Hi,
I was testing the current draw from a sample of servos last night, none of them were 'giant' and none of the had a particularly high torque specification.
One of the servos was able to draw 1.5 Amps from four AA Batteries, its highly unlikely you will get this from AAA batteries, its possible from AA's but if your servo really is a giant, you would be much better of with RC Batteries such as the previously suggested D or C cells, look for '7.2 NIMH' there are lots out there. An even better if a little more expensive option is LIPO batteries, these are light, available in more sizes, hold more charge and deliver far more current.
So your options are -
Cheap and cheerful -
- Get some bigger batteries of the type you are currently using
More expensive, higher performance -
2) Get a dedicated hobby battery such as an 7.2 Volt Nimh pack designed for RC Cars - you will need a 5Volt or 6Volt regulator to get the battery voltage down to the servo voltage, there are lots available for around 10 dollars.
3) Get a dedicated LIPO hobby battery, 7.4 to 8.4 volts, also needs a regulator to get the voltage down, but uses the most uptodate battery technology with better performance than NIMH.
Options 2 and 3 require a hobby quality battery charger which also adds to the cost.
A final option is a bench top power supply.
If I get a chance over the next day or two I will post some results from running servos against various battery packs with a load applied.
In the meantime - http://rcarduino.blogspot.com/2012/04/servo-problems-with-arduino-part-1.html
Duane B