I always get flight prior to motorized transportation and I find getting a stack of bombers is vital if you are going to wage war in the time period between replaceable parts and motorized transport-- I find by the time I have flight I have a few cities capable of building bombers in 2-3 turns, so within 3-4 turns of getting flight I am able to use bombers where they are needed... bombers make it possible for cavalry to take down cities defended by infantry without losing more units than it's worth. Angmar is right, 1 bomber is useless but 10 are very helpful. I often use even more than 10; once I get flight I usually have a reasonably sized cavalry army already so I focus my unit production on bombers... by the time I switch to tanks (depending on the game this can be anywhere from 8 to 20 turns after I get bombers) I have a reasonably sized bomber fleet capable of doing a number of important things that artillery is capable of doing, but without the need to protect them with additional infantry that would be needed with an army of artillery.
Once tanks do come along, I find bombers are essential in minimizing my tank losses (lots of people will say to just build a ton of tanks and throw them at your opponent, but in my experience I find the cost of the bombers more than compensates for the tanks I would have lost in a situation aimed at overwhelming an opponent). Anyway, you can argue that anythign a bomber can do (with a bombard rating of 8) a unit of artillery could do better (with a bombard rating of 16, and 20 shields cheaper). However, artillery armies tend to move slowly and always need infantry escorts; bombers speed this process up greatly allowing you to take more cities per turn than you are capable of doing with the limited mobility of the Infantry/Artillery combo.
I imagine if you were to do a cost/benefit analysis of the damage caused by a bomber compared to that of artillery (taking into consideration infantry, even) the artillery would end up cheaper as its bombard rating is significantly better, but the added cost of the bombers is more than accounted for in the speed with which you can transport bombers and easily conquer entire regions of the map, averaging more cities per turn.
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As for recon missions, it can be helpful to probe enemy borders and find out what units they have heading for your borders without actually risking a unit, many times (playing in prince) I'll get flight and have a few planes while the computer is still upgrading its defenses, it can be nice to know which cities on the borders are protected by infanty and which ones are still protected by ... spearmen or whatnot
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Let me know if im way off the mark
