When an electronic flash is fired at anything other than full power, it isn't less bright, it is just fired for a shorter duration.  

In other words if you reduce the flash power by half you should half the flash duration and double the "stopping power".

In order to stop humming bird wings, speeding bullets or drops of milk in a saucer, you need

very fast flash durations.

Harold Edgerton used some very powerful flashes at MIT which I have been told were

salvaged from systems used in the war to take aerial photographs at night.

Small shoe mount flashes with very small tubes fire at very high flash durations.

One low budget technique is to use a lot of them.   (My Nikon 

SB-20 fires at 1/15,000 of a second at 1/16th power), However, at such

high speeds you have a problem with getting them all to go off

at the same time.

 Therefore I reasoned that if you got a very high power flash and reduced 

the power to a fraction of its full power, you could get a lot of light in a very 

short time.

I got a Norman LH4000 strobe head which fires in 1/2000 of a second at full power

which is 5000 Watt Seconds.  Logically at 2500 Watt seconds it should fire at

1/4000, 1250 Watt seconds at 1/8000 and so on.

Although I have a photo cell and an oscilloscope, I decided to measure what 

I cared about; stopping power.

Therefore I decided to spin a 16" target disk at 30,000 Rpms.  This put the speed 

of the outside edge at about 2000 ft. per second or about as fast as a rifle bullet.

I promptly burned the brushes out of my Drimmel tool so I moved to a trim router.

The technique was to set the camera up in the dark room, turn the lights out, trigger the timer on the camera and turn the router on.

  Note: at 30,000 rpms the card board disk could probably take your head off.  I was very careful.

I used a Nikon SB-20 shoe mount flash for a reference.  At full power the published flash duration is 1/1200 of a second and at 1/16 power it is 1/15,000 of a second.  I got the following results.

Note that at 1/16 power you can actually start to resolve the test 

target that was glued to the edge of the disk.  Note that the center white

stripe which has straight sides distorts to the shape of a cone because the 

outside edge is spinning faster then the center which has not relative 

motion.  These are exactly the results that I expected.

Now for the Norman studio flash.

Even at 400 Watt seconds where the Norman should have a calculated duration in the 1/15,000 of a second range

it isn't even stopping motion as well as the Nikon at full power and 1/1200 of a second.

I surmise that the problem is that the wave form of the small flash is more nearly flat with straight sides.  While the large flash tube 

takes a while to build to full power and then decay again, giving it a wave shape more like a bell curve.

Published flash durations are measured at T= .5 which I take to mean half way between dark and full luminance.

So even though the Norman T=.5 duration might be as fast as the Nikon shoe mount, the amount of light at the bottom of the bell 

curve is obviously enough to destroy the stopping power.