30 ‘Useless Yet Interesting Calculations’ To Get Your Mind Reeling (New Posts)

"So the ave stump height is cut to 0.45 m. Let's assume an oak, with an ave height of 20m. Thats about 2.3% of overall height.

This tree would therefore be around 11.7km high using that ratio. Almost high enough to tickle the stratosphere at 12km

So if I used the horizon calculator right, you could still see the bastard 387km away

EDIT: Just to answer a few of the many questions. In American that'd be about 7.3miles, or 13,760 washing machines"

"The quote is "I'm sexy and I know it"

sqrt(1+tan^2) can be verbalized as "sec" and so this formula is the "sec of c"

"I'm sec C and I know it""

"They’re called crinkle crankles. A single leaf wall over that distance would need brick piers approx every 1.5-2m if it was a retaining wall it would need to be at least 9” wide (2 bricks). The crinkle crankle has more strength due to it’s curved nature so can be 4” wide or a single leaf of bricks.

For the maths if we can assume they’re true semi-circles then each semi circle would be 1/2piD or 1.57D whereas a double leaf wall would be 2D for the same length D

Therefore using 21.5% less bricks than a double leaf wall"

"Quick eyeballing suggests a curvature of about 30°; that's 1/12th of a full circle, so given that the Earth's circumference is just over 40,000 km, the car would have to be about 3333 km long, or about the driving distance from Chicago to Los Angeles, or about 5.5 million washing machines (in case you're too American to understand kilometers)."

"One source says the “minimum actuation force” of a key is 47.6 grams. If we assume the kitten is standing on 4 keys (only one per paw) 4*47.6 is 190.4 grams or 0.4 pounds. Ao the kitten would be under that weight. It appears that the kitten is standing on more than 4 keys though so maybe 1/2 pound."

"$9.33 on the left and $21.51 on the right"

"Each ingredient can either be included or not -- that's 2 possibilities. Multiply out all 9 ingredients and we have 29 = 512 in total. I presume you'd want to exclude the 1 possibility where none of the ingredients are included, so that leaves 511."

"Quite the opposite, it will leave you with less sandwich. Since no cut is perfect, some of the sandwich molecules will stay on the knife or there is more crumbs on the cutting board. Therefore, cutting on a diagonal (longest cut) will dislodge more material of the sandwich than cutting along shorter line"

"Return flight JFK - Madrid: ~€750 Minimum income in Spain: €850/mo; 24 months amount to €20400. We'll assume that since a lot of people in Spain have to make do with this much, you will figure it out too. Learning Spanish is pretty straightforward, if you live in Spain for 2 years, you're practically guaranteed to pick up enough of it to get by, but let's say you spend €100 on a couple textbooks and a dictionary, just to get you started. Depending on where in the US you live, there might even be a solid chance that you already speak the language, after all it's the country's second language, with more speakers in the US than in Spain. You will also be spending a bit on visas and other bureaucratic requirements, let's call that another €200. Running with the bulls and getting trampled can be had for free. And then there's the hip replacement itself, at $7,371, or €7074. However, depending how you play it, you could actually take a minimum-wage job in Spain, and qualify for public healthcare, in which case the hip replacement might actually be covered. But let's just assume you have to pay for it out of pocket (which, frankly, is a pretty unusual thing in Europe, and typically only happens when people have to get treatement abroad and the insurance situation hasn't been figured out, or for a couple religious weirdos who object against having health insurance on moral grounds).

So let's ring you up; grand total: €28524, that's about $29700.

Not only does it fit comfortably into the US figure, you even have some $12,000 to spare"

"The average emperor penguin slaps with about the same force as a middleweight boxer. 800-1000 PSI"

"Assuming those are $100 bill stacks at $10,000 each. I count 12 stacks across and 15 stacks deep and assuming that each stack is ~0.5 inches tall with a total height of ~30 inches.

12 * 15 * (30 / 0.5) * 10,000 = $108 Million dollars."

"36,567,729 sheets of letter sized paper according to Excel (single sided)

According to Google a pallet contains 200,000 sheets

Therefore 182 pallets of paper would be needed.

A photocopier can apparently print 500,000 sheets in its lifetime, so you would need 73 photocopiers"

"The total area of ocean is about 361 million square km, or 3.61 x 1014 square meters.

The highest point of Denmark is about 171m.

The earth is large enough that we can choose to ignore the curvature over a change of radius of 171m (compared to the radius of 6300km it’s less than a rounding error).

What we can’t ignore is that there is about 30 million square km of land that is 171m or less above sea level which will also be flooded (estimating from a hypsographic curve). I’ll factor in a mean of half of that to give the new earths surface figure of 3.76 x 1014 square meters.

This means that there would need to be 171 x 3.76 x 1014 = 6.43 x 1016 cubic meters of water displaced.

If we assume a good throwing rock has a volume of 1 litre, then you would need 6.43 x 1019 rocks.

At 1 rock per day that’s going to be 1.76 x 1017 years, or 12 900 000 times the age of the universe.

If all 8 billion people on the world threw one rock per second, it would only take 250 years"

"According to a google search, it takes about 4,000 newtons to crush a bone, & I’m going to assume that an average person has a frontal surface area of 1 m2 for ease.

A nickel weighs 5 grams, which equates to about 0.05 newtons of gravitational force… you’d need at least 81,578 nickels on top of the person, or about $4,078.90"

"Beginner: 1 in 102 million
Intermediate: 1 in 6.1 million
Expert: 1 in 477,000"

"Oh come on this is doable from an engineering point of view:

One sip per second of 10ml (a shot glas' equivalent in a few seconds)

90°C tea, 0°C water (I see ice?), ∆T =90

Conduction in the thin straw is negligible, basically water-to-water heat transfer at a slow rate: the convection coëfficiënt for that is about 1000W/m²K (forced convection water to unforced water essentially)

Straw is 5mm diameter, 150mm length is submerged. Total area = 5π*150 = 2350mm² heat exchange area.

As such, the heat (power) transferred per second is = 9010002350/1e6 ≈ 211W

211W for 0.01kg water (tea) per second is ∆T = 211/4200/0.01 ≠ 5°C difference.

This matches my experience: the straw is simply not big enough to offer proper area for heat exchange:

Source: 10 years of steam boiler engineering

Hope you enjoyed!"

"Im gonna assume the loop is about 60m based on the height of the building next to it.

At the top of the circle, the two forces are mg and centripetal force. The two together equal ma (a being v2/r.) So mg + Fc = m(v2/r). Set Fc to 0 as you would have to have a centripetal force slightly above 0 to complete the loop. This gives us v2 = sqrt(gr). For a 60m loop (30m radius) v = 17.1m/s.

This is the speed at the TOP of the loop. Using conservation of energy, we can say that 1/2mv2 + mgh = 1/2mv2 (the first part is top of loop, second part is bottom of loop). Cancel m and plug in numbers.

You would have to travel 38.34m/s or 138kph (85.7mph) to make the loop."

"NASA did the math on this

"If the Sun was replaced with a black hole that had the same mass as the Sun, the Schwarzschild radius would be 3 km (compared to the Sun's radius of nearly 700,000 km). Hence the Earth would have to get very close to get sucked into a black hole at the center of our Solar System.""

"He's a corporate executive of some sort and the trip was being paid for by the family member in Paris. His wife was also a fairly successful artist.

A 800k house in Bay Area probably cost >5M today"

"A circle has 360 degrees, so 60/360 is 1/6th of a pizza, and 45/360 is 1/8.

The area of a circle is (pi)r2

The area of the 6" pizza is 1/6(pi)(62 )=6(pi)

The area of the 7" pizza is 1/8(pi)(72 )=6.125(pi)

6.125/6=1.021, so the 7" pizza is 2.1% bigger

$1.70/$1.50 is 1.13, or 13% more expensive.

The 7" pizza is 13% more expensive, but only 2.1% bigger, so the 6" pizza is a better deal."

"500,000 tons is its downward force due to gravity. It has a gravitational pull, but minimal compared to the earth (6,000,000,000,000,000,000,000 tons)"

"If only contacting the floor with the heel then yes.

An elephant's foot is 15-19 inches across, so assuming it's vaguely circular gives an area of at least 0.114m2 per foot. Elephants when walking depending on the gait will have 2/3 feet in contact with the floor - so that's at least 0.228m2 in contact with the floor. (Going for minimum area as this will give the highest pressure for the comparison)

6000lbs under Earth's gravity is a force of 26.7kN, which when divided by area for a pressure of ~117kPa - if it's just standing still this could actually be halved to approx 58kPa

If a 100lb woman (445N) is standing on only her heels (~1cm2 x 2) this is a pressure of 2,224kPa which is indeed about 20 times higher than the elephant on 2 feet.

However that's not really representative of how heels are worn, even the picture shown has the shoes in contact with at least 20x the area of the ground than just the heels"

"Yes, a 33 round single elimination bracket would have 233 participants, which is about 8.5 billion. So it is actually possible, since the world pop is probably just under 8 billion, that the winner would be someone who had the 1st round bye and only had to win 32 times"

"I believe blackjack gives the house a 0.61% edge over the player on average when played absolutely perfectly. Assuming the same odds for every game, .493932 leads me to a .000000000157% chance of winning 32 games in a row."

"Rough estimate: 8 *109 people , Assuming a 10 cm2 signature/person to make the numbers easy. This comes from a 10cm long signature 1 cm in width.

Gives 8*1010 cm2 = 8*106 m2 in area. If we model the bat as a cylinder of length L, the surface area is SA = 2 pi r2 + 2 pi r *L, so if the bat has a length of 1 meter to fit in our hand, the second term is negligible, as r will be huge.

So A / 2pi = A/6 ~ 1 *106 m2 , square root to get the radius,

R = 1 * 103 m = 1 km

So if the bat is a meter long, it would have to be around a kilometer in radius to fit everyone’s signatures."

"Each pod is capable of holding 25 people at maximum safe capacity. Assuming each person can reasonably be 100kg, that means the safe load placed on any one pod is 2500kg.

The pods themselves weigh 10,000kg. The radius of the London eye is 67.5m.

Since at the bottom apex of the rotation the total force from centrifugal/centripetal force is equivalent to weight, a centrifugal force equal to 2500x9.81=24,525N is the maximum safe level.

F=MV2/R

V=sqrt(FR/M)

V=sqrt(24525x67.5/10,000)

V=12.9m/s

The pods could travel at approximately 28mph, or complete one rotation every 33 seconds, before the forces on the pods exceed safe levels. Theoretical maximum levels would be higher, but without stress testing the material cannot be precisely calculated."

"Counter tops are usually 34 to 36in.

It was 5 phones to the top of counter 5.75"*5=28.75"

So I think they are off by a factor of 1.18 (34/28.75)

That would put her height around 5ft1in."

"Slow apartment sized elevators (which this looks like) go about 1mph. Let's say it takes an average of 10 months for a dog to go from puppy to a fully grown adult.

10 months = 305 days = 7320 hours.

Short elevator ride = 7320miles (close to the diameter of the earth)

Assuming dog is 16 years old in second photo:

16 years = 192 months = 5856 days = 140,544hours."