That depends on the battery, how long the lamps will be operated for, the output of your current alternator at the planned operation RPMs, and the load of all other accessories. Figure those lamps will draw about 16-18 amps when both are in operation. If you have an alternator that puts out 100amps at 3000 engine RPM but you drive around at 1500 rpm you are not getting the full 100amps from your alternator. If your alternator puts out 100amps at 3000 engine RPM and your current accessory load is 90 amps (stereo, A/C blower motor, fuel pump, headlamps, engine ECU, etc..), flip on those lights and you'll have a shortfall of juice by 6-8 amps - something a healthy battery should tolerate for a reasonable amount of time. Without knowing what you've got, what condition it is in, and what you're powering it's impossible for one of us to say yes, you need a new alternator, or, no you don't. My guess is you'll be fine.
If you have a 4 liter or a 4 cylinder I think they use the same alternator and they are pretty crappy. I have gone through 4 of them as well as our prerunner and both are differnet brands and vendors. If you get one for a Mazda Navajo I think they are 130 amps and bolt right in. Be sure to get one that you ahve to solder in the lower plug. That lower plug is what "they " say is the problem with them. THe minute I got a good one to last more then a few months, the bearing on it took a [censored]. So get it from a reputable place with a lifetime warranty and then you have no worries cuas you cna jsut keep returning them, jsut dont tell them about the lights and any extra hi amp running gear( stereo, race radio etc..). The place I got mine from switched their policy over from lifetime warranty to limited, but they still warrant mine for life so I am happy.
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Something you may want to consider is getting an alternator out of a wrecked police car-usually they are 100-150 amp and would require new brackets, but they put out lots of power at the lower rpm ranges. Chrysler used to use my personal favorite- a 105A Leece-Neville that put out 105 amps at 2000 engine rpm and 90A at idle speed (750rpm).
If you do a search on "Leece Neville" you can get to their web site (they were purchased a while back by Prestolite, I believe).
If your stock alternator is putting out 60 amps you could only run 720 watts if nothing else was operating on the system. Add a stereo, blower for the A/C or heat, and all the other electronics that are operating while the truck is running and you will overwhelm your battery because the alternator cannot produce the number of amps needed. Keep in mind that unless the alternator is operating at its most efficient speed it will not put out the maximum number of amps. If you have a cheapo battery and start driving around at low RPM with 720 watts of auxilary lighting that will kill it (the battery) dead in a short amount of time, not to mention the voltage will probably drop to the point where things will start to fumble and bumble.
I have a friend that bought a Chevy 1 wire alternator out of summiit and got it to work on his Toyota, pretty inexpensively, although it was an 89 I don't know what the differences are. Had to modify brackets though.
Yes, 720 watts in total. And no, I never thought you had 720 watts of lights on your truck. You are only running 520 watts in lamps alone, minus your marker lights and brake lights (low watt). Your system is probably right on the edge of maintaining adequate battery output with all the lights on and everything else running. What I was originally trying to say is that with a 60 amp alternator you can support a maximum of 720 watts at maximum alternator output without tapping into the battery power. No more on this subject from me...
I have a tacoma 3.4L V6 and I want to run 3-130 watt Hella 8" lights. I dont even know what the output of my stock alt is. I currently have a Optima deepcycle battery, and am planning on adding another soon. one will be used for starting, while the other for running the truck while the 1st gets recharged. Do I need to get a higher output alternator? I have a stock AM/FM radio, but also run a race radio. I am planing on racing, so I will have some more goodies added later.