Seriously, if networks can superimpose graphics on the field in real-time (I can't seem to find a screenshot, but I hope you know what I'm talking about), then surely there's a better way to measure 10 yards:
So, getting the position of the ball on the field to within one length of the ball would require a system that could detect differences of about one nanosecond in the arrival times of pulses from the ball. Other positions on the field are pretty comparable. I calculated positions for a few different cases, and the smallest difference I got was for a ball exactly on the goal line, at the center of the field. Moving that ball back one foot changes the difference between arrival time by a hair under a nanosecond (unless I made a horrible math error, which is possible).
That's challenging, but might be doable. Of course, the length of the ball is pretty coarse by the standards of farcical distance measurements in football, so you'd like a system that could do much better. And that starts to get tough-- getting the position to a centimeter would require time resolution of about three one-hundredths of a nanosecond. Getting transmitters and receivers that are stable to that precision is difficult proposition.
OK, scientists, now it's time to figure out a way to rethink the whole damn BCS system.