Ponies Versus Physics II – It’s The Great Pony Charlie Brown

And for today’s entry it’s a quick (and rather silly in it’s underlying assumptions) question about the articles on MLP:FIM. It’s…

Who’s the most powerful pony?

The correct answer is “whoever the script has put in that role for this episode”, but I’m going to take it as a physics question, just so I can play with some numbers. Just looking at the Mane Six…

Rainbow Dash can clear a cloudy sky in ten seconds flat.

• Presuming a basically earthlike planet, clouds are usually seen at altitudes of 6500 to 45,000 feet.
• The distance to the horizon at 45,000 feet is about 260 miles. Of course, that would be clouds on the horizon – and we’re only interested in those that are substantially above it. That gives us a radius of about 200 miles.
• Given that this is a pretty crude calculation, I’ll just treat the area as if it was flat to get the volume she’s affecting. That will somewhat reduce the figure for total volume, but it’s going to be absurd anyway.
• So she’s altering a layer of atmosphere seven miles thick (45,000 feet minus 6500 feet) over a radius of 200 miles. This gives us a total volume of somewhat over 900,000 cubic miles of atmosphere and a total mass of more than 400 trillion tons with a specific heat capacity of .24 BTU/Lb.
• It wouldn’t be nearly enough, but lets say that it only takes a temperature change of five degrees farenheit to eliminate the clouds (dissipating them will just lead to more forming and transmuting the matter involved gets even more absurd than this will). That will require adding some 192,695,500,800,000,000 BTU’s – or about 200,000,000,000,000,000,000 Joules worth of heat energy to the atmosphere in ten seconds. Ergo Rainbow Dash is putting out 2 x 10 to the 19’th power Joules per second.
• A one megaton nuclear weapon releases 4.18 x 10 to the 15’th power joules.
• Rainbow Dash’s energy output would thus equate to nearly 4800 Megatons per second.
• Earths total global nuclear arsenal is about 7000 megatons. Given that I’ve rounded down on Rainbow Dash in a lot of places, that says equating One Rainbow Dash to One Global Thermonuclear Arsenal per second is just about right.

For comparisons, a hurricane releases about as much energy every day as Rainbow Dash does every 2.6 seconds. The eruption of Mount St Helens came in at about 24 megatons (five millidashes, or her power output for one 200’th of a second), and a supervolcano causing mass extinctions across the earth has a total power output of about 1 Dash over it’s lifetime. A city-destroying, potentially tidal-wave causing, magnitude nine earthquake (remember the 2004 Indian Ocean Tsunami? 226,000 people dead and millions homeless as multiple cities were devastated? Magnitude 9) releases about 100 megatons worth of energy – about .02 Dashes.

Even if we cut things down to a twenty-mile radius, and thus reduce her power requirements a hundredfold… that’s still 48 megatons per second. similarly, crossing the sky even ONCE while clearing it would call for her traveling forty miles in ten seconds – giving her a cruising speed of mach 20. And she zig-zags around while sky-clearing.

Now it may take a crew of a dozen “normal” pegasi to cover for Rainbow Dash, but that still gives Derpy a power output of at least 5 megatons per second. Perhaps her accidentally destroying the town hall, smashing pillars, and crashing through floors is more plausible than it looked.

Does that make it less surprising for Rainbow Dash to shatter rocks many miles away when performing a sonic rainboom?

And what do these calculations really tell us?

They tell us that the physics of Equestria bears not the slightest resemblance to real physics, that Equestria doesn’t even pay attention to geometry and prospective much less to math, and that any attempt to calculate the capabilities of magical ponies based on earthly physics or assumptions is completely pointless. This is sort of belaboring the point from the first Ponies Versus Physics article, but people keep asking and I rather like calculations, so why not?

You ponies… have POWER. And you don’t even know it. The strength to mold the weather and the seasons. To transmute tons of earth and stone into fruit and living wood. To bring bounty from the wastes. To light the world and bend it to your wills. You GLOW with it. What you radiate without even knowing it… A portion of the power of a single stallion granted our queen strength beyond anything she had ever imagined even as he commanded the guard and sustained a city-wide shield that it took our entire army to break – and HE recovered from weeks of her draining him within an hour. Yes, Queen Chrysalis was drunk with power and mad with jealousy to even THINK of trying to attack you – but couldn’t one or two of you spare a few minutes worth of your power every week or two to feed our species? We’ll be good! Maybe we could do your dusting or something?

-Trotsky Commune, Changeling Scout

For a bonus calculation we can consider Alicorns, and try to see how much they surpass normal ponies.

Shall we presume that Celestia actually moves an Sol-like Star about an Earthlike World?

Well…

• One Solar Mass = 2 x 10 to the 30’th kilograms
• The average distance from the Earth to the Sun = 150,000,000,000 meters.
• The daily distance travelled = 2 Pi x R = 942,000,000,000 meters.
• If the sun went around the earth once every 24 hours, that would be devided by 86,400 seconds per day, giving an “orbital” velocity of about 11,000,000 meters per second.
• That gives us a Centripetal Acceleration (Velocity Squared/Radius) of about twelve to thirteen gravities – and a generated force of at least 2.4 x 10 to the 32’nd power newtons.
• Unfortunately, this doesn’t neatly translate to energy. It’s enough force to accelerate the earth (6 x 10 to the 24’th kilograms) at about 40 million meters per second squared – making it approach the speed of light in less than eight seconds – but since it’s always being applied at right angles to the current direction of motion of the sun, there’s no actual change in speed, no work being done, and no energy being expended on the sun itself. If whatever-it-is that’s doing it requires energy (it may or may not) I have no method of calculating that.

But wait! We also see Celestia making the sun “tick” ahead one hours worth of movement in a fraction of a second.

• That means that the sun starts at a near halt, abruptly reaches a speed of at least 120 x 10 to the 9’th power meters per second (figuring a third of a second for the “tick”), and then comes to a near-halt again. OK, that’s almost four hundred times the speed of light, but that’s still a quanity of kinetic energy that we can calculate if we ignore relativity.
• Kinetic Energy = 1/2 MVV = 1.44 x 10 to the 52’nd power Joules.
• Which would be how much energy Celestia would need to generate, and then dissipate again, every time she pulled that trick. That’s about the energy released by 144,000,000 supernova.

What’s bigger? Well, the total barayonic mass of the observable universe is (crudely) estimated at 1.5 x 10 to the 53’rd power kilograms, equating to 1.35 x 10 to the 70’th power Joules – So if Celestia can generate that energy in – say – a tenth of a second, it would still take her almost three billion years to create the observable universe.

Or about one day to create an average galaxy from nothing.

The total mass-energy of the sun is about 1.8 x 10 to the 47’th power Joules. That would mean that Celestia can personally generate and dissipate enough energy to create or destroy some 80,000 suns per second.

When making a star disappear and creating another one nearby and counting on persistence of vision to make it look like it is moving – basically performing stop-motion animation with solar systems – is the EASY way… You know that you have chased the math down a rabbit hole.

Yet Episode One pretty firmly establishes that Celestia and Luna control the day-and-night cycle of Equestria. Perhaps they’re rotating the planet? That would be a lot easier. We can reduce the energy demand even further by stretching the time a bit.

So – over the course of a few seconds – they’re twisting an apparently earthlike planet through a substantial arc (enough to take the sun or moon from too far below the horizon to illuminate it to well above it) and stopping it again.

But rotational inertia is a pretty major thing. The calculation is too crude to bother writing out – but this stunt will still require that Celestia or Luna generate, then dissipate, roughly 2 x 10 to the 35’th power joules (or up to a hundred times that if we go by the “ticking sun” episode). The Gravitational Binding Energy of the Earth is 2 x 10 to the 32’nd power joules – one thousandth of that. The total power output of the sun for a YEAR is 1.2 x 10 to the 34’th power joules. The total amount of energy that the sun provides to the earth each year is 5.5 x 10 to the 24’th power joules.

Thus spinning the planet means that Celestia routinely, over the course of a few seconds twice a day, first puts out and then dissipates enough energy to rip the earth to monoatomic dust hurtling outwards at escape velocity somewhere between a thousand and a hundred thousand times. At a minimum. as much energy as the sun puts out over the course of nearly seventeen years. As much energy as the earth would recieve from the sun in thirty-six billion years. And she apparently exerts such fine control over that power that no one notices any inertial effects.

It’s a LOT more reasonable to simply have Equestria be a rogue planet and have it’s “sun” and “moon” be nearby energy-effects being generated by Celestia and Luna. While that leaves them directly powering the weather, ecology, and tides of Equestria all by themselves, it still reduces the amount of power they need to supply by a factor of ten trillion or so – to a mere 1.5 x 10 to the 22’rd power Joules per day.

But wait! Rainbow Dash could generate 1.7 x 10 to the 24’th Joules per day. She, however, spends a LOT of her time sleeping, eating, and doing other things – cutting down her net power output by at least an order of magnitude and probably by two.

So, according to this theory, Celestia ‘s minimal, casual, continuous power output is roughly equivalent to Rainbow Dash’s peak power output. Depending on her losses and just how casual this is… her peak power output could reasonable be anywhere from ten to a hundred times that of Rainbow Dash.

You know, that’s the most reasonable number that any of these calculations have produced so far. Despite the completely unreasonable method of arriving at that number, I think that I’ll keep that one.

And hopefully that will about do it for this particular topic. What’s the point? It’s simply that it’s a CARTOON. If I pick the right examples… I can “prove” pretty much anything that I want to.