People who think persistent contrails indicate some kind of conspiracy (which they call “chemtrails”), sometime point to the “dark lines” that sometimes accompany contrails. Since they can’t immediately think of why these dark lines should be there, they assume it’s part of the conspiracy. Either there is some kind of “dark chemtrail”, or the plane is projecting a dark beam of some kind of negative energy, or it is following a dark beam.

In reality these “dark lines” are simply the visual effects of shadows. There are actually three main kinds of dark line that are formed by contrail shadows.

Self-shadowing contrailsSelf Shadow - where the contrail itself is in shadow and appears dark. This can happen a number of ways. The sun can be low on the horizon and the contrail can be shadowed by a mountain or a thick cloud bank (such as in this video). In rare cases the plane can be flying directly towards the sun, and the contrail will shadow itself. When self-shadowing, the leading edge of the contrail will be brightly lit, with a dark area behind it. The photo on the right here shows some thick contrails (or possibly just row clouds) that are self shadowing. The sun has just set in front and to the right of the contrails.

Parallel Shadow - The contrail is simply casting a shadow on a layer of cloud beneath it. The cloud layer is thin enough so you can see through it, but it’s visible, so you can see the shadow on it. Theoretically you could cast a shadow on a cloud layer above or behind a contrail, if the sun were low enough, but this would be rather difficult to observe. Most “dark lines” are of this type. There’s an excellent explanation of these shadows over at Atmospheric Optics.

Edge shadow - The most interesting type of contrail dark line is when the contrail is lined up with the sun. This produces a slice of shadow through the atmosphere that looks like a dark line when viewed edge-on. It is quite difficult to visualize what is going on since you have to think in three dimensions, and we are accustomed to thinking of shadows as being flat, since they are usually cast on surfaces. You are not seeing a thin dark shadow here, you are actually seeing a huge slab of very faint shadow, but it’s viewed from looking along the edge. Imagine you have a thick sheet of glass. Viewed head on, it’s transparent, but if you look at it from the edge, it seems a lot darker.

The photo on the right is a rather dramatic illustration of this effect. The “dark line” here is caused by the slab of shadow cast by the portion of the upper part of the exhaust trail of the space shuttle Atlantis that is lined up roughly in a flat plane with the camera and the sun. The sun has just set, so the rays of the sun are almost parallel to the ground, so the upper portion of the plume is casting a long tall shadow through the air towards the horizon. This is viewed edge on from below, and so looks like a dark line. Since it’s a full moon, the sun is directly opposite the moon, so the “shadow” looks like it’s pointing at the moon (if you look closely, you’ll see it continues past the moon). This is particularly dramatic because of the combination of the setting sun and a vertical exhaust trail. With normal contrails, the sun has to be higher in the sky to cast the slab of shadow downwards.

[Math Warning] It’s a bit difficult to explain these edge shadows (also called volumetric shadows, or anticrepuscular shadows). You can think of them in terms of three dimensional geometry. The contrail is a line in three dimensional space. The camera (or observer) is a point in three dimensional space. The sun is essentially infinitely far away, and so is only really relevant as a directional vector (a vector in three dimensions, where the magnitude is unimportant ). These three quantities are what you need to consider to understand the condition for the edge shadow.

Given the line (contrail) and direction vector (sun) we can form a plane that contains the line, and is parallel to the direction vector. This plane cuts through the contrail, the atmosphere, and intersects the ground. Projecting two end points of the contrail along the plane in the direction of the sun’s vector, we get essentially a two dimensional parallelepiped (although the far edge is not very well defined). This parallelepiped is quite thin (it’s as thick as the contrail), so when viewed from the side, you won’t see much. But when the viewer is in the plane of the parallelepiped - specifically anywhere along the line on the ground formed by the intersection with the plane formed by the contrail and the sun - then they will be viewing the parallelepiped from edge-on, and so it will seem to be a dark line that intersects the contrail.

Since only the portion of the contrail that is roughly within this plane is contributing to the shadow, there may be other potions of the contrail that are not in the the plane, and hence do not seem to be casting a shadow. In fact they are, but since it is in a different plane, they are not visible unless the viewer was to move to a new position. This can be seen in the two photos above. In one it looks as if the plane was following a dark line, and then veered off. In the Shuttle photo, the highest portion of the trail, although brightly illuminated, is not contributing to the visible shadow. However a viewer in another location may have been able to see a different edge shadow trailing from this upper portion.