I saw a guy on youtube measure the speed of a supersonic baseball using a highspeed camera and two posts in the ground. Could a smartphone do the same thing for arrows? I think so, because a 150 fps arrow travels 30 ft in .2 seconds. This means a camera with at least 5 frames per second would be enough.
My idea is to place two stakes in the ground 30" apart and film an arrow shot straight over them. All you have to do is note the time it takes it to travel between the two and do a little math.
This is harder than using a chrony, but a lot less expensive than the good ones, and probably more accurate than the cheap ones.