**WARNING:**Full understanding of this topic requires at least knowledge of Algebra.

**MATH ALERT!**

I was messing with my 2L homemade again yesterday. I range tested it, and measured with a tape measure for maximum accuracy. It got 43 feet, which is really good for a XP type soaker. I then tested for shot time. It got about 24 seconds, which started to make me think. Only about half that shot past 20 feet. I did the calculations to get output, and it got really pathetic. That was because the drop-off rate in a XP soaker is almost linear. I remember that from the Aqua-NeXuS, back when I was a inexperienced user here. I wanted to see my drop-off rate in a equation, for both output and range. I then output tested it first for 10 seconds, and then for 20 seconds. 10 got 85 ml's a second and 20 got 62.5 ml's a second. Now, those numbers actually are the numbers for 5 seconds into the shot and 10 seconds into the shot, because when you think about it, it is the average output over a period of time. I then took out my trusty TI83+, and used it's LinReg(ax+B) function to find out the drop off rate for the output. LinReg(ax+B) looks at some lists of numbers I entered and turns them into an equation. It spat out y= -4.5x+107.5, where y is the output and x is the time into the shot. 107.5 is the maximum output this soaker can produce, the output once I pull the trigger. Lets call the max output mo for short. I then thought that the range equation should be similar, so I divided 107.5 by 43, the maximum range this soaker can put out, and I got exactly 2.5. Let's call the max range mr for shot. So in this soaker, and maybe all XPs, 2.5mr=mo. I then used this new knowledge to make an equation for the range drop-off, y= -1.8x+43. I think that you are seeing a trend here. I'll explain this:

*max refers to the stat once the trigger is pulled*

mo=max output

mr=max range

odr=output drop rate

rdr=range drop rate

To find the output of a XP soaker, use the equation y= -(odr)+mo

To find the range of a XP soaker, use the equation y= -(rdr)+mr

After than I wanted to find out the full shot time(until no water comes out) exactly. Let's call this fst. I did the math and when output and range = 0, time = 23.89 seconds. Isn't this fun?

I couldn't stop the soaker math. I wanted to find out how the output was in X. So, I looked around and found a bottle. It said that 473 ml = 16 oz. I knew that 1 oz is the output of a XP 70, what X is based off of, so I did a little math. The maximum X of this soaker is 3.6X, and when the output was 85ml's a second, it was 2.9X. So, this soaker has about a 3X nozzle? That's what I guesed when I made it, and it looks like I was right.

I started thinking about how all this info could help soaker mods and homemades. So I figured out the psi in my soaker. I knew that ther was 2L of air when empty in it, and I already measured in the past that the capacity of the soaker was 1.6L exaclty. So I did some more math. The 2L of air was compressed to the size of 400ml of air. So the pressure in there was 5 atmospheres. I did a quick google search and found out that 1 atmosphere = 14.6 psi. So I did 5*14.6 and got 73 psi. I then used that useful LinReg funtion again, knowing that the pressure at second 0 was 73 psi, and at 23.89 it was 14.6(1 atmosphere), and I got the equation y = -2.445x+73 to solve for the psi at any second in the shot. I then looked at the table funtion of my TI83+ and I saw that at 109.67 psi, the range should be 70 feet, and the output would be 175ml's a second. I know that the range won't be 70 feet due to stream breakup, and I also know that that output is only about 6X, but that really is amazing for a XP type soaker, and it is 100% possible. Maybe through better nozzles and rifling this could be achieved...

So what do you guys think about this almost article I posted? I think I'll post it at WWN.