How can the lift produced by animal wings be calculated?

[Necronox]

Firstly, I'm new to these forums, and I'm not sure what the prefixe in creating this thread is supposed to be... (i'm assuming it is to judge to question's level)? saw some threads without prefixes but i can't post one without... maybe i missed a stickied thread or a readme?

Alright, so, first of all let me give a bit of a backstory as to where this question comes from, it might help answer the question a little bit better. I am in the process of writing a book, I'm doing research in animal flight physics so i can know how big the animals in my world can be before it can physically no longer fly (I'm trying to make things 'real', to make sense in terms of physics, biology and all, as my "world" does not have "magic" or thing that just happen for not apparent reason), I'm not exactly sure this is the place to post this, but it seemed the most appropriate i could find.

The first question is, how big can an animal be before it becomes to large to fly? there are some large birds like the vulture, but from my calculations, their wing size is, propotionally speaking, significantly larger then let's say a common pigeon. This seems to agree to some other research i found that says thrust produced by muscles increases more slowly then the drag and resistance increase as the animal becomes bigger. and it seems the easiest and most ecological way of bypassing this is simply to have larger wings producing larger amounts of lift. (this is to say, if you took any animal and simply scaled it up, it will not be able to fly as well)

Secondly, according to this post: https://www.physicsforums.com/threads/lift-calculations.630078/ one can calculate the lift of a plane, but this is hardly comparable to the wing of a bird or a bat, i believe the bat's wing is flat (flat aerodynamics or something?), then what of a bird? they both bend and "flaps" which planes do not. so i assume the calculation those not work for bats, birds and etc... So, is the calculation simply the displacement of the air? does the mass of the air moved (displaced by the wing) equal to the lift produced? and if it does, or if it is close enough to be used as a rough method of telling the lift, how can it be calculated?

So, summing it up, here's a few question I'd like to find an answer to:

how can one person calculate the lift produced by a wing from an animal? (other than physically measuring a bird's lift - i do not have the capability to do this)
Is there a size or weight limit on this animal's size?
There are different types of wing, those of insect are different then those of bats or birds, which produce the most lift? which are more efficient? i assume each are more specialized or suited to different styles of flight, what are they?

 

[256bits]

Last page of this site gives a graph of size vs speed.
Speed would be the normal un-agitated flight speed ie cruising speed.
Bursts of power, acceleration, maximum speed is not shown, which is what one would need for say size of landing strip and takeoff speed rate of climb,..
You can see that there is a general pattern from all the way from small insects to large aircraft.

The graph is on,
http://ocw.mit.edu/courses/material...ering-fall-2005/projects/flght_of_brdv2ed.pdf

You can have a look.

Birds produce their thrust to gain speed by wing flaps, a flat plate drag might give an idea of what size this force could be, but it won't be exact.
Flight, or soaring, has the wings acting as, well, a wing, hence the name.

 

[CWatters]

Some long extinct birds were so large that they didn't/couldn't have enough muscle power to flap their wings sufficient for a take off from level ground. They needed to launch themselves from high places into thermals. If you don't have to flap the wings then they can be much larger than they would otherwise be. If you are only interested in birds that can take off from level ground then I think it may make a difference what the oxygen levels are?

There is some debate about how big and heavy the largest really was, even if or how well they flew...
https://en.wikipedia.org/wiki/Quetzalcoatlus

PS In short I think this question has more to do with the biology and biomechanics of animals than the physics of flight.

 

[Necronox]

Fair enough, i did think it would be more biology orientated, but I've never done biology beyond high school, and I've never done biomechanics, so I'm at a loss there.

according to 256bits' link, it seems to be some correlation between weight and speed. but that doesn't necessarily mean they can fly well, as you pointed out, some extinct animal didn't have the muscle power to take off from ground level, so, do you know what the limit was?

Could the animal's muscle be somehow different? or perhaps more dense? i know jumping spiders use a hydrolic system to jump 50 times their own length, while grasshopper's muscles are more powerful then human's if they where the same size. couldn't you use this to make the muscle more efficient? or perhaps, if that particular bird for example had one exeptionally large heart, or perhap two or three of them, would that make them somewhat more powerful? perhaps enough to overcome the weight and size?

Excuse me if i seem to ask too many questions, but I've done little biology and no biomechanic, and i want and like, to get my creatures right.

On a side note, what is the carry load of some predatory birds? some eagles can carry off rabbits, which albeit are not heavy, but are of comparable weight to the bird itself?

ps: I'm still working on the creatures, and hence my questions, but if it helps you get an idea of the size and weight I'm looking at then the creatures I'm working on must have the ability to fly well (and being able to take off from ground level), but still able to prey upon men, and perhaps even small horses, deers, and similar sized creatures. I'm not sure what is plausible and what isn't, and perhaps this is just wishful thinking - I do want/like to get the physics right.

 

[sophiecentaur]

Would the best thing be just to look at present day birds and just use their performance as a guide? You could change things a bit; for instance you could inflate the the load carrying performance to make things more interesting. I think it may be a step too far to suggest a capability of lifting humans (as in Lord of the Rings) if you want to avoid getting into fantasy.
I saw a YouTube movie the other day in which an eagle pulled a goat off a mountain ledge and killed it that way. The goat was far too big for a straight lift but the eagle managed to glide it away from the cliff and arrange so that it fell a long way. The goat appeared to weigh quite a bit more than the bird but we're a long way from eagles lifting people. Sorry1
Sea eagles achieve some pretty impressive lifts, right out of the sea. Some of those salmon look huge - several kg, at least and it's a 'dead lift' with no help from a launch elevation. There may be some help from the wind at times.

 

[Necronox]

well, it is a fantasy world. So that is the general idea, but as i said, i like, and want, to have something that is able to fly physically speaking, be realistic and not use typical fantasy things like magic. (no magic in my world - there are thing that people call magic, but it isn't - it is just some physics or chemical reaction they cannot explain/understand)

interesting, it seems that most predatory can lift more then their own weight, the heaviest eagle weighs up to 8kg, a goat is at least 50 kg i'd say, it's seems improbable that they can lift so much? even it the eagle was just gliding away.

 

[CWatters]

Perhaps look at wing loading...

http://sciencelearn.org.nz/Contexts/Flight/Science-Ideas-and-Concepts/Wing-loading

Wing loading for birds is generally between 1 to 20 kg/m2. The maximum possible wing load before a bird is unable to fly is about 25 kg/m2. This is when the bird is too heavy for its wings (like the kiwi, which has tiny wings and a large body mass). The wing loadings of some of the lightest planes fall within the bird range. A typical hang-glider may have a maximum wing loading of 6.3 kg/m2. On the heavy side, a Boeing 747 has a maximum wing loading of about 730 kg/m2. Although it has a huge wing load, it can fly because of its incredible speed.

A typical full size glider (eg ASK 21) can operate with a wing loading of say 6.8 lb/sqf about 33kg/sqm

So I'd say for a fictional bird the size of a glider you should aim for around 10-20 kg/sqm. Perhaps push it to 30kg/sqm if you must.

 

[sophiecentaur]

If you want to have some justification for this sort of 'stretching' of reality, perhaps you could envisage your 'humans' and their associated livestock having become smaller in size. It's a theme in Brian Aldis's story 'Hothouse', which explores the life of some much-reduced humans in a tropical rainforest environment. Alternatively, you could introduce a more dense / viscous atmosphere, which would have the effect of producing more lift for 'flapping flyers'. There could be issues about breathing with conventional lungs in such an atmosphere.

I know it's easy for us, on the sidelines, to chuck in comments like the above and I appreciate that it is a can of worms for a would be author of an alternative reality story. But . . . . you did ask. Light blue touch paper and retreat.

 

[Necronox]

Any input is good input, at least that's what i think.

Making the atmosphere denser would screw up some other parts of my world.

As for making humans smaller, then that's also a little screwy since that put human out of proportion to everything else, i suppose it wouldn't be that far fetched it would be, however, a pain in the neck to change everything tho.

So, in relation to CWatter's post, a bird with a 15m wingspan from tip to tip, that would be what, roughly 1800kg? give or take. does this stand up to other creatures like bats of flies?

 

[sophiecentaur]

At least all this 'realism' hasn't out you off.
The problem with trying to scale things up in this way is that things just don't go nicely. If you double the length of wing and keep everything to scale, the area will go up by 4 times (x²), the mass will go up 8 times (x³) and the stresses go up by 16 times (x⁴). That calls for even stronger and even lighter materials.Then, unless your birds are just going to glide, they will need greater power, which means more energy input per day so they have to spend more time eating. In fact, the same limits apply nowadays to the size of birds. They would need a special niche in the ecology in order to allow this. Not totally impossible, perhaps but they would have to be the dominant top level predator. As an example, the ostrich and elephant survive simply by being big enough to deal with big predators and there would be immense competition for the sort of food supply that these fictitious birds would be using. Perhaos the birds could be eating some very high energy substance that's only available on mountain tops? That could give them the advantage (four star lichen that needs UV for it to grow).

Scaling everything down in size (all mammals) wouldn't be that screwy - some past environmental change could have had the same effect on everything - except for some of the birds (?) I think my idea of a change in atmosphere could be worth thinking about because, at a stroke, you can get more lift for flying. Bats and flies are of appropriate sizes to allow them to fly more easily. For insects, the atmosphere is more like treacle than how we perceive it, at our size.

 

[Necronox]

fair enough, so, in short, there no simple way to scale thing up realisticly? eventually, if i want to use those sizes, i would have to use stronger-but-lighter-then-bone replacements and muscles that give out more power, and to explain all this, give the said creature larger lungs, two large hearts to be able to supply such powerful and demanding muscles?

so, if you have a common every-day pigeon that way 2 tonnes, how big would his wings be to lift him? Assuming stress and power was not an issue?

On a side note, found a rather interesting pdf file: http://jeb.biologists.org/content/jexbio/130/1/235.full.pdf althought some of the details goes beyond me. i will have to go over it more thoroughly... perhaps there is something in there that can help me.

Edit: After some calculations (https://docs.google.com/spreadsheets/d/1P8ewGi4m23ulE13mTx1xwqsq3xNjY7GoPV8A-wMiXW8/edit?usp=sharing) it seems that something so big would either need a ridiculous strength and a feasible wing size, or a ridiculous wing size and a feasible strength... ugh. reality sucks... damn you physics! but i will make this work!...

 

[NTW]

As it is a 'fantasy world', you can also try reducing gravity. A world with a fraction of the Earth's gravity will make flying much easier...

 

[Necronox]

I suppose so, even by a small fraction it would help, but then again, i can't really explain that the planet, which is already a little bigger then earth, has similar gravity (i've chalked up the difference to a lighter planet - not as dense) I expect that sooner or later, i will have to make something not add up in terms of physics if i want to get my way. It would take me the better part of a whole lifetime to try and make an entire planet, right down to the last animal, that fits all together an makes sense. Thing is, where do i draw the line where such accuracy is simply too far or not important? maybe I'm a bit obsessed to make my world realistic in such a way it could happen in terms of physics, but well, i'll have to draw the line somewhere, ugh, the *dilemma*.

 

[A.T.]

A world with a fraction of the Earth's gravity will make flying much easier...

Like the Moon? Less gravity would affect the density of the atmosphere, which in turn affects aerodynamics.

 

[NTW]

You can have a density like the Earth's atmosphere with a less massive planet, and hence less gravity. Look at the case of Venus, with a similar mass to the Earth, but a much, much denser atmosphere...

 

[NTW]

I suppose so, even by a small fraction it would help, but then again, i can't really explain that the planet, which is already a little bigger then earth, has similar gravity (i've chalked up the difference to a lighter planet - not as dense) I expect that sooner or later, i will have to make something not add up in terms of physics if i want to get my way. It would take me the better part of a whole lifetime to try and make an entire planet, right down to the last animal, that fits all together an makes sense. Thing is, where do i draw the line where such accuracy is simply too far or not important? maybe I'm a bit obsessed to make my world realistic in such a way it could happen in terms of physics, but well, i'll have to draw the line somewhere, ugh, the *dilemma*.

You can resort to another variable: the rotation velocity of the planet and the resulting centrifugal force. With a fast enough rotation, the apparent weight of any object will be much reduced, specially at latitudes near the Equator. Besides, you'll have some nice effects resulting from Coriolis acceleration...

 

[Necronox]

What kind of effects would result from the Coriolis effect? besides, just how fast would the planet need to spin for the centrifugal force to affect flight? I'm not sure what other effects would that result in other then a faster day-night cycle?

but in any case, I'm reluctant to be changing too many variables in terms of the planet and it's characteristics, it seems too affect just too much, including Aerodynamics.

would it be possible for the upper atmosphere to be layered? so when it's close to the ground it's relatively the same as earth, but further up it's denser then become lighter again as it goes towards the stratosphere? perhaps due to charged particles or magnetised iron particles or something?

 

[A.T.]

besides, just how fast would the planet need to spin for the centrifugal force to affect flight?

If the effect was significant for flight, it would also affect the shape of the planet (flatten it).

 

[CWatters]

So, in relation to CWatter's post, a bird with a 15m wingspan from tip to tip, that would be what, roughly 1800kg? give or take. does this stand up to other creatures like bats of flies?

Lighter. There is a glider competition class for aircraft with a 15m wing span. An example would be the ASW 27 which has a wing area of 9sqm (97sqf). In an earlier post I said...

So I'd say for a fictional bird the size of a glider you should aim for around 10-20 kg/sqm. Perhaps push it to 30kg/sqm if you must.

So I would suggest that a bird that big would be limited to around 20*9=180kg or perhaps 30*9=270kg. At that sort of size and weight it would be unrealistic to have it flapping it's wings to take off. A typical flight would consist of it walking to the edge of a cliff, unfolding it's wings and launching itself off the edge like a hang glider. If it did land somewhere flat it would have to be able to climb up high enough to take off again.

 

[Necronox]

i see, but gliders don't "flap" wouldn't that generate more lift? since you're actively spending energy to fly, instead of just gliding where you're not spending energy to keep flying?

It seems that something that big or heavy will simply not be able to fly because of so many different reasons, not enough lift, not enough strength, too much stress. I hate physics sometimes, ugh. damn who ever came up with them laws... xD. Either way, i'll have to bend a few things to make it fly, I'm reluctant to change gravity, of the spin of the earth, the size of mammels or the density of the atmosphere, those i'd rather like to stay close to earthly values. I suppose i could make it significantly lighter, boost it's lift a little and ignore the fact it doesn't quite have the strength to deal with such strength requirement, giving it two hearts, large lungs and the like i could use as an excuse for it's larger strength. Assuming it still can carry away large game for birds like humans, deers, and the likes, it would need to at least have a life of 100kg. so, what size and weight does that make it? allowing for a little bit of pushing here and there, how close can i make it reality?

 

[A.T.]

i see, but gliders don't "flap" wouldn't that generate more lift? since you're actively spending energy to fly, instead of just gliding where you're not spending energy to keep flying?

You will notice that the bigger a bird is, the less flapping it is doing.

 

[sophiecentaur]

So I would suggest that a bird that big would be limited to around 20*9=180kg or perhaps 30*9=270kg. At that sort of size and weight it would be unrealistic to have it flapping it's wings to take off. A typical flight would consist of it walking to the edge of a cliff, unfolding it's wings and launching itself off the edge like a hang glider. If it did land somewhere flat it would have to be able to climb up high enough to take off again.

Alternatively, it could do what an albatross has to do in order to take off from the sea, after catching a fish. It relies on the fact that the Southern Ocean is constantly windy and the waves are big. It waits till it's on the crest of a wave, faces into the wind and starts running and flapping its wings as hard as it can so that there is just enough lift to get it off the surface. Apparently, they also use the gradient of the wind speed near the surface and (with a sort of tacking motion) pinch enough power to allow them to stay aloft between the peaks of the swell with very little expenditure of energy.
These massive predatory birds could perhaps use a strong prevailing wind (in a rare bit of topography and climate) and use a slope soaring method to get the required power.

 

[Artribution]

As big as you want it to be.

Any large creature in sci-fi is going to be criticized. People will point to square-cubed problems, say their muscles can't be strong enough or they would weigh too much, etc. But that's overlooking the fact that creatures that evolve to large sizes also, by necessity, evolve ways of overcoming those problems. For example, large dinosaurs evolved lightweight bones filled with air sacs to reduce their actual weight, extraordinarily growth-optimized metabolisms, etc. Biological history has shown in the evolution of organisms all the way up from the microscopic scale that if there's an evolutionary mechanism that favors larger size, life finds a way.

 

[Necronox]

As big as you want it to be.

Any large creature in sci-fi is going to be criticized. People will point to square-cubed problems, say their muscles can't be strong enough or they would weigh too much, etc. But that's overlooking the fact that creatures that evolve to large sizes also, by necessity, evolve ways of overcoming those problems. For example, large dinosaurs evolved lightweight bones filled with air sacs to reduce their actual weight, extraordinarily growth-optimized metabolisms, etc. Biological history has shown in the evolution of organisms all the way up from the microscopic scale that if there's an evolutionary mechanism that favors larger size, life finds a way.

well that makes sense. =)

 

[Artribution]

That link was supposed to go here.

Yeah, though, I think you're scientifically licensed to ignore any smartypants who tells you your creature can't exist. You might want to avoid being overly detailed in its biology until you're comfortable you can, but if natural selection can evolve microbes into dinosaurs, it can certainly evolve them into Godzillas (or Rodans). The difference is insignificant. All it needs is pressure and time.

A few biology suggestions:

• A highly efficient metabolism. Sauropod chicks are no bigger than human babies, but grow thousands of times faster. Sadly they're not so efficient as adults.
  
• Lighter, tougher tissues. Maybe its muscles/wings/organs/etc. aren't made of cellular tissue at all, but woven like spider silk from some lighter, stronger material.
• Maybe they are cellular tissues, but made of structurally superior cells - plantlike walls instead of membranes, a cellular skeletal structure, or just stronger membranes or a lighter kind of cytoplasm.
• (added from below) Also, water. On this planet, most of an animal's weight is water. An animal that didn't need so much water could grow to ridiculous size and would certainly fly a lot better.

 

[Necronox]

0.0 there's some good ideas there.

On a side note, what would good substitute for keratin (which is used in nails, hair, scales, etc...)?

 

[Artribution]

Also, water. On this planet, most of an animal's weight is water. An animal that didn't need so much water could grow to ridiculous size and would certainly fly a lot better.

On a side note, what would good substitute for keratin (which is used in nails, hair, scales, etc...)?

No idea. =s

Although insects substitute chitin.

 

[Necronox]

but isn't water kind of necessary for the almost any animal being? how could an animal simply not need as much? would there be another lighter substitute to take on the roll of whatever water does in the animal body?

 

[Artribution]

It's needed for chemical reasons, yes. And there's where I run out of ideas, because I know not of "chemistry." I just know that water is heavy, and that it's most of the reason animals are heavy. So if you want lighter animals, cutting down on water seems like a good thing to consider.

I guess as a start, an animal that relied less on cellular tissue might need less water. The cellular structure on this planet might also be fundamentally different - maybe most of the animal's cells don't contain its full genome. but get DNA instructions from other cells instead. That might save on redundancy. And also prevent cancer.

 

[Necronox]

okay, I've got no idea what your second paragraph means, went straight over my head.

 

[Artribution]

Well, every animal cell has a nucleus with DNA inside. I was saying maybe that's not the case with animals on your planet. I'm not sure how much of an effect that would have on water, but an animal's mass is largely in its cells, so, differences in cellular chemistry could greatly reduce the overall weight of animals on your planet compared to ours.

 

[Necronox]

so, they have bones made of some wooden-like structure and some of their cells are not strictly organic, but simply neutral compounds that don't degenerate but carry out the same similar role? Interesting idea, but wouldn't a result of this allow for prolonged life expectancy? All thought that's not a problem, I never thought about the life expectancy of my creatures. but I'm liking some of these ideas... ultra-light massive flying animal that can carry away large pray and lives an extraordinary long time, is quite powerful and has a strong body and is quite resistance to attack? looks like my antagonist's weapons/slaves/corrupt creatures are more powerful then i was expecting... me like.

 

[Artribution]

Seems there'd be less that could go wrong, yeah.

 

[Necronox]

what do you mean?

 

[Artribution]

I was replying before the edit to your question about longevity. I agree that it seems animals could (not necessarily would) live longer that way, yeah. Not necessarily would, because you still have predators and diseases, and evolution still depends on the animal dying at some point to make room for its descendants. But it does seem that it could, because cell tissue is complex, and the more complex something is, the more ways it can fail.