Until the introduction of the Intrepid Class Starship (Voyager et al), the Oberth Class was the workhorse of the Federation science fleet. With sensor capabilities far outstripping even the most sophisticated of sensor suites equipped on more run-of-the-mill starships, the Oberth Class was designed to measure...well, everything. It would function well as a reconnaissance vessel during wartime were it not for its mediocre shielding system, pitiful top speed and limited defensive capabilities. As it is, Oberth Class starships function beautifully as peacetime science and low warp exploratory vessels.
The Oberth Class made its first appearance as the USS Grissom in Star Trek III: The Search for Spock, charting the development of the genesis planet. From that point on, ships of this class were seen fairly frequently on The Next Generation, generally as the ships the Enterprise-D had to go to extraordinary lengths to rescue from subspace anomalies, rifts in the space-time continuum, extremely virulent diseases and what have you.
Hull configuration
The saucer section is tiny, comprised of three or four decks. An impulse engine extends from the back of the saucer and the warp nacelles are mounted at the saucer's port and starboard sides. Extending down from the nacelles are two cantilevered struts that connect to a large, strangely aerodynamic-looking pod that contains a massive sensor system and extends far aft of the primary hull. The actual deflector dish is contained internally at the front of the sensor pod. How this works, I have no idea.
The class is a total departure from what we know of Federation starship design. Nevertheless...the spaceframe makes very little sense. There's no easy way to get personnel from the primary hull to the sensor pod. There's also no way to get the deuterium and antimatter stored in the sensor pod to the warp nacelles. It has been suggested that turbolift shafts and fuel conduits run down the support struts between the two hull sections. Fuel lines, I can buy, but the angles are all wrong for a turbolift - the cabs would enter the sensor pod horizontally. It would take an immense feat of engineering to make that work, a feat that wouldn't be necessary with a more unified spaceframe structure.
The only reason to separate the sensor pod in this way would be to avoid Electromagnetic interference produced by the ship's systems to obtain a clear sensor reading. This is pure speculation.
Weapons and Armaments
None. Ok, that's not strictly true - there are a few phaser emplacements located around the saucer section, but they're mostly for scientific purposes. The class has no photon torpedo capability and is a sitting duck if attacked. This would be fine, except that ships of this class seem to get the crap beaten out of them on a pretty regular basis. It's mostly for this reason that they have been superseded by the Intrepid Class.
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A noder says "Just one more bit of speculation on my part: perhaps the sensor pod is designed to be released and jetissoned in case of accident? I suppose if you *really* need to get down there you could use the transporters. Keeping everything dangerous (antimatter fuel and ultrahighpower sensors) in one place let's just get rid of it all at once in case of any emergency. And if these are short range ships, help would just be a couple days away."
Their point is valid, and I have a few more of 'em: intraship transport was considered dangerous during The Original Series and I'm not sure whether they'd fixed that problem by the time this class came into service. Also: I said the ships were short range, but that's a bit inaccurate - they're not short range, they're low warp. With the amount of fuel contained in that storage/sensor pod, their range is pretty standard for a starship and excellent for a ship of that size. (which reminds me - I forgot to mention exactly how small the thing is - it's 120 meters long).
There's one added benefit of being able to jettison the sensor pod: Federation security. There's a good chance that the sensor systems on this class of ship are classified. In the event of imminent capture, it's possible that the secondary hull could be jettisoned and set to self destruct at a safe distance.
(just thinkin', is all)