If a UFO is moving too fast for your eyes to notice it, your video camera probably won’t catch it either.

Since reading about the Denver UFO the other day — this is the supposed air/space-craft that supposedly cavorts over a crowded metro area too swiftly for nearby people to see — I’ve been wondering: how fast would a flying saucer have to be moving, to be effectively invisible to unaided eyes?

There’s no single, simple answer, of course. The “invisibility speed” would depend on the ambient light level, the relative size of the object in one’s visual field, the relative direction of motion, the presence of other sensory cues such as whooshes or flashes, the direction of your visual attention, and a host of other factors. You can’t see a speeding rifle bullet, for example, but you can see a much larger military jet moving at the same speed. This treatment here, in the bulletin of a medical research institute, gives a good overview of the problem.

It isn’t hard to come up with a seat-of-the-pants estimate, though. The binocular field of view of a person with normal vision is about 120 degrees. Let’s imagine an airplane-sized object that speeds straight across this binocular field of view, with a closest approach of one mile. How quickly must it get across to be effectively invisible?

The human visual system starts to lose its ability to distinguish stimuli — even under optimal conditions — when they are separated by less than about 1/50th of a second. That isn’t strictly relevant to this problem; the question here is whether you can detect a single novel stimulus moving against an ordinary background. But the 1/50 sec figure gives us a rough idea of the effective “refresh rate” of the human visual system, and I think we can all agree that just about anything crossing our visual field in 1/50 sec. would be invisible, unless it is highly luminous against a dark background. In bright daylight even a much slower object — even at airplane scale, at an easy, one-mile viewing distance — could still be unnoticeable to most or all viewers if it is not luminous. Human eyes frequently dart around (saccade) for about 1/5 sec at a time, during which the visual feed is interrupted; also our eyes blink a lot, for intervals that can be even longer. These interruptions are effectively random, so they wouldn’t blind everyone at once. Also, like other mammals we have a visual system that is highly sensitive to moving objects, even if we can’t perceive them with sharp resolution. But surely the effective FOV-crossing limit is higher than 1/50 sec.

What’s the upper limit on this transit time? I think that if I were staring out onto a clear, sunlit expanse of ground or water, an airplane-sized object speeding across my binocular visual field a mile away would have to cross in well under a second, to go unnoticed. Let’s say 1/2 second. (Count ‘one-mississippi’ but stop halfway — it’s a longer interval than it might seem.) I’m pretty sure that an object of that size, moving that fast, at that distance, would still be perceptible to a significant fraction of onlookers. I’d bet that even a 1/4 sec transit would be noticed by some people, especially if they’re expecting to see something. But let’s stick with 1/2 sec to be (I think) conservative. What speed does that represent?

If you work out the simple trigonometry of it, you come up with a figure just shy of 25,000 mph — which is faster than low-earth-orbit satellites move. It’s also faster than a simple, earth-technology aircraft could move through the lower atmosphere without quickly burning up. And again, I believe that’s conservative. The real speed for effective invisibility of a large object before a multitude of onlookers could be double or triple that figure.

At closer ranges, the same object would be larger and in that sense more perceptible, but also would spend less time crossing people’s fields of view, so it could well have a lower invisibility-speed. Clearly invisibility-speed is neither static nor simply linearly varying with distance. But even if you were to halve the distance and assume a halved invisibility-speed, you’d be talking about something that has to move at more than 10,000 mph.

These calculations are relevant, I think, to video-only UFO incidents like the Denver one. Such incidents tend to bring with them the assumption that ordinary, non-zoomed video cameras can catch stuff that unaided eyes can’t detect. In the recent Denver case, for example, the “UFO” was caught from a distance on camera with minimal blur (at presumably 1/100 shutter speed) but supposedly was moving too fast to be visible to people who were closer to it.

My suggestion is that the real, too-fast-for-people-to-notice speed for airplane-sized objects, at modest ranges in full daylight, is going to be so high that they would show up only as blurs on ordinary video. An object at 10,000 mph, for example, would move about 150 ft during a typical (1/100 sec) video shutter interval. That would be all blur, even for a 747-sized craft. Conversely, an airplane-sized object that is moving slowly enough to appear with minimal blur on a camera one mile away should be easily noticeable to most people at closer range.

The Denver case is hard to judge definitively at this point, for a number of reasons: the object (or objects) is small compared to the video image field, we don’t know whether the camera operators used zoom, we don’t know whether they tried to perceive the object without a camera, and of course we don’t know the true distance of the object from the camera. But count me among the dubious. As many have suggested, the object might be only a bumblebee-like insect in the near-field (or medium-field viewed with zoom). If so, that would explain why no one downrange sees it. It also would account for the blunt, tubular appearance of this “UFO” on film: that would be the insect’s body, the wings being too fast-moving (and probably too transparent) to show up at all.