The Magic Air comes in at least two 110v versions: DIDA2 and DIDA4 The DIDA4 takes 11.25 amps at 110 volts to operate. Thats ~1200 watts. 1200 Watts at 12 volts is 100 amps. The DIDA2 takes takes 7.5 amps at 110, or 825 watts, which requires 68.75 amps. If your inverter only has a 40 amp fuse then the most that it could sustain is 40 x 12 = 480 watts, which would only provide 4.3 amps at 110 volts. The situation gets worse if the wiring to the inverter is a little under sized and there is a voltage drop. If the voltage drops to 11 volts then the maximum power you can sustain on a 40 amp fuse is only 440 watts. To further confound things, the inverter is probably only about 80% efficient, so to get 800 watts to the inflator would require drawing 1000 watts from the battery, which at 11 volts would require 90 amps. If you want that inverter to operate reliably then you need to supply it with a much larger current capacity. I would follow the manufacturers recommendation and use a 200 amp fuse with wires that will handle that load (like, #2 awg) and keep the wires as short as possible to the battery.
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