[Note that this article is a transcript of the video embedded above.] If you have a fluid-filled system of pipes in your life, whether liquid or gas, (and who among us doesn’t?) there’s a very good chance that it passes through a simple device at some point on its journey to you. This device is almost unbelievably reliable for a purely mechanical system, and it has changed very little since the mid 1800s. So reliable that there’s a good chance you’ve probably never serviced or replaced one and maybe never even noticed one, despite them controlling so many aspects of our everyday lives. Of course, I’m talking about pressure regulators. But don’t let the jargon bore you, because these things are fascinating. They’re basically Victorian-era mechanical computers, and I cut one in half so we can see how it works. I’m Grady and this is Practical Engineering. “Control theory” is the branch of engineering that we use to describe managing dynamic systems, including the flow of fluids in pipes. I have a bunch of videos and demonstrations of just how dynamic those systems can get. A fundamental idea in this field is that, to garner any amount of control, you need some kind of feedback. And this is not a complicated idea. Say I want to control the pressure in my garden hose. I can put a pressure gauge on it, look at that gauge, and adjust the valve until I hit my setpoint. If something changes, like someone flushing all the toilets in the house simultaneously, I’m the feedback loop. I look at the gauge and make the change to get the pressure back to where it’s supposed to be. In fact, this exact situation (more or less) contributed to the pressure regulation equipment that we know and love today. The legend goes that in 1876, a massive fire broke out in Marshalltown, Iowa. William Fisher, a city engineer, spent all day and all night adjusting the throttle on steam-driven pumps by hand to manage the water pressure in the system to help the firefighters. Exhausted by the effort, he went on to develop the constant pressure pump governor, a precursor to the modern pressure regulators that are absolutely ubiquitous today. And I really mean that. Let’s take a little tour. One of the easiest regulators to find is on an air compressor. You generally want the reservoir as full as possible, which means pressurizing it to a level higher than what you would actually want out of the hose. Every air tool has its own maximum pressure, so you have a knob like this so that, no matter how much higher the pressure in the tank is, you get a consistent and controllable pressure out. If you use pressurized tanks of gas like oxygen, argon, or propane - exact same thing. You’re almost always going to see a regulator on top to control the pressure leaving the tank. Maybe you have a natural gas connection to your house. In most cases, residential plumbing and appliances are designed for very low pressures, like a half a psi or about 30 millibar. That’s great for getting gas from your basement up to your kitchen, but it’s hard to get gas to flow long distances at those pressures, so the lines feeding houses are usually at pressures quite a bit higher. You don’t want high pressure explosive gas in the walls of your house, so it has to be regulated down at the meter. That’s the pancake shaped device you often see outside. Even a standard pressure cooker has a regulator on top. A weight on top of a small pipe balances the steam pressure inside, providing only enough release to maintain a constant pressure inside. It’s not just gases either. The pressure in your water main can be too high for residential plumbing, so you might have a pressure reducing valve on your water service line. Most internal combustion vehicles have regulators that manage fuel pressure between the pump and injectors. And, of course, there are countless industrial applications of pressure regulators used in factories, power plants, and more. If you can find a pipe anywhere in the world, there’s a good chance that, no matter what’s in it, somewhere along it is a pressure regulating device. By the way, the stakes associated with pressure regulation are extremely high, particularly when it comes to natural gas. In 2018, the Merrimack Valley in Massachusetts saw over a hundred structures damaged by fire and explosions, 22 people injured, and 1 dead all as part of a single incident. It all came down to a mistake made during a pipe replacement project that kept the regulators from working correctly. This was a system where pressure was regulated down at a district level instead of each individual meter. The mistake sent natural gas into homes and businesses at pressures way above what the plumbing was designed to handle, ultimately resulting in one of the worst natural gas disasters in American history. I covered the whole story in a video a while back if you want to learn more after this. Here’s the thing: it’s not that complicated to reduce the pressure in a stream of fluid. Basically any kind of obstruction to the flow will do it. A simple way to do it is to put a flat plate with a hole inside the pipe. But a graph will show you why it’s not quite that easy. Let’s assume you have a constant pressure on the inlet side. If you graph the outlet pressure as a function of flow rate through the pipe, you don’t get a flat line, but a curve. And, critically, when there’s no flow, the pressure on the outlet side is the same as the inlet. There’s no reduction at all. If you let the pressure on the inlet vary, things get even more complicated. It’s easy to see why a static device, like an orifice plate, is not a very good regulator. There’s no feedback and no control. You definitely get a lower pressure in some situations, but if you need a consistent pressure that doesn’t exceed some maximum level, this is not going to work. Early gas regulators were bulky contraptions, but actually pretty simple. You could suspend an iron bell in a tank of water. A cast iron cone was attached to the top of the bell, sliding inside the inlet pipe. If the pressure inside the bell rose, it would float upward, pulling the cone too. The higher the cone is, the more restriction you get on the inlet pipe, decreasing the flow to maintain a consistent pressure leaving the device. It’s a pretty clever invention, but not entirely practical. The water level had to be maintained; it could freeze or get gross; the metal corrodes. And importantly, when it failed, it didn’t fail safely. If the bell sprung a leak or the counterweight cable broke, the cone would fall downward, fully opening the inlet. Modern regulators have a few features that improve on the original idea, and I happen to have a natural gas regulator so we can take a look inside. This is a used regulator that probably came from a large commercial building or a light industrial setting. And it’s actually built by Fisher Controls, the company William Fisher started after his firefighting pump throttling experience. Not a sponsor, but I like to think he would appreciate us cutting it up to learn more about it. I tried to be strategic about this to allow a look inside without it completely falling apart. From the outside, it kind of looks like gas would make a straight shot through, but when you cut it open, you can see that there's a separation here where the regulator connects to the line. I have it set where the discharge is pointed down. Gas has to pass through this valve to make it to the discharge side, and you can see that, past the valve, the discharge side is connected to this chamber in the main body of the regulator. Inside the chamber is this flexible membrane called the diaphragm sandwiched between the two sides of the housing. It’s a little floppier than usual, since I cut the whole thing in half, but hopefully you can still see how this works. This regulator has a stiffening plate attached to the diaphragm that acts against a spring at the top. The spring is a little too stiff for me to show you the full range of motion, so I’m going to take the seat off just to demonstrate. Let’s say there’s no demand for gas downstream. In that case, the pressure in the discharge line will build up, pushing the diaphragm upward. The diaphragm is connected to this lever, which is connected to a poppet, which pushes up against an orifice to close the valve, preventing gas from flowing. Let’s say someone opens a valve downstream, like a stove or a heater. As the gas flows out of the system, the pressure in the discharge line will fall, reducing the pressure on the diaphragm. The spring at the top will push the diaphragm down, lowering the lever, and opening the poppet so that gas can start flowing. If the demand increases, the pressure will drop further, lowering the diaphragm and opening the valve even more. And this system will constantly adjust to the downstream pressure, throttling the valve to keep it consistent - a completely mechanical control loop maintaining equilibrium. Any difference in the setpoint and actual downstream pressure creates a proportional movement of the diaphragm and poppet valve. And it’s adjustable too: The compression of the spring at the top can be increased or decreased, which allows you to dial in the exact pressure the regulator will supply. This is just so impressive to me. It’s a dead simple idea, but it does such an important job. But one of the difficulties, especially with natural gas, is that, like all mechanical devices, there’s some friction in the system. I mentioned that the downstream pressure of natural gas is pretty low. This regulator has an outlet range of about 1.5 to 3 psi above ambient air pressure, or about 100 to 200 millibar. Force is pressure times area. If the area of the diaphragm was small, the total force from the gas pressure acting against the spring would be practically indistinguishable within that range, especially when you consider the friction of the lever and valve. That’s why the diaphragm in natural gas regulators is so big. Even small changes in pressure create large difference in force, so you get more sensitivity, and the valve positions are more closely tied to the actual changes in pressure. You might see an issue with this design though: For the valve to open wider to allow more flow, the diaphragm must move down. For the diaphragm to move down, the pressure holding it up (the downstream pressure) must drop. Engineers call this droop, which I love. But there is still some variability in the downstream pressure. Pressure is tied to the valve position, so it’s necessary that it be allowed to fluctuate some. It will never be rock solid in this model. If you need that, the solution is usually a pilot-operated regulator. In this design, the downstream pressure is connected to a tiny, ultra-sensitive pilot regulator, and that regulator basically uses the higher-pressure inlet gas to move the main valve. In this way, you can go from 0 percent to 100 percent flow with almost no change in downstream pressure. Regulators can also be sensitive to inlet pressure. You can see on my model that the inlet pressure acts against the spring to open the valve. Of course the valve is a lot smaller than the diaphragm, so the effect isn’t as big, but there’s still a relationship between inlet pressure and outlet pressure, which isn’t always ideal. A lot of regulators work the opposite way, where the inlet pressure acts to close the valve. If you use a regulator on a tank, this can cause the counterintuitive issue of discharge pressure spiking as the tank empties, since the inlet to the regulator isn’t pushing as hard to close the valve. If you want to reduce this sensitivity, you can use a two stage regulator where you drop the pressure in steps. Let the first stage handle the coarse reduction, providing a more consistent inlet pressure to the second stage which can then keep the discharge pressure rock steady. One thing this regulator doesn’t do is fail closed. If this diaphragm rips, the outlet pressure won’t be able to push it upward to close the valve. So we have to account for that potential in other ways. Lots of gas systems will use a secondary, redundant regulator set to a slightly higher pressure that will take over if the primary fails. There is also a circuit breaker equivalent for gas systems called an overpressure shut-off or slam-shut. This model uses another option: an internal relief valve. Say the pressure on the discharge end somehow got too high. Maybe something got stuck in the valve, keeping it from fully closing. Or maybe the discharge line was exposed to sunlight, expanding the gas inside. In this case, the diaphragm can bottom out and act against this secondary spring, lifting off this plate. Gas is allowed to escape through a hole in the center of the diaphragm into the top half of the casing and out of this vent hole. And here we have another valve called a flapper. It can open inward to balance the pressure inside the regulator. And it can open outward if the relief valve activates, letting the excess pressure escape. The regulator would normally be mounted like this so the vent points downward, keeping rain out. And it has a screen so bugs don’t make a home inside. Obviously, this has some tradeoffs. This regulator has to be mounted outside or be attached to a ventilation pipe running outdoors to make sure it’s not releasing gas into a closed space. Even so, you don’t necessarily want to vent a bunch of natural gas outside. But because of the odorant that’s added to it, the idea is that someone would notice pretty quickly that some part of the system is malfunctioning and shut the line down for repairs. Like every part of engineering, it’s a game of tradeoffs: pressure versus flow, capacity versus cost, accuracy versus redundancy, and safety here versus safety there. I just love that there’s stuff like this out there, pretty much anywhere you’re willing to look, doing an essential job that few people even consider, and that their basic function really hasn’t changed in centuries. Samuel Clegg, one of the early engineers in natural gas systems had this to say about the pressure regulator: “Its use is nowhere sufficiently appreciated. Had it been a complicated piece of machinery, or expensive in its first cost and after application, objections to its adoption would not have been surprising; but it is perfectly simple: its action is certain and unvarying, and its first cost inconsiderable.” Nearly 200 years later, I couldn’t have put it any better myself.

[Note that this article is a transcript of the video embedded above.] I love the periodic table of the elements. I love it because it reveals the deeper order of what seems like an otherwise wildly disparate collection of atoms with different physical forms, chemical properties, and nuclear stabilities. I love it because, even before we actually found the elements that fit into each box, we knew that something did and could even predict some things about those elements before they were ever discovered. And finally, I love it because it’s a bit messy. Not everything lines up perfectly, and in some ways, it’s still a work in progress. In many ways, human-created standards follow that same form, and I want to try and convince you that they deserve the same affection. Let me present the periodic table of standard North American electrical connections. Isn’t it beautiful? I’m fascinated by stuff like this: a diversity of needs and purposes put into a relatively nice, neat order. But why do we need so many? And where do any of these actually get used? Well, I’ve spent the past month reading just about everything I could find on electrical plugs and receptacles to figure those questions out, and I even have a few of them here so I can show you what I learned. I’m Grady, and this is Practical Engineering. Electricity is something we really don’t want to be proprietary. It’s one thing if your charger doesn’t work on your buddy’s cell phone. It’s another thing entirely when you have to rewire your house because you bought a different brand of toaster. The National Electrical Manufacturers Association, or NEMA, was founded in 1926 as a coalition of companies making electrical equipment. Their members realized that life would be better with some standards, so that any company making an electrical device could be reasonably confident that the people who might want to buy that device would be able to use it, and more importantly, use it safely. This didn’t happen overnight. It took a diverse group of manufacturers, engineers, and testing labs to form a consensus around the system we use today. And it’s far from a perfect system. My friends Mehdi and Alec have covered receptacle-related topics on their channels, including the merits and disadvantages of the NEMA designs. But it works pretty well. Well enough that the NEMA connector standards have been adopted not just in the US, but all of North America, Central America, parts of South America, Japan, Taiwan, the Philippines, and beyond. Here’s that table again. You probably noticed that every type of plug and receptacle has its own special number. They seem a bit arcane at first glance, but it’s actually a handy naming scheme that’s pretty straightforward to understand. The first number is the configuration that defines the combination of voltage rating, wire count, and grounding style. These numbers are a bit arbitrary, but they kind of represent a certain class of receptacles and plugs. For example, NEMA 1 receptacles are rated for 125 volts and have just 2 poles (a hot and neutral) with no ground. The NEMA 1-15 was the classic North American outlet until the 1960s, and you still see these in older buildings. Lots of devices made today can still use them, especially low-voltage equipment like chargers, and, critically, those without external metal parts. If an energized wire inside the device comes loose and contacts the case, there’s still an insulating barrier protecting someone from being shocked. The reason NEMA 1 receptacles are mostly a thing of the past is what could happen when equipment didn’t have that protection. If a device with a metal enclosure or exposed metal parts had an energized wire come loose, that metal would be energized too. But, critically, it might not create a short circuit. With nowhere for current to flow, the device could just sit there, indefinitely dangerous, until someone happened to touch it, allowing current to flow through them to a lower potential. The ground wire we see in nearly all plugs and receptacles today fixes that specific hazard. Bonding exposed conductive elements and connecting them to ground makes sure that if they somehow become energized, current will flow, a short circuit will form, and protective devices like breakers will activate. Today we use the NEMA 5 standard for the vast majority of receptacles and plugs. Even if you’ve never heard of NEMA or seen the other plugs on the periodic table, you’re almost certainly familiar with this design. They have a 125 volt rating to handle the standard 120 volt service for most electrical devices with a little buffer. They have an energized pole, called the hot; a neutral pole to provide a return path, and a separate ground return that is bonded to the neutral line in the main electrical panel. The ground pin on most outlets is round instead of flat, and that’s the reason why nearly all electrical outlets kind of look like they’re screaming. Or at least they do to me. One thing about NEMA 5, and actually most of the NEMA configurations, is that the outlets have polarity. On the NEMA 5-15, the neutral slot is a bit wider than the hot, making it so the plug can only go in one way. In function, polarity often doesn’t matter for AC circuits. Current travels in both directions, so the equipment inside the device can’t really tell the difference. And some devices, like switch-mode power supplies, don’t care which direction they’re plugged in. Both blades are the same size. For safety, though, a lot of devices do. You really don’t want heating elements, motor coils, and circuit boards energized and waiting for a ground. It’s less hazardous to put the switch on the hot wire so that nothing beyond the cord is energized until it’s turned on. Enforcing polarity at the plug prevents “switched neutrals” along with other issues like electrical noise. The NEMA 5-15 plug and outlet were designed to be backward compatible with the older 1-15 standard. 1-15 plugs work just fine in the modern 5-15 outlets, and there are quite a few interesting compatibility cases like that in the NEMA standards. For example, the “15” in 5-15 refers to the current rating. Nearly every household device and appliance that runs on 120 volts is designed so that it never draws more than 15 amps, and actually, if the device is meant to run for more than 3 hours continuously, like a space heater, it can only draw 80% of that (which is 12 amps if you’re keeping score at home). That limit is obviously fine for most household appliances. But, especially in commercial spaces, it’s not quite enough power for certain devices like kitchen mixers, treadmills, copy machines, and power tools. Of course, we could just change the codes to require 20-amp circuits everywhere, but that has huge implications: larger circuit breakers, heavier-gauge wiring, and more expensive receptacles. And in many cases, it’s just not necessary. So instead, NEMA created a different receptacle and plug for 120-volt, 20-amp circuits, the 5-20. I have a bunch of these in the studio. You can see they have that T shape on the neutral slot. And 20-amp devices have the neutral blade rotated 90 degrees on the plug. But here’s the backward compatibility: regular 15-amp plugs fit into the 5-20 receptacle as well. NEMA 5 has 30 and 50 amp receptacles too, although they aren’t used very often these days because of a quirk about the historic availability of voltage. Today, split phase electrical service is basically standard for residential power. You get two 120-volt hot lines which can be used individually for smaller circuits or combined to get 240-volts for circuits that need more oomph. In the early 20th century, 240-volt service wasn’t always available, so you have these very-high-current 120-volt receptacles that could power heavy commercial cleaning equipment like floor burnishers and blowers, kitchen equipment like warming cabinets and steam tables, and large shop tools like table saws and compressors. Also, not all portable generators run at 240-volts, so older models used the larger NEMA 5 receptacles as well. These are still available and installed in places where, for whatever reason, a higher-voltage circuit is hard to come by. But in most cases, the more power-hungry devices are going to run on 240-volts. That brings us to NEMA 2. Like NEMA 1, these are ungrounded receptacles, but instead of a hot and neutral, they have two hots. Each is 180 degrees out of phase with its neighbor, so you get 240-volts across them, handled with a little cushion by the 250-volt rating. There were 20 and 30 amp receptacles, but, also like NEMA 1, these are mostly obsolete now that a ground is required by code. They’ve been replaced with NEMA 6, which has 15, 20, 30, and 50-amp receptacles and plugs. Of course, with double the voltage, you also get double the power compared to the NEMA 5 equivalents at the same current rating. The 6-15 is common for window or wall-mounted air conditioners. The 6-20 is used for heavier-duty air conditioners plus commercial kitchen equipment and shop tools. The 6-30 is used with large heaters, kilns, and heavy power tools. The 6-50 is kind of the standard welder outlet, plus it’s pretty common these days for level 2 EV chargers, capable of delivering nearly 10 kilowatts of continuous power through the receptacle. Like NEMA 5, the NEMA 6 has some backward compatibility, allowing 6-15 plugs to fit into 6-20 receptacles. This is kind of clever, but it doesn’t work all the way up the different current ratings. Of course a 50-amp outlet could easily handle a 15-amp device. And it would certainly be possible to design a series of outlets where each successive jump in current rating allowed those smaller devices to plug in. But there are two main reasons why they don’t: One is practicality. The blades on plugs aren’t all the same thickness. Designing a single receptacle slot that can safely grip both a thin, 15-amp blade and a massive 50-amp one would make manufacturing more difficult and increase the chances of developing loose connections inside the receptacle over time. Two is safety: circuit breakers are sized to protect everything downstream, including the plug and the appliance cord. If a thin cord on a low-current device develops an internal short, the resistance of that thin wire itself will cap the fault current so that a larger breaker might take much longer to trip or not trip at all. That could allow the wire to reach high enough temperatures to start a fire. Of course you don’t want a high-current device plugged into a lower-current-rated circuit, but if you trace out the things that can go wrong, it turns out that you also don’t want lower-current devices plugged into a high-capacity circuit. So, the plugs and outlets are designed to prevent both cases, except for the 15 and 20 amp situation, where the current is close enough that a breaker should still work as intended. 240 volts are useful to supply more power at the same current rating, but of course it comes at a cost. Higher voltage means more potential, literally, for arcs to occur. Equipment designed to handle the higher voltage needs better insulation and more careful design. Take a clothes dryer for example. You want the extra voltage for the power-hungry heating elements, but all the other stuff inside (like timers, controllers, and clocks) can easily run on 120 and those lower-voltage components are more affordable. That’s where NEMA 10 came in. You get three poles: two hots and a neutral. In that way, you get dual voltage: 240 between the hots and 120 between each hot and neutral. Of course, NEMA 10 receptacles also lack a ground connection, so they’re mostly obsolete. Plenty of houses still have them installed for clothes dryers and kitchen ranges, but since the 1990s, they’ve been supplanted with the NEMA 14 configuration. This is the most widely-used 240-volt standard in North America today. It’s versatile, providing both voltages. And there are a full range of current capacities, allowing you to design a circuit that’s well-suited for a device, from 15 all the way up to 60 amps. The 14-15 is pretty rare. I couldn’t even find someone making the receptacle. The 14-20 is also not that common. Some food service equipment uses this like certain coffee makers. The warmers rely on 240 volts while the fans and timers run on 120. Same with some jobsite heaters and specialized laboratory equipment. The 14-30 is the standard residential electric clothes dryer plug and is often used for EV chargers. Some server and mainframe equipment uses it as well. The 14-50 is the standard residential cooking range and oven plug. It’s also widely used for EV chargers and pretty common at RV campgrounds as well. The 14-60 is more of a commercial or industrial receptacle, used for large kitchen appliances and distribution of power at events like concerts. Single phase electrical service covers nearly all residential and lots of commercial buildings. But, the grid runs on three phases and it’s pretty common for larger commercial buildings and essentially all industrial facilities to have three-phase service. It’s particularly useful for devices that use large motors. And of course, if you have the service, you’re going to need receptacles and plugs for those devices, or at least the ones that aren’t hard-wired. NEMA 11 was the standard for up to 250V with receptacles and plugs ranging from 15 to 50 amps. Those have been replaced by the new NEMA 15, again because of grounding requirements. And this is going to almost always be relatively specialized industrial devices: woodshop and machining tools, laboratory testing equipment, grinders, pumps, dust collectors, heavy welders, plasma cutters, and so on. It’s not stuff most people see in everyday life, and in many cases, each receptacle is going to be custom-installed for a specific piece of equipment. And since hard-wiring equipment directly to the service panel is typically the default, that makes receptacles like these even more rare. You really only see them in places that need a high degree of modularity, allowing for rapid reconfiguration of workspaces like jobsites, certain manufacturing facilities, and short life-cycle equipment that needs to be easily swapped out. There are two main three-phase service classes used in most commercial and industrial buildings in the US. The most common is 208 volts phase to phase, which uses the NEMA 15 configuration. There’s also 480 volts phase to phase, but like I mentioned before, you can get a lower voltage between phase and neutral (in this case, 277 volts). So NEMA 7 has plugs and receptacles specifically for using just one phase from buildings wired with 480-volt, three-phase service. A lot of commercial and industrial lights use these receptacles, like warehouses, factories, and arenas, making them easy to swap out without hard-wiring. Commercial ventilation and air conditioning systems use them too. And just like the dual-voltage 240-volt plugs, there are also dual-voltage three-phase plugs, delivering equipment with all three hot phases plus a neutral so different components can run at different voltages. NEMA 18 has receptacles for 208-volt service, although they don’t have a ground, so they’re mostly obsolete. There are no straight-blade plugs that have replaced NEMA 18. Aligning and inserting a 5-blade plug would be tricky and take a lot of force. And I’ve kind of buried the lede here only talking about the straight-blade NEMA standards. The reality is that a large number of the NEMA receptacles and plugs have an equivalent locking version. These use curved blades that twist inside the receptacle so they can’t be easily pulled out. Actually the locking versions are more common than the straight-blade equivalents in many cases, especially when it comes to portable generators, jobsite equipment, and events where things are always moving around. If your vacuum cleaner unplugs itself because you’ve gone too far into the hallway, that’s usually not a big deal, but if a three-phase 600 volt plasma cutter does the same thing, you can get serious damage from arcing. That’s why the locking standards extend beyond the voltage ratings of the straight-blade ones up to three-phase 600-volt circuits. They even have receptacles for 400-hertz power used in aerospace, submarine, and military systems. Of course, sometimes the standards make themselves. When it comes to RVs and travel trailers, (from what I can gather) the industry had already developed a 120-volt, 30-amp receptacle before NEMA formalized its catalogue of standards. Instead of forcing an entire industry to retool, NEMA just adopted what everyone was already using, calling it the TT-30. TT for travel trailer and 30 for the current capacity. In function, it’s not any different than the NEMA 5-30 receptacle and plug, but you’ll almost never see one of those, because the TT-30 is far more common. It’s a face only an outlet enthusiast could love. I haven’t really talked about the smaller versions of the locking connectors used where space is an issue. And there are even more specialized standards like ship-to-shore power, aircraft, and military uses. Of course, when you look beyond NEMA, there are way more standards out there. But I feel like this is enough to get you excited about the weird, wide world of electrical receptacle standardization. There are all kinds of practical considerations that make it much more complicated than just a 2D chart with voltage on one side and current on the other. Just like the periodic table of the elements, the NEMA connection standards are a bit messy. And that’s what I love about them.

[Note that this article is a transcript of the video embedded above.] Flaming Gorge Dam rises from the Green River in northern Utah like a concrete wedge driven into the canyon, anchored against the sheer rock walls that flank it. It’s quintessential, in a way. It’s what we picture when we think about dams: a hulking, but also somehow graceful, wall of concrete stretching across a narrow rocky valley. But to dam engineers, there’s nothing quintessential about it. So-called arch dams are actually pretty rare. For reference, the US has about 92,000 dams listed in the national inventory. I couldn’t find an exact number, but based on a little bit of research, I estimate that we have maybe around 50 arch dams - it’s less than a tenth of a percent. The only reason we think of arch dams as archetypal is because they’re so huge. I counted 11 in the US that have their own visitor center. There just aren’t that many works of infrastructure that double as tourist destinations, and the reason for it is, I think, kind of interesting. Because an arch dam isn’t just an engineering solution to holding back water, and it’s not just a solution to holding back a lot of water. It’s all about height, and I built a little demo to show you what I mean. I’m Grady, and this is Practical Engineering. Engineers love categories, and dams are no exception. You can group them in a lot of ways, but mostly, we care about how they handle the incredible force of water they hold back. Embankment dams do it with earth or rock, relying on friction between the individual particles that make up the structure. Gravity dams do it with weight. Let me show you an example. I have my tried and trusted acrylic flume with a small plastic dam. Once this is all set up, I can start filling up the reservoir. This little dam is a little narrower than the flume. It doesn’t touch the sides, so it leaks a bit. The reason for that will be clear in a moment. And hopefully you can see what’s about to happen. This gravity dam doesn’t have much gravity in it, so it doesn’t take much water at all before you get a failure. I’m counting failure as the first sign of movement, by the way. That’s when the stabilizing forces are overcome by the destabilizing ones. And the little dam by itself could hold until my reservoir was about a quarter of the way to the top. Gravity dams get their stability against sliding from… you guessed it… friction. Bet you thought I was going to say gravity. And actually, it kind of is gravity, since frictional resistance is a function of just two variables: the normal force (in other words, the weight of the structure) and a coefficient that depends on the two materials touching. Engineers analyze the stability of gravity dams in cross-section, essentially taking a small slice of the structure. You want every slice to be able to support itself. That’s why I didn’t want the demo touching the sides of the flume; it would add resistance that doesn’t actually exist in a cross-section. The destabilizing force is hydrostatic pressure from the reservoir, which increases with depth. And the stabilizing force is friction. There are some complexities to this that we’ll get into, but very generally, as long as you have more friction than pressure, you’re good; you have a stable structure. So let’s add some normal force to the demo and see what happens. [Beat] You can see my little reservoir gets a little higher before the dam fails, about halfway to the top. And we can try it again with more weight. But the result gets a little more interesting… the dam didn’t actually slide this time, but it still failed. Turns out gravity dams have two major failure modes: sliding and overturning. Resistance to sliding comes from friction, which really doesn’t depend on how the weight of the dam is distributed. That’s not true for overturning failures. Let’s look back at our cross-section. For a unit width of dam, the hydrostatic pressure from the reservoir looks like this. Pressure increases with depth. And the area under this line is the total force pushing the dam downstream. We can simplify that distribution and treat it like it’s a single force, and it turns out when you do that, the force acts a third of the way up the total depth of water. Most dams want to rotate about the downstream toe, so you have a destabilizing force offset from the point of rotation. In other words, you have a torque, also called a moment. The dam has to create an opposite moment around that point to remain stable. Moment or torque is calculated as the force multiplied by its perpendicular distance from the point of rotation. So, the further the center of mass is from the downstream toe, the more stable the structure is, and the demo shows it too. Here’s where we left the weights the last time, and let’s see it happen again. The reservoir makes it about two-thirds of the way up the walls before the dam overturns. Let’s make a simple shift. Just move the weights further upstream and try again. It’s not a big difference. The reservoir reaches about three-quarters the way up before we see a sliding failure, but shifting the weights did increase the stability. And this is why a lot of gravity dams have a fairly consistent shape, with most of the weight concentrated on the upstream side, and usually a sloped or stepped downstream face. Interestingly, you can use the force of water against itself in a way. Watch what happens when I turn my little model around. Now the hydrostatic pressure applies both a destabilizing and stabilizing force, so you get more resistance for a given depth. A lot of deployable temporary storm barriers and cofferdam systems take advantage of this kind of configuration. You can imagine if I extended the base even further, I could create a structure that was self-stable just from its geometry alone. The weight of the water on the footing would overcome the lateral pressure. But there’s a catch to this. This is fully stable now, but watch what happens when I give the dam just a bit of a tilt. All of a sudden, it’s no longer stable. This might seem kind of intuitive, but I think it’s important to explain what’s actually going on. Hydrostatic pressure from the reservoir doesn’t only act on the face of a dam. With smooth plastic on smooth plastic, you get a pretty nice seal, but as soon as even a tiny gap opens, water gets underneath. Now there’s upward pressure on the bottom of the dam as well. If you’re depending on the downward force of a dam from its weight for stability, it’s easy to see why an upward force is a bad thing. And it’s so dramatic in the example with the upstream footing specifically. In that case, the downward pressure of the reservoir is acting as a stabilizing force, but if water can get underneath that footing, it basically cancels out. The pressure on the bottom is the same as the pressure on the top. But this isn’t only an issue in that case. The ground isn’t waterproof. In fact, I’ve done a video all about the topic. Soil and rock works more like a sponge than a solid material, and water can flow through them. That’s how we get aquifers and wells and springs and such. But it’s a problem for gravity dams, because water can seep below the structure and apply pressure to the bottom, essentially counteracting its weight. We call it uplift. Looking back at the cross-section, we can estimate this. Of course, you have the triangular pressure distribution along the upstream face. But at this point you have the full hydrostatic pressure also pushing upward. And at the downstream toe, you have no pressure (it’s exposed to the atmosphere). So, now you have a pressure distribution below the dam that looks like this. Of course, this part can get a lot more complicated since most dams don’t sit flush with the ground, and many are equipped with drains and cutoff walls, so definitely go check that other video out if you want to learn more. But let me show you the issue this causes with some recreational math on our cross-sectional slice of the dam. The taller the dam, the greater the uplift force. That happens linearly. In other words, the force is proportional to the depth of the reservoir. But look at the lateral force. Again, remember it’s the area under this triangle. Maybe you remember that formula: one-half times base times height. Well, the height is the depth of the water. And the base is also a function of the depth. More specifically, it’s the unit weight of water times depth. Multiply it together, and you see the challenge: the force increases as a function of the depth squared. So for every unit of additional height you want out of a gravity dam, you need significantly more weight to resist the forces, which means more material and thus a lot more cost. Hopefully all this exposition is starting to reveal a solution to this rapid divergence of stability and loads as a reservoir increases in height. Dams don’t actually float in space like my demonstration and graphics show. You know, by necessity, they extend across the entire valley and usually key into the abutments on either side. Naturally, that connection at the sides is going to offer some resistance to the forces dams need to withstand. And if you can count on that resistance, you can significantly lower the mass, and thus the cost, of the structure. But, again, this gets complicated. Let’s go back to the demo. Now I’m going to replace my gravity dam with something much simpler. Just a sheet of aluminum flashing, and, to simulate that resistance provided by socketing the structure into the earth, I’ve taped it to the bottom and sides… with some difficulty, actually. When I fill up the reservoir with water, it holds just fine. There’s a little leaking past my subpar tape job, but this is a fully stable structure. And I think the comparison here is pretty stark. When you can develop resistance from the sides you can get away with a lot less dam. But it’s harder than you might think to do that. For one, the natural soil or rock at a dam site might not be all that strong. The banks of rivers aren’t generally known for their stability, so the prospect of transferring enormous amounts of force into them rarely makes a lot of engineering sense. But the other challenge is in the dam itself. Take a look back at this demo. See how my dam is bending behind the force of the water. It’s holding there, but, you know, we don’t actually build dams out of aluminum flashing. Resisting loads in this way basically treats the dam like a beam, like a sideways bridge girder. Except, unlike girder bridges that usually only span up to a few hundred feet, dams are often much longer. Even the stiffest modern materials, like prestressed concrete boxes, would just deflect too much under load to transfer all the hydrostatic pressure across a valley into the abutments. Plus we usually don’t like to rely on steel too much in dams because of issues with corrosion and longevity. So where a typical beam experiences both tensile and compressive stress on opposite sides, we really need to transfer all that load, creating only compressive stress in the material. I’m sure you see where I’m going with this. How have we been building bridges for ages from materials like masonry where tensile stress isn’t an option? It’s arches! The arch is a special shape in engineering because you can transfer loads by putting the material in compression only, allowing for simpler, cheaper, and longer-lasting materials like masonry and concrete. You basically co-opt the geology for support, reducing the need for a massive structure. For completeness’s sake, let me show you how it works in the demo. I’ve formed a little arch from my thin sheet of aluminum. Now when I fill up the reservoir, there’s no deflection like the previous example. And again, side by side, it’s easy to see the benefits here. You get a lot more efficiency out of your materials than you do with an earthen embankment dam or a gravity structure. Of course, there are some drawbacks here. For one, arches create horizontal forces at the supports called thrusts that have to be resisted. Sites that use this design really require strong, competent rock in the abutments to withstand the enormous loads. And just like with bridges, the span matters. The wider the valley, the bigger the arch needs to be, so these dams generally only make sense in deep gorges and steep, narrow canyons. The engineering is a lot more complicated, too. You can’t use a simple 2D cross-section to demonstrate stability. The structural behavior is inherently three-dimensional, which is tougher to characterize, especially when you consider unusual conditions like earthquakes and temperature effects. And since they’re lighter, arch dams don’t resist uplift forces very well, making foundation drainage systems more critical. All this means that it’s really only a solution that makes economic sense in a narrow range of circumstances, one of the most important being height. For smaller dams, the additional complexity and expense of designing and building an arch aren’t justified by the structural efficiency. Gravity and embankment dams are much more adaptable to a wider range of site conditions. And there are other types of dams, too, that blend these ideas. Multiple-arch dams use a series of smaller arches supported by buttresses, dividing the span into more manageable components. Even what is perhaps the most famous arch dam in the world - Hoover Dam - isn’t a pure arch structure. Technically, it’s a gravity-arch dam, meaning it resists part of the water load through mass while also distributing the forces into the canyon through arch action. The proportions are carefully balanced to take advantage of the unique site conditions and relatively wider canyon than most arch dams are built in. And so, when you look at the tallest dams on Earth, one structural form dominates. By my estimation, around 40 percent of the tallest 200 dams in the world incorporate an arch into their design. There aren’t that many places where it makes sense, but when you compare what it takes to hold a reservoir back in a narrow canyon valley, I think the case for arches is pretty clear.