Roughly, these regulations correspond to making sure that if a plane were to hit your unmanned balloon on the way up or on the way down that the plane will survive and that your package won't be dragged along; and, that the package itself won't be hazardous to folks on the ground.
(IANAL) Conformance with the rules means that no single payload is more than 6lbs, that the side-wall density of your payload does not exceed 3oz/sq in on the smallest side, and that the cabling you use will break with an impact force of 50lbs. We could debate about how you measure impact force, but most folks in this hobby read it to mean "tensile" strength. For 6lbs payloads, to meet the density requirement, you want a box about 1x1x1ft, which is often why most of the pictures of payloads that people send up in the sky look about the same size and shape.
Last, you need to conform with the safety regulations in FAR 101.7. The gist here is that you need to make sure that your payload isn't a danger to others on the ground, and not a danger to those in the air. Compliance here is more subjective, but a parachute and padding box go a long way to making others on the ground safe.
It's relatively easy to file a Notice To Airmen (NOTAM) that indicates you'll be launching a balloon. A courtesy call to your local Air Traffic Control office wouldn't hurt either. If you don't have a local ATC, the nearest airport is good place to start.
My familiarity with these regs comes from actually launching several helium-lifted payloads to near-space a few years ago and talking through the regs with the FAA and ATC to make sure we didn't need an official waiver (we didn't). My group had a slightly higher budget, but we went higher, longer and farther than these young Canadians, making two launches within an hour and sending the first balloon about 2000 miles over 34 hours starting at around 80,000ft, and sending the second balloon + payload to 123,000ft with about 3 hours of flight time.
Like many enthusiasts, our project used amateur radio frequencies to communicate, which qualified us to be listed on the Amateur High Altitude Radio Balloon (ARHAB) website for our achievements, we're listed as PBH-9 and PBH-10, for the duration and distance records.[2]
[1]:http://ecfr.gpoaccess.gov/cgi/t/text/text-idx?c=ecfr&rgn...
We had a pretty intense model that we ran with some probabilistic ambiguity and live weather data; it's written in C and unfortunately locked behind a proprietary wall from my previous employer. The physics in the sim were mostly described by Rodger Farley (IMO he's the world expert on the subject), the short version of his paper is available here[1] (we contacted him directly to get the full version from NASA). The model also reads live weather data, which helps with figuring out direction.
The hard part to measure is heating effect from the sun and indirect heating effect from ground and cloud albedo. You can get pretty close, but IR sensors would probably have done the trick.
One cool thing about our flights were that they had 2-way comms; we could actually instruct the payload from over 1000 miles away by sending Morse Code to it. Morse Code might seem like an odd choice for a protocol, but we were required to use it so that other amateurs could communicate with the payload to cut it down if we were in a signaling dead-spot. Another fun fact is that it used a custom-designed Morse decoder that performed pretty near 0dB SNR.
[1]:http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/2005024...
Rank 3, 1,965.23 mi, April 19th 2009, PBH-9 (Cornell U/LM) last known position
Rank 5, 1,259 mi, April 4th 2010, PBH-10
From the article:
Lawrence Richard Walters, nicknamed "Lawnchair Larry", was an American truck driver who took flight on July 2, 1982 in a homemade airship. Dubbed Inspiration I, the "flying machine" consisted of an ordinary patio chair with 45 helium-filled weather balloons attached to it. Walters rose to an altitude of over 15,000 feet. After 45 minutes in the sky, he shot several balloons and descended slowly, until the balloons' dangling cables got caught in a power line. Walters was able to climb to the ground. He was immediately arrested by waiting members of the Long Beach Police Department. "We know he broke some part of the Federal Aviation Act, and as soon as we decide which part it is, some type of charge will be filed. If he had a pilot's license, we'd suspend that. But he doesn't."
"If the FAA was around when the Wright Brothers were testing their aircraft, they would never have been able to make their first flight at Kitty Hawk." Walters committed suicide at the age of 44 by shooting himself in the heart.
* ... captured photographs of the figurine posing with a Canadian flag at 78,000 feet
for me that smells as "assassinated in the woods but the case was never investigated"
Wait, it's the NSA that has the mind control ray...
They "checked to make sure the flight wouldn’t be dangerous or illegal", and they used forecasts from "a website that calculates a weather balloon’s estimated landing spot based on input launch coordinates, prevailing winds, and balloon specs" to time the launch so that the balloon would land in Canada in the US.
http://www.thestar.com/news/article/1120808--toronto-teens-s...
UPDATE: Never mind, I think I found it: http://nearspaceventures.com/w3Baltrak/readyget.pl