Daniel and his tripod ("The Economist") (promotional still)
As a physicist, Daniel Faraday seemed particularly interested in some of the unique properties encountered on the Island. In the episode "The Economist" in particular, Daniel conducted an intricate experiment while communicating with the Kahana.
"The Constant" experiment
When Desmond suffered from side-effects caused by electromagnetic radiation and leaving the Island, it appeared that his consciousness was transported back in time. In trying to understand his condition, Desmond met a young Daniel Faraday, who was a Professor at Queen's College, Oxford. Daniel showed him a machine he had built, one which he claimed could "unstick" a consciousness within time so that it can travel to different points within a subject's life, in the past or in the future.
"The Economist" experiment
In Daniel's timing experiment, the beacon was mounted on a tripod with a clock on it. He then phoned the freighter, getting Regina. He asked her to send a "payload" in a small rocket to the beacon. Regina did so and began counting down the geographic arrival of the payload in rapid 5-kilometer-steps, starting with 40 km. But when she reached zero, the rocket had not reached the beacon. Regina said that it was "weird" while Daniel responded that it was "far more than weird". The rocket did eventually arrive a while later. He compared the time on a digital clock from the rocket with the one from the tripod and saw that they were different by 31 minutes, 18 seconds. Daniel commented that the result was "not good".
Clock from rocket ("The Economist")
There is a great deal of uncertainty about the velocity of the rocket as it traveled to the Island. Calculations lead to velocities that would seem infeasible given the rocket's construction.
The position of the freighter relative to the Island when the rocket was launched is unknown. The most that can be assumed is that the freighter was between 40 kilometers and 150 kilometers (80 nautical miles). The lower bound is from the countdown to theoretical impact on the Island. The upper bound is from Naomi's report of the position of the freighter when she arrived on the Island.
Daniel's clock ("The Economist")
The payload is a blur just before it slams into the earth. ("The Economist")
At the upper bound of distance, intuition tells us that in the eight seconds between Regina launching the rocket and her breaking the silence and counting down from 40 kilometers away from the island, the rocket traveled 110 kilometers. This means the rocket was going 13.75 kilometers per second, or 49,500 kilometers per hour. The fastest missile ever is said to be the Russian made Topol SS 27, which goes less than 18,000 kilometers per hour. 
- The prop / equipment used to create the beacon is simply a Swann Night Hawk Wireless Outdoor Camera.
- Originally the time difference was only about 31 seconds, but it was later changed before the episode aired.
- For fan theories about these unanswered questions, see: Daniel's experiments/Theories