I've heard of people using audacity and radar guns. But Chronies would be nice for a good release velocity. Only problem I foresee is the high likelihood of destruction. Maybe cut out some sort of shield for the actual machine?

They aren't really expensive and a shield would be rather easy to build.  You can get an inexpensive one for a lot less than a phone or I pad.

The main problem will be the window, it's actually rather small.  And you will have to have the shades for it to work properly.  So, you would have to throw through a port in the shield for it to work. 

So, we'd need a really super accurate slinger, who can throw at full power and not get squirrely with his accuracy when he does so.

This actually sounds like a job for Timpa.   

MidwayUSA had an inexpensive model, last time I checked.  And it will record arrows.

goth dave has a chrono.

Dunno if he's posted any videos of it in use.

@Morphy that's the way i do it. but there might be errors.
wait until weekend. i'm making a video with speed measurements by camera frames.

720p 30fps the same you see in the videos i've uploaded.
hopefully i will find a phone with more fps in the future.

I like the board and side camera idea. I'll have to try to set something similar up in future as well. Right now, I just don't have anywhere to do it.

I'm starting a new thread in the "Here Be Maths" section for your speed recordings and using what method. I'll create a similar Google Form to the one I've done for target results and we can compile some decent statistics from that over time.

I'm looking forward to hearing about the results in future!

(Also, when I create my regular slinging club in Northern NY/Southern VT, I'll be regularly uploading such results and I'll have both standard targets and a speed rig like the one described above. I'll let you know when that's established.)