I’m so hungry I could eat a whole cow.
I think the expression typically cites a horse, but I don’t know anyone who actually eats horsemeat, so this version seems a little more reasonable.
Have you ever heard that expression and wondered, jeez, how many calories would that be? I have, and I’ll take it a step further, what could you do with all that energy?
You’ve probably heard the number 2000 kcal floated around as the minimum daily amount of energy a person needs to function properly. In reality, that number depends on a number of factors, and the average requirement for a full-grown adult is probably closer to 2500 kcal. The typical American consumes over 3700, and you can find the full breakdown of calorie consumption per capita by country here.
But what does that number mean? What do our bodies do with all that energy? Most of it is used to maintain our necessary biological processes, and to keep our internal temperature constant. Some of it is stored in fat cells for later use. Very little of it is used to actually do physical work – the amount of energy required for someone my height to lift a 105kg (230lb) weight above my head (my reach is about 2.5m/8ish ft) is < 1 kcal! And yet, this miniscule energy output is the best I’ve done in my entire life.
I should note that since our bodies are not perfectly efficient machines, it would take more kcal than that for me to get the job done, but it would still be an insignificant percentage of my daily intake. I should also mention that since a clean + jerk might occur in about a second of total movement, my momentary power output is much more impressive – about 2600 W.
So how much energy is 2500 kcal? What could we do with it if it was available to us all at once? That’s the minimum energy needed to lift 430,000 kg above my head – twice as heavy as the biggest tree in the world, General Sherman!
If we could perform such a feat with our daily energy intake, what could we do with all the energy in a single cow? It depends on what you mean by ‘total energy.’ The total amount of calories yielded by the beef? How about all the calories consumed by the cow during its lifetime? What about the energy the cow loses due to thermal radiation? The energy yield of the manure it produces, if we were to set it on fire? How about Einstein’s mass-energy equivalence?
good ole’ fashioned calorie content
A typical beef steer is about 600kg ( > 1300 lbs) at slaughter. Of this, only about 42% is converted into edible meat. That’s 252 kg (~550 lbs) of steaks, burgers, beef ribs, roasts, etc.
A typical sample of (raw) beef is about 20% protein by mass, and 10 % fat. Cooking removes some of the weight- but the loss is mostly moisture and leaves the calorie count mostly unaffected. This means that our cow yields about 50kg of protein, and 25 kg of fat. Using the standard conversions of 4 kcal per gram protein, and 9 kcal per gram fat, that’s a grand total of 430,000 kcal according to the conversion above.
To put that number in perspective, one cow could feed a person (at 2500 kcal/day) for nearly half a year!
If I managed to channel that energy into a clean and jerk, that’s enough for me to lift 73 million kg above my head- heavier than the Titanic!
okay, but how much did the cow eat?
Of course, it makes sense that it takes a lot more energy to grow a cow than we end up getting in return. After all, beef steers don’t just pop out of the womb at 600 kg- it takes about two years for them to reach market weight (which is not quite their mature weight).
A beef steer is born at about 40 kg (~ 88 lbs), and consumes about 3% of its bodyweight in dry food per day, at the hungry end of the spectrum. Assuming a linear growth curve of .77kg per day (which is wrong, but a reasonable approximation), our cow ends up consuming 7000kg of a carb-heavy (hay, grass, etc.) diet during its two year lifetime. Because of our assumption concerning the growth curve, this likely ends up being an underestimation.
At a reasonable guestimate of 2000 kcal per kg of dry food, the cow consumes a staggering 14 million kcal during its lifetime – 32x the calorie yield that consumers see.
That’s enough energy to launch the full-sized cow out of a cannon at 14 km/s (~31,000 mph)! Meanwhile, the escape velocity on Earth is only 11.2 km/s – we’ve literally launched our cow over the moon!
Of course, that’s ignoring drag on the cow. When air resistance is put back in, our cowstronaut does not fare nearly so well. At the precise moment he leaves the cannon, his power loss due to air resistance is 1.4 teraWatts. That would be like sticking the cow’s face directly into the engine of the Apollo 11 rocket at takeoff.
What happens next is difficult to predict. The cow likely explodes into a bunch of fiery pieces, all of which have widely varying drag coefficients. The more svelte chunks make it into orbit at varying altitudes (barbeque at the International Space Station, anybody?), others burn up completely. If you launch at noon, some bone splinters might land on the other side of the planet, under the cover of night. Some cow dust would get suspended on the other side of the tropopause, ensuring a light sprinkling of cow for a long time to come.
okay, but how much did the cow poop?
Cows poop a ton.
Each day, a cow produces about 6% of its body in manure – twice as much as it eats! This means that over the course of its (two-year beef-steer) lifetime, the cow pooped out 14,000 kg. However, 90% of that weight is just water – which leaves 1,400 kg of dry manure. So, cows don’t actually poop a ton: they poop one and a half tons.
Cow manure is actually a pretty viable energy source- providing 4800 kcal/kg via combustion. That’s comparable to the energy density of coal! The difference is that it doesn’t take millions of years to make.
If we burned all of it, that’s 6.7 million kcal, about half of the energy the cow consumes over its farm-restricted lifetime. Meanwhile, the energy required to power my 1000 square foot, 2 BR Texas apartment was about 860,000 kcal last August according to my energy bill. That means one cow’s poop could power my apartment for 78 Texas summer months- over 6 Texas summer years! For reference, our energy consumption in October (without AC) was about half our summer consumption. So really, one cow’s poop could provide all the electricity my roommate and I need for nine years or so.
Keep in mind that these numbers completely ignore cow flatulence, which produces natural gas (methane) at a staggering rate. Methane is an even better energy source than coal, because the principal byproduct of its combustion is water vapor. Theoretically, if you could devise an effective system for capturing cow farts, you could reduce greenhouse gas emissions (methane is one of the most nefarious greenhouse agents), generate cheap electricity and produce clean drinking water all in one go!
My proposition is to attach a balloon to every cow’s butt, and have a handler change it out whenever it gets near to bursting.
So, that’s cool and handy and all that we can use cow waste to power our homes, but it’s boring to spread all that energy over nine years or one hundred apartments in Texas. What if we tossed a match on the poop pile?
If you could get the entire pile to combust at once, the resulting explosion would rival that of the Mother of all Bombs, the most powerful non-nuclear weapon ever detonated by the United States (the Russians have since detonated the Father of all Bombs, about 4x as powerful).
The blast radius of our poopsplosion would be over 100m, completely leveling everything within an area equivalent to 6 American football fields!
Blackbody radiation is a thermal equilibrating process, by which heated objects release energy in the form of light. The wavelength (equivalent to color in the visible spectrum) of the light released depends only on the surface temperature of the object. The hotter the object, the shorter the wavelength. Every thermal object releases energy in this way- a typical fire’s peak wavelength is red, the sun’s yellow, a hot fire’s blue, and humans release light in the infrared range, which is how thermal goggles allow you to see people at night.
The total energy released in this fashion is related to the temperature of the object and its surface area. We can use this statement to help explain why big poofy jackets keep us warm. While they increase our surface area, they increase our volume more so (more volume = more capacity to hold heat), and the surface temperature of the jacket is much less than our skin temperature. Therefore, we end up losing many fewer kcal to blackbody radiation with a jacket on than in our birthday suit.
So what about cows? Cows are pretty fat, and therefore pretty good at retaining their own body heat. And they don’t move around much, so overall they’re pretty efficient eating machines.
The skin temperature of a cow is about 298K (77 F). Meanwhile, its surface area can be related to its mass according to the equation:
SA = .12 * m.6 
while the rate of blackbody radiation loss is given by:
P = SA * σ * ε * (T4 – To4)
Where σ is the Stefan-Boltzmann constant, ε the emissivity of the cow hide, T the skin temperature and To ambient temperature. Using the values above, our linear growth curve, 285 K as the average ambient temperature (a decent approximation for middle latitudes over the course of a year, day and night), and approximating cow hide emissivity as 1, we get
Pn = 8.8 * (.77t+40).6 * 86400
where Pn is the daily power output n days after birth, and 86400 is the number of seconds in a day. Using Excel to sum this over two years, we get a total output of 4.1 million kcal, a little under one third of the total energy consumed by the cow. That’s enough energy to boil a small swimming pool, with a starting temperature just above freezing!
You may have noticed that with each new energy consideration, we get closer and closer to the energy consumed by the cow. And in fact, if you add up all the energy you could harvest from eating the cow (keep in mind that humans are not the only organisms on the planet that consume dead animal meat), burning its poop and farts, and the heat loss over its lifetime, you should exactly equal the cumulative calories it consumes, plus the amount of extra calories the mother consumed during its gestation period. When your physics teacher told you that energy is conserved, he (or she) meant it!
Environmental scientists take note: this is probably the most plausible method by which to calculate the methane emissions of our cattle industry.
This is the fun one.
You have probably heard or seen Einstein’s famous equation the equates energy and mass:
E = mc2
It’s a beautifully simple statement with tremendous implications: mass is energy and vice versa. That means you can obliterate mass into pure energy, and create mass from the ether!
We only ever see these reactions on Earth in the most extreme of circumstances. Nuclear fission and fusion reactions convert tiny bits of mass directly into energy, making nuclear fuel far and away the most energy dense substance available to us. One gram of uranium yields 21 million kcal in a fission reactor- 30% more energy than the cow consumes in its entire two year lifetime.
Meanwhile, we have managed to create elementary particles via super-energetic collisions in particle accelerators. This is how scientists at CERN discovered the Higgs Boson in the Large Hadron Collider- they made one!
But even nuclear fusion seems like a hamster spinning its wheel when compared to the most energy dense reaction in the known universe: matter-antimatter annihilation. Think of antimatter as some sort of bizzaro world material- it behaves exactly like regular matter, only the charges are flipped (antiprotons are negatively charged, etc.). When antimatter collides with matter, the colliding particles annihilate into gamma rays or higher energy photons.
We only ever observe antiprotons and positrons (anti-electrons) on Earth, and they’re pretty hard to detect because of their propensity to explode. Usually, we detect them via the resulting gamma rays produced by the explosion. So far we’ve observed ephemeral units of antimatter in particle accelerators, in the upper reaches of our atmosphere, and in thunderstorm clouds. [WIKI]
But what if we had an entire anti-cow? Theoretically, such a thing is possible, though it would be tough to get it back to Earth. If we did manage to smuggle one here, it would be just as tough to properly smash it into our regular cow before the anti-hide began annihilating itself against the atmosphere.
There are some other logistical issues I will ultimately and happily ignore. Once the cows touch tips, the two carcasses would accelerate away from each other at high speeds due to radiation pressure. That would send a jet of vaporized cow flesh in one direction, and a constantly exploding anti-cow jet in the other, raining down gamma rays in the process.
The lingering effects of this streaking gamma ray hose might be the most dangerous outcome of this whole experiment. Not only can gamma rays cause serious cellular damage and cancer, secondary radiation emitted when the rays interact with matter would be highly carcinogenic too.
If we conducted this experiment on the moon, the resulting flash might be many times more intense than the sun’s rays, depending on the timescale of our reaction. Most of the released gamma rays would be filtered by our atmosphere. Secondary radiation would reach the surface, and might inflict radiation sickness on a good chunk of the organisms who happen to be on the wrong side of the planet. Our only hope to directly observe the explosion would be an intense but fleeting beam of blue light propagating through our atmosphere due to Cherenkov radiation.
But what if, through some miracle of ingenuity, we smuggled the anti-cow into our cow pasture and used it to ram an unsuspecting steer, immediately converting all 1200 kg of cow + anticow into energy?
The explosion would be like nothing before seen by humankind.
Plugging the numbers into Einstein’s equation, we get a yield of 26 quadrillion kcal. That’s on the same order as the total amount of energy used by all of humankind in a year. It’s equivalent to the entire energy expended by an average hurricane over the course of two days.
Most of a hurricane’s energy expenditure is used to move moisture around, only a small percentage actually drives its horizontal winds. If we used all that energy to power a cyclone’s winds, you could expect wind speeds of up to 4000 km/h (2500 mph)! At that speed, cow’s wouldn’t just be thrown around like in Twister- they’d be obliterated, torn flesh from bone. Any bits of cow meat lucky enough to be shielded from the wind by bone would be cooked to ash- crispy cow brains would become a donation staple during the relief effort.
And here we are releasing all of energy instantly, within one tiny cow pasture.
The explosion would be more than a million times more powerful than the atomic bomb dropped on Hiroshima. It’s 500 times more powerful than the Tsar Bomba, the most powerful weapon ever detonated on Earth, whose explosion shattered windowpanes up to 900km (>500mi) from ground zero. The Tsar Bomba’s mushroom cloud penetrated into the mesosphere- the cow cloud would surpass the exospheric origins of the aurora borealis, and perhaps even smother the International Space Station.
The immediate blast would destroy everything within an area larger than the state of New York. Smoke and debris would be launched above our atmosphere’s cloud forming layers, where they would remain free from fear of rain for a very long time (this is the nuclear winter scenario feared by many during the Cold War). Depending on the volume and type of debris uprooted by the explosion, the cow cloud could reduce the solar energy the Earth receives from the sun by a noticeable margin, with disastrous effects on our climate.
Ground zero would be energetic enough ignite hydrogen fusion, giving an extra kick to our mega-event, but the reaction would not be self-sustaining with the sparse density of material found on Earth. This means that the ending to Spiderman 2 was complete bullshit.
All this from one teenage cow and its bizzaro world twin.
SOURCES AND RELATED INFORMATION
I near-ubiquitously used the term ‘cow’ for habit’s sake. ‘Cow’ technically refers to a female that has birthed a calf and can give milk. Meanwhile, a ‘steer’ is a male that has been castrated and is the most likely origin of the steak on your plate.