Topic: Back of the envelope calculations

[Chew]

Hoover dam can produce up to 2080 MW of electricity.
Its reservoir, Lake Mead, occupies 640 km².
Solar thermal power plants' average conversion of solar radiation into electricity is 2.7% (each collector is about 20% efficient, but the collectors have to be spaced apart, so the average over the entire area of a plant is 2.7%).
Lake Mead receives an average solar radiation of 6.29 kWh/m²/day (fixed tilt=latitude).
If Lake Mead were paved over and a solar power plant installed it would generate 52 2.2 times as much electricity as the Hoover dam.

Edit: Dammit! I forgot to divide by 24 hours in a day. So it's not 52 times, it's 2.2 times.

[Citizen Skeptic]

Wow. Far be it from me to question your math but assuming you're correct, we ought to be getting started on blanketing the nearby desert. 52 Hoover dams is a lot of power.

[Chew]

Are you going to tell this poor little guy he must die just so you can play your xbox?

(click to show/hide)

[Citizen Skeptic]

Are you kidding? I bet it would welcome the extra shade on those really hot days.

[Chew]

There is a blog called Do the Math that covers a lot of the energy topics discussed in this thread and elsewhere on the forum.

[Lancezh]

Ha! How about you build the solar panels OVER the lake ? Doublewin!

[amysrevenge]

Here's one I like.

A human diet is (very roughly) 2000 calories per day - this converts out to (really roughy now, but within napkin range) an average power of 0.1W per person.

The earth (atmosphere, land, and water) absorbs about 3.85E24 Joules/year of solar energy (lots gets reflected away).  That's just over 1E17 Watts, let us call it 1.2E17 W

That would mean that the largest sustainable human population, stacked up Matrix style and converting 100% of absorbed incoming solar energy directly into sustaining human biological function, would be 1.2E18 (about half a billion times as many people as there are now). Since the people are stacked Matrix-style they probably don't need 2000 calories per day so you might be able to double that number, lets call it 2.4E18 (this also makes the division in the next step trivial lol).

However, the surface area of the earth (land and water added) is on the order of 5.1E14 square metres.  That would mean that you'd have 4000 people per square meter - not very comfortable.

The city today with the highest population density is Manila, with 4.3E4/square km (or 4.3E-2/square metre - inverted means something like 25 square metres per person).

At that density, utilizing land and sea (and mountains and Antarctica), you're looking at a maximum population of 2E13 ("only" about 3000 times the current population).  To maintain their biological function you'd only need to attain on the order of 0.001% efficiency from the incoming solar energy.  That leaves lots of room for other energy requirements such as computers and internets.

So I'm gonna say that, barring either extra-terrestrial energy sources or Matrix-style stacking, and assuming that just 1/10 of the planet's surface is actually hospitable for life (taking away oceans, mountains, deserts, and polar regions) you can make a good stab at determining the largest truly sustainable, long-term human population on eart.

With the collected assumptions of:
-The ability to utilize at least 0.001% of the total incoming solar energy from the sun to the earth
-A 2000 calorie diet for human beings
-A population density similar to Manila's today
-Roughly 1/10 of the earth's surface suitable for habitation

The final estimate is on the order of 2E12/two trillion/2,000,000,000,000.

[Chew]

So I happened to see a video about a bunch of soccer fans getting crushed to death by a crowd trying to push their way into a stadium. Then I got to thinking about castles being besieged in the good old days and how crowd mentality could be used to defend a castle. Dig a deep pit just inside the castle door, the attacking army breaks down the door, and rushes in. The soldiers in front will get pushed into the pit by the soldiers behind them. A pit 10 feet on a side and 50 feet deep, assuming an average weight for a soldier is 150 pounds and a packing fraction of 80%, could hold 1706 soldiers.

[Citizen Skeptic]

You sir, are a deep thinker.

[Chew]

no one can accuse me of not thinking outside the box.

[Guillermo]

Let's see. Considering that terminal velocity for a person in a belly position falling from a sufficiently high place, would have a terminal velocity of 54 m/s in average. Given that "The NHTSA standard for a sudden impact acceleration on a human that would cause severe injury or death is 75 g's for a "50th percentile male"" and using the following formula:

a = (v²-u²)/2d

I get that the minimum leeway allowed for a net to stop that falling person with a more likely probability of survival (>50%) is d = -(54)²/2(75)(9.8 ) =~ -1.98 meters. If the net is strong enough and capable of constant deceleration, It needs to stop a falling person in more than 2 meters for them to survive (Most of the time).

An average females body' Impact accelaration limit is 65g, so under that premise, d = -(54)²/2(65)(9.8 ) =~ 2.3 meters, then If Superman where standing on the ground, he'd have to be taller than 2.3 m at the shoulder in order probably save Lois Lane from falling from the Daily Bugle. At least he should know that he needs to fall down with Lois in order not to kill her with his arms of steel.

[Chew]

Excellent!

Some have said Superman grabbing Lois Lane after she falls from the helicopter in the original movie would have killed her. But if you watch it carefully you can see he decelerates her.

https://www.youtube.com/watch?v=fVWrUT1CvvA

[Guillermo]

When researching the terminal velocity, I found this tid bit of information that I found interesting. That a baby, due to terminal velocity would survive a fall of 4 to 5 stories high 50% of the time. That totally undermines when my wife tells me that a baby fell from a 5 story building and survived.

[Citizen Skeptic]

When researching the terminal velocity, I found this tid bit of information that I found interesting. That a baby, due to terminal velocity would survive a fall of 4 to 5 stories high 50% of the time. That totally undermines when my wife tells me that a baby fell from a 5 story building and survived.

I'd like to see some real data on that. When do we start dropping babies? 

[Henning]

When researching the terminal velocity, I found this tid bit of information that I found interesting. That a baby, due to terminal velocity would survive a fall of 4 to 5 stories high 50% of the time. That totally undermines when my wife tells me that a baby fell from a 5 story building and survived.

Not undermines but supports? Undermines your initial skepticism?
I would think the survival rate would have more to do with a babies basically being amorphous blobs of flexible bone and goo at their age. But what is the contention... that the lesser mass of a baby makes the difference?