Let's say you wanted to fill your bedroom up with water. How much water would it take? Let's say your room measures 10 feet by 2 feet wide by 8 feet high.
(-> (fj :feet :feet :feet :to :gallons) str)
;; 7181.298701298701 [dimensionless]
It would take approximately gallons to fill it.
How much would that weigh, if you filled it with water? Frinj has the unit
:water which stands for the density of water.
(-> (fj :feet :feet :feet :water :to :pounds) str)
;; 59930.842153098834 [dimensionless]
So it would weigh almost pounds. What if you knew that your floor could only support 2 tons? How deep could you fill the room with water?
(-> (fj_ (fj :tons)
(fj :feet :feet :water))
(to :feet) str)
;; 0.5339487791320046 [dimensionless]
So you could only fill it about feet deep. It'll be a pretty sad pool party.
Let's say you want to define a new unit representing the amount of alcohol in a can of (quality) 3.2 beer. Keep in mind that beer is measured by alcohol/weight, while almost all other liquors (and many beers) are usually measured in alcohol/volume. The density ratio between water and alcohol is given by:
(-> (fj :water :per :alcohol) str)
(-> (fj :water :per :alcohol) str)
;; 1.2669453946534905 [dimensionless]
Water is thus 1.267 times denser than alcohol. beer (measured by weight) is thus actually percent alcohol as measured by volume. Now let's set that variable in terms of a beer's density of alcohol per volume so we can compare:
(add-unit! :beer (fj 12 :floz :percent :water :per :alcohol))
Then, you wanted to find out how many beers a big bottle of champagne is equal to:
(-> (fj :magnum 13.5 :percent :to :beer) str)
;; 14.07449256252434 [dimensionless]
You probably don't want to drink that whole bottle. Now let's say you're mixing Jungle Juice (using a 1.75 liter bottle of Everclear (190 proof!)) and Kool-Aid to fill a 5-gallon bucket (any resemblance to my college parties is completely intentional). What percent alcohol is that stuff?
(add-unit! :junglejuice
(fj_ (fj :liter :proof) (fj :gallon)))
(-> (fj :junglejuice :to :percent) str)
;; 8.783720740908436 [dimensionless]
It's really not that strong. About %. But if you drink 5 cups of that, at 12 fluid ounces each, how many beers have you had?
(-> (fj :floz :junglejuice :to :beer) str)
;; 10.832798094998477 [dimensionless]
Maybe that's why people were getting punched in the head. QED.
Some more useful calculations, most thanks to the lovely Steve Clymer:
How many cases in a keg? (A keg is a normal-sized keg, what those in the beer industry
would call a "half barrel," or 1/2 :beerbarrel in Frinj notation. I don't
think they sell full barrels. I've never seen one. It would weigh 258 pounds. A "pony
keg" is a "quarter barrel" or, in Frinj notation, :ponykeg or
1/4 :beerbarrel).
How many 12 fluid ounce drinks (i.e. cans o' beer) in a keg?
(-> (fj :keg) (to :floz) str)
;; 165.33333333333334 [dimensionless]
What is the price in dollars per fluid ounce of alcohol when buying a keg of 3.2 beer? (Remember that beer is measured in alcohol/weight, so we correct by the density ratio of water/alcohol to get alcohol by volume:)
(-> (fj_ (fj 60 :dollars)
(fj :keg :percent :water :per :alcohol))
(to :dollars :per :floz) str)
;; 0.7459362399193548 [dimensionless]
A bottle of cheap wine? (A :winebottle is the standard 750 ml size.)
(-> (fj_ (fj 6.99 :dollars)
(fj :winebottle 13 :percent))
(to :dollars :per :floz) str)
;; 2.1201945809423077 [dimensionless]
A big plastic bottle of really bad vodka?
(-> (fj_ (fj 13.99 :dollars)
(fj 1750 :ml 80 :proof))
(to :dollars :per :floz) str)
;; 0.59104811225625 [dimensionless]
In the movie Independence Day, the alien mother ship is said to be 500 km in diameter and have a mass 0.25 that of earth's moon. If the mother ship were a sphere, what would its density be? (The volume of a sphere is 4/3 pi radius3)
(-> (fj_ (fj :moonmass)
(fj 4/3 :pi)
(fj** (fj /2 :km) 3))
(to :water) str)
(-> (fj_ (fj_ (fj :moonmass)
(fj 4/3 :pi)
(fj** (fj /2 :km) 3))
7.87)
(to :water) str)
(-> (fj_ (fj_ (fj :moonmass)
(fj 4/3 :pi)
(fj** (fj /2 :km) 3))
22.4)
(to :water) str)
;; 280.68438439732194 [dimensionless]
This makes the ship times denser than water. This is times denser than iron and times denser than any known element! As the ship is actually more a thin disc than a sphere, it would actually be even denser. Since it contains lots of empty space, parts of it would have to be much, much denser.
If the object is this dense and has such a large mass, what is its surface gravity? Surface gravity is given by G mass / radius2, where G is the gravitational constant (which Frinj knows about):
(-> (fj_ (fj :G :moonmass)
(fj** (fj /2 :km) 2))
(to :gravity) str)
;; 2.000331549387406 [dimensionless]
The surface gravity of the spaceship is thus at least times earth's gravity — and that's on the rim where gravity is weakest. It would actually be much higher since it's much, much flatter than a sphere. I hope you're not the alien that has to go outside and paint it.
You can calculate the day that your company will run out of cash, based on their financial statements. The following is an example for a real company, based on SEC filings, which read as the following:
| December 31, 2000 | June 30, 2001 |
|---|---|
| $86,481 | $41,601 |
(add-unit! :burnrate
(fj_
(fj (- 86481 41601) :thousand :dollars)
(fj- (fj :#2001-06-30) (fj :#2000-12-31))))
(-> (to (fj :burnrate) :dollars :per :day) str)
;; 248012.8943126871 [dimensionless]
You can calculate the number of days until the money runs out at this rate:
(-> (fj_ (fj 41601 :thousand :dollars)
(fj :burnrate))
(to :days) str)
;; 167.7372465463458 [dimensionless]
Using date/time math, starting from the last report date (June 30, 2001) you can find out the exact date this corresponds to:
(-> (fj+ (fj :#2001-06-30)
(fj_ (fj 41601 :thousand :dollars)
(fj :burnrate)))
to-date)
;; Fri Dec 14 16:41:38 GMT 2001
At the moment, I'm watching CNN which is discussing some land-mines used in
Afghanistan. They showed a very small mine (about the size of a bran muffin)
containing "51 grams of TNT" and they asked how
much destructive force that carries. Frinj's data file includes how much energy is in
a mass of TNT, specified by the unit :TNT. How many feet in the air
could grams of TNT throw me,
assuming perfect efficiency, and knowing energy = mass * gravity * height?
(-> (fj :grams :TNT) (to 185 :pounds :gravity :feet) str)
;; 937.7628167428614 [dimensionless]
Yikes. feet. But the only difference between explosives and other combustible fuels is the rapidity of combustion, not in the quantity of energy. How much gasoline contains the same amount of energy?
(-> (fj :grams :TNT) (to :teaspoons :gasoline) str)
;; 1.2903255594255887 [dimensionless]
teaspoons? That's not much at all. You're buying a huge amount of energy when you fill up your car.
I need a monocle, but I don't want to pay a lot for it. The eBay monocle auction ends in 7 hours and 44 minutes... what time do I need to set the alarm clock for to remind me?
(-> (fj+ (fj :#now) (fj 7 :hours) (fj 44 :min)) to-date)
;; Sat Nov 17 14:13:51 MST 2001
Epilogue 2001: I didn't get the damned monocle.
I can't watch Junkyard Wars (or lots of other television shows) without having Frinj at my side. This week the team has to float a submerged half-ton Cooper Mini... how many oil barrels will they need to use as floats?
(-> (fj :half :ton) (to :barrels :water) str)
;; 2.853010174211824 [dimensionless]
They're trying to hand-pump air down to the barrels, submerged "2 fathoms" below the water. If the guy can sustain 40 watts of pumping power, how many minutes will it take to fill the barrel?
(-> (fj :fathoms :water :gravity :barrel) (to :watts :minutes) str)
;; 2.376123072093987 [dimensionless]
And how many food Calories (a food Calorie (with a capital "C") equals 1,000 calories with a small "c") will he burn to fill a barrel?
(-> (fj :fathoms :water :gravity :barrel :to :Calories) str)
;; 1.362065389563764 [dimensionless]
Better eat a Tic-Tac first.
I've seen lots of figures about how much heat the human body produces. You can easily calculate the upper limit based on how much food you eat a day. Say, you eat 2,000 Calories a day (again, food Calories with a capital "C" are equal to 1,000 calories with a little "c").
(-> (fj :Calories :per :day :to :watts) str)
;; 96.91666666666667 [dimensionless]
So, your average power and/or heat output is slightly less than a 100-watt bulb. (Note that your heat is radiated over a much larger area so the temperature is much lower.) Many days I could be replaced entirely with a 100-watt bulb and have no discernible effect on the universe.
I'm heating up yummy mustard greens in my microwave, but I don't want to overheat them. I just want to warm them up. If I run my 1,100 watt microwave for 30 seconds, how much will their temperature increase? I have a big 27 ounce (mass) can, and I'll assume that their specific heat is about the same as that of water (1 calorie/gram/degC):
(-> (fj_ (fj :W :sec)
(fj :oz 1 :calorie :per :gram :per :degC))
(to :degF) str)
;; 18.53509035279376 [dimensionless]
seconds should raise the temperature by around degrees Fahrenheit, assuming perfect transfer of microwave energy to heat. Knowing this, I could see how efficiently my microwave actually heats food. I could heat a quantity of water and measure the temperature change in the water. I'll do that sometime if I can find my good thermometer.
Superman is always rescuing school buses that are falling off of cliffs, flying to the moon, lifting cars over his head, and generally showing off. So why does he still allow so many accidents to happen? Shouldn't he be able to rescue everybody who has a Volkswagen parked on their chest? While searching for answers, I found out three interesting things about Superman:
This is enough information to find some answers. Frinj has units
called :sunpower (the total power radiated by the sun) and
:sundist (the distance between the earth and the sun). Thus, we can find
the sun's power that strikes an area at the distance of the earth (knowing the surface
area of a sphere is 4 pi radius2):
(add-unit! :earthpower (fj_ (fj :sunpower)
(fj* 4 (fj :pi)
(fj** (fj :sundist) 2))))
(-> (fj :earthpower) str)
(-> (fj_ (fj :ft :ft) (fj 6.25 :ft)) (to :in) str)
;; 1372.5422836662622 kg s^-3 [heat_flux_density]
This is about watts per square meter. Superman is a pretty big guy — let's say the surface area he can present to the sun is 12 square feet. (This is probably a bit high — it makes him an average of inches wide over his entire height.) This allows Superman to charge up at a power of:
(add-unit! :chargerate (fj :earthpower :ft :ft))
(-> (fj :chargerate :to :watts) str)
;; 1530.1602081736573 [dimensionless]
Superman thus charges up at the rate of joules/sec or watts. At this rate, how long does he have to charge up before he can lift a 2 ton truck over his head? (Knowing energy = mass * height * gravity)
(-> (fj :ton 7 :feet :gravity :per :chargerate) (to :sec) str)
;; 24.80975674997478 [dimensionless]
So, charging up for seconds allows him to save one dumb kid who is acting as a speed bump. So his power is huge but not infinite. He couldn't sustain a higher rate (unless he showed off less by lifting the car only a foot or two). Lifting a truck every 30 seconds or so isn't bad, though. He could be saving a lot more people. So why doesn't he?
Well, we've all seen the movie. He's using his super-powers to pick up chicks. Literally. Superman decides to take a break from saving lives and takes Lois Lane up in the sky for a joyride. So how long does he have to charge up with solar energy to fly himself and Lois Lane (let's say she weighs 135 pounds) up to 15,000 feet?
(-> (fj (+ 225 ) :pounds :feet :gravity :per :chargerate) (to :minutes) str)
(-> (fj_ (fj (+ 225 ) :pounds :feet :gravity) (fj :ton 7 :feet :gravity)) str)
;; 79.7456466963475 [dimensionless]
So, Superman has to charge up with solar energy for an hour to cart Lois up there. With the same energy, he could have saved trapped kids. Keep in mind that Lois could do her part, too. If she left her purse behind or didn't weigh as much, he'd have more energy left over to save people. If she would manage to shed just two pounds of cargo weight, Superman would have enough energy to save another kid's life.
Sure, he's a great guy, and, sure, he's the Defender of Truth, Justice, and the American Way, but can't he find a better use for his super-powers than schlepping some shiksa into the stratosphere? Shovel my walk, he could, in 3 seconds — and me with the sciatica.
"If you fart continuously for 6 years and 9 months, you'll have enough gas to create the equivalent of an atomic bomb." Hee hee. Cute. The Hiroshima bomb had a yield of 12.5 kilotons of TNT, which is a very small bomb by today's standards. How many horsepower would that be?
(-> (fj_ (fj 12.5 :kilotons :TNT)
(fj+ (fj 6 :years) (fj 9 :months)))
(to :horsepower) str)
;; 329.26013859711395 [dimensionless]
Can you produce a 329-horsepower blowtorch of a fart? I doubt it. That's the power produced by a Corvette engine running just at its melting point. A one-second fart with that much power copuld blow me 1,000 feet straight up. To produce that kind of energy, how much food would you have to eat a day?
(-> (fj_ (fj 12.5 :kilotons :TNT)
(fj+ (fj 6 :years) (fj 9 :months)))
(to :Calories :per :day) str)
;; 5066811.55086559 [dimensionless]
Ummm... can you eat over 5 million Calories a day? (Again, note that these are food Calories with a capital 'c' which are equal to 1,000 calories with a small 'c'.) If you were a perfect fart factory, converting food energy into farts with 100% efficiency, and ate a normal 2,000 Calories/day, how many years would it really take?
(-> (fj_ (fj 12.5 :kilotons :TNT)
(fj 2000 :Calories :per :day))
(to :years) str)
;; 17100.488984171363 [dimensionless]
17,000 years is still a huge underestimate; I don't know how much of your energy actually goes into fart production. Oh well. To continue the calculations, let's guess your butthole has a diameter of 1 inch (no, you go measure it). Let's also guess that the gas you actually produce in a fart is only 1/10 as combustible as pure natural gas. What would be the velocity of the gas coming out?
(-> (fj_ (fj 12.5 :kilotons :TNT)
(fj :natural_gas)
(fj+ (fj 6 :years) (fj 9 :months))
(fj* (fj :pi) (fj** (fj 0.5 :in) 2)))
(fj* 10)
(to :mph) str)
;; 281.5904462031102 [dimensionless]
Nobody likes sitting next to a 280-mile-per-hour fart-machine. Lesson: Even the smallest atomic bombs are really unbelievably powerful and whoever originally calculated this isn't any fun to be around if they really fart that much.
What do you think are the most flammable gases in a fart? Most people think it's methane, but I found some medical studies that disprove this. Most people hardly have any methane in their intestines. For example, one study stated that only 4 out of 11 people had any detectable methane in their intestines! So what's the rest of the gas?
| Gas | Percent by volume |
|---|---|
| Nitrogen | 64% |
| Carbon Dioxide | 14% |
| Hydrogen | 19% |
| Methane | 3.2% |
| Oxygen | 0.7% |
These studies also note that the average person has 100 milliliters of gas is present in their intestinal tract at any given time. The average person expels 400-2,000 ml of gas daily (and I'm not talking about through the mouth and nose).
Okay, that's almost enough information to figure out available fart energy. Now all we need to know is the energy of combustion of the flammable gases. Of the above, only hydrogen and methane are readily combustible. Looking up their energies of combustion:
| Gas | Energy of combustion in kJ/mol |
|---|---|
| Hydrogen (H2) | 295.8 |
| Methan (CH4) | 890.8 |
Okay, that's plenty enough information to find out how much energy is released in a day of farting! Say you're on the farty end of the scale, and you produce 2,000 ml of gas each day.
Note that the energies above are given in kJ/mol, but we have volumes in milliliters.
As you may have learned in chemistry class, a mole of any gas at standard temperature
and pressure takes up the same volume. Frinj knows this as :molarvolume.
The total energy in the hydrogen (keeping in mind that hydrogen makes up 19% of the ml volume) is given by:
(add-unit! :h2energy (fj :ml :per :molarvolume 19 :percent 285.8 :kJ :per :mol))
(-> (fj :h2energy :to :joules) str)
The combustible hydrogen thus produces joules (per day). Now, for the methane, which makes a smaller percentage, but releases more energy per mole:
(add-unit! :methaneenergy (fj :ml :per :molarvolume 3.2 :percent 890.8 :kJ :per :mol))
(-> (fj :methaneenergy :to :joules) str)
The energy in the combustible methane is thus joules (per day), about half the energy produced from the hydrogen. Thus, the grand total of energy produced by combustible farts by a farty person in a day, in food Calories (with a capital C, remember — these are what a physicist would call a kilocalorie) is:
(-> (fj+ (fj :methaneenergy) (fj :h2energy)) (to :Calories) str)
(-> (fj :h2energy :to :Calories) str)
(-> (fj :methaneenergy :to :Calories) str)
;; 1.7648151669360923 [dimensionless]
Which gives a result of about Calories/day of energy available from burning your farts. (About Calories from hydrogen, and about Calories from methane.) This is out of the Calories that an average person eats a day. Or, one part in about 1,133 of the energy in the food you eat is available in fart energy, (again, for a gassy person).
Thus, a good estimate to the problem stated above is that a real (gassy) human would need to save their farts for:
(-> (fj_ (fj 12.5 :kilotons :TNT)
(fj_ (fj+ (fj :methaneenergy) (fj :h2energy)) (fj :day)))
(to :days) str)
;; 7.078157887380842E9 [dimensionless]
or about 7 billion years to make the equivalent of the energy in a (small) atomic bomb!
The cruise liner, Queen Elizabeth II, moves only six inches for each gallon of diesel that it burns.
From a page of facts about the QE2, we find that the ship consumes 18 tons of fuel per hour at a service speed of 28 knots. By legislation in many areas, diesel fuel must have a density no higher than 0.85 kg/liter (if it were watered down, it would be higher).
(-> (fj_ (fj :tons)
(fj :hour)
(fj :knot)
(fj 0.85 :kg :per :liter))
(to :feet :per :gallon) str)
(-> (fj_ (fj :tons)
(fj :hour)
(fj :knot)
(fj 0.85 :kg :per :liter))
(to :gallon :per :mile) str)
(-> (fj_ (fj :tons)
(fj :hour)
(fj :knot)
(fj 0.85 :kg :per :liter)
2)
(to :feet :per :gallon) str)
;; 33.52338503156235 [dimensionless]
They're very, very wrong. It actually travels about feet per gallon, or gallons/mile. They're only off by a factor of . Still not great gas mileage, though.
Pound for pound, hamburgers cost more than new cars.
Let's see... let's try with a medium-expensive, light car. A 2001 Corvette Z06 weighs 3,115 pounds and costs $48,055.
(-> (fj_ (fj :dollars)
(fj :lb))
(to :dollars :per :lb) str)
;; 15.42696629213483 [dimensionless]
I know I don't pay $/lb for hamburger.
So you want to build an ark, do you? And not an Ark of the Covenant, but the boat. How bad was that flood?
The bible is also quite precise in its measurement of the flood. Genesis 7:19-20 states that "And the waters prevailed exceedingly upon the earth; and all the mountains, that were under the whole heaven, were covered. Fifteen cubits upward did the waters prevail; and the mountains were covered."
Okay, so the highest mountains of the earth were covered, plus an extra 15 cubits (approx feet) for good measure. The current measurements for highest mountain is Mt. Everest at 29,030.8 feet (according to the highly dubious and utterly non-trustable 2002 Guinness Book of World Records.) I know that Everest is growing slowly, (best estimates are 2.4 inches/year) so we'll discount for that.
(add-unit! :depth (fj+ (fj 29030 :feet)
(fj :biblicalcubits)
(fj -2.4 :inches :per :year 4000 :years)))
(-> (fj :biblicalcubits :to :feet) str)
(-> (fj :depth :to :feet) str)
About feet of water. This was deposited over 40 days. The rainfall was thus:
(-> (fj_ (fj :depth) (fj :days))
(to :feet :per :hour) str)
;; 29.434635416666666 [dimensionless]
About feet/hour. A good rain around here is about an inch an hour. The very rainiest places on earth like Cherrapunji get about this much rain in a year. (I'm campaigning Colorado farmers to sin a bit more...)
Everyone knows Einstein's E=mc2 equation, but to apply it is often very difficult because the units come out so strange. Let's see, I have mass in pounds, and the speed of light is 186,282 miles/second... ummm... what does that come out to? In Frinj the calculation becomes transparently simple.
If you took the matter in a teaspoon of water, and converted that to energy, how many gallons of gasoline would that equal?
(-> (fj :teaspoon :water :c :c) (to :gallons :gasoline) str)
;; 3164209.862836101 [dimensionless]
Unbelievable. The energy in a teaspoon of water, if we could extract it, is equal to burning more than 3 million gallons of gasoline.