I was thinking releasing the single for free is a great way of getting the music and word out quickly from Beady Eye.

Do you think it will be a free download for a limited time? This way it could still chart and have an additional B-side.

Coldplay did it with Violet Hill

From Wiki -

"The band announced on 28 April 2008 that the single would be released on the official Coldplay website on 29 April 2008 for free for one week before the paid download on 6 May. The song was downloaded for free by over 600,000 people in the 24 hours since it was made available at 12:15 p.m. on 29 April. In the subsequent week, the single was downloaded 2 million times from the Coldplay website.

Coldplay released "Violet Hill" in the US on 9 May 2008 as the album's first single. A promotional 7" vinyl release of the single was given away free in the 10 May issue of NME, including non-album track "A Spell a Rebel Yell" on the B-side. On subsequent physical CD releases, "Lost?", an acoustic recording of album track "Lost!" serves as "Violet Hill"'s B-side instead.

The single debuted on the US Billboard Hot 100 on 24 May 2008 at number 40. The song stayed in the peak position from its release. Three weeks after its release, the track entered at the number nine position on Hot Modern Rock Tracks. The song peaked at number six in Canada Singles Chart and number eight in the UK Singles Chart, making it the second single to reach the Top 10 to have not having a single released physically"