Quick! Manual GN question

Two flashes on manual, I know the guide number for both of them, the will both light the same area (more or less, they are both set on wide and will fill more than the angle of view the lens gives), can I just add the guide numbers to get the correct exposure?

Ex, distance 10 meters, flash 1=GN 45, flash 2= GN 64, hence I would get an f/stop of roughly (109/10)~=f./11 ?

no the guide number is

sqrt( 45^2 + 64^2)= 78 so it's f/7.8 or about f/8

okay, thanks!

You don't have to, but if you wouldn't mind, can you explain why the relationship is like that?

OK I will try to explain as I am not good at this.
First I would give you an example just to prove that it works. Take your example but change the flashes to 2 identical units with the GN of 56. Using the formula it came out as 80 for the combined GN. Which give you f/8, 1 stop more than with 1 flash.
The reason has to do with the inverse square law that states that the illumination at the subject is inversely proprotional to distance squared. And so if we are to keep the same amount of illumination but increasing the distance then the flash power has to be increased proportionally with the distance squared. The aperture number in similar fashion that the intensity of the light fallen on the film is proportional to inverse of the aperture squared because light intensity is proportional to the area of the lens opening not its diameter. With this 2 factors the square can be removed and form a simple relationship between distance and aperture. However, when we deal with power we have to put the square back before we can add or mutiply. I hope it helps because like I said I am not good at this.

Hi Chan,

Wouldn't the smaller flash just be ignored as if you were using it as a fill?

Yes if the smaller flash is significantly smaller. Fill light generally in the opposite direction and fill in the shadow of the main and thus doesn't really contribute much to the main exposure. However in this case, the 2 flashes are in exactly the same position and the smaller flash isn't that much smaller than the larger flash. As you can see with the larger flash alone it's f/6.4 and with the smaller flash it's f/7.8. A differenet of 0.57 stop.

Wow, thanks, I suspected it had to do with the inverse square relationship. I blasted the living be jeepers out of an empty parking lot during a rain storm last night. I hope it will come out good. It did in the viewfinder at least.