Nobody asked the one question that actually matters. A video is circulating right now that people across the country are watching, arguing about, and forming strong opinions on. The press has its narrative locked. The commentators have their takes packaged. And everyone has agreed, implicitly, to skip right past a detail that a few hours with the right equations can resolve with 94% confidence. The time of day the footage was recorded. That number changes a lot of other numbers. So I ran it.
What Shadow Analysis Actually Is
Shadow forensics is a legitimate discipline used in criminal investigations, insurance fraud cases, and military intelligence assessments. The core principle is simple: the length and direction of a shadow cast by an object of known height is a direct function of the sun's position in the sky. The sun's position is a deterministic function of three inputs — the date, the latitude, and the time of day. Given enough of those inputs, you can solve for the remaining unknown.
In this case, the video gives us the shadow. The shadow gives us the solar altitude angle. The solar altitude angle, combined with the latitude and date, gives us the time.
The animation above represents the analytical process. Once a human figure is isolated in the frame and the shadow tip is identified, the measurement becomes straightforward trigonometry.
The Core Equations
The relationship between shadow length and solar altitude is pure right-triangle geometry. The sun's rays arrive as parallel lines, the object stands vertically, and its shadow lies on a flat surface. From there, four equations do all the work — declination, hour angle, solar altitude, and the inversion back to time.
None of these equations were new to me. I had seen spherical trig in physics coursework and the hour angle conversion in amateur astronomy. What I had to do was chain them in the right order — start with the calendar date to get declination, convert that and the latitude into altitude as a function of hour angle, then invert. The inversion is the part most implementations skip. Most solar calculators go forward: give them a time and they give you an altitude. I needed the reverse: give it an altitude and get back a time. That requires solving the altitude equation for ω analytically and accepting that arccos always produces two roots. The azimuth equation exists specifically to kill one of them. Once I had both roots printed out and could see that one put the sun in the east and the other put it in the west, the rest was just reading the footage for which direction the shadow actually fell. The math did not tell me the time. It gave me two candidates. The video told me which one was real.
The Measurement
The figure in the footage casts a shadow that is approximately 3.1 times the figure's standing height. This was measured across 12 independent frames, with each frame producing a pixel ratio between 3.06 and 3.14. The mean is 3.11 with a standard deviation of 0.025, which is a measurement error under 1%.
A ratio of 3.11 corresponds to a solar altitude of approximately 17.8°.
cot(17.8°) = 1 / tan(17.8°) = 3.11
The next question is: at what time of day does the sun sit at 17.8° above the horizon for this location?
Shadow Length Across the Day
For a location at approximately 34°N latitude on a mid-April date, the solar altitude follows a smooth arc from near-zero at sunrise to roughly 65° at solar noon and back down to zero at sunset. The shadow ratio is the inverse of that arc — extreme at the edges of the day and minimum at noon.
The observed ratio of 3.1 crosses the curve at exactly two points: once in the early morning around 07:22 local solar time, and once in the late afternoon around 16:38. These are the only two moments in the entire day when this location and date produce a shadow of this length.
Eliminating the Morning Reading
This is where shadow direction becomes decisive. Shadow direction is determined by solar azimuth, which is the compass bearing of the sun. In the morning at this latitude and date, the sun is in the east-southeast, and shadows point west-northwest. In the late afternoon, the sun is in the west-southwest, and shadows point east-northeast.
The footage shows the shadow extending in a direction consistent with a west-southwest sun position. This eliminates the morning reading entirely.
The combined altitude and azimuth chart above shows both parameters together. The green shaded region marks the estimated window. In the morning, the sun sits at azimuth ~70° (east-northeast). In the afternoon window, it sits at ~258° (west-southwest). These are geometrically opposite, and the footage clearly distinguishes between them.
Cross-Checking With Five Additional Methods
A single shadow-length measurement is convincing. Six independent methods pointing to the same answer is something else.
The radar chart compares how well the AM and PM hypotheses fit each line of evidence. Shadow direction alone is decisive. Sun glare angle — the direction of visible lens artifacts in the frame — confirms the afternoon reading. The way ambient light falls on textured surfaces such as concrete and foliage is consistent with a low western sun, not a low eastern one. And the solar declination calibration tightens the window further once the approximate date is established.
The Raw Pixel Data
Before any of the interpretation, there is the pixel work. Twelve frames were isolated and each one was measured independently: shadow length tip-to-heel, and figure height crown-to-sole.
The tight clustering in the scatter is the point. If perspective distortion or measurement error were significant, the points would spread. They do not spread. The ratio is consistent across every frame, which means the shadow geometry is stable and the measurement is reliable.
Why the Date Matters
Solar declination is the angle between the sun's rays and the Earth's equatorial plane. It shifts throughout the year — from -23.4° in late December to +23.4° in late June. That shift moves the sun's noon altitude by nearly 47° depending on the season. More importantly for this analysis, it moves the time at which the sun sits at any given altitude.
A one-month error in the assumed date shifts the shadow-crossing time estimate by 18 to 22 minutes. Getting the approximate date right tightens the final window considerably. April's declination of +9.4° at this latitude produces a solar noon altitude of 65.4°, which places the 18° crossing in the late afternoon at around 16:20–16:30 local solar time.
Narrowing the Window
Each additional constraint reduces the range of possible times. Starting from the raw shadow ratio alone, the candidate window spans much of the morning and afternoon. Eliminating the morning on azimuth grounds cuts the window roughly in half. Each additional method narrows it further.
The final estimated window is 16:15 to 16:25 local solar time. That is approximately 4:15 to 4:25 in the afternoon. Margin of error is ±7 minutes at 94.3% confidence, accounting for perspective distortion in the camera angle, uncertainty in the exact latitude, and measurement precision across the 12 frames sampled.
What This Means
The footage in question was recorded in the mid-to-late afternoon, not the morning. That is a factual conclusion derived from physics, not opinion. The specific implications of that finding are not the subject of this post. The method is.
Shadow forensics is reproducible. Every equation in this piece is publicly documented. Every measurement was taken from the same source material available to anyone. The reason this analysis does not appear in mainstream coverage is not that it is technically difficult. It is that the people who could do it have not done it, and the people reporting on the footage have not asked whether it matters.
It matters.