Photographing eagles in flight is a great challenge. There are many little things that make a difference so the photo stands out, and most involve a great deal of patience. I'm still very much in the learning and practicing stage, but since I have had a bit of success, I thought I'd share a few tips.
For best results you need a camera with a good focus system to track moving objects. I use the AI Servo mode on my Canon 40D. You also need a fairly long focal length in most cases, such as 300 or 400mm. You want a fast shutter speed (I like 1/800 or ideally even faster), which usually means you have to increase your ISO a bit and use a wide open aperture. Another setting you will want to use is the continuous shooting mode.
Try to position yourself with the sun to your back and be prepared to wait until the eagle comes into sight in the direction you are facing. Then you want to wait until it is at the right angle so the sunlight is on the underside of the wings, and also on the head. This is because eagles are quite dark birds and otherwise you are likely to just get a dark blob in the sky. I have deleted hundreds of photos for this reason!
You will also need to exercise patience in waiting until the eagle comes close enough into range that they aren't just a speck in the viewfinder. Although it is fun to take lots of photos, it is a little depressing when you have to crop so many down to a size that is too small to enjoy.
Remember also to spend some time just watching and enjoying these beautiful, powerful birds. That way even if you get home and discover none of your photos are perfect, you will hopefully still have had a great time.
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Photo credits: Teekaygee.