The Meyer Box: A Fire Sprinkler Layout Theory

Most of my articles don't necessarily break new ground - and that's intentional. There are a lot of people smarter than myself who volunteer for many years to contribute to the codes and standards we have today.

My role, as I've seen it for some time, is helping share lessons learned and my understanding of those topics. When we share our knowledge, we all help create a world a little more safe from fire.

After writing off and on for five years now (woah!), I finally have something that might be a new contribution to the industry. Not in a real or tangible way, but something that may just not have been thought about exactly like this before. I've asked around and I haven't seen this concept out in the world before, so I think this could be something new.

It could also have very well been thought about and published 30 years ago and just got buried in history. If so, I'll disclaim credit.

My father in-law is a mechanical engineer in research and product development, and for years he's help spur ideas and help kick around new things to try. He once said (perhaps jokingly) that to really make a dent in the world you have to name some kind of industry contribution after yourself. 

Well, today's the day. I'm calling this concept the Meyer Box. 

I know, I know. This is so profound and earth-shattering. I'm so glad I've come up with such a great name for what could be my only real new-ground breakthrough to date.

Also, if there aren't enough things named Meyer-something around here, I felt it my duty to throw yet another thing into the mix. So if you were itching for more Meyer, then my friend today is your day.

---

The concept started with the way we lay out smoke detectors. We're allowed to space smoke detectors 30-feet apart, or, as an alternative, any location as long as all points within a room are within 21-feet. I wrote an article about this (often-overlooked) method some time ago.

Sprinkler spacing follows similar logic; except there is an allowable coverage area, per sprinkler, and a maximum spacing that sprinklers can be apart.

Why isn't there some shape for a sprinkler, that if all floor areas are covered in it, that protection is appropriate?

Like all my typical daydreaming, I immediately was forced to spend the rest of the billable hours that day jumping further and further down a wormhole of algebra and confusion.

If you've ever worked with an architect on a sprinkler layout, you know they love to draw circles around sprinklers and spot-the-dot in a very crude way. Is it accurate? No. Does it meet code? No. Does it get them where they need to go? Not really, but they seem to think so.

If a circle doesn't work, there's got to be some natural geometric relationship (a shape) that would work.

That's when I got to experimenting and back to some basic math.

​Light Hazard
Light Hazard rules are basic, and they result in a basic shape. Non-combustible (or combustible unobstructed) standard spray upright & pendent sprinklers get 225 sqft per sprinkler, and a maximum spacing of 15-feet according to NFPA 13.

First, I drew a sprinkler (above). Next, I copied the sprinkler to the maximum spacing for Light Hazard, 15-feet to the right:

What is the maximum distance these two sprinklers can be copied vertically and not be overspaced? For Light Hazard, that's easy - 15-feet. The 15-ft x 15-ft spacing is exactly 225 sqft total, which is right at the maximum spacing per sprinkler:

Now, if we attribute sprinkler coverage to each of these sprinklers, the dividing line would simply be the midpoint between each sprinkler, effectively creating just a 15-ft x 15-ft box around each sprinkler.

For light hazard, this "box" is easily understood, and is basic. Things get more interesting when our coverage area is limited to 130 square feet per sprinkler, like we often see for Ordinary Hazard. 

---

Ordinary Hazard
Using the same approach, let's start with a single sprinkler, ad then copy to a maximum spacing of 15-feet to the right:

Now, in order to not exceed 130 square feet per sprinkler, what is the maximum these two sprinklers can be spaced in the opposite direction? That would be 130 sqft / 15-feet, or 8.67-feet to the north:

Now for the sake of trying to attribute an area to each sprinkler, let's identify the exact intersection of coverage between these four sprinklers. It would be the midpoint of all four sprinklers, here:

Note here that if the north-to-south distance was less than 8'-8", we would still have compliant coverage. This is the maximum spacing between these sprinklers to still accommodate 130 sqft per sprinkler.

But what if our spacing in the east-west direction was less than 15-feet? Say it's 13-feet. Here's where that new midpoint lands:

Keeping that original sprinkler in the same place, we can repeat this process over and over again re-spacing the other three sprinklers in their maximum configuration:

If we keep running this process over and over, we start to see a trend in how this boundary exists:

Around each sprinkler, there's a natural boundary line, where if every sprinkler's box covers the floor area, then the 130 sqft-per-sprinkler coverage area is met.

This new box around the original sprinkler is what we're talking about. If this box stays with each sprinkler, then as long as all of the floor area is covered within a sprinkler's box, the coverage rules are met. Let's look at what this does practically when laying out sprinklers: 

Why would this be helpful?

For one, you can now instantly see whether a layout adequately covers all floor areas. Think less dimensioning and hand-calculating whether a sprinkler is overspaced at 130 sqft.

For two, as you're laying out a system, it's easy to snap to the maximum opposite dimension. In the video above, I entered in 13-feet in the east-west direction, and 10-feet in the north-south direction. That's 130 sqft per sprinkler. However, with this box I could also just select the box and copy from the intersection of the boxes.

Above, this would be a code-compliant layout. There are no gaps in these coverage boxes.

There are exceptions to this to watch, though. Irregular boundaries might be inside a coverage box, but would exceed the maximum spacing or 130 sqft for the sprinkler. 

These are exceptions though, and don't come up often. When I lay out sprinklers I evaluate these one-off scenarios when they crop up, and address them at that time.

Could the same shape be performed for a 100 sqft limitation? Yes, it can. Here's what a 100 sqft limit with 12-ft max spacing would look like:

Mathematically, how are these curves defined?

If a sprinkler is at (0,0) on an X-Y coordinate graph; to get any Y-coordinate on the 130 sqft box the equation would be

Y = 32.5 / X
(where X is the X-coordinate, and is between 4.3 and 7.5).

Why is this a power function? Simple - X x Y = 130 sqft. If we're drawing a curve to represent one-fourth of the overall area, then we take X x Y = 130 / 4, or, rearranged, Y = (130/4x) = 32.5 X.

Where would we draw the line for the 100 sqft box? Similar premise:

Y = 25 / X
(where X is the X-coordinate, and is between 3.9 and 6)

---

Importance
Why is this relevant? 

Having coverage boxes for sprinklers can be a huge time saver if used appropriately. Model these in CAD blocks or Revit families and the time saved on sprinkler layouts and review alone could be major. 

How do I draw these up? Are there familes or CAD blocks I can use? Yes - I've drawn these myself and uploaded the files for paid members here. Just login and download these files.

---

Feedback
Have you used anything similar before? What are your thoughts? Comment on the blog here (www.meyerfire.com/blog) or shoot me an email at joe@meyerfire.com. Always interested in your take. 

​Have a great rest of your week!