A Problem of Perspective in the OC – New Year’s Eve Contrail
An interesting contrail cropped up off the coast of San Clemente, Orange County, California on December 31st 2009. The curious shape led some people to think it’s a missile launch, which it does kind of look like (all taken from San Clemente)
http://sciencedude.freedomblogging.com/2009/12/31/mystery-launch-visible-off-oc/75161/

Click these for larger images:

The idea that it’s a missile launch comes from three misconceptions. Firstly that the trail is vertical – it’s not, it’s a horizontal trail, at around 32,000 feet (about six miles). It’s the same as this:

This contrail is no more vertical than the road is, and nor are the power lines at 45 degrees. Everything is horizontal – it’s the just the angle you are look at it from. All of these show horizontal contrails.
Secondly there’s the misconception of direction, that it’s flying away from the viewer, when it’s actually flying towards the viewer. This is because the “base” of the contrail seems wider than the tip. Perspective tells the brain that this mean the base is closer. But actually you can see the base has been greatly spread by the wind. Since it’s still so far away the effects of perspective are greatly diminished, meaning the actual width of the contrail is what is creating the illusion. Imagine is a plane with a 100 mile long spreading contrail were coming towards you; what would it look like? It would look exactly like this.
Thirdly there’s the idea that it goes all the way down to the ground. Now that might be true if the Earth was flat, but the Earth is round, and things go beneath the horizon eventually, no matter how high they are. A plane 200 miles away but five miles up is always below the horizon. If the horizon is raised (as it is here, with Catalina Island), then the distance is less. Here’s some math:

This diagram is not to scale, but the math is the same regardless. The solid curved line is the surface of the earth. The dot at the top is San Clemente. The little triangle is Catalina. “d” is the distance to Catalina (d=35 miles). “c” the amount of Catalina that is visible above the horizon (c=0.05 miles, really a bit more, but let’s be conservative). “a” is the altitude of the plane, (a = 6 miles). “r” is the radius of the earth (r=3963 miles).
The green wavy line is the contrail. Notice it’s at a fixed height above the surface of the earth, and is going directly towards the OC.
The point labeled (0,0) is the center of the earth. (0,0) means X=0, Y=0, where X is horizontal and Y is vertical. What we want to know is how far away the plane is, the value x. We do this with cartesian geometry, noting that the lowest visible point of the trail is at the intersection of the dotted line, which is a circle of radius (r+a), hence the equation x^2 + y^2 = (r+a)^2 and the line labeled “sight line”, which is has the equation y=x*c/d. Combining these equations to solve for x yields a quadratic equation, which we can solve with Wolfram Alpha:
intersection of (y=r+x*c/d) and (x^2+y^2 = (r+a)^2)
and with the real numbers:
intersection of (y=r+x*c/d) and (x^2+y^2 = (r+a)^2) where a=6 and d=35 and c=0.05 and r=3963
Which gives x = 212, meaning that the bottom of the contrail is around 200 miles away. So if the front of the contrail (the actual aircraft) is somewhere above and behind catalina, then that means the contrail is over 100 miles long. At 500 mph, that means it could have formed in 12-15 minutes, which seems consistent with the descriptions in the discussion above. (feel free to play around with the numbers there to see the affect of various assumptions)
Looking at the satellite image for noon on that day (12/31/2009) and the next day (1/1/2010), we see contrails in approximately the same position, and around 100 miles long, showing it’s quite possible, given the right weather.
Really what makes this odd looking is the position of the people taking the photo. Obviously the same contrail would be visible all the way up the coast, however the only people who though it was really odd were those who were lined up with it, in OC. People in LA would see a dramatic looking contrail, but more obviously just a contrail, so less worthy of writing to the newspaper about. I actually saw it myself, but was in a car, and could only get a poor cell-phone snapshot:

That was from somewhere around San Diamas, on the 210 freeway, so I’m looking South West, probably around 45 degree the the contrail, which you can only see a bit of behind the Home Depot sign. It looked quite impressive at the time. I’m sure there are other photos of it from various other angles which show it’s contrail-ness more clearly, and I’d appreciate it if someone could send me some.
[UPDATE] I found this photo of the same contrail, taken from Santa Monica:

You can see from this angle (and taken a bit earlier) it looks far less interesting, as it’s very apparent it’s just a contrail.
In the meantime, here’s a similar photo, but with the contrails going in the other direction (away from the camera):

[Update 1] Here’s another image of the New Year from another angle, from Corona del Mar, about 20 miles Northeast of San Clemente:

A photo from the Oxnard/Ventura region should put the matter to rest. Anyone?
Here’s a similar photo (of a different contrail, obviously) on the same day at the other side of the country:
Here’s some more contrails at sunset (From a very nice set of contrail photos), note how they look exactly the same as sections of the New Year contrail:

4 comments Tuesday 19 Jan 2010 | Uncinus | contrails
4 Responses to “A Problem of Perspective in the OC – New Year’s Eve Contrail”
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To quote someone, please use <blockquote> and </blockquote> tags, for example:
<blockquote>But surely the contrails would evaporate?
How do you explain that, given those facts?</blockquote>






Ah, Uncinus, you’ve caught me on the hop!
Perhaps I’m lucky you did, because you have certainly addressed this badly-understood topic with a greater panache and with better evidence and argument than I would have mustered.
You have made it so much easier for others to understand and for me to explain: I can just direct those describing “steep angles” and “vertical trails” and even “loops” straight to your page here.
It’s true, of course, that non-persistent contrails do this too. It’s just that they have “vanished” before you get to see the complete track of the contrail.
By “vanished” I mean “sublimed back into water vapor”, and we all know water vapor is invisible, don’t we? It hasn’t really gone away: you just can’t see it anymore.
Great disinfo site you have here, I know what I see every day when I look at the horizon, and the Earth is FLAT!
*end sarcasm*
These are some great pictures of beautiful sunsets! I was in San Clemente on the 12/31/2009 and watched the thing through my binoculars and through a Barska 20-60×60 spotter scope and caught about 20 seconds of digiscoped video through the Barska. It was very odd. Check it out at http://www.groovetraveler.com or
http://www.youtube.com/watch?v=88XaLNzysJ0
Hi GrooveTraveler, note that several of the above photos are from the actual incident, and clearly show it to be just a contrail when viewed from a side angle.