How Do You Get 1.21 GigaWatts For Your Time Machine?
Here’s the important lines in this scene from Back to the Future.
Doc: 1.21 gigawatts? 1.21 GIGAWATTS!? Great Scott!
Marty: What? What the hell is a gigawatt?
Note: they pronounce this as jiga-watt instead of the usual “hard g”.
What the hell is a gigawatt?
Let’s break it down. A watt is a unit of power. What is power? Power can be one of several things. The most often way to describe it is the change in energy in a certain amount of time.
La te xi t 1
If energy is measured in units of Joules and the time interval is in seconds the power would be in Watts. So, 1 watt = 1 Joule per second. Horsepower is another unit for energy where 1 hp = 746 watts.
What about the giga? Giga is a prefix for units that typically means 109. This means that 1.21 gigawatts would be 1.21 x 109 watts.
Is that a 
What Does Doc Brown Even Mean?
How much power does it take to travel through time? Well, Doc said 1.21 gigawatts. To me, this would be like asking how much power it takes to make toast. Yes, you could use a 500 watt toaster. However, you could also use a 250 watt toaster but it would take longer. Maybe there is something special about time travel such that there is both an energy requirement and it has to take place over some time interval. That’s what I am going to assume.
If I want to calculate the energy required for time travel, I will need the power (given) as well as the time.
How Long Does it Take to Travel in Time?
That’s actually looks like a stupid question. Oh well. Let’s take a look at the actual real life footage of the time machine (from the historical archives).
Time travel is possible if you get the car up to 88 mph. Is this car going 88 mph? Is there any way to tell? Oh, yes. Yes, there is. All I need to do is to look at this car (a DeLorean) and use video analysis. The clip isn’t perfect, but I think it will give a good enough estimate. I can scale the video using the wheel base of 2.413 meters.
Here is a plot of the position of the DeLorean in the first time travel (with the dog in the car).
Data Tool
The slope of this line puts the car’s speed at 56.7 m/s (127 mph). Yes, that is faster than 88 mph. I’m not sure why the one frame repeated. Also, there could be a problem with my scale since it was rather difficult to see the car. Here is the next time the car gets to a speed near 88 mph (when Marty first goes back in time).
Data Tool
Well that’s not good. This give a speed of 29 m/s (65 mph). For this video, the car isn’t quite up to 88 mph so this seems ok. I guess I should look at the last time travel speed (when Marty goes BACK TO THE FUTURE). Oh, actually there is not a good shot to analyze there. Oh well, the second shot is close enough to 88 mph, that I will just stick with that.
What about the time interval? For the first test, I looked at the time from just when the car started to shoot sparks until it “exploded”.