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For starters, allow me to define more carefully what I am asking. For now I am not worried about any of the following, as if this question is answered they will be covered in later questions:

  • Bones breaking, tissues tearing etc. caused by the dragons large size, and organ systems required to support this creature. Both covered Here
  • Metabolic requirements.
  • How such a creature evolved or the plausibility thereof.

What I am asking is if I have made any mistakes or am missing any factors as to the mechanical ability of this dragon to fly.

I figured that whether or not my dragon could get off the ground, this question and subsequent answers might supply some basis to work off of for others who come to this site to ask about large flying creatures.

Warning - Math Ahead - Warning - Product of Someone with too much Free Time

I started with a sketch of the Dragon (Updated with Structure on tail to add some stability) Dragon

Using this Drawing I treated the body as a series of ellipsoids to calculate the volume. From there I ran numbers to find an appropriate wingspan etc. and edited the images to match.

The Dragon is designed with a head modeled loosely after a false gharial, wings and a chest modeled after those of a bat for flight, and a toads legs+a kangaroos tail to aid in liftoff.

Height: 6.5 meters

Length: 19 meters

Volume: 11.9 cubic meters

Average Density: 0.614 g/cm^3*

Weight: 7310 kilograms

Wingspan: 38 meters

Wing area: 304 square meters

Wing loading: 23 kg/m^2

Wings+Legs+Tail muscle cross-section: 43,000 cm^2

Muscle strength*** newtons/cm^2: 35 n/cm^2

Wings+Legs+Tail muscle strength: 1,474,900 watts

Liftoff time: 1 second

Height leaped in Liftoff**: 20.6 meters

Wing muscle cross-section: 21,600 cm^2

Wing muscle strength: 756,000 watts

Flap time: 2 seconds

Flap acceleration**: 21 meters a second

Coefficient of lift****: =<3.9

Coefficient of drag****: =>0.12

From nasa.gov

L = (1/2) d v2 s CL

L = Lift, which must equal the airplane's weight in pounds

d = density of the air. This will change due to altitude. These values can be >found in a I.C.A.O. Standard Atmosphere Table.

v = velocity of an aircraft expressed in feet per second

s = the wing area of an aircraft in square feet

CL = Coefficient of lift , which is determined by the type of airfoil and angle >of attack.

(I'll be using metric) Density of air at 3km above sea level and -4.5c = 0.9093 kg/cm^3

0.5 x 0.9093 x 10^2 x 304 x 0.6 = 8292.816 kg of lift, more than enough to get this guy off of the ground.

Drag = Cd (d v^2)/2 x reference area

The density of air at sea level and 20c = 1.225 kg/m^3. The reference area I calculate is (1.5 x 2)m^2 for the face and torso + (36 x 0.4)m^2 for the wings, or 17.4 m^2.

0.2 x (1.225 x 10^2)/2 x 17.4 = 213.15 newtons of drag, though I am not sure how to calculate the effect of this on the dragon.

*Density of bird lowered further by certain adaptations which will be discussed in another question.

**Found using a simple work-over-time equation.

***There is no difference in strength between fast and slow twitch muscle fibers, only in contraction speed and endurance. Paper which shows this.

****Actual Coefficients of bats, if there is some reason these would not be close enough, please let me know.

I was surprised after looking at these numbers that I wasn't actually seeing anything that as far as I could tell stopped the dragon from flying. But this is my first time doing any of the math involved, and even if I got all of it right I could be missing something, so I thought I'd ask some of the smart folks over here at Stack-Exchange and see what they told me.

Assuming that this creature runs and then leaps, using arms then legs+tail, to liftoff, followed by a few flaps of its wings, could it get air-born as my numbers imply? From there could it maintain flight?

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Myrdden Wyllt
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  • What are its bones made of? Can you compute the required strength for, e.g., the humerus bone or the proximal phalange of the 5th finger? And what about sustained mechanical power, because I have no idea what "explosive" power means... – AlexP Apr 06 '17 at 23:47
  • @AlexP as I said at the top of the question, I'll be addressing bone strength and whatnot in another question. As for sustained mechanical power, I'll add data on that if I can find it, but it's much easier to find information on "explosive" strength, so that's all I have for now. Explosive strength referring to being able to lift an object for a short period of time, as opposed to being able to carry it. – Myrdden Wyllt Apr 07 '17 at 00:02
  • I will edit the OP to make what I mean by explosive strength more clear. – Myrdden Wyllt Apr 07 '17 at 00:16
  • It's not clear to me how the structure of the wings and motive power of a creature do not fall under "mechanical ability to fly". – The Nate Apr 07 '17 at 00:22
  • @The Nate, perhaps I could have phrased that a bit better. But to be clear, I am interested if muscle strength will be sufficient, but bone strength will be addressed seperately. – Myrdden Wyllt Apr 07 '17 at 00:25
  • You will find that bone strength is critical. I suggest some sort of composite of carbon fiber and titanium... The point of requesting sustained power is that brief bursts are of no interest. Humans can easily jump off the ground, but they need strenuous training and very elaborate mechanical devices to fly by muscle power alone... – AlexP Apr 07 '17 at 00:50
  • @AlexP yes, I see the point of requesting sustained power, I just haven't found a way to compute that yet, I'm limited to what I can google and I have only been on this project for ~3 days, I'll update with information when I find it. I also agree bone strength is critical, my thinking was to replace the strength giving minerals in the bone with graphene foam, it's made of carbon, incredibly strong, and reduces the density of the dragon by about 50 kilos per m^3. I will however address bone strength and similar issues in another question. – Myrdden Wyllt Apr 07 '17 at 00:56
  • @AlexP I just learned that there is no inherent difference in strength between the muscles responsible for explosive strength and sustained power, so the value listed above will work for both. – Myrdden Wyllt Apr 07 '17 at 01:57
  • I think you're going to run into problems due to scale. There's a limit to how large the wings can grow before they start tearing under their own weight; I can't recall the precise figure, but I think your limit is a wingspan of about 8 to 10 metres for a purely biological creature (no artificial materials). There's also a limit on how fast signals can pass along the nerves, in the range of hundreds of milliseconds for humans; with your 38-metre wingspan, the delay between thinking flap the wings and the wings actually starting to move will be noticeable and potentially problematic. – Palarran Apr 07 '17 at 03:06
  • @Palarran from the list of issues I will address in another question "Bones breaking, tissues tearing etc. caused by the dragons large size". I have some ideas addressing patagium strength, but they will be addressed in a later question. As for nervous signal speed, that is a good point, I think I have some ideas regarding it, but they will be addressed along with the earlier points about tissue strength. – Myrdden Wyllt Apr 07 '17 at 03:11
  • @MyrddenWyllt I raised my eyebrow seeing a Coefficient of Lift of almost 4. Bear in mind that bats (the source of your number) fly at much lower Reynolds numbers than your much larger creature. I'm betting on the Cl being 2 or less, at least for gliding flight. – Steve Apr 07 '17 at 06:31
  • 2 MW sustained power is a lot of power. Let's say that the muscles of this superdragon have 25% efficiency at converting chemical energy into mechanical energy, comparable with the best motor-car engines; that's 8 MW thermal power, which means that the dragon must dissipate 6 MW as heat. In a very short time it will be flying ball of fire. – AlexP Apr 07 '17 at 07:27
  • @AlexP it has that much sustained power available to it, it won't necessarily be using all that power all the time, as it's enough power to push the dragon 20 meters over about one second. Assuming it uses half of it, 1,474,900*3, that's 23,313 Celsius to dissipate, over 700 m^2 of surface area, or about 33c power m^2. Unless I'm missing something, that's around the same range as human core temperature, if it needs to be lowered that I think is something that could be addressed in the other question I've asked so far. – Myrdden Wyllt Apr 07 '17 at 12:31
  • @Steve that's the highest number I've seen for bats, but I agree it would be too high for gliding, notice in my lift equation I used a Cl of only 0.6 . I don't know what the best number to use would be as I am a layman, so I aimed low. I don't know enough about Reynolds numbers to look at that math, but I'll try and see what I can learn, I suspect you're right and the max Cl should be much lower, but I don't think the dragon needs​ to approach 4 to stay in the air either way. – Myrdden Wyllt Apr 07 '17 at 13:33
  • @Steve depending on the exact structure of the wing, the dragon has a Reynolds number between 4 and 5.6 million (according to my math checked with online Reynolds number calculator), which is ~400 - 60 times that of a bat. What I'm reading says that larger Reynolds numbers are better, however, not worse, than low ones, as they allow higher Cl's and lower Cd's. So, unless I'm missing something, it actually seems to be good news for the dragon. – Myrdden Wyllt Apr 07 '17 at 14:06
  • Previous comment is Reynolds number at 10m/s. – Myrdden Wyllt Apr 07 '17 at 14:16
  • This dragon seems like a dead ringer for Rhamphorhynchus. Though I think Rhamfy would be a bit miffed to be called a gharial-bat-toad-roo. – cobaltduck Apr 07 '17 at 20:23

3 Answers3

8

It looks like you don't want to pull the magic card.

I think that you can do without the webbing between the legs. I think that it is too close to the wings to provide much stability. I'd flatten the tail instead (or make the body longer and the tail shorter but that'll add mass).

Otherwise, unless the body is much denser than a mammal's, I don't see any reason why it shouldn't fly.

Walking, on the other hand may be an issue given its total size. Unless the leg bones are much stronger than ours, I think that the legs are too thin for its size.

Also, don't just look at loading on the surface of the wing but follow that load along the structural members. The shoulders (wing root) will be under a lot of stress. It might need to get beefed up. You might also need more "fingers" in the wing to reduce the stress faced by the root of each finger.

Though if it had hollow bones, that would work but it would be much more fragile.

It will also have the issue of being unable to pump the blood up from its legs back up to its heart. Take a look at elephants. The skin around it's feet and lower legs are very strong and is designed to act like a pressure sock to help muscle movement pump the blood back up.

So, aerodynamically, it looks good but I think that the cubed root law is going to bite you in the structure.

ShadoCat
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    I'm going to attempt to address many of the issues you raised in another question (organ systems, bone and tissue strength, and whatnot). For this question I'm concerned mainly with if I've got the aerodynamics right, if as you say at the end of your answer I'm good there, I'll begin to write up my next questions concerning this dragon. – Myrdden Wyllt Apr 07 '17 at 00:09
  • As for the membrane between the legs and tail, that was an attempt to slightly reduce wing loading, as I would like to keep that as low as I can. If there is some reason that would not work, I would appreciate it greatly if you could elaborate on that. – Myrdden Wyllt Apr 07 '17 at 00:27
  • For reference, I believe mammal density is ~1.5g/cm^3. Making the density of my dragon a little under half. – Myrdden Wyllt Apr 07 '17 at 00:36
  • @MyrddenWyllt, the leg membrane will indeed reduce wing loading but it will not add much stability. All in flight stability will have to be "active." It will be constantly using energy by altering the flapping of its wings to remain stable. It's doable especially if there is plenty of prey but flying will be more cost effective if there are some control surfaces farther back. – ShadoCat Apr 07 '17 at 00:42
  • @ShadoCat ah, thank-you for the clarification, I shall keep that in mind. – Myrdden Wyllt Apr 07 '17 at 00:46
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    Remember that this is a [tag:hard-science] question and, as such, requires citations to support your conclusions. You should [edit] this to include references to supporting evidence; otherwise, this may be deleted as inadequate, as the answer banner indicates. – Frostfyre Apr 07 '17 at 12:10
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    As Frostfyre mentioned, this has the tag hard science so you will need to back your claims with either citations (which I presume will be rare for dragons) or equations. The lack of supporting material have led to that your answer is in the review for low quality answers. – Mrkvička Apr 07 '17 at 17:33
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The area of a bat-shaped wing is calculated by A = (F x D5) + 0.5 (D5 x D3). F = the forearm length, D5 = digit 5, D3 = digit 3 Each square on your chart is ~1.85 meters, so your dragon has a wing area of ~220 m^2 including the hind legs and tail. Assuming normal air density at sea level, it should have a stalling speed of 42.5 km/h. So as long as your dragon can launch itself at or greater than 42.5 km/h, it should fly.

Praearcturus
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0

Wings are not propellers

Bats only have a coefficient of lift of ~3.9 because their wings do a lot more up/down movement than they do back and forth. For reference: a fixed wing airplane has a theoretical max of about 2. This means that for your dragon to get that coefficient of lift AND fly 10m/sec that your wings will actually be accelerating much more than 21 m/sec.

In these videos (https://www.youtube.com/watch?v=Ni_mS4cKPXY, https://www.youtube.com/watch?v=JAP2I-t3FGs), you can see that a bat's wings covers about a 130-140 degree arc per stroke and that each stroke only moves it about 1/6th as far forward as the wing moves up or down. So, if your wings are about 17m each, that means your wing tips are moving about 40m per full flap moving you forward ~6.67m; so, to get to 10m/sec speeds using bat wing mechanics, your dragon has to complete 1.5 flaps per second where your wing tips are actually covering about ~60m/sec while accelerating at an average of ~120m/sec^2 at any given time...

Since your wings are actually exerting a lot more force than you were accounting for, you will need to scale some things down a bit and figure out a wing flap profile that works for you. Instead of the lift coeffect of a bat, you should probably be looking at large birds like the Albatross or Andean Condor which actually flap very little. Less flapping is better for large flying animals because it reduces stress on not just the bones, but the muscles and ligaments that give the bones structure.

Nosajimiki
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