Struggling to work out where was best for this topic. I know its been covered numerous times before, but I'm after more reach than 200mm of my 70-200 on my 7D. It would be used primarily for motorsports, airshows and wildlife
A couple of years ago, I faced the same issue: I found that my 70-200mm on my 50D didn't have enough reach for shooting motorcycles on racetracks, and I was looking to get (significantly) closer.
After trying a 400mm and a 300mm in a shop and some "thinking", I decided that 300mm wouldn't be enough and splurged on a used 400mm/2.8L Mk I. Only to find out that a 400mm on a APS-C got me too close to the action to be useful for me. I had to practice quite a bit to learn how to properly use the 400mm.
So my advice to you would be to check out if a 1.4x TC or a 300mm might suffice for what you want to do, or you really need the 400+mm.
Now that I have a 5D3, I'm looking forward to try the 400mm again to see if it has become more "user-friendly" for me.