A discone is much more broad banded, and as such, is a better choice when trying cover a wide range of frequencies It has little or no gain because of this, and is a good choice for an antenna in an urban area, where a large amount of gain may overload your receiver.
However, don't let that stop you - a ground plane is a sound, simple choice - and as my old Marine DI used to say (he had retired from Parris Island, and was my first boss in the DP industry)...KISS 'Keep It Simple Stupid' (actually he had something more colorful for the second 's' but this is a family board....) It's much easier to build and won't cost an arm and a leg to get together.
As for the formula - interestingly, the much respected Antenna Elmer website has an online calculator- however, he doesn't lengthen the radials by 5% as the HamUniverse site suggests. I suspect the extra 5% is for pruning to get a good match - not really what we need to worry about here. Here's the URL for that online calculator...
http://www.qsl.net/w4sat/gndplane.htm
73s Mike
[edit] Since we're on the subject of broadbanded antennas, don't forget to look at the AC6V supersite - there are TONS of antenna links there, and I wouldn't doubt that he'd have something on discones. The link is in our Scanner Antennas wiki.
Something else that's quite broadbanded, and has attracted a good deal of attention in the past - the Off Center Fed Dipole. Again, from our Scanner antennas wiki...
http://wiki.radioreference.com/index.php/Homebrewed_Off-Center_Fed_Dipole
Several folks on the Antennas board have built this and had good success with it. The guy that put that article up is a member of this board.
Finally, to divert from antennas for a moment, what about frequencies...again, the Wiki comes to the rescue
http://wiki.radioreference.com/index.php/ARTCC
use the Washington DC page (at the bottom of this page) - the FAA ATA100 freqs are not the most accurate (as has been discussed here, on Larry Van Horn's Milcom blog, and other places) - though I'd take special note of the 'Do Not Publish' frequencies
(edit on that) I've been told by another source that those 'Do Not Publish' freqs are quite outdated - not very surprising - so stick with the data that appears after the ATA100 - and perhaps put the 'discretes' in a lower priority bank, since we're not very sure about how good they are...
http://wiki.radioreference.com/index.php/Potomac_Consolidated_Terminal_Radar_Approach_Control
which covers areas north of you, but with the number of flights coming and going, I have no doubt that you'll hear lots on these frequencies
http://wiki.radioreference.com/index.php/Andrews_Air_Force_Base,_MD
I'm not sure if you're in the flight path of aircraft leaving or going to Andrews, but if you are....'nuff said.