Calculating The Approximate Density of the Cake from S2E24

[Evilshy 5,091]

WARNING: MATH CONTENT

 

 

 

also, I did A LOT of estimation. Like, a metric shitton of estimation. I mean, it's not like we have accurate measurements of the size of the cake or anything...

 

I went off the following assumptions:

the average adult pony is a little over 1m tall (some brony calculated them to be about 4 feet tall or something)

the house that big mac pulled was a legitimate house, made of wood.

big mac legitimately pulled it, it wasn't just a visual gag (yes, I know it actually was, but bear with me here)

the amount of weight I can drag easily is about the weight I struggle to lift, making the cake approximately the weight of the house (yeah, this is probably wildly inaccurate, but by the time I was this far into calculations, I didn't care about precise or even accurate estimation anymore)

 

 

okay, so going off an adult pony to be a little over 1m, and applebloom to be a little under 1m, I estimated the house to be about 6m long, 5m wide, and 4-5m high, making the volume 120-150m³

 

If it is indeed a wooden house, then it is made of wood (woo tautology). What kind of wood? Well, we know there are apple trees aplenty, but judging off of other screenshots, I'd say the area around ponyville, as well as Everfree has Oak, Beech, Elm, and Willow trees. I have their apporx. densities in kg/m³

 

apple - 656.7 - 832.9

oak - 672.8 - 752.8

beech - 704.8 - 736.8

elm - 560.6 - 704.8

willow - 432.5 (only found one value for willow :/

 

I spoke to my father, a construction manager, and he said that the most commonly used building wood is Pine, usually some sort of Fir, often Douglas Fir. He wasn't sure what other woods would be used, since he's never encountered any other types of wood used (well, not for structure, anyway. plenty of types of wood are used for decoration.) Anyway, I found the density of Douglas Fir, for comparison

 

doug fir - 480.5 - 528.6

 

Which makes the range for (maybe) possible densities of the wood in the house 432.5 - 832.9 kg/m³

 

Now, I did some weird math involving the approx amount of board feet (a carpenters measurement, 12"x12"x1") of wood used in a house, scaled it down it to reflect the smaller pony house, and converted it to m³. I seem to have done this on a different piece of paper than all my other calculations, and also seem to have misplaced it, and only have the final answer on my main piece of paper Suffice it to say, the house has about 31.86m³ of wood.

 

Using that with the range of densities, the house has an approx mass of 13,780 - 26,536 kg.

 

That's quite a range. It was at about this point I almost gave up, seeing as with a range that wide, whatever I came up with at the end was sure to be absurdly wrong. But I soldiered on, because I didn't really have anything else to do tonight :/

 

For anypony who is interested, that makes the density of the house 92-221 kg/m³. But that doesn't affect the other calculations.

 

Something else that doesn't affect them that I calculated anyway is friction. The coefficient of friction between concrete (which is what goes on the bottom of houses) and soil (which is what the house was resting on while being pulled) is about 0.3. This makes the force of the friction about 40,513 - 78,016 N. I think.

 

Using some EXTREMELY ACCURATE measuring techniques (aka watching this video a bunch of times and using the stopwatch on my phone), I found that big mac was pulling the house at about 4-4.3 m/s. And because they just HAD to cut to the pony in the house when mac started to pull, I don't really know when he started to pull and when he reached his final speed, so finding the acceleration was quite hard. I ended up just starting the timer when his face started to strain (when he started pulling, I presume) and when it cut back to the house being pulled at the 4-4.3 m/s. I calculated the acceleration to be about 4 - 6.1 m/s². This means Big Mac was pulling with at least 55,120 - 161,870 N of force. Damn, son.

 

 

Anyway, onwards to the cake!

 

So it has 4 layers, right? I estimated the bottom to have a diameter of about 2/3 of a meter, but then while typing this, I realized that I forgot to halve it to get the radius before calculating the volume and surface area and whatnot, and swore very loudly when I did so. I then briefly thought about giving up, but no, I wasted this much time on it, and I'm going to damn well waste some more...

...

...

...

(this is me recalculating a bunch of stuff)

...

...

...

 

Yeah, so it's about 1AM here, so instead of calculating all that shit myself, I stuck my measurements of the cake into a cylinder calculator I found online to get those particular measurements. Assuming that the top layer of the cake is half the size of the bottom, and that the two layers in between are equal increments between the two (cuz that's what it looks like to me), the cake has a volume of about 0.334m³.

 

Now, like I said a long time ago, waaaaaaay back at the beginning of this post:

 

the amount of weight I can drag easily is about the weight I struggle to lift, making the cake approximately the weight of the house (yeah, this is probably wildly inaccurate, but by the time I was this far into calculations, I didn't care about precise or even accurate estimation anymore)

So the cake is about 13,780 - 26536 kg.

 

Taking into account the many estimations and inaccuracies of my numbers, this makes the cake's density somewhere within a lightyear or two of the ballpark of about 41,257 - 79,449 kg/m³.

 

Which means the cake is AT LEAST almost twice as dense as Osmium, the densest element known to man, and up to four times as dense. It could be about half as dense as the core of the freakin' sun. That's pretty dense.

[Swordfishtrombone 384]

Badass! Ah jeez, that is some amazing math skill. Good job on that one. Haha.

[Evilshy 5,091]

Eh, I'm more impressed that I remembered all the formulas for everything. I haven't taken any math or physics for over 2 years :/

 

MODS BE EDITIN' MAH TOPIC TITLE??!

Edited April 12, 2012 by Evilshy

[Swordfishtrombone 384]

Actually I hate dense cake, so that is just downright evil. How long did that take? And what inspired you to wake up one day and go "today I'm gonna accurately approximate that cake from MLP"?

[Evilshy 5,091]

OOOOOOOOOOHHHHHHHHH... I'll figure out the sugar content next!

 

took like an hour or two to do it (including looking up all the desinties of the wood and the amount of wood in a house, friction coefficients, etc). and almost another hour to type this damn thing >_<

 

And honestly, I don't know. I just like this kind of stuff, i guess :/

Edited April 12, 2012 by Evilshy

[Starshine 16,335]

So the cake is about 13,780 - 26536 kg.

Uh... what?

 

1 bite could easily scoop out at least hundreds of kilogram, and yet RD and others took more than one bite.

 

These ponies are crazy

[Sunny Fox 5,952]

Don't you use your fancy mathematics to muddy the issue!

[Znex 936]

That is pretty hardcore I must say, though I do have some niggling problems with it:

1. What specific frame of reference are you using when you say that normal MLP ponies are taller than 1m? There are several different ones you could be using

2. Mac was in a mad state of love in the Hearts and Hooves Day episode, so it seems quite likely that pulling the house is in no way some ordinary feat for him and probably shouldn't be used to estimate his actual strength

 

And of course clearly the cake was made out of dark matter

[Evilshy 5,091]

I used this:

 

And the assumption that Big Mac is a bit bigger than the average pony.

[Runty 41]

Who said that house was made of wood? Maybe it was a house made like these in the country i live in, out of bricks.

 

And not to brag but iv done my fair share of mansion lifting...

Well i didnt lie about that the average person doesnt pick up any mansions

[The Awesome One 1,315]

He's roughly 4.5 to 6 feet based on a little studying I did using a freeze frame of Big Mac standing next to Applejack.

 

Applejack's approx. height: 4 feet

 

Big Mac's approx. height : 5 feet (most likely)

 

NEXT QUESTION:

How tall is Spike?

 

We should probably use the estimated height of ponies to solve this one.

Edited April 12, 2012 by The Awesome One

[Evilshy 5,091]

Who said that house was made of wood? Maybe it was a house made like these in the country i live in, out of bricks.

 

I did, remember:

 

the house that big mac pulled was a legitimate house, made of wood

I had to make some assumptions, since we don't know everything about what's was going on in the show. Nobody can really tell what that house is made of, but I decided to base my calculations off the assumption that it was made of wood, a common house building material.

[I used to be a stranger 7,994]

So the cake is about 13,780 - 26536 kg.

 

That means his back is tough enough to take in the order of 60,000kg/m² of pressure.

 

He's tough enough to scuba in the mantle of Jupiter.

[Discovery Dream 592]

I love dense cake but man, that is just...the Cakes really did out-do themselves.

[MVC NVMXD JVRXD 2,406]

Calculating the density of the cake is one thing... But MAKING the cake.... Hmm....

[Eenohay 318]

Note that Big Mac pulled the house under the effects of the love poison. It probably granted him a lot of extra strenght.

[Fox 5,331]

[Akemi Homura 7,681]

This is totally Kyronea's type of thread.

[MissDo 195]

That is some heavy cake! Though it does sound unreasonable, I guess your explanation is correct...

 

You have reinforced my thoughts that Big Mac is actually strong.

[I used to be a stranger 7,994]

That is some heavy cake! Though it does sound unreasonable, I guess your explanation is correct...

 

You have reinforced my thoughts that Big Mac is actually strong.

 

What, did you think his hulking frame was just him being big-boned?

 

(No euphemism intended.)

[letterone 1,204]

Oh my... that's one heavy cake!

[The Alpha Team 51]

I'm saying its made of Black Matter

[Marcusaralius76 151]

I did just a little research on my own (It would require a bit of follow-up) on the sugar content of the cake. The average cake has a serving size of 50g with 199 calories and 19g of sugars.

 

Now if that cake has around 13780-26,536 kg in mass, or 13,780,000-26,536,000g, then the cake has between

54,844,400 and 105,613,280 calories. a healthy person should consume around 2000 calories per day, and there are 365.25 days in a year. So if a person ate nothing but this cake, they would have enough calories to last them 144.6 years.

 

Now for the sugar! there are around 5,236,400 to 10,083,680 grams of sugar in this cake.

 

The human body has 5.6 liters of blood in it, and a person is at serious risk for diabetes at 215 mg glucose per deciliter or blood. Would anybody like to do the math to figure out how many times over Pinkie Pie is at risk of diabetes?

[KakeiTheWolf 652]

The cake actually is significantly lighter.

 

See, when Big Mac pulled the house, he was under the effect of a love poison, which would create a flood of seretonin. Naturally, physical pain lessens and strength rises in dual inverse and obverse proportionalities as expressed in a limit stating that dy/dx (the derivative of the function) is a limit expressed by the conditions that, as x approaches infinity, y will approach zero and z will approach infinity, whilst x is not equal to z.

 

Such an effect is noted in drugs like PCP, which give no sense of pain yet incredible strength. That is because the mind is more powerfully focused on the chemicals it is being flooded with than the sensations of pain or exertion. It is notable that, under the influence of his infatuation, Big Mac would be flooded by ATP, adenosine triphosphate, more commonly known as adrenaline or epinephrine.

 

This chemical is known for vastly increasing how powerful the body of the effected subject. It is calculated that a human without ATP influences could pull 25 tons using all muscles in their body. Though we cannot do that easily, horses can. A well-known case of ATP influence was when a rock climber threw a several ton rock mass off his body, saving his life and separating his muscles from his bone from this indescribable force. As well, 200 ton 747 Jumbo Jets have been pulled by single humans.

 

Horses are far more powerful than humans. Note that in real life, the average horse can pull 0.5 times it's body weight of an unwheeled mass without strain. The average weight for a pony of Big Mac's size is 750 pounds. However, ponies can pull more pound for pound than horses. According to what I have read, even small ponies can pull 4.5 times their body weight. However, normal sized ones can pull around the same loads as a draft horse, which can pull 6 times their weight, with their weight averaging 1,500 pounds, adding up to a strain-free pull of 9,000 pounds.

 

Assuming Big Mac is 750 pounds, being able to pull a 9,000 pound load without ATP, Big Mac can pull an uninfluenced strain-free load of 12 times his weight. The average house in Ponyville is a 2-story house made of what we can assume is pine. Judging by the size of the house by pixels, the candy cane comparison, and the known height of Big Mac (via Candy Cane measurements and the knowledge he is a 12hh horse, meaning he is 48 inches or 4 feet tall), and the calculation of Big Mac's height recopied to compute the house dimensions (2 Appleblooms and 2 Big Macs tall, according to calculations, meaning the house is 14 feet tall, 1 Applebloom and 3 Big Macs for width, after adjusting parallax dimensions, totalling 15 feet wide, and 3 Big Macs long, after parallax adjustments, totalling 12 feet long, meaning a 15x14x12 house), we can begin to calculate the weight, assuming the rough calculated equivalent of 315 8' sections of wood would make a solid cube of these dimensions, that the eliminated exterior (Rough pattern and two 6.5x9x6.5x6.5 sections of triangular form are removed, and calculating the tangent, sine, and cosine of angle theta that defines the triangles defines the removed triangular space as 32 spaces, and 4 spaces as the space for the rough patterns according to universal cube measurement made after calculative dissection of the triangular forms' areas), that the eliminated interior is an inverse function assuming the inversal triple integral of the outer dimensions, and assuming a nominal 6" thickness to walls, 124 sections further are removed, totalling 160 totall removed sections, or 155 total remaining sections.

 

10.24 lbs is the weight of a pine 8' 2x4, and calculating for all dimensions, the unpainted wood weight is 12697.6 lbs. The average weight of unleaded paint (The type assumed to be used in Ponyville) is 10 lbs per gallon. Assuming a traditional two-coat practice, and calculating the surface area of the house (which is ~1680 ft²), one can assume an even two-coat weight adjustment would be 672 pounds, assuming 1/5th of a gallon is used per square foot of exterior and the two coats double weight, bringing our new total to 13369.6 lbs. For the interior the addition is ~195.1 lbs, assuming rounding is used and the inverse remains the same despite the addition of atomic matter from the air particulates surrounding the house and from various other factors, like the paint, and assuming the surface area of the interior was not modified by any factors like atomic matter addition. This brings us to a new total of ~13564.7 lbs. We will assume the knick knacks and furniture add 1000 pounds, and that the pony inside is the only pony inside and adds 550 pounds, bringing this addition total to 1550 lbs, making the new total ~15114.7 lbs. for the house in it's entirety.

 

This is approximately 1.679410752688172 times Big Mac's normal strain limit, but it is assumed that ATP makes up for this. Assuming Equestria uses Avoirdupois weight, and the nominal acceleration of the OP's post was true, the Newton force exhibited by Big Mac (Who we can assume was under the influence of ATP) was approximately 30371.6927951368 Newtons. The house, however, was PULLED. It is far easier to pull than to carry.

 

Carrying implies the force is the mass of the cake being forced down at 9.8 m/s². It is reccomended for the health of a pony that it not carry a vertically imposed burden of any more than 20% of it's body weight. This is due to the fact that ponies pull with all their muscles, but push against both mass and the force of gravity to sustain a carried load. Assuming Big Mac weighs 750 pounds, this means he starts to become stressed at 150 lbs. or greater (Remember, no ATP to help him here). Judging by the fact the cake is 2 Big Macs tall and 0.5 Big Macs wide, judging by the weight of the likely ingredients, the cake is likely to be 250 pounds (A likely weight for a 8 foot cake).

 

So while Big Mac can pull extraordinary loads, especially under the influence of ATP, the cake is of no similarity in weight, and this is mainly a problem of physical and biological confusion. The cake is just as dense as a normal cake.

 

Sources:

 

Wikipedia: Pony and draft horse pull statistics, and pony weight statistic.

Wiki answers: Paint weight, pine weight, and pony carrying statistic.

http://www.smartconversion.com/unit_calculation/Force_calculator.aspx: Newton calculation.

http://easycalculation.com/area/prism.php: House size calculation.

Yahoo answers: Pony height statistic and addition pull statistic.

My Little Brony: Source of picture of the house pull scene, used for calculations.

 

I hope this cleared some stuff up.

[DrOphthalmos 497]

.I hope this cleared some stuff up.

 

So basically, the cake isn't made of dark matter but is actually a legit cake that would give Big Mac problems?

 

Still doesn't explain why they didn't just put the cake on a cart and made Big Mac pull it.