As far as Back To The Future lore goes, it's the biggest question that bugged me for several years. It's explained in the first film that to operate the time machine, you begin by turning the time circuits on. You enter your destination time, get the DeLorean up to 88 MPH, and there you go, you've traveled through time!
But that wasn't good enough for me. I always assumed the time machine required precise math to arrive at the precise time, and traveling faster than 88 MPH could throw those calculations off with disastrous consequences. But that was under the assumption the time machine did it's magic by traveling faster than the speed of light. At least, hanging around nerds at an impressionable age, it's what they all thought. Turns out though, that's not how it works. If you look at the roof of the DeLorean in the middle-back, you will see a small silver box. I would post a screenshot from the movie, but I currently have no way of watching the movie besides on my iPad, which of course doesn't allow screenshots in the Videos app, so you'll have to do with this picture I took of the 1/64 Hot Wheels model. I've added an arrow to show where to look:

So what is this box? According to these TMR Trading Cards, it's a "Tachyon field generator", which for simplicity's sake, works in much the same way as a wormhole generator.
How I interpret this is the time machine never reaches light speed, instead it's actually a wormhole generator on wheels. Using this conclusion it's logical to assume the reason the DeLorean must reach 88 MPH is that the wormhole can only stay open for a very brief moment, and 88 MPH is how fast it must travel to make it through in one piece before it closes and cuts it in half.
So to answer the question, what happens when you turn on the time circuits when the DeLorean is going past 88 MPH? It's hard to know how the time cicuits handle flukes like this, but my guess is it will immediately send the time machine back to whatever was last entered. And as for messing up the accuracy of temporal displacement, it doesn't matter because the time machine is making it through the wormhole anyway.
This of course is partly in-universe canon, partly fan-canon. None of this applies to technical or production decisions in real life, for example, how 88 MPH was chosen as the magic speed because it lights up every segment of a seven-segment display, looking far cooler than had the display been partially lit. This is just trying to explain the logic inside the world of Back To The Future.
That's basically all, I just felt like sharing this with the world, as not many people have talked about this on the net. Other than one person asking this question on Quora some time ago *EDIT, 2020-9-23, I just learned a user on Stack Exchange by the name of Sobrique discussed this same topic in 2015*, that's about it. Well, thanks for reading. Stay safe, take care and carry on.
Argot
Page created: Thursday, May 28th, 2020