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Bird Size and Bird-Brained Math

Hi all,

Oh, you're going to love this one - determining bird size from a photograph. For the backyard birder, this is pretty easy as long as you have a known reference. (Though for a nature birdwatcher, I'd imagine the task is a bit more formidable.) Alrighty then... Where to begin? Well, how about at the beginning Beguine? Here's the pic and we want to know the length of the crow...

crow with pizza in mouth1_enhanced_300.jpg

(Before we get to truly rocking and rolling, be forewarned that I'm using a digital microscope and a digital caliper, so if the following photograph strikes you as odd, that's OK. I'm just trying to introduce as much accuracy into the process as possible. There's no reason why you can't use a magnifying glass and a decent rule to perform the same steps...)

And away we go!

  1. Right off the bat, we're going to have to relate the unknown length of the beastie to a known length in the image. Well, it just so happens that I built that crow feeding tray and know that the rail that goes around the top is .75" tall. So now we have a reference.
  2. Next, I used the microscope and found the length of the bird in the picture.

    400_crow length from microscope.jpg

    Hmmm... Looks to be about 31 mm

  3. I repeated the step above and found that the .75" rail was about 1.4 mm
  4. So what is the ratio of the image railing to the real railing? It's about 13.25.
  5. Onward! To get the real length of the creature, we'll have to multiply the picture length of 31 mm by 13.25 and that gives us 410 mm, or about 16.125". That sounds right and looks right. Granted, the bird might be crouching or the snapshot angle may not be at a true 90 degrees... But close enough.
Well, that's about it... Sibley says that the length of a full-grown American Crow is 17", so if anything, this is probably a first-winter critter. Yeah, I know... That kind of info won't make the world spin off its axis, but it still is kinda cool...

See you by the feeders,


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Can't help myself. So where did your multiplier number, 13.25, come from?
Harry "Gipper" Morris

Hi Harry,

Thanks again for your readership!

I got the number 13.25 by looking at the ratio of the known, real-world tray rail size (3/4" or ~19 mm) to the tray rail size in the photo (~1.4 mm). Given rounding "slop", that comes out to roughly 13.25. (In order to earn my engineering degree, I had to suffer through a brutal class that explored the +/- accuracy of manipulating irrational numbers (including binary...) I figured I'd skip this stuff for fear of boring the readers to the point of tears.)

In short, there were too many factors to sweat the details:

* I'm not sure that I captured the bird at full length. (Was the crow sticking its neck out?)
* Because of pixilization in the photo, I'm not sure of the exact measurement of the length of the bird in the image.
* Because of camera angle, some more accuracy may be lost.

Beyond all that was the accuracy of the magnification of the computer magnifying glass - once again, roughly 13.25

But in general, I think the measurement and technique used to reach that measurement was sound within expectations.



Hi Alan,
I guessed that it came from there. Try another way to solve the problem. ie,
1.4mm is to .75inch as 31mm is to X. The equation would be thusly:
1.4/.75=31/X, solve for X.
Don't have to worry bout how long a millimeter is with this method and it reduces error. Either case, we get similar answers. Heehee!!!
BTW, I liked the photo and how you were able to use your measuring stick to measure the photo.
Harry "Gipper" Morris

Right on Harry!

One of my first physics profs used to hold his fingers out as if he was a hypnotist trying to put us students asleep... And he'd stare into our eye's and say "Magnitude... Magnitude..." It took me a decade to figure out what he (and others!) were trying to say... "Be able to work precisely (I designed a CNC machine that was accurate down to the thousandths for OFC in Natick, MA), but don't waste effort over-engineering a club". In this case, all I wanted was a way to approximate the length of the crow within half an inch or so. As you know, depending on the angle of the camera to the bird, the measurement will change. Also, if a crow is "caw-cawing" the length of the neck will change... No point in over-engineering a variable.

But we arrived at a number I think all will agree upon... The crow was roughly 16" long... Not 15" and not 17".

I hear you on dimensional analysis... Reduce the units conversions, and you reduce the error. The problem is that when the initial system parameters (camera angle, pixilization of the pic, etc.) are shaky, making up accuracy later on in the system becomes moot.

But I am tickled that we both ended up in the same ballpark which is all I was looking for.

As for that photo... I took that with a Celestron 44302 digital microscope (about $55 new on Amazon... ) This thing just rocks! Name your hobby, and it applies.

Superb comment Harry!


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