimwing has the same speed as Flying fish, then SSW2 = SFF2
AFF = 15167 ∙ AFF
This means that the length and width of the wing must become 123 times larger instead of the original 35.7 times. This is still preposterous.
16 comments:
Thats a very enjoyable read, math and all; thank you for making it.
I suppose that not even thinning the wings and using lightweight supermaterials (in parallel to their use in Pandoran land animals) would really help much; thats a shame. But now we know, thank you.
>taxiing
When I saw that, I thought "don't ducks and swans use that?" And now, much later after that thought, I'm wondering it it helps any that waterfowl can use the ground effect, without being hindered by having part of their bodies in the water?
*shrugs*
Great work, and I'm looking forwards to Part II.
-Anthony C. Docimo
Very interesting, I now wonder about the feasibility of some of the other giant flyers of Pandora: an Italian Instagram page https://www.instagram.com/p/CoAJAc2KEXw/?igshid=YmMyMTA2M2Y= claims to have calculated a lift coefficient of 6 for the toruk, compared to a value of 2.7-3.0 for small airplanes, but they didn't publish their calculations and I didn't take the effort of replicating them.
Regarding the next article, will it maybe be about the plausibility of a sapient species developing philosophy and sciences without apparent means of manipulation?
Anthony: Thank you. I wondered about that too. The density of fish appears to be something like 1085 kg per cubic meter, which has to be compared to that of seawater at about 1027 kg per cubic meter. Fish have a swimbladder to achieve the same overall density as the water around them to maintain height. You wouldn't want a 'lighter than water' fish, so the minimum density of the overall animal should probably be that of seawater, reducing the weight to something like 1027/1085 = 0.95 of what it was. That will not be enough, I am afraid.
Davide; Thank you for that page; my Italian is just good enough to understand it. I cannot understand their calculations either. At the very least you would have to know the velocity of which the animal flies. In the film, the Leonopteryx can seem to fly slowly, but that involves flapping flight, not gliding. I saw that you commented on the site; perhaps you can ask them for the full calculations, as my Italian is not good enough to ask such questions?
As for carbon fibre, I had a quick look at its density, and to my surprise I found 1.75 tot 1.93 kg per cubic meter. That is heavier than I thought, although it is certainly lighter than aluminium, itself a light metal (2.7 kg/ cubic meter). Out of curiosity I tried finding the density of bone, and to my surprise I found 1850 kg per cubic meter! What!? Carbon fibre is about as dense as bone? So no magic weight saving for Pandoran animals at all?
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I will try to write a post every two weeks from now on; I have three lined up but do not know their order of publication yet: one will be a Furahan hexapod muscle study, one deals with some TWOW species (with a few words on the likelihood of water creatures understanding the spoken language of a terrestrial being), and one will stay a surprise for now.
I've asked for the calculations, I'll post a comment here when (and if) they reply.
From a purely qualitative point of view, Pandoran flyers do seem to have very large wings with a comparatively small body, typical of giant flyers on Earth like azhdarchids and pelagornithids, but then again the scale, especially with the great leonopteryx, is totally different and I don't know if the local gravity and atmosphere density would be enough to make flight (with passengers nonetheless) feasible, especially given what you found about carbon fiber. Could it at least make the bones stronger while having the same overall body weight? According to this paper https://www.sciencedirect.com/science/article/pii/S1369702110700201#:~:text=Steel%20has%20about%20the%20same,the%20elastic%20energy%20of%20bone. "A typical carbon fibre composite has a similar total energy but about 10 times the elastic energy of bone.".
Davide: Let's wait and see. I agree that the Leonopteryx has a very large relative wing area, which is good. But the weight of only 3000 kg seems rather low for an animal with a 24 m wingspan.
After all the discussions here I started to look at the first Avatar film again, and in the beginning there is a statement that Na'vi bones have natural carbon fibre in them, not that they are made of carbon fibre. I guess that that might help. You may first have to set out what you want if you would want to replace bone with another biologically feasible material. Lighter with the same strength would be good for flying animals, or for enormous animals. I liked the post you provided, although the writer seems more interested in a comparison with metal than with carbon fibre. I am still thinking about the consequences of finding out that carbon fibre doesn;t seem to be lighter than bone... Perhaps Abbydon could comment too.
Good post, though perhaps I am biased...
Anyway, I just had a look at the discussion about the leonopteryx. My ability to speak Italian is non-existent but Google translate works quite well using the camera on a phone to replace the text with English. I may have misunderstood something though.
It's definitely unclear what their calculation is as they specify takeoff, however, the leonopteryx presumably won't take off in the same way as a plane, i.e. by running very fast and letting the wings redirect air to produce lift. Instead it will have to flap its wings to produce lift or throw itself off an edge.
Flapping its wings would be difficult as to get space for that it first has to leap into the air. My understanding is that the maximum height produced by leaping is what limited the size of pterosaurs as this in turn limits the maximum size of wing that can be used at take off. While gravity is 20% lower than on Earth the 3 tonne mass isn't going to allow a high jump. This means it would be really difficult to generate sufficient lift to take off.
This means leaping off a floating rock is likely the only way it could take off. Consequently, landing on Pandora's surface might prevent it ever flying again. That's perhaps a viable approach though not consistent with the film.
While you might be able to reduce the total mass by changing the bone composition, I'm not sure that would allows such a large flying organism. While it would help, the proportion of the total mass that is due to the skeleton is only between 5% and 25% in birds (that was from a quick Google search). So perhaps what's really needed is a reduction in the mass of muscle to allow more force to be exerted at take off.
Either way, strength is the key parameter to withstand the rigors of flying. This is even more of an issue if the animal weighs 3 tonnes. Carbon fibre does have a significantly greater yield strength than bone I believe, so perhaps that can help explain things, but taking off is still difficult for a large winged animal.
Finally, this does bring to mind a paper I read a while ago: Why are your bones not made of steel?.
Incidentally, I had linked to the same paper earlier in the discussion!
Oops. That would explain why I was thinking of it. I should have checked the URL.
To redeem myself, another slightly relevant paper by Professor Taylor is: Shape optimization in exoskeletons and endoskeletons: a biomechanics analysis. It models skeleton limbs as hollow tubes and discusses how the optimum ratio of radius to thickness (r/t) differs for bending versus axial compression.
For the leonopteryx bending would be the problem while flying so a low value of r/t would probably be expected (i.e. low radius, high thickness bones) for the long slender wing bones. This would however make them less resistant to axial loading. Presumably this would hamper jumping on take-off or upon impact with the ground on landing. Falling off of the floating islands definitely seems the best approach I guess.
Very enjoyable to read and very informative! The numbers have gotten very ridiculous very fast!
Davide and Abbydon: I wonder if we ever get to see the calculations from the Italian site Davide found, but meanwhile I'll stick to our own views on the matter.
Petr: Thanks!
I asked for them, but I doubt they'll ever answer
I wonder if there's a way to make the skimwing possible. Let's say it had the mass not of an isometrically scaled flying fish, but of an isometrically scaled Quetzalcoatlus: possibly a better analog, being a giant winged animal. Quetzalcoatlus was about 8.5 meters from feet to beak in flight (assuming a pose with semi-outstretched legs), and recent mass estimates are about 150-200 kg. That would scale up to a 12.5 meter skimwing with a mass of 480-640 kg.
The question could be raised of whether an animal with this length and mass could have enough muscle to swim at taxi speeds. I think it's not impossible, since swimming is less energetically costly than walking, and Quetzalcoatlus is believed to have been well-adapted for walking. (A dolphin can swim faster than a pony walks while using less energy: https://academic.oup.com/icb/article/42/5/1060/659876 )
Flying fish weigh about 0.05 kg ( https://journals.biologists.com/jeb/article/213/19/3269/9762/Aerodynamic-characteristics-of-flying-fish-in ).
This makes the Quetzalcoatlus-like skimwing 9600-13000 times the fish's mass, instead of 45500 times. Using your equations, a skimwing with fish-proportioned wings would need to fly at a speed of 45 to 53 m/s (still faster than the fastest swimming speed on Earth). If the wings are enlarged instead, they would have to be approximately 2.2 to 2.6 times the proportional length and width of the fish's wings, which might come with too great a burden of increased weight.
But there's a middle ground where the skimwing is 480 kg, swims at a more believable speed of 30 m/s, and manages to stay in the air with wings 1.5 times the proportional length and width of the fish's wings. So maybe there's a way for this creature to at least be on the edge of possible.
Avatar 2 has honestly taken an even looser approach with biology than the first. Once again its alien animals are too-easily recognizable as their earth counterparts, and have body plans that make no sense, such as cetacean-analogues bearing ridiculous arrays of horns and crests that completely would interfere with streamlining.
Though on a speculative biology sense one decision I do admire was the portrayal of a new sapient species: and it's the whale-like tulkun! It aggravated me to no end in the first film how the Na'vi looked far too human to the point of outright breaking the internal consistency of Pandoran anatomy. I would have greatly preferred a story about humans making contact with an alien intelligence so vastly different from our own both in physical and psychological aspects that they're not even recognized as a sapient "people" at first, as opposed to a cliched Pocahontas-esque love story between a human and a blue lemur Native American pastiche.
Akavakaku: sorry about the delay in answering; I had too many things going on at the same time. I like your reasoning but wonder what the resulting animal would look like. My starting point was the appearance of the animal in the film, meaning it looked like a large scaled-up flying fish. My calculations were based completely on that appearance and scaling laws, leading g to the sad conclusion that the result is unworkable. Your idea is better that the film maker's one in that it takes a large flying animal to start with. That makes sense, but the result must look radically different than a large flying fish. If I understand you correctly, you envisage something that would look unique. Have you made sketches of its appearance? Mind you, large pterosaurs must have been able to deal with forces of flying and landing, but this creature must be able to propel its tail forcefully and at high speed against water. That may call for some serious heavy-duty engineering.
Shando: I agree that fast-swimming animals are VERY unlikely to sport all kinds of projections. I once designed a Furahan whale-analogue. It had a sieve in its jaws that were completely different from those of Earth whales, but when it closed its four jaws, the need for streamlining made it look so much like a whale that I never finished the painting...
I agree that it is nice to have intelligent species that does not look like a primate. Then again, the idea that Cetacea are intelligent is not exactly a new one, so that concept cannot surprise the audience. In contrast, you could say that it plays on concepts that whales are benevolent intelligent creatures (it may be best to ignore that orcas may play with seals as cats play with mice).
It seems I used a weight estimate for a much smaller flying fish species than the one whose length (.35 m) was used in the calculations. A flying fish .25 m long is .191 kg.
https://www.researchgate.net/publication/335769633_Why_does_a_flying_fish_taxi_on_sea_surface_before_take-off_A_hydrodynamic_interpretation
So, redoing my equations using this new flying fish length and weight, a Quetzalcoatlus-like skimwing is only 2500-3400 times the fish's mass while being 50 times its length. With Pandora's gravity and atmosphere, the skimwing needs 1700-2300 times as much wing area to stay up as the fish does with the same 20 m/s taxi speed, so it needs wings 41-48 times the absolute size of the fish's wings, meaning the wing size can actually remain the same in proportion to body length!
Here's a simple image I constructed comparing a flying fish, a Quetzalcoatlus/flying fish composite using the proportions above, and a skimwing (not to scale with each other).
https://i.imgur.com/3TaBfIw.png
Conclusion: Rather than being too large to taxi, the movie's skimwing might just be too bulky.
Akavakaku: I haven't had the time to look at the calculations. It seems we agree that a skimwing as shown in the film will not work. It may indeed take a pterosaur approach to make extremely large animals fly. Even so, that leaves the question open whether the animals can fly while carrying several humanoids on their back. I also still worry about how strong and therefore heavy the animal needs to be to propel its tail against the water.
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