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A general rule of thumb to use the Shark.
1) Determine the number of LEDs you want to drive in series. Example: 4 Lux3s.
2) Determine the series voltage of the LEDs at the desired current. Example: 1A which means ~4V/LED and 4LEDs = 4 * 4V = 16V (approximately)
3) Determine the operating and min battery voltages using the total Vf output. Operating is > 1/2 output and min is approximately 1/3 Vout.
Operating should be greater than 1/2 of 16 Volts or a fresh battery pack should be 8+ volts.
At end of battery life your battery voltage should not drop below ~ 1/3 Vout or 1/3 of 16 = 5.3V
In this example a 9V stack of AAs batteries or a 12V stack of AA batteries would be fine for this example. What won't work is 2AAs, 4AAs since the current demand will approach the limit of the regulator.
Example 2:
Three low Vf LuxV. say you have 3 LuxVs with Vf of approximately 7V @ 700mA. That's 21V which is below the 22V open circuit protection (with J1 jumpered).
1/2 21V is 10.5V and 1/3 21 is 7V.
A 12V battery pack would suffice for this application. A 9V battery pack would be marginal for this application.