Finding the most remote point to the nearest exit

Everytime I draft a fire safety plan and show travel distance to an exit, this question comes to mind…

Is there a technique using geometry to determine the most remote location of a space to the nearest exit? Most times I will pick a point in a space that I THINK is the most remote point to an exit and show the travel distance, but I am hoping someone on here has a technique they use to find the exact point where this occurs in a space.

Thank you!

 

[walker.t]

Is there a technique using geometry to determine the most remote location of a space to the nearest exit? Most times I will pick a point in a space that I THINK is the most remote point to an exit and show the travel distance, but I am hoping someone on here has a technique they use to find the exact point where this occurs in a space.

Not sure what you mean when you say a “technique using geometry” to find the most remote point in a space. I’ve always used a point in the corner of the room farthest from the door then set that point about 12” from the adjacent walls. I’ve always done it “by inspection” - just kind of look at the plan and use my best judgement. If you’re not sure about which point is actually most remote you’ll have to trace the paths from those points to confirm which is the longest.

As far as “techniques” related to travel distance, the closest thing to a “technique” I’ve heard of was something a code official told me, he said that I should draw the route parallel to the walls and not use a line from the most remote corner of a room straight to the door. The 2018 International Building Code Illustrated says a few things which may be of interest to you:

1. “Travel distance is one of the most difficult features of the egress system to determine in either the design or the plan review stage.”
2. “The preferred approach, conservative in nature, would dictate using the right-angle method for measuring travel distance.”
3. “Care should be taken to measure the travel distance in a manner that best represents the actual means of egress through the space.”

See also this post:

Measurement of Common Path of Travel Distance

Are there more specific instructions on how to measure this distance apart from this definition? For example, if you have a corridor that is 8' wide, does your measurement line need to be in the center, or can it be a certain distance from the wall?

www.thebuildingcodeforum.com

In that post Yankee Chronicler shares a commentary that is similar to what I found in the Illustrated Handbook. He mentions taking the measurement down the center of corridors, that’s what I’ve done in the past, in the room I generally run the line about 12” away from the wall.

 

[BrendanLead]

Not sure what you mean when you say a “technique using geometry” to find the most remote point in a space. I’ve always used a point in the corner of the room farthest from the door then set that point about 12” from the adjacent walls. I’ve always done it “by inspection” - just kind of look at the plan and use my best judgement. If you’re not sure about which point is actually most remote you’ll have to trace the paths from those points to confirm which is the longest.

As far as “techniques” related to travel distance, the closest thing to a “technique” I’ve heard of was something a code official told me, he said that I should draw the route parallel to the walls and not use a line from the most remote corner of a room straight to the door. The 2018 International Building Code Illustrated says a few things which may be of interest to you:

1. “Travel distance is one of the most difficult features of the egress system to determine in either the design or the plan review stage.”
2. “The preferred approach, conservative in nature, would dictate using the right-angle method for measuring travel distance.”
3. “Care should be taken to measure the travel distance in a manner that best represents the actual means of egress through the space.”

See also this post:

Measurement of Common Path of Travel Distance

Are there more specific instructions on how to measure this distance apart from this definition? For example, if you have a corridor that is 8' wide, does your measurement line need to be in the center, or can it be a certain distance from the wall?

www.thebuildingcodeforum.com

In that post Yankee Chronicler shares a commentary that is similar to what I found in the Illustrated Handbook. He mentions taking the measurement down the center of corridors, that’s what I’ve done in the past, in the room I generally run the line about 12” away from the wall.

Thank you for the response. I understand how to calculate the path of travel and how to account for potential furniture etc, it's primarily trying to determine the actual most remote location from the closest door. In my case, I'm designing a 135,000 sf indoor rec facility that's being designed as two buildings due to use plus max allowable sf of a building based on construction type. I have attached a pdf of the life safety plan for reference. The large open indoor turf field has numerous egress doors around the perimeter, so somewhere in the center of the space is the furthest travel distance to the closest egress doors.

Many years ago an architect showed me a method using a series of triangles to determine the actual furthest travel distance but I can't seem to remember it. I can eyeball it and verify to the best of my ability, but I'd like to know if there's a simple way based on geometry to determine that point.

Thank you.

 

[wwhitney]

If you have a rectangular room, and you are only allowed to travel on paths parallel to one of the walls, then measuring distance between two points this way is called the "taxicab metric." That's named after the idea of a taxicab traveling through a square grid of city streets.

If your rectangular room is free of obstacles and you're away from the walls, then the "circle" of radius r around a given starting point (the points in the room at most a distance r away in the taxicab metric) is a diamond shape (a square with sides turned 45 degrees relative to the rectangle's sides) of diagonal length 2r. If your center point for that "circle" is a door on one of the walls, then only half the diamond is inside the room (as long as r is less than the distance to the corner).

So conceptually, you can think of a little movie or animation where at time t you draw the half-"circles" of radius t around each of the exits. As time advances, these half-"circles" cover more and more of the room. Visually, this is like wave fronts on a pond expanding from each starting point (exit), but in diamond shapes rather than the usual circles. At some value of t the very last point of the room is covered. The location(s) last covered is the most remote point(s) in the room from the exits in the taxicab metric, and that value of t is the distance from that point to one or more of the exits.

This is hopefully a useful way to think about the problem, but it doesn't give you a direct algorithm for finding the most remote point. It does provide you a way to check a guess, though--given the guess, you get a distance, and given that distance, you can draw the "wavefronts" or half-"circles" or half-diamonds around each exit for that distance. If your guess is conservative, those will cover the entire room. And if your guess is sharp, either two of those wavefronts will have just met at some point or line that is the farthest distance, or one of the wavefronts will have just hit some corner.

If your guess is close but not sharp, you'll find that your point lies between two wavefronts that have swept past each other. If they are parallel lines then half the distance between them is how far you've overestimated (assuming this is the thinnest area of double coverage).

I'll think a little more about an algorithm to directly give the farthest point without guessing, and post if I come up with anything.

Cheers, Wayne

P.S. If each exit from the room was itself a different distance from some exterior exit that you need to add to your actual calculation (no idea if that is what the building code may require), then you can do something similar, conceptually. The "wave fronts" at each door would not all start at time t=0, but instead at a delay equal to the additional distance you need to add if exiting via that door.

 

[Yankee Chronicler]

The triangle method only works for large spaces, such as big box stores. For a building such as an office building or a school, with a number of individual, smaller rooms occupying a floor plate, the only way is trial and error. You pick what looks like the most remote point and check the travel distance to the two exits nearest to that point. Then you check the most remote point in the room on each side to verify.

 

[wwhitney]

I'll think a little more about an algorithm to directly give the farthest point without guessing, and post if I come up with anything.

So I think the following should work for a room with no obstacles, although I've not gone through and rigorously proved it. We can approach this by steps:

Step 1: A polygonal room with one exit. Then we just need to check the corners of the room to find the farthest one.

Step 2: A polygonal room with two exits. We're going to draw a possibly zig-zag line across the room that separates the part of the room closer to one exit from the part of the room closer to the other exit. Then consider each side of this separating line as an example of Step 1, and find the farthest point within each side. Compare the two; the farther one will be the farthest point.

To find this dividing line through the room, draw the line between the two exits, and find the midpoint. This is a point that is equidistant from each exit under the taxicab metric, for some distance d. Draw the diamond of distance d (which I previously called a "circle") around each exit; our midpoint will lie on each diamond. Where the two diamonds coincide, that line segment (if not just a point) is on our dividing line. Where part of the room is outside of both diamonds, the two diamonds will meet at a 90 degree angle on the boundary of the region outside the both diamonds. The dividing line will extend out of that corner bisecting that 90 degree angle.

Step 3: A polygonal room with more than two exits. Look at all pairs of exits, and construct the dividing line as in Step 2 for each pair. The farthest point should be one of the corners of the resulting polygons within the room.

Cheers, Wayne

 

[walker.t]

Thank you for the response. I understand how to calculate the path of travel and how to account for potential furniture etc, it's primarily trying to determine the actual most remote location from the closest door. In my case, I'm designing a 135,000 sf indoor rec facility that's being designed as two buildings due to use plus max allowable sf of a building based on construction type.

Thank you for the clarification, knowing now that you have multiple exits helps me see why finding the most remote point is not as simple as I had pictured in my mind.

I have attached a pdf of the life safety plan for reference.

Here’s a cropped view of your plan, hope you don’t mind my sharing a few comments but I noticed a couple things for your consideration:





1. Turf Playing Field (Room 101) 220’ “travel distance.” I assume you are referring to the exit access travel distance when you say “T.D.” in the symbol. But Lobby (Room 100) doesn’t appear to be an exit component of the means of egress (no indication of fire-rated separation around it or fire-rated doors.) Wouldn’t your travel distance from the playing field room go to the exterior doors in the lobby? If the exit access travel distance stops at the fire wall then I would assume you’re using a horizontal exit, but I don’t see any indication of or calculations regarding the refuge area required by 1026.4 if that’s what you’re thinking.
2. Both restrooms shown on this plan have six or more lavatories. All the lavatories look the same, I would expect one in each restroom to look different to indicate that it has the enhanced reach range required by 1109.2.3 and A117.1 606.5.
3. Do you need an ambulatory accessible toilet stall in the men’s restroom? 1109.2.3 says that when the total of toilets and urinals is six or more that 5% have to be ambulatory, but it doesn’t say “but not less than one” in regards to the ambulatory stalls. You do show an ambulatory stall in the women’s restroom.
4. The doors in the wheelchair accessible stalls should be located in the corner diagonally across from the toilet per A117.1 604.9.3.1 which refers to Table 604.9.3.1.
5. Regarding the drinking fountains, I assume one is low for wheelchair access and the other is high for standing use. I don’t know what your standing use drinking fountain looks like but it will be considered a protruding object if the bottom edge is above 27”. Here’s a link to the U.S. Access Board guide on that:

U.S. Access Board - Chapter 3: Protruding objects

The U.S. Access Board is a federal agency that promotes equality for people with disabilities through leadership in accessible design and the development of accessibility guidelines and standards for the built environment, transportation, communication, medical diagnostic equipment, and...

www.access-board.gov

6. Is the door to the women’s room allowed to overlap the door maneuvering clearance for the door into the janitor’s closet? I don’t know the answer to that, A117.1 doesn’t tell us what door clearances can overlap like it does about the floor clearance at toilets.

 

[mtlogcabin]

The janitors closet is not an occupiable space IMHO and therefore is not required to be accessible

 

[walker.t]

The janitors closet is not an occupiable space IMHO and therefore is not required to be accessible

Definition of “occupiable space” is:

“A room or enclosed space designed for human occupancy in which individuals congregate for amusement, educational or similar purposes or in which occupants are engaged in labor, and which is equipped with means of egress and light and ventilation facilities meeting the requirements of this code.”

The mop sink tells us that someone will be spending at least a few minutes in the room doing some sort of work or preparation for work. As far as light and ventilation, the room is large enough they’ll put in a light, I would think there’s probably not a supply air duct in the closet.

I personally don’t have a big problem with the women’s room door overlapping the door clearance at the janitor’s closet. I only noticed last fall that A117.1 404.2.3 doesn’t give a detailed list of what may or may not overlap the door maneuvering clearance. By comparison, A117.1 604.3.3 provides a nice list of things that can overlap the floor clearance at toilets.

 

[Yankee Chronicler]

I think spaces such as janitor's closets, store rooms, and toilet rooms are considered to be "not normally occupied" spaces. Those are the types of rooms and spaces that are not allowed to open directly into an exit enclosure.