How this instrument works
Implied speed is nothing more than the oldest kinematic identity there is, v = d ⁄ t, aimed at a specific kind of input: a distance and a duration that nobody measured with an instrument. A sighting report gives two numbers a witness estimated by eye and by feeling — how far away the object seemed, and how long the object took to cross that distance. Divide one by the other and the arithmetic is exact, even though the numbers feeding it are not; the honest way to describe the output is 'the speed implied by what was reported,' not 'the speed of the object.'
The two inputs fail for different, well-studied reasons. Distance to a point of light in a dark sky has no depth cue to anchor it — no tree line, no aircraft fuselage for scale — so a small object twenty metres up and a huge one two kilometres up can look identical, meaning the same apparent motion could imply speeds separated by a factor of a hundred. Duration fails for a psychological reason instead: perceived time compresses under sudden fright or surprise, a documented effect in eyewitness research, so a genuine four-second event is commonly reported as two.
Because the formula divides by whatever duration is entered, its output is only as trustworthy as the shakier of the two inputs — and duration is usually the shakier one, since a distance can sometimes be checked against a landmark while an unaided sense of elapsed seconds cannot. Halve the reported duration and the implied speed doubles; the instrument will faithfully report a doubled figure with no way to know the halving happened. That is not a flaw in the arithmetic — it is the correct behaviour of a division, applied honestly to imperfect inputs.
- Enter the Reported distance traveled — the witness's best estimate of how far the object moved, in metres or kilometres.
- Enter the Reported time elapsed — how long that distance took, in seconds.
- Read the Implied speed in m/s, then switch its unit to mph if that comparison is more familiar.
- Compare the result against a known figure: sound travels near 343 m/s, a cruising airliner near 250 m/s, so context is immediate.
Worked example — 5,000 metres in 2 seconds
A witness reports an object covering about 5,000 metres — roughly three miles — in 2 seconds. Enter 5000 for Reported distance traveled and 2 for Reported time elapsed: v = 5000 ⁄ 2 = 2500 m/s, or about Mach 7. No aircraft is known to sustain that speed, which is exactly why a figure like this one gets flagged rather than dismissed — the instrument only performs the division, and it draws no conclusion about whether the underlying estimates were accurate or the object was genuinely extraordinary.
Change only the time and the picture changes completely. The same 5,000-metre distance reported over 10 seconds instead of 2 gives v = 5000 ⁄ 10 = 500 m/s, close to Mach 1.5 and well inside the performance of a fast jet at low altitude. The distance estimate never moved; the clock estimate did — and that two-number sensitivity is the entire reason investigators treat duration as the weaker of the two figures in any sighting report.
Questions
Why does a small error in the reported duration change the speed so much?
Because duration sits in the denominator, so halving it doubles the implied speed and doubling it halves the speed — the relationship is inverse, not proportional. Distance errors scale the result directly, but duration errors get inverted first, which is why a witness misjudging '2 seconds' when the real figure was '4 seconds' alone doubles the reported speed with the distance estimate untouched.
Does this calculator decide whether a sighting is a genuine UFO?
No. It performs one division, distance over time, and reports the speed those two numbers imply. It has no way to judge whether the underlying estimates were accurate, whether the object was misidentified, or whether the sighting was extraordinary — that judgment needs corroborating measurements, not a bigger calculator.
Why is distance usually the least trustworthy number in a sighting report?
Because a point of light at night carries no size cue. Without something familiar nearby for scale — a plane, a bird, a rooftop — the eye cannot tell a small object close by from a large one far away, and both can produce the same apparent size and the same apparent duration while implying wildly different real distances, and therefore wildly different real speeds.
What implied speed lines up with a known aircraft?
A cruising airliner sits near 250 m/s; a fast military jet at altitude can reach roughly 600 to 700 m/s. An implied speed climbing toward 1,000 m/s or beyond, at low altitude, sits outside any publicly known aircraft's performance envelope — which is a cue to re-examine the reported distance and time, not proof of anything unusual.
Can I use a stopwatch-timed duration instead of a memory-based guess?
Yes — the formula does not care how the two numbers were obtained. A duration timed on a phone and a distance measured against a known landmark separation feed into the same v = d ⁄ t and produce a far more defensible implied speed than two figures recalled from memory after the fact.