There are lots of commercial rebounders out there (we own this one), but all of them remove a lot of pace from the ball. This is fine and quite appropriate for many drills, but to work on catching fast throws the best target is one that sends the ball back sharply (i.e. the collision is elastic). For that, you need a hard, flat, angled surface and serious mass, which can be achieved if you have a huge tree handy. We were lucky enough to salvage two rounds from such a colossus when our neighbors had their 125 year old Douglas Fir felled by the city (it had signs of rot). Here's how I turned one into a lacrosse rebounder. Bonus: it's almost totally silent in use.
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Step 1: Find the Wood
Get yourself the biggest chunk of wood you can find. It needs to be massive and roughly flat. You'll get it properly flat in a later step. This trunk was over 3' in diameter.
Step 2: Build a Flattening Frame
I have lots of stuff in my garage, including some caster wheels, and I used these along with some recycled wood to make a trolley for my router. The idea was to have the router at a fixed height that I could move around over the log, skimming a small amount off all the high bits until eventually the whole thing was perfectly flat. If the ball is coming rocketing back off the stump, you want the bounce to be true.
It's easy to mount a router into a temporary surface - just remove the screws on the face, and use it as a template to cut holes into whatever surface you want the router in. I used a sheet of 1/4" plywood, which I cut to the router width + 3".
The frame was joined together with deck screws for easy dismantling. The dimensions were matched to my particular rounds and the recycled wood I had handy; it needed to clear the wood in height and be at least 50% wider than the largest diameter (so it can reach the middle of the log). Mine was a fair bit bigger than it needed to be, but I was disinclined to cut any of the wood for a one-use purpose like this. Once I finished the routing I disassembled it all and put the wood back in my lumber rack (OK, with the exception of the short end-pieces).
For a smaller levelling jig for logs, check out seamster's excellent instructable on the subject.
Step 3: Flatten
This part is messy and will take a while, and you really want the log to be as flat as possible before you begin. Do some cleanup with a chainsaw and/or hand planer and level the log as much as possible on the floor. The two faces don't need to be parallel, so use wedges to make it level. Use the plunge feature on the router to progressively lower the bit. If your log is sufficiently un-flat that the travel of your router doesn't get the whole thing, you will have to lower the frame (you did assemble it with screws, didn't you?).
I did three passes removing about 2 mm at a time. The first pass just removed the highest peaks, the second removed material from about one third of the surface, and the final pass covered nearly the whole thing. I then ran over the whole surface again with the hand planer set to remove about the smallest amount of material I could set it to, and it was pretty smooth after that. I forgot to take any photos during the routing process, I got distracted by the fun process of making so much sawdust.
I just used a square bit in my router, but ideally for this sort of task you should use a surfacing bit instead.
Step 4: Make Supporting Leg
I used a 2×6 attached by hinges on the back to prop up the round of wood. This makes the angle of attack adjustable. I plan to slap some clear coat on the front.
Step 5: Set Up and Practice
The log target is smaller than the average rebounder and you should consider putting up a net behind/around it to catch stray balls. Also be conscious of the fact the ball is being returned at high speed, so be aware also of what is behind the thrower. Hits on edges can rebound erratically. You should probably wear protective gear while practicing (and don't throw while other people are around), so the gif above is not setting a great example...
Post a picture of your own home-made rebounder (any design) and I'll send you a 3-month pro membership.