Perhaps acquiring an UPS for your rigs would be profitable in the long term, keeping them mining while you go rearm the breaker?
I think this is a bad idea. If you are tripping the breaker, your are overheating the wiring. You really should wait at least 5 minutes before rearming the breaker.
IlbiStarz needs to put each machine on a separate circuit as far as I can tell. He/she already started the circuit mapping by tripping the breaker. IlbiStarz, you did write down what plugs and lights were on the breaker that tripped, right? For lights you can estimate the power draw by adding up the ratings on the bulbs.
PS: For running off of battery power for any length of time, you probably want your rig to draw less than 60W. I think it may be feasible for me to do some mining using solar power at 12watts. 12 Watts is 288 Watt-hours (1.04 MJ) per day. A 12V battery would need a capacity of at least 24 Amp-hours to supply that much load all day (6 amp-hours for a 48V battery). You will want to be able to fully charge the battery in full sun during the day. To do this, the solar panels must charge the battery within ~8 hours (preferably 6). That will take at least 36Watts (assuming 100% battery efficiency) + the 12Watts you are constantly drawing (48 Watts). Round up to a 60Watt panel. For a 60Watt load, you need to multiply all those numbers by 5 (30 amp-hour 48 Volt battery, 300 Watts of panels).
Why am I bringing this up? A UPS loosing power in the form of waste heat will make the breaker problem worse. Sure, you may be able to run for 5 minutes while the wire cools. But then, you will trip the breaker immediately because your 1600 Watt load will become 2000 Watts as you charge the UPS battery. Note: batteries take at least an hour to charge; if you don't want to degrade them over time.
PPS: power usage for computers is difficult to estimate without actually using a watt-meter. Most power supply calculators online over-estimate the power requirements to sell you a bigger power supply. Cheap power supplies can't even supply their rated power. In other words: if both rigs have approximately the same hardware, they should have approximately the same power draw, despite the power supply ratings.
PPPS: for ball-park, 30W for board + rated CPU wattage + Rated GPU wattages + 6W/ hard-disk).