If a miltary jet flies overhead at supersonic speed it goes across the sky from horizon to horizon in just a few seconds but it’s slow enough such that you can watch it. If you doubled it’s speed it might go across the sky in two seconds but you’d still see it. Double the speed again and it would pass in one second but still slow enough to catch a glimpse.
If it went at something approaching the speed of light then it would fly over so fast you wouldn’t even see it making it effectively invisible. What’s the cut off point? How fast would it need to go to cross into invisible territory?
There are things in nature that move too fast to see - that shrimp that flicks a leg, some plant that releases it’s pollen, a Bruce Lee punch - but I was thinking of a big thing like a train or a plane.
So if a typical jet takes 10 seconds to cross your field of vision, you’d have to go a few thousand times faster than that. Let’s say 1% of light speed, give or take.
Hmm, light moves at the speed of light, and we can see it.
How fast would something have to move to be invisible… at what distance? I’ve seen satellites move at 17,000 mph, but they pretty much crawl against the sky. On the other hand, I’ve launched model rockets from 15 feet away that accelerated from 0 to over 40 in the space of 3 feet, and continued to accelerate to around 100 in the next few feet. In too many cases, the last time I saw them was when they were still on the launch pad.
Assuming you’re not standing in a grove in the middle of the forest, I don’t think there is any terrestrial craft that crosses from horizon to horizon in mere seconds.
Light speed is 671 million miles per hour so 1% of that would be 6.71 million miles per hour. You reckon it would have to go that fast to not be seen? Seems a little on the high side to me
Actually, an airplane’s propeller is invisible (enough) when it is turning at speed. The Cessna I flew had a “normal” high propeller speed of 2400 RPM, or 40 RPS. Estimate the propeller length (i.e., radius) to be about 3 feet. Do the “2 pi r” stuff and you’ll have, oh let’s see, about 784 feet per second. Which is about 535 MPH. Well below the speed of sound. And, actually, the propeller was invisible at half that RPM. So even at about 267 MPH it was invisible.
That’s a pretty low quality video, and at that altitude is pretty similar to my “standing in a grove in a forest” scenario. Actually, if you look closely, the aircraft was noticeably BELOW the horizon for quite some time…so I say it doesn’t count.
Aside: Amusingly, it was a plot point in Master of the World (Jules Verne) that a vehicle travelling at 120mph would be invisible. Not one of his better guesses.
The real issue is persistence of vision - there was a prototype drone developed that looked a bit like a boomerang and rotated so rapidly that from a distance it was effectively invisible (but not inaudible, sadly). There was a ton of computing to construct stable images from the thing, though.
This is thinking aloud - I may be making unwarrented assumptions, please correct my math if you see something glaringly obvious:
For something to be not seen due to this effect, it would have to cross the fovea (about 2 degrees of arc) in about 1/25th of a second, if the eye was fixed. Pursuit tracking of the eye is about 30[sup]o[/sup]/sec, so an object would need to subtend 30*(1/25) degrees of arc in 1/25 of a second.
So for a given range (in meters), the lateral velocity (in km/h) is given by (Range*SIN(RADIANS(30/25)))253600/1000, giving:
Now, this is probably only valid for point objects, other physiological factors may enter into play that I don’t understand, but you may get an idea of the scale of speeds involved. For example, I would see a person moving at 1.8km/h at a distance of 1m, but maybe not a fly. However, at a distance of 10000m an aircraft would have to be doing 20,000km/h (mach 20 or so) to be invisible, and at that speed you would not hear the sucker till it was long gone.
It was just a random video I found of a military jet flying fast but allow me to prove it to you using maths:
Military jets (eg an F22 Raptor) can fly at mach 2
Mach 2 is 1317 mph
Divide that by 60 and you get 21.95 miles per minute
Divide that by 60 and you get 0.365833 miles per second
So a Raptor will cover a third of a mile in one second
The horizon at sea level is three miles away so that’s 6 miles from horizon to horizon.
So it will cover one mile in three seconds and six miles in 18 seconds.
I originally said a military jet would go from horizon to horizon in “just a few seconds”. So it depends how you want to define a few seconds - less than 10? less than 20?
Si said:
20,000 kph would be 12,427.4238 mph.
That’s pretty amazing really. 10000m is about normal cruising height for aircraft so it would be easily low enough to see. And 12 000 mph isn’t all that much faster than a military jet goes now - about 10 times quicker.
So if our military jets went a measly 10 times quicker than they do now, we wouldn’t be able to see them.
What about a train passing right in front of your eyes a few metres away?
I suspect they can. If you stand behind a shooter the sun behind you, it’s easy to see a .45 bullet in flight - I’ve done this many times. These have a muzzle velocity close to supersonic. Based on how easy this is, it should be possible to see a similar bullet traveling 50% faster.
Obviously, it’s important that the bullet have a low angular velocity with respect to the observer.
