[I never did understand how renewable energy sources were never a thing in Star Trek. Voyager was having so much trouble with finite power reserves, why not just stick a solar panel array on the hull, park next to a star for a bit to recharge, then on your way! No more Janeway bemoaning the lack of replicator coffee, and no more crew having to put up with Neelix’s cooking.]
Just for fun, I decided to do the math:
MASS WE NEED TO REPLICATE:
Let’s start Captain Janeway’s day off with a nice 12oz cup of coffee. Coffee is almost the same density as water, so that’s 0.3538 kilograms. But we also need to make the mug to drink it from. Cursory Googling shows an average 12oz coffee cup itself weighs about 13 oz, bringing our total to 0.7223 kg.
ENERGY NEEDED:
Thank you to Einstein for the classic e = mc^2, which tells us:
e = (0.7223)(speed of light)^2
e = 6.4917087 x 10^16 joules to fabricate a cup of coffee, assuming the replicator and associated power transfer conduits are 100% efficient. (They’re not because that violates the laws of thermodynamics, but this is Star Trek and/or America circa 2018, where laws are suggestions at best).
Converting to kWh because that is a handier unit for solar panel calculations, that’s 18.03 billion kWh to create our coffee and mug from scratch.
POWER GENERATION OPTIONS:
The International Sapce Station generates 84 to 120 kilowatts of energy from 2500 square meters of cells. Rounding to 100 kilowatts for 2500 square meters (on average), that gives us 1 kilowatt per 25 square meters of solar panel. For kicks let’s double it to 2 kilowatts per 25 square meters, they have super science in the future.
Voyager is 342.5m long and 55.42m tall (http://techspecs.acalltoduty.com/intrepid.html), and let’s say it’s deploying a separate panel rather than just being covered in panels (trying to calculate the surface area of an Intrepid class is beyond my abilities).
If Voyager deploys a solar panel that’s the size of the entire ship along its side, that gives us 18981m^2—let’s round it up to 19,000 square meters. So our solar panel generates 1520 kW.
(Side facts: 1520 kW is roughly the amount of power generated by one wind turbine or used by approximately 375 American homes, according to Wolfram Alpha)
This is going to take a long while. I’m going to re-interpret the parameters of this meme a little and say that instead of pulling up next to the star, we’re going to sunbathe—the whole of Voyager’s top (or bottom) will be the solar panel. That ups our surface area to just under 50,000 square meters, or 4000 kW.
SETTING OUR COURSE FOR HOME:
How long does it take to generate 18.03 billion kWh at 4000 kW? Or, put another way, how long does it take for a Voyager-sized solar panel to generate enough energy for Captain Janeway’s first morning cup of coffee?
It takes about four and a half million hours, which is a hair over 500 years.
For kicks: if we wanted to generate enough power to create Kathryn’s cup of coffee in 5 seconds (roughly the amount of time it takes for the cup to materialize in the replicator), we would need to generate 12.9 trillion kW, using a solar panel that is 1.613 x 10^4 meters squared. That’s about 110% the size of all land on Earth.
All of this to say: warp cores are the way to go when you’re generating power for that sweet, sweet coffee.
#im so sorry #i miss doing math
never apologize for genius
I’m in awe.
Wow. Science the science!
bekjaneway 