Zipp and Flight · 11:41am Oct 17th, 2021
I do love a good blackboard shot.
The scene where Zipp stands in front of such a board in the derelict Zephyr Heights station, while confessing her deep frustration at living a ridiculous lie, was a great scene that had me pressing the pause button and taking screen shots. What does this board tell us?
There aren’t any juicy equations on this one (unlike the last movie) but it has clearly been carefully drawn, with streamline diagrams, plots, tables, and maths you might find in an aeronautical engineer’s notebook. The result provides a perfect illustration to Zipp’s background. She is a pony who longs to take to the sky as pegasi once did, but no matter how hard she trains, it remains out of reach. As a princess, she has to keep up the fiction of flying royalty by flapping her wings while being lowered on wires into the throne room. That’s enough to make you pull a face when told to remember to smile. Yet Zipp keeps her cool. She is a smart strong mare who thinks tactically. As the heir to the throne, she has likely been well educated.
It’s left to us to fill out further details of this story. Zipp wants to understand flight. With no magic, you may as well study the science. Has Zipp taught herself physics with the dream of finding a way to fly? Or is this just another hobby to get away from her day job?
It is made clear throughout the film that pegasus flight is magic. I approve of this message. Many scriptwriters would not think it unreasonable to expect a young audience to go along with the fiction that you can just attach wings to a horse and have them fly like a bird. If anyone asks why not, it is not so easy to give an answer beyond just saying that ponies are too heavy.
Let’s look at how wings work. The principle is to lift yourself up by pushing against the air molecules around you. The trouble is that there are usually just as many pushing you down as up. You need a pressure difference. If you have a big fan blowing lots of air upwards, you can spread your wings and rest on the rising stream. Easy.
Without such help, you can try flapping your wings to create a higher air pressure underneath than above and thus produce lift. How exactly does this work? Zipp’s blackboard scribblings look like she may have been trying to understand pegasus flight using aerodynamic theories for fixed wing aircraft. If so, she will have found that this approach is a dead end, not just because pony flight is magic, but because when you start flapping, things are much more complicated. Simple theories work for aeroplanes but are of limited use in explaining avian flight beyond the fast gliding of large birds. For much of the 20th century, even as engineers were designing supersonic jets, the details of flapping flight were a mystery. There is a story that early researchers used their theories to prove that bumblebees should not be able to fly.
There has been a lot of progress in this field in recent years. Insects are better understood than birds. A key mechanism is the leading edge vortex, a swirling region of air formed on the edge of wings as they rotate with each stroke generating lift. The review paper: Flapping wing aerodynamics: from insects to vertebrates lists five mechanisms to let insects fly, with fascinating sounding names like clap and fling and wing-wake interaction. The authors then explain that knowledge about bird and bat aerodynamics is much more limited. Even when a good model has been developed to explain basic flight, there are many more advanced manoeuvres, such as how birds change course in mid flight to dodge obstacles, attack prey, and avoid predators. This is subject of ongoing research by groups like the Oxford Flight Group using multiple cameras, high speed digital photography, and advanced computer modelling. The hope is that this could lead to more efficient designs for micro drones.
The aerofoil cross sections on Zipp’s blackboard look more like the solid wings of metal aircraft than the thin feathered curves of pegasi. Could Zipp have been working on a design for a heavier-than-air flying machine? We don’t see any flying ships in this film, but what Zipp calls ‘some sort of station’ looks like an air terminal with deflated balloons hanging from the ceiling. This is made clear in this concept art by artist David Alcarria.
This raises the possibility that when magic disappeared from Equestria, it not only stopped pegasi flying, but also grounded the balloons and zeppelins of the earlier era, which had nowhere near the volume to float just by buoyancy. With one exception: the earth pony balloon escape pack shows at least one instance of physics-defying pony flight has survived. Maybe the engineers at Canterlogic know something the pegasi don’t, even if they still need to perfect their design.
See also:
Pegasi versus Pterosaurs
Looks like it. Just to the right of her you have Sin(theta) = V(?) / V(pony). It took some digging, but that appears to be an equation for estimating projectile flight arcs. (The graph above that could be an accomanying parabola.)
I'm not sure what her numbers relate to, but at a launch angle of 28 degrees, a pony would need a velocity of 834.06... something, to accomplish I don't know what. Hopefully Zipp does.
It probably makes some sense. In order to properly choreograph "natural" flight using wires and theatrics, you'd probably need a good math background to estimate how a full grown pegasus would flop about on their way down.
5596730
When I first saw that, I wondered if it was taken from the sonic rainboom analysis in https://www.youtube.com/watch?v=muVfidujxRg which calculates Rainbow Dash's hypersonic velocity from the angle of the Mach cone. But the numbers don't fit. 387m/s is too fast for the speed of sound, unless the atmosphere around Zephyr Heights is very dense, and the 28 degree angle doesn't seem to come from anywhere. But the idea of Zipp studying legends of the sonic rainboom with the goal of doing one herself has great potential for a fanfic.
5596733
I hadn't actually mathed it out, but that is actually 387m/s... I'd assumed that I just wasn't seeing a decimal (3.87, or some such), but no...
Maybe that is rainboom calculations. Huh.
Excellent! Loved every word.
Also, Zipp is best pony.
Excellent blog. The lack of flight capability without magic provides a satisfying continuity with G4.
I couldn't help but notice that Zipp's flight feathers are properly asymmetric and overlap in the correct (functional) way. The designers and modelers put a lot of thought/research into their work, which is so very gratifying.
Excellent and fun blog!
5596805
Having a 3D animation degree, I went into the movie hoping to see some great wings. (Weird specific, I know) One of the first things I did afterward was tell everyone just how gorgeous the wings were.
Wiiiiiiings...
I did notice how authentic the wings look. They have a curve to them that real wings do, and animated ones generally don't. I have no training to describe it further, but they look right.
The animation team on this movie really paid attention to details. I love any movie where I find myself repeatedly pausing and taking screenshots to examine background details. IIRC, Cheerilee had some equation with the del operator on her blackboard somewhere way back in FiM.