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I've been reading articles that talk about using multiple strobes next to each other, all pointing in the same direction: as a means to add more light over what one flash can do.
Does the addition of another strobe directly add to the light such that one more strobe provides twice as much light, and two more provides three times as much, and so on and so forth?
If this is the case, is there a point of diminishing returns, and if so, where is it?
The amount of illumination increases as you add more strobes, but not linearly. The point of diminishing returns is, basically, right away. This is because flash power is proportional to the square of the guide number. Or to look at it the other way around, the guide number is related to the square root of the flash power. Why all these powers and roots? It's the inverse square law in action.
Practically speaking, this means that when you add another flash, the resulting guide number is the square root of the sum of the squares of the guide numbers of each individual flash.
For example, if you have two flashes with guide numbers of 36, the resulting guide number is about 51:
sqrt(36²+36²) = 50.91...
Or, if you mix a relatively powerful flash with GN 50 with a little GN 20 unit, you get a very unimpressive-sounding increase:
sqrt(50²+20²) = 53.85...
It logically follows that if you want to double flash power, you need four of the same flashes. For example, with some hard numbers:
sqrt(36²×4) = 72
So, basically: increased power gets expensive quickly. This is true whether increasing the power of a single flash or adding in a second — the math is the same. To increase the guide number — the distance to which you can cast a useful amount of light — by a small amount requires an ever-increasing amount of additional power.
The main advantage of multiple flash units is the ability to shape light and shadow. That little GN 20 flash might not add much sheer brightness, but it could soften shadows or add a sparkle to someone's eyes.
You mention in a comment that you want to overpower sunlight. I made some charts for another answer which also might be useful here:
First, the sun is bright:
People often underestimate the difference between indoor lighting and sunlight, because our vision system is great at adjusting to be (relatively) comfortable in both situations. So, while a flash may be powerful indoors, it takes a lot to overpower the sun, as you want to do:
Basically, to really overpower the sun, you need a lot of power (or to get much closer).
Yes, adding strobes does add to flash power, but you'll encounter the inverse square law - doubling flash power only increases distance that can be lit by 1.41 times. Three flashes will illuminate 1.73 times further than one (1.22 times further than two). To double the distance, you'll need to quadruple flash power - and it's only 1.15 times further than you got with three flashes. So yes, adding flashes one by one does have diminishing returns - you'll need to double the amount of flashes to get the same effect that you got on previous step. You'll get most effect out of the first flash, each next one will have less impact.
If you don't want to have higher flash power for longer distance, but lower ISO or smaller aperture, the same law still applies. You must double your lighting to get one stop advantage in ISO or aperture.
The only areas you can expect roughly linear return in is recharging time and battery life - if you use n flashes instead of one at n times less power, they will recharge about n times faster and last for n times more shots.
Yes, it is true, as long as we are speaking of the same distance between flashes and subject. The answer to the question about diminishing returns depends on what do you want from the quality of light, as opposed to the quantity of light. For example, two speedlights put next to each other tend to result in a nasty double shadow and so on. With today's technology, it is hardly the amount of light that gets on the way, it is rather the way the light can be directed and modified.
Adding another identical flash will double the amount of light the flashes give, this in turn will double the amount of light hitting you subject (compared to the exact same setup with just one flash)- but it will not double the range or guide number of the flash (as everyone else said you need 4 flashes for that)
The more flashes you add, the more light you get, and this is linear.
If you want to keep the illumination constant changing distances or you use different lights modifiers, filters, pollarizers, etc., then yes, you would have to consider the inverse square law, and many others things that have been pointed in some comments.
