Fun with units
(1.21 gigawatts) / (88 miles per hour) = 30,757,874 newtons
Heh...this is from Back to the Future. If you never saw the movie,in this 1980s sci-fi classic, small-town California teen Marty McFly (Michael J. Fox) is thrown back into the '50s when an experiment by his eccentric scientist friend Doc Brown (Christopher Lloyd) goes awry. Traveling through time in a modified DeLorean car, Marty encounters young versions of his parents, and must make sure that they fall in love or he'll cease to exist. Even more dauntingly, Marty has to return to his own time and save the life of Doc Brown.Now, a movie that starts off with time travel probably shouldn't take itself too seriously, and this one doesn't. But on another level, any movie—any work of fiction—has to take itself seriously, in the sense that it has to create a credible narrative, or else the audience won't be able to engage with it.
The setup for this movie is that Marty travels from 1985 back to 1955 in a nuclear-powered time-traveling gull-wing DeLorean automobile. (This was back before DeLorean got busted for cocaine trafficking and DeLoreans were still cool.) This immediately creates two big problems for the screen writers:
1. Well, why doesn't he just get back into his nuclear-powered time-traveling gull-wing DeLorean and return to 1985?
The problem being that if he does this, then you don't have a movie. And the solution is that, see, he used up all the nuclear fuel on the trip into the past, and now he can't return to the future. Which leads to the second big problem:
2. Well then, how does he get back to the future?
The solution to this one is more complicated.
To travel through time, the DeLorean needs 1.21 gigawatts (GW) of power. That's 1.21 billion watts. For reference, the power consumption of the United States is around 12 kilowatts (KW) per capita, so 1.21 GW is the power consumption of a small city.
You can't get 1.21 GW from a wall socket, but Marty does know where he can get 1.21 GW. He knows (because he's from the future) that lightning is going to strike the clock tower in the town square at exactly 11:58 PM on a particular day in 1955. He knows this because the lightning strike stopped the clock, and no one ever fixed the clock, so the clock has been stopped at 11:58 PM his whole life, memorializing the event.
So what he's going to do, see, is drive through the town square at exactly 88 miles per hour (uhhh...because that's how fast you go when you travel through time...) at exactly 11:58 PM on the designated day, and the lightning bolt is going to strike the car, and that will deliver the requisite 1.21 GW of power, and that's how he is going to get back to the future.
Really. That's the setup for the movie.
Again, you can't take this stuff too seriously. It's a movie, not a physics text. But the funny thing is, the screen writers used real numbers, and real units, for their setup. 1.21 GW. 88 mph.
Screen writers don't always do this. For example, when Captain Kirk goes zipping around the galaxy in the starship Enterprise, the ship travels at "warp" speeds. They talk about speeds like warp 1 or warp 4. We're given to understand that warp 1 is the speed of light, and that the higher warp numbers are faster than that. But in the whole history of the show, the screen writers never nailed down exactly what any of those higher speeds are. They just seem to be fast enough to get the Enterprise to interesting places in interesting lengths of time—where interesting means on the order of days to weeks.
And this is a real issue for a screen writer. If it takes a thousand years to get to the next planet, then the entire crew will be dead before you get there, and you don't have a story. If it takes 15 seconds, then it's more like an elevator ride than a journey. You might still have a story, but it's hard to maintain the sense of exploration and adventure.
So screen writers need to be careful about what they commit to when they create their worlds. And the screen writers in Back to the Future were careful. Not everyone knows what a gigawatt is, but it is clearly some large amount of power. If they had said that Marty needed 100 watts for the return trip, then the audience would be rolling their eyes and saying, "So get an extension cord and get going!"
Similarly, 88 mph is an exciting, but plausible speed for a DeLorean. If the car didn't need to be in motion, then he could just park it under the clock tower and wait for the lightning strike. (Bonus points if he runs jumper cables from the car battery to the grounding wires that connect to the lightning rod on top of the clock tower.) He gets home, but it lacks high-speed split-second drama.
Conversely, if the DeLorean needed to go 88 thousand mph, then the audience would be smirking. Not even a nuclear-powered DeLorean is going to go 88,000 mph. That's comic book territory, at best.
So the screen writers were careful, and they chose numbers that maintained the dramatic structure that they wanted, and that the audience could accept without giggling.
But...there are relationships between physical quantities. Physical relationships that always hold. For example
speed = distance / timeIf you travel 60 miles in one hour, then your speed is 60 mph. That's how speed works. Or
area = length × widthIf you have a piece of fabric that is 3 feet long and 2 feet wide, then it has an area of 6 square-feet. That's how area works.
If you understand the quantities and how they relate, then these relationships are obvious—nearly tautological. If you don't understand the quantities, they can seem mysterious. For example, Einstein famously wrote
E = mc2which is shorthand for
energy = mass times the speed of light squaredIf you don't understand how the quantities work, then this sounds like nonsense. What does it mean to "square" the speed of light? And how can you multiply that by mass? But if you do understand the quantities, then E = mc2 is as straightforward as area = length × width. It's just how mass and energy work.
And that gets us to today's fortune cookie. There is a relationship between power, force, and speed
power = force × speedThis means that when you push on something (force), and it moves (speed), then the product of force and speed is the power that you are expending to move the thing.
This relationship always holds when you move something, just like speed = distance / time always holds when something moves. If you know the power that you are expending, and how fast the thing is moving, then you can rearrange the equation to find out how hard you are pushing on it
power / speed = forceAnd if we plug in the numbers from Back to the Future, we get
(1.21 gigawatts) / (88 miles per hour) = 30,757,874 newtonsA newton is a unit of force. 30 million newtons is about 7 million pounds. So what this equation is telling us is that if something is moving at 88 mph, and you drive it with 1.21 GW of power, then you are pushing on it with 7 million pounds of force.
Another way to push on something with 7 million pounds of force is to simply put a 7 million pound weight on top of it. 7 million pounds is 3500 tons. For reference, here is something that weighs 3500 tons.
A 3500 ton weight pushes down, while the lightning bolt (presumably) pushes forward, but 3500 tons is 3500 tons, and if you put 3500 tons on a DeLorean, then it is going to squash flat (like a pancake) no matter which direction you are pushing. The only difference is that the weight will squash it top-to-bottom, while the lightning bolt will squash it front-to-back.
Granted, this is reading a lot into a situation that is impossible to begin with. Even within the logic of the movie, you could argue that the 1.21 GW of power is expended to move the car though time, not space, and so maybe the car doesn't experience forces in the same way.
But in the real world, power = force × velocity always holds, and to anyone who understands that relationship, 30 million newtons is as silly as 88 thousand miles per hour. It's pancake territory.
In fact, if a supra-linear scale were in use, it would almost certainly be exponential, something like s = c × 10w. On that scale, warp 7 would get you across the galaxy in a few days. However, it has the drawback that the speed of light is then reckoned as warp 0, which would be confusing to the casual television viewer.