Applejack is a Vine-Chopping Double-Airplane.

Mon Nov 25, 2013, 7:12 PM

Think for a second about the nearly impossible amount of strength it would take to cut a living vine the thickness of a small tree with something as dull as a window without being able to build any momentum.

Alright, let’s do this.

Applejack exerted a certain amount of psi onto a large vine and broke it. How much psi can Applejack generate without a sweat?

We’ll work in SI units in this exercise.

One pascal (SI unit of pressure) is N / m^2

• N = newtons of force applied
• m^2 = meters squared where pressure is applied.

Let’s first find how many pascals the windowframe first exerts on the vine because of gravity.

N = 9.8 (the gravitational pull of the earth).

A dull window would have a large area exerting force, compared to a sharp, small edge. Various window measurements from Home Depot's website and my house reveals that an average window's edge dimensions are roughly 3/4 inches x 36 inches. An inch is 0.0254 meters.

3/4 * 36 * 0.0254 = 0.6858 meters squared.

m = 0.6858 meters squared.

Let’s calculate.

p = N / m^2

p = 9.8 / 0.6858

p ~= 14.29 pascals

The window exerts 14.29 pascals on the vine naturally.

Let’s assume the vine is made of black oak. The tensile strength of black oak is 6,520 psi (when the oak compresses and crushes). Wolfram|Alpha tells me that that is equal to 44,950,000 pascals. Woah. Let’s subtract the natural gravitational pascals from the overall tensile strength to find out how much Applejack has to exert manually.

44950000 - 14.29 = 44949985.7 pascals

There’s our answer (a lot). But how much is that in psi? Let’s have Google finish it off.

44949985.7 pascals = 6519.44424 pounds per square inch.

Applejack has to exert about 6519.44424 psi of pressure onto the vine. That’s just about the equivalent of twoairplane hydraulic systems.

Applejack for best vine-chopping double-airplane, 2013.

I did not math this. Thanks to SgtPiggy for the calculations.

Applejack is a Vine-Chopping Double-Airplane.by Foxy-Noxy

Featured By Owner Nov 26, 2013  Hobbyist Artist
Crossposted from my reply to Darkflame75's calculation:

Consider that there is no deformation of the window frame. That means that the frame itself was not subjected to a pressure larger than its yield strength, so the vine must be of a softer material than speculated. Since Applejack only has one hoof on the frame, the area that supports whatever force she exerts must be the shadow area of her hoof onto the frame. If we consider the frame to be 19mm broad, and for simplicity's sake have half that area on the inside of the glass, that allows only a segment of her hoof to actually transfer force. A hoof is roughly circular, and if we estimate Applejack's shoe size to be radius r=50mm (no insult intended, miss!), the area of the circular segment that can touch the frame is:

A = (r^2)/2 * (θ-sin(θ)).

θ is equal to 2 * acos((r-h)/r), where h is the length from the glass to the edge of the frame (19mm).

The maximum force transferred is therefore the yield strength of the frame times the area under the hoof. Since it is the "Golden Oak" library, let us use that material for the frame. Oak has a maximum yield strength of σ = 60 MPa (N/mm^2).
Maximum force is therefore:

F = σ * A = 60 N/mm^2 * 379mm^2 = 22 740 N.

Observation shows that the mare's weight is not enough to cut the vine. Only when she uses her famous earth pony strength does the window slam shut. If we assume that her legs are 0,5m long, her forelegs must muster a moment of:

M= F*L = 22740N * 0,5m = 11370 N*m

For comparison, that is about 15 horsepower seconds. Applejack cuts the vine in roughly one second with her front legs, using her hind legs for bracing, meaning that she utilises her entire body. My conclusion is therefore that Applejack is approximately 15 times as strong as a standard horse
Featured By Owner Nov 26, 2013
You didn't take friction into account, that window would of already been open, and because of the friction, it wouldn't be putting gravity force on the vine
Also from the way the vine broke, it looks pretty hollow
Featured By Owner Nov 26, 2013
Here I thought Trekkies over analyzed things. Great maths!
Featured By Owner Nov 26, 2013  Student General Artist
It struck me as how impossible that would be when I saw it.
Featured By Owner Nov 26, 2013  Hobbyist Digital Artist
I love how you've worked this out. I'm like how so many other people have noticed this XD
Featured By Owner Nov 26, 2013

I think there's a far simpler explanation:

Featured By Owner Nov 26, 2013  Student Writer
Natural Earth Pony strength + Active Apple Farmer lifestyle + Adrenaline Rush = Super Strong Applejack. Huh. I wonder if her superhero persona in "Power Ponies" will have super strength as a superpower? Maybe she'll transform into an Incredible Hulk or The Thing comparison? It would match her coat color. XD
Featured By Owner Nov 26, 2013
AJ op plz don't nerf
Featured By Owner Nov 26, 2013  Hobbyist Digital Artist
I know that this post is just for fun and that you didn't do the math, but I'd still like to point out some mistakes in the calculations because physics is serious stuff:

- First of all, you shouldn't use symbols of SI units as symbols of quantities like you did when writing N= newtons of force applied, as it can get quite confusing. Instead you should write, for example, F = force applied, A = area where force is applied and pressure = p = F/A.

- Unit conversions: The calculation for the area of the window is wrong, it should be A = 3/4" *36" * (0.0254 m/")^2 = 0.01741932 m^2. Luckily this doesn't really affect the final result.

- Rounding the result: there's no point in writing the result to nine significant figures when the calculations are accurate only to two. The result should be written as 6500 psi.

Sorry about lecturing on a post about cartoon ponies, but you know what happens when someone is wrong on the internet.
Really fun post though, otherwise I wouldn't have bothered writing all this.
Featured By Owner Nov 26, 2013  Student
nobody cares
Featured By Owner Nov 26, 2013  Professional General Artist

Featured By Owner Nov 26, 2013
Wasn't it proven that Applejack is dark matter?
Featured By Owner Nov 26, 2013  Professional General Artist
uh.... 9.8 isn't the FORCE exerted by the earth, it's the ACCELERATION. The force is 9.8 times the mass of the object. If we assume AJ is "the object," then she would have to be using her entire weight to crush it, which she is definitely not.
Featured By Owner Nov 26, 2013  Professional General Artist
Also you're calculating pressure... Applejack is not a fluid, it would probably be better to calculate either pure forces or energy transfer.
Featured By Owner Nov 26, 2013  Professional General Artist
Oops, ignore this second comment. My first point still stands though.
If you say the force is 9.8 N, then you're implying that Applejack weighs 1kg, or roughly half a pound.
Featured By Owner Nov 25, 2013
Appleplane! Airjack? Aplaneck?
TwistedOmniscience Featured By Owner Nov 26, 2013
Applemerian airlines
Featured By Owner Nov 25, 2013  Hobbyist General Artist
Why is the bit of the fuselage on the upper airplane between the wing and tail of the lower one missing?

Oh, and uh... nice maths... too.
Featured By Owner Nov 25, 2013  Professional General Artist
This is hilarious! I love it!
Featured By Owner Nov 25, 2013
So, Applejack is made of dark matter after all?
Carmine96 Featured By Owner Nov 27, 2013  Hobbyist General Artist
Everypony is made of dark matter.
Featured By Owner Nov 25, 2013
Well...
She's an earth pony. Earth ponies are believed to be good with plants.
Maybe they are good at killing them too XD
Featured By Owner Nov 25, 2013  Hobbyist Digital Artist
Just talking about how much pressure she's exerting is fairly meaningless. An average car is held up by about 30 psi of tire pressure, but I can easily exert far more pressure than that with just one finger by sticking a thumbtack into some cork. (You also made a mistake converting the window area, but I won't get into that now)

Now if we multiply the pressure by the contact area, the force Applejack would have to exert is (44950000 N/m2) x (0.01741932 m2) = 782998 Newtons (minus whatever the window weighs, but that's negligible). Under Earth gravity this is 79,898 kg, or 176,144 lbs.

In conclusion, Applejack is still badass.
Featured By Owner Nov 26, 2013  Professional General Artist
Actually, cars aren't held up by 30 psi in the tires. The 30 psi is what's called Gauge Pressure. Gauge pressure is the difference between the actual pressure and 1 atm (The pressure the atmosphere exerts on you, which is quite a bit).
Featured By Owner Nov 26, 2013  Hobbyist Digital Artist
Gauge pressure is what's important for how much weight the tires can support though. If the total pressure inside the tires was 1 atm (gauge pressure of 0), then they wouldn't be able to hold any weight at all (besides what the sidewalls are able to carry).
Featured By Owner Nov 26, 2013  Professional General Artist
True, but there are four tires and each tire alone has more surface area than the window. A LOT more. That's why you don't pump your tires all the way up, so that there's more surface area with slightly less pressure.
Featured By Owner Nov 25, 2013
What?
Featured By Owner Nov 25, 2013  Hobbyist Writer
Science
Featured By Owner Nov 25, 2013  Hobbyist Digital Artist
Translation for the stupid (like me) here:
AJ Is strong as shit.
Featured By Owner Nov 25, 2013  Hobbyist General Artist
I say the Element of Honesty gives her super-strength.
Featured By Owner Nov 25, 2013  Hobbyist General Artist
*sees update*

What
Featured By Owner Nov 25, 2013  Student Digital Artist
Hahaha, yeah. It wasn't completely accurate at first. XD
Featured By Owner Nov 25, 2013  Hobbyist General Artist
There's also the possibility of you reading too much into a kids show about talking magic horses. Oh, wait, we're bronies; that's ALWAYS a possibility with us.
Featured By Owner Nov 25, 2013  Hobbyist Digital Artist
haha. Earth pony has da super strength ja! (I lift zings up and put zem dowwwwn)

I thought it was sorta odd that they were having so many problems with the tiny saplings on the farm and then she just goes WINDOW SLAM NOPE CHOP CHOP. But I just sorta accepted it since it didn't really make a difference either way
Featured By Owner Nov 25, 2013
I'm more concerned with her apparent ability to generate glass from thin air. That window lacks any moving parts.
Featured By Owner Nov 25, 2013
This is an awesome post.
Featured By Owner Nov 25, 2013  Student General Artist
the mare is sooooo strong!
Featured By Owner Nov 25, 2013  Student General Artist

I'll just take your word on it.
Featured By Owner Nov 25, 2013  Hobbyist Digital Artist
This is all assuming the vines weren't made of marshmallow of course.