# Anatomically Correct Pegasus

This is part of the Anatomically Correct Series. I've been wondering how an anatomically correct pegasus could evolve.

### Pegasus characteristics

They are pretty obvious, but just in case:

• Horse size and form
• Wings
• Being able to fly and gallop

### My questions

As in the anatomically correct creatures series, I follow a line of questions about possibilities:

• Is it possible?
• How would they evolve?
• Would it be possible to ride one?
• – Theraot Sep 21 '16 at 12:24
• @Theraot wow, didn't find this while I was looking before asking, may delete question if duplicated – Yacomini Sep 21 '16 at 12:26
• It isn't exactly a duplicate because you are asking two questions (angel and pegasus) and Anatomically Correct Pegasus is yet to be done. So you could convert this question into that. – Theraot Sep 21 '16 at 12:28
• And vote retracted :) – Mołot Sep 21 '16 at 12:38
• Also highly related, not dup: worldbuilding.stackexchange.com/q/38550/10851 – cobaltduck Sep 21 '16 at 13:47

# Weight vs. Wing length

The approach I'll follow to decide if the Pegasus is possible is to analyze the Weight vs. Wing length. The first problem I have is to find a good enough data source.

In the past (old version of this answer) I had used third party analysis based on Wikipedia data. This time I'll get a better data source and work estimation by myself.

## Extracting the data

The data source I found is the information published by the British Trust for Ornithology. In order to extract the data, I've created a custom software. Using that software I got the raw data that I will be working on.

In order to process the data, I used an online spreadsheet.

The extracted data, once curated (removed entries with not enough data) consists of 540 data points corresponding to averages of weight and wing length. This data came from multiple measurements of the individuals per species. I'm disregarding the distribution of those values and only using the average.

Note: if you want to compile the software you need a C# compiler and my libraries available from nuget.

## Processing the data

Once curated, I did the following plot of the data:

Plot Weight (?) vs. Wing length (mm)

In the plot we can see that some of the data points lay very close to the horizontal (wing length) axis. The rest of the data points seem to follow growing curves.

Actually the data is wrong, turns out some data is in kg and other in g (my software doesn't read the units) - after fixing the unit we have the following plot:

Plot Weight (g) vs. Wing length (mm)

My next step was to plot the natural logarithm of the values for the same data points. The result is as follows:

Plot Ln(Weight(g)) vs. Ln(Wing length(mm))

In this plot we can see that a linear function seems to be a good enough approximation.

Remember that the wings are at least as big as needed, and not as big as too increase Weight to a point that impedes flight. So, it is expected that for each Weight value, there actually exists a range of plausible wing sizes (the original plot supports that idea too).

## Adjust to a linear function

Plot of the first cluster + approximation to a line

In the plot the added line follows the equation:

$$Ln(Weight(g)) = \frac{1640}{1379}Ln(Wing length(m)) - \frac{2102}{2167}$$

Oops... that's the wrong way around - of course, I have weight in the vertical - let me fix it:

$$Ln(Wing length(m)) = \frac{1379}{1640}Ln(Weight(g)) + \frac{7357}{9020}$$

Keep in mind that we are working with the natural logarithms.

Of course, the wings add weight to the animal. So using the weight of the animal without wings is inaccurate. But it should be noted that due to the estimation method, this value is somewhere near the middle of the range of valid wing lengths. Thus, I’ll consider this method to be good enough.

In case of doubt, BTO defines Wing Length as follows:

Wing Length

Maximum flattened chord measured on live birds, this measurement will be greater than that of the natural, resting wing, or of measurements taken from museum skins (see Svensson (1992) for details).

Also, it is a measurement of a single wing; it should not be confused with wingspan.

# Horse computing

## Subject 1: Thumbelina

Thumbelina compared to a dog.

Thumbelina, the world smallest horse has 26Kg.

So we have:

$$Weight = 26Kg$$

But we need grams, so:

$$Weight = 26000g$$

Next we need the natural logarithm in order to feed it into the function we found:

$$Ln(Weight (g)) = Ln(26000)$$

We compute Ln(26000):

$$Ln(Weight (g)) = 10.165851...$$

Plug it in the function:

$$Ln(Wing length(mm)) = \frac{1379}{1640}10.165851... + \frac{7357}{9020}$$

Compute that and we have:

$$Ln(Wing length(mm)) = 9.363625...$$

Now we get the wing length:

$$e^{Ln(Wing length(mm))} = e^{9.363625...}$$

$$=>$$

$$Wing length = 11656.574347... mm$$

$$=>$$

$$Wing length = 11.656574... m$$

So, we have Wing length of 11.65 m (38.22 feet).

That's HUGE for poor Thumbelina!

## Other subjects

I'll be using data from the paper Estimating a horse’s weight from the Department of Primary Industries of Australia.

Subject 2: Anatomically Correct (Flying) Pony

The large pony has 360kg. Wolfram|Alphing we get: 106.233559... m (348.535 feet)

Ok, that's ridiculous.

# Evolution

Before we consider the case of riding the animal, we need to consider that the non-ridden modes of locomotion would have evolve naturally, and then for it to be ridden it would require domestication. In particular breeders would select the stronger animals for reproduction in order to make offspring strong enough for carrying a human.

## The Six-limbs problem

As with Anatomically Correct Angels, we run into the problem of six-limbed mammals. There are no examples in nature, and there reason to believe that the DNA structure doesn't support it※ - of course, a different structure could also evolve.

※: Researchers have created mutated fruit flies that have legs where they should have antennas. This was done by swapping portions of DNA, this suggests that there is a limited number of locations where you can insert limbs in the DNA.

It is also worthy to look at the lore:

Bellerophon on Pegasus spears the Chimera, on an Attic red-figure epinetron, 425–420 BC

The depiction above gives some insight on the six-limb problem as we can imagine the wings as ramifications of the frontal legs.

I also want to note on the wing aspect ratio, that different wing aspect ratios are characteristic of different flight styles:

Examples of Wing aspect ratio

If Pegasus is used for battle, it probably has high agility as to avoid attacks and approach the target from different angles. So, a wing with similar proportion to the crow depicted above example is expected.

# Conclusion

Giving wings to horses result in exaggerated size

There is no way around it, if want something that resembles a Pegasus, you need to evolve the horse to have less mass. Similarly to the Anatomically Correct Angel, the Anatomically Correct Pegasus needs to have thinner bones...

The Anatomically Correct Pegasus has two solutions:

It can fly but you can't ride it because the bones are too weak to support a human. You can ride it, but it can't fly, the wings are only an ornamental vestige kept by the breeders.

• You meant ridding as in riding right? Cos I just read it as getting rid of the animal... – Skye Sep 21 '16 at 14:04
• I think you've got your math wrong in the equation and graphs. Squaring the wingspan does not automatically get you the surface area of the wings, unless the wings are perfectly square. Those things tend to be far longer than they are wide (you might have a 2 metre wingspan on a bird 3 feet long), so your estimates will simply be wrong. – Palarran Sep 23 '16 at 16:19
• @Palarran That was what WIRED used to make the estimate, and it got very close for humans as they later reviewed. And of course it is wrong, it is an estimate! Now, I know it can be done better, in fact WIRED found that doing a logarithmic plot makes a near perfect fit of the curve – this computation is just easier to use. – Theraot Sep 23 '16 at 16:23
• "With the formula above, we get a wingspan of 17.3 m2. But that's area..." Remember this statement from your post? That's dead wrong. Wingspan is not defined in square metres, and squaring wingspan gets you, at best, an overestimate of wing surface area. Those are two entirely different things. – Palarran Sep 23 '16 at 23:17
• @Palarran I see. Alright, I'll redo this. I'll skip WIRED and find an estimate from raw data, it will take a while. – Theraot Sep 24 '16 at 3:13

I found good points in all the answers so far.

I disagree with the ones that say it's not possible, though. I say it's possible.

I believe that, as always is the case with the anatomically correct series, people are taking a very stiff aproach when it comes to mysthical beasts. In this case, people would like to see an Equus ferus with bird wings attached to it, obviously leading to problems related to weight.

(Unicorn horn entirely optional)

I'd like to take a different approach. I'd like to base the feasibility of my pegasus, henceforth known as the Hippopterus renanii, on three pillars:

• There have been really big critters flying on Earth before. I present you Quetzalcoatlus northropi and Quetzalcoatlus sp.:

Weight estimates vary, but the bigger guy in the pic above could probably reach 200 kg and still fly like a vulture.

The ribs and their connecting membrane may be extended to create a wing

• It is believed that mammals evolved from reptiles, so if we stretch our suspension of disbelief enough, then a mammal species could evolve to have traits that in our real world have only ever been perceived in reptiles, extinc or extanct.

With these three points in mind, imagine if you will a genus of mammals that branched off from the Equidae family a few million years ago. These beasts were originally very small, and at some point developed the following characteristics:

• Their ribs are articulated, with the first articulation close to the vertebral column. They fold a couple times before enveloping the torso, and they don't support the structure of the thorax. They can open up like wings. A thick hide membrance, called a patagium, connects them. All in all their wings will resemble something between the wing of an eagle and the wing of a vulture.

• A smaller, secondary patagium connects their legs, from the ankle up, to the ribs when they open up. The secondary patagium only serves to add to surface area during flight. Yes, our pegasus is going to fly with its legs spread open to the sides.

• To make up for the loss of the bone ribs, a secondary set of hard, cartilagenous ribs has replaced them as the supporting structure for the thorax.

• The Hippopterus has about the body size as an adult horse, but due to lighter bones and organs its weight is about 80 kilograms. Compare with the 380 to 1,000 kilograms provided by Google, and you see it's quite light when compared to an Equus ferus. The Hippopterus also looks very skinny, like an undernourished greyhound or whippet.

• Last but not least, the wingspan. It is a little more than that of the Quetzalcoatlus sp., the smalled of the two in the diagram above. Small Quetz has around 5,5 meters of wingspan. I'm eyeballing a 6 to 6.2 meters wingspan. This should give it about the same weight to wing surface ratio as the smaller Quetzacoatlus.

So, all in all... Our flying horse has a very bizarre appearance. It will probably fly by soaring over thermal currents. It can flap its wings but cannot sustain powered flight for more than a few seconds. It can, however, glide for miles once it reaches a high enough altitude. It probably evolved this method of flight as a succesful migration strategy.

Weighting less than an adult ostrich, it is probable that a human would only be able to ride it while it walks, but not while flying. The Hippopterus would also be a very bad ride, and would neither tolerate nor withstand a human sitting on it for long periods.

So, to summarize:

• Horse size and form: check
• Wings: check
• Being able to fly and gallop: check

• Is it possible? Yes.

• How would they evolve? As an offset of the Equidae, developing both Draco and Azhdarchidae reptilian characteristics.
• It would be possible to ride one? Only on land, only for a very short while, and you'd probably be in for a very rough ride. If you want a flying ride that badly you'd probably do better by getting a microlight.

No, Pegasuses are Not Possible

Ah, the Anatomically Correct series - where we all learn that just because you can draw something doesn’t mean it would work.

The Primary Issue: Wingspan

First let's start with the size of horses. Per Wikipedia, "Light riding horses usually range in height from 14 to 16 hands (56 to 64 inches, 142 to 163 cm) and can weigh from 380 to 550 kilograms (840 to 1,210 lb)". So let's say our horse is on the lighter side, at 380kg/840lbs.

Next let's consider the necessary wing size. As outlined in this academic paper on the topic of wing size to speed physics, let's use the equation:

W/S = 0.38v^2

Where;

W = Weight (Newtons) per Wing S = Surface Area of the Wing (square meters) V = Velocity (Meters per Second)

Note: This equation assumes air density at sea level.

So how fast should this horse fly? Traditionally a Pegasus has demonstrated a speed faster than a running human, so let's go with that. The fastest human speed is 12.4m/s, so we'll go with 12.5m/s just to edge it out.

Result: The resulting surface area of the wings must be at least 23.84 square meters per wing. Compared to the human in a hang glider above, which has a surface area less than 11.9 square meters... for both "wings" put together!

This probably puts wing length in the area of 10 meters (33 feet) to a side.

Now imagine a horse dragging a 10 meter (33 foot) wing on each side while it tries to gallop!

NOTE: The wingspan would actually have to be larger, to additionally account for the weight of the wings themselves!

• Not only do you have to have larger wings to account for the weight of the wings, you should also have to have larger wings to account for the weight of the rider and saddle since in general we are interested in a pegasus you can ride – Kevin Wells Sep 21 '16 at 17:45
• Fair point; what's the point of a Pegasus if you can't ride it? I forgot to mention that the size would ALSO need to increase due to the drag of the much-less-than-aerodynamic shape of a horse! At some point the anatomically correct pegasus is going to have to start evolving a jet-based propulsion system to handle all these challenges; I just hope I'm not standing behind it during take-off! – GrinningX Sep 21 '16 at 18:45

# No - Not Possible

Is my call.

The largest known flying bird (living or extinct) appears to be Pelagornis sandersi

This bird had a wing-span of some 20-24ft (up to 7.3 metres) and weighed something between 50 and 90lb (22-40 kilos)

The average horse weighs something between from 380 to 550 kilograms (840 to 1,210 lb). For a good sized Pegasus, let's take the larger of the two to make it rideable.

So that's over 10 times the weight of the largest bird. How big are those wings going to be, and how massive will the muscles that drive them have to be? And muscles aren't the lightest of tissue types. Then there's the bones to support those wings and the muscles that drive them. And how much larger will those wings have to be to support a rider...?

It's all too much for reality as far as I can see.

• Well there was a nifty site I found talking about why humans(as we are) can't have wings that allow flight as the wings need to be big to support our weight and the bigger the wings are the more weight there is from the wings so it's impossible unless your wings are like super light. – Skye Sep 21 '16 at 14:03

Well adding onto all the answers here. It should be noted that a horse is HEAVY. Its stability and speed on land come because of its weight and anatomy.

Imagine a horse, light as a feather, with hollow bones and zolatific wings!