How does Picard, or anyone for that matter, decide at what warp speed to travel? Obviously there are times when they need to get somewhere in a hurry and he says, warp 9 or maximum warp, but the rest of the time he just seems to pick a number at random. He rolls a warp 6.5 Is there some guide as to recommended speeds that he's following? Is there a speed that is the most efficient?
One major consideration when determining the what warp factor to travel at is energy consumption: starships—even in the 24th century—did not have infinitely renewable sources of energy, requiring massive amounts of deuterium and antideuterium to power the matter/antimatter reaction assembly in the warp core.
A second consideration is the wear and tear on the warp drive: starships, for all their sophistication, are also fine-tuned instruments that will fail under stress, especially under the strain of sustained travel at high warp.
The final consideration, that you touched upon, is the urgency of the matter at hand. The captain must take the previous considerations into account and weigh them on the pressing urgency of the current mission.
So when a starship is commissioned, it's rated for different types of travel:
- Normal cruising speed until fuel exhaustion. On a Galaxy-class starship like the Enterprise-D, this would be Warp 6.
- Maximum cruising speed. Traveling at this speed would be tremendously inefficient, but should cause minimal wear-and-tear. For Galaxy-class starships, this is Warp 9.2.
- Maximum top speed. Traveling at this speed would be inefficient and would not be sustainable after 12 hours due to the damage it would cause to the propulsion system. Warp 9.6 on a Galaxy-class starship.
So when Picard commands Warp 6.5, he's not picking a number at random: he's considered the urgency of the mission and decided that it's worth traveling faster than the normal speeds to get to the destination.
In "Force of Nature", it's determined that high warp speeds harm the fabric of subspace, and the Federation issues a speed limit of Warp 5 unless in the case of a dire emergency. Naturally, Enterprise-D often broke or ignored that limit (episodes are rarely if ever about the non-emergency missions). By the time Voyager was commissioned, Starfleet was able to develop a warp system that overcame this problem by creating a substantial warp field (the movement of the nacelles).
A good engineer always knows how to push the engines beyond their rated speeds: it wouldn't be unheard of for the Enterprise-D to run consistently a notch or two above the rated speeds due to La Forge's engineering skill.
Source for the speeds is from the Star Trek: The Next Generation Technical Manual.
There are almost certainly guidelines laid down for each class of ship regarding energy usage versus travel speed.
As no system is 100% efficient, there will be a law of diminishing returns when picking a warp number to travel at. For instance, Warp 6 under the original scale (it's easier) is approximately 216c. Warp 9 is approximately 729c. So, Warp 9 is approximately 3.375x faster than Warp 6. A system with even, say, 80% thermodynamic efficiency (only 20% lost to entropy) would have to put roughly 25% more energy in than it saw in returns, so travelling at Warp 9 would cost approximately 4.2 times as much energy as travelling Warp 6, for only 3 times the gain. And that's if the system is equally efficient through its performance envelope; usually entropy becomes a larger percentage of input as the amount of energy in the system increases, meaning it might cost 10 or even 20 times as much energy to travel at maximum warp than at the ships "cruising speed" (typically the speed at which the engine is most efficient).
So, the consideration is between speed and efficiency. The faster the Enterprise travels, the more often it will have to refuel, on a disproportionate scale to the number of light-years traveled. Other maintenance will be required more often as well; in the episode where the Enterprise undergoes a baryon sweep, the base engineers state that the Enterprise has travelled more distance (and acquired more harmful subatomic particles) in one year than most ships do in five. However, sometimes you simply have to travel as fast as the ship can take you (such as to drop Deanna Troi's mother off at the nearest starbase).
I agree with the above answers, but I had a few other ideas of reasons not covered in the above that I thought I'd throw out there:
- Sometimes they are on a specific schedule but understand that there can be delays. If they are meeting the Cardassian ambassador somewhere that takes 1 week to get to at warp 9 and 2 weeks to get to at warp 6, they can leave 2 weeks before the event and cruise at warp 6, then if something comes up en route make up time "in the air" by going at a faster speed.
- They're a science vessel, so they're constantly running long-range and short-range scans, gathering data and looking for anomalies and such. It seems very likely to me that if they're just cruising around or they don't have to be anywhere any time soon, they just set the value at the fastest speed they can go while getting thorough scans of the area. Of course, maybe this is way off and you can't even run sensors from within a warp field.