Wednesday, January 23, 2019

Shower Design, Tradeoffs, and Gift Horses

The nice thing about the shower in the hotel room where I recently spent a few days was that the enclosure was quite long, long enough so that towels hung up at one end of it were a safe distance from the shower head at the other end. Also, and more important, long enough so that I could use the shower control at one end of the enclosure while a safe distance from the water at the other end whose temperature I was adjusting. That eliminated the usual problem of getting frozen or scorched while getting the water to my preferred temperature.

The not nice thing about the shower was that it took a long time for the temperature of the water to respond to a change in the control, which made the whole process of adjusting the shower to my preferred temperature more difficult than usual.

It eventually occurred to me that these two features were connected. The farther the control is from the shower head, the longer the pipe between them. The longer the pipe, the longer it takes for the changed mix of hot and cold water to get from the control to the shower head, hence the slower the process of adjustment. The feature I did not like was part of the cost of the feature I did like.

This is one example of a general point. Consider any system—a shower, a car, the human body—that has been optimized. If changing the system in some way, in my example moving the control farther from the shower head, produces a benefit, it must also produce a cost—otherwise the change would already have been made in the process of optimizing the system.

The human body has been optimized by evolution. But the purpose it was optimized for, reproductive success, is not my purpose. Hence there might be changes to be made that are to me unambiguous improvements—dollar bills lying on the pavement to be picked up. Still, it is prudent to suspect any obvious improvement of a downside. 

Many years ago my father decided to stop using the phrase "there is no such thing as a free lunch" on the grounds that it was not literally true—consider consumer surplus and producer surplus. If someone pays me a thousand dollars to give a talk I would be happy to give for free, I have just gotten a thousand dollar free lunch.

His substitute: "Always look a gift horse in the mouth."


William H. Stoddard said...

After thinking about Israel Kirzner's book Competition and Entrepreneurship for quite some time, I realized that Kirzner's analysis implied that there are free lunches all over the place, and that entrepreneurs are the ones who watch for them and eat them. TANSTAAFL really only seems to apply in an economy at equilibrium; and while that's a useful intellectual construct, it doesn't describe market economies at all well.

TruePath said...

Yah I recently spent some time thinking about this and I really want a digital shower control that can remember the temperature I want and adjust the mixture in real time to retain that temperature. By making it digital one could put the actual valves right behind the shower head in the wall and the control panel wherever you want.

Anonymous said...

I makes me very sad that the late Milton Friedman was "found deceased in shower". Milton is extremely intelligent and his beliefs may have made enemies of crooked politicians that benefit from his demise.
I call it a conspiracy. The day he was found dead he was to deliver a speech, but he never made it out the door. The police didn't even investigate the death of one of the most important figures in history. He had decades of life left.
In the far future if mankind becomes space-faring, we need to devise a time-machine to clone or to bring Milton back to life.

Fortnit said...

This does not pertain the moral of the story, but they do make hot water circulation systems in homes , where the water does not get cold, and it is also possible to install electric water heaters next to the bathroom or kitchen sink. These have instant hot water and it does not run out. There is only the cost of buying an addition electric heater to have it specifically used for the individual bathroom.
Many hotels on the other hand are built for pure profit, they care little,or are ignorent of long term costs or small comforts over fast and cheap solutions. They will use the lowest bidding contractor, painting and to coverup all the shortcuts they used.

As for the saying there is no such thing as a free lunch, that can be ambiguous, but it still remains true. There is no such thing as free, it is the 2nd law of thermodynamics. You may perceive something to be free, but your opinion would be false. You received something free at the cost of someone else. He would have had producer surplus as he would have been willing to pay $2000, but it was never free, and that speech you would give, that is your life energy, your brain power, your time spent. Doing nothing is technically not free! Any choice means there is a alternate dimension where you did something else.

I had to do a search on what a gift horse mouth is, what an absurd expression. It is meant to imply that gifts shouldn't be measured in value, just be grateful for the gift, especially in the presence of the gifter. But anyone who values anything should and will measure it when the gifter has left the room.

Paul Sand said...

I'm too improvement-averse to get one, but this looks like the kind of thing Peter Gerdes wants: Charmingwater Shower Mixer Valve with LED Digital Display, LED Digital Fahrenheit Display Bathroom Wall Mounted Shower Mixer Valve Control Ceramic Valve, Brushed Nickel

Gordon said...

Point taken, but the solution in the shower case is to build the shower wide enough so that you may stand to the side while adjusting a close-to-the-shower control. For shower/tub combinations (by far the most common situation in hotel rooms), however, this significantly increases the size of the tub. Although, that, too, may have value.

Are you willing to pay more for a room with this feature? Who will begin the market discovery process?

Sound and Fury said...

This seems related to the Algernon Argument about why interventions like supplements and nootropics are so limited in their effect.

As for the showers, there's no need for Peter Gerdes' digital suggestion — why not just have a mechanical linkage between the controls and the valves? For waterproofing's sake, I'm imagining something like the cable-in-tube system used for the brakes and gear-change on bicycles.

Fortnit said...

@Sound and Fury - thank you for your comment! I did a search on your topics and learned very much!

Actually I just read the first google link and the first few paragraphs from the linked article.

Last year, Elon Musk made ridiculous statements about simulated universes. Regarding that possibility, in the far future it would be nice to have computer models and simulations which could play out all the results from the smallest enhancements or changes in a system. Like what if you did increase the life span of a population or raise its IQ. Have a computer play out the results and show it to us in 5 seconds, show us the results of a trillion variable, and in a snap of a finger, you would see the the results instantly of instead of having to wait out centuries to see what would happen in real life. Science fiction.

On the other hand, in China, scientists working to cure many diseases just recently succeeded with "gene-edited donor monkeys using CRISPR-Cas9 to edit the BMAL1 gene of in vitro fertilized monkey embryos."
Then there are already plans of making new laws banning that type of research.
Even though the implication is that the concept that is may be possible to eradicate genetic defects to making humans more intelligent, healthy, and longer living.

Big government and Christian fundamentalists have routinely held back the progression of mankind, from "On August 9, 2001, U.S. President George W. Bush introduced a ban on federal funding for research on newly created human embryonic stem (ES) cell lines." to "In 2000, the U.S. Congress authorized the modernization effort, GPS III. During the 1990s, GPS quality was degraded by the United States government in a program called "Selective Availability".
A senator purposely made it so that GPS would be highly inaccurate by 10 miles, at the cost of what?
Because of politicians crippling service and restriction,
"Korean Air Lines Flight 007, a Boeing 747 carrying 269 people, was shot down after straying into the USSR's prohibited airspace,...Ronald Reagan issued a directive making GPS freely available for civilian use".

Fortnit said...
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gurugeorge said...

This is why I'm much less gung-ho about technological change than I used to be, and less against some of the economics of the Left (e.g. welfare state level, not full-on socialism level ofc), while at the same time (like quite a few ex-libertarians and ex-ancaps today) I have also moved away from pure libertarianism, to the libertarian wing of the Alt Right.

The point about trade-offs goes deep, and economic efficiency, while a very important value, is one among several for a society. Individual liberty, also, is one important value among several, but a precondition of individual liberty is civic/ethnic fellow-feeling, or thumos, which (from a cold, blind start) is the most salient and obvious Schelling point to get society and civilization off the ground, to solve market failure problems, game-theoretic impasses, etc.

I think the abstract prettiness of Ayn Rand's thought, while it was a useful foil against pervasive abstract socialistic indoctrination for a window of time, misled a lot of us down a hyper-individualistic cul-de-sac. More sensible were some of the old guard like Hayek, your father, etc., who understood that there's a place for some elements of collectivism even in a society that treasures individual liberty, and that some majorities (particularly in relatively ethnically homogeneous cultures) may be willing to make the trade-off between some measure of economic efficiency and the implementation of the principle (and sentiment) that "we" look after "our" old, poor, sick, vets, dysfunctional, etc.

From the other angle, thumos is also important for inculcating a sense of noblesse oblige in elites, with the end result (of thumos across the entire social spectrum) being that politics ends up as simple horse-trading between the classes, rather than a deathmatch between mutually exclusive ideologies.

Fortnit said...

So it seems even smart of people like you have no idea on what is the most correct and effective form of society. Let's start with America, it works because of Capitalism, but yet the nation has soo many problems. So you would blame Capitalism on all the nations failures, but that original assessment was totally wrong in the first place! America is 50% socialism. That 50% socialism is what is hindering the nation. For example, Social Security? What kind of garbage is that, a guy wanted to be President so he decides to win by stealing from the unborn and lying about it? That President is long and dead now but we are stuck with his massive paycheck tax forever?
One of the first persons to get paid by Social Security was Ida May Fuller, and her first paycheck was for more than she ever put in. During her lifetime she collected a total of $22,888.92 in Social Security benefits and paid in $24.75. How is that not infuriating? Of course she and others would vote for anyone who promised that, they are evil because they were complicit in passing that evil law.
At the cost of $732 billions, SS is now larger than all other welfare programs in the world, combined!
Now look at China, they are evil because they are communists and socialism would never work, but it is only 50% communist/dictatorship. 50% of China is now Capitalism, they are using the profits of free market to sustain their oppressive government.
There are other extreme examples of how full-on Communism is bad and doesn't work, but we can't really gauge how bad or fast they would fail because Cuba, North Korea, and other Oil nations who are not democratic, have been strangled by the United States! Of course their people are starving, the US will not allow anyone to trade with them. Since WWII, the one hand of the USA has been culvertly engaging in many acts of immoral behavior. From the creation of Hamas, the Taliban and ISIS, non would exist if not for the direct involvement of US politicians. Ironically those that profit from war are the CEOs of military companies. Same for US gun manufacturers, who cares where the mass production of firearms end up, as long as they get rich! This goes back to the southern Slave owners and Big Tobacco, to the oil companies of today. You don't think those robber barons don't own a few politicians of their own?
Power corrupts and absolute power is absolutely corrupt. Fix that problem first.

Fortnit said...
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Fortnit said...
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Simon said...

There is no need for remotely operated valves as suggested by Sound and Fury - there's a simpler solution.

You just need a valve system that keeps the hot and cold water in separate flows insulated from each other and mix them only at the shower head. That way, the change in flows from the valve should affect the flow rates of hot and cold at the shower head at about the speed of sound, not the speed of the water flow.

This should be simply implementable by using separate hot and cold water faucet, insulating the hot water tube, and merging the lines at the shower head. If you want to use a single faucet handle, it will presumably require a redisign of the faucet so as to have separate hot and cold water valves internally, but I don't imagine this would be that hard to do. In fact, I looked up "faucet valve" on Google Patents and quickly found an example (US5573037) that looks like it has these (but then mixes the fluids immediately).

I have no idea why this delaying of the mixing of hot and cold flows is not already done.

Augustin Moga said...


I believe all of you are ignorant of the most obvious solution in regards to the shower issue. Hotels, small and large, should simply provide enough space in the shower so that one can sit on a horse and have the shower head straight into its mouth. Then, judging by the horse's reactions, one can adjust the water temperature accordingly.

And yes, the horse's mouth should be thoroughly inspected during the process of receiving the room's key. Also, a free dinner for the horse should be provided, no questions asked.

Anonymous said...

Simon - how would you adjust the valve in the shower head without exposing your body to the scalding hot water or freezing ice cold water? The entire point of moving it to the other side was to not get too near to the water until the temperature was right.

If you kept the basic setup in the original post, and to avoid the delay, you would need to change to a remote switch and electrically actuated valve located near the shower head.

While this would be doable in your home, I imagine it is no longer optimized for cost, even at hotel scale.

An even more complex optimization matrix that I've been following lately is lithium ion batteries for electric vehicles.

Cost, safety, energy density, rate of charge/discharge, cycles...etc. Then all of the various possible materials.

Tesla has achieved high energy density and low(er) cost at the expense of safety by minimizing use of cobalt. While all other manufactures are using a different chemistry, which is more stable, but less efficient in energy density.

Will one chemistry win out?

Simon said...

Unknown: You misunderstand my proposed solution. The valve is in the usual place, well before the shower head. However, it does not mix the water, merely control flow in both pipes. The two pipes are insulated from each other until the shower head, where they combine and the water mixes.

Should be low cost, low delay, unless the non-mixing valve is hard to make, and I doubt it is.

There is still some time it would take initially to replace the room temperature water in the pipes with hot and cold water.

Simon said...

I retract my proposal. I thought a change to a rate of flow through a pipe could propagate through the pipe much faster than the fluid itself moves through the pipes. But now I've done some math on it and realized that this actually isn't the case.

When you adjust the valve, the change in flow rate occurs gradually depending on the pipe length. It should approach the new flow rate asymptotically, but you can define an effective propagation rate of the change in flow as the time it the change would occur if it occurred at the rate it starts to occur at, divided by the length of the pipe between the valve and the shower head.

---Badly formatted and sloppy math, ignore this section---

Lets suppose we can model everything up to and including the valve as equivalent to a large reservoir with an adjustable pressure, and everything after the valve as a constant diameter frictionless tube with an open end. For this to be valid, you would want the pipes leading up to the valve to be much wider than the pipes after the valve. Otherwise the length we would need to take into account is the full length of thin pipe, I think.

v= flow speed
r= fluid density
p=pressure in the imagined idealized pressure source that the valve approximates
dp, dv = changes in p, v
t=effective time for change dv or dp to occur
a= instantaneous acceleration of fluid when dp and dv occurs

OK, since the tube is open at one end, we have zero pressure at the end, and within the thin frictionless tube. By bernoulli's principle, ignoring gravity, p=(r/2)v^2 or v= sqrt(2p/r)

If we change pressure by a small amount dp, flow speed would change by dv=dp/sqrt(2pr)

the acceleration initially imparted on the fluid is a=(dp)*area/mass = dp*area/(r*volume) = dp/(r*length)

effective time for the change to occur: t = dv/a = r*length/sqrt(2pr)= length*sqrt(r/2p)=length/v

So the effective propagation rate of the change in flow rate is:

length/t = v

-----end badly formatted and sloppy math--------

So, it effectively propagates at the fluid's flow speed (and since the change equilibriates asymptotically, it's actually slower in practice).

I guess I could try to salvage it by imagining a valve that, when you adjust it to make a change, automatically makes a much larger change for a short time to change the flow rates quickly, then dials back to avoid overshooting. This combined with delayed mixing could get you a faster response, but it would be complicated, so whether it would actually be better than other complicated solutions is doubtful.

Simon said...

And of course, "define an effective propagation rate ... as the time ..., divided by the length ... " is inverted.

Simon said...

Thinking about it some more, actually it wouldn't necessarily be that complicated to have the valve have a much stronger initial response when an adjustment is made. It could be like a thermostat, you set a desired flow rate, and it lets flow through very easily or strongly restricts it depending on whether the actual flow is higher or lower than the desired level. You'd also need it to damp oscillations though. You'd need two of them, one for each of the hot and cold pipes, ideally controlled by a single handle.

TruePath said...

I think the link broke since I wasn’t looking for a towel rack but I searched for it and found it and it only DISPLAYS the temperature it doesn’t adjust the flow to maintain a given shower temp.

TruePath said...

I still think my solution of digital controls that control valves right before the shower head (and have temperature gauges installed there and up pipe) is much better.

I mean any kind of weird initial burst system is going to be complicated enough it needs to be digital anyway so why not just ensure both immediate change AND thermostat control so temp doesn’t fluctuate as warmer water arrives?

TruePath said...

I loved your idea about late combining tho...too bad it doesn’t work.

I’m still quite surprised by that actually. I mean electrons actually move pretty slowly but a change in voltage (analagous to pressure change) propagates extremely rapidly.

Simon said...

The onset of the change propagates quickly, but the water has momentum, and you need to apply enough force to change it to close to the new value, which takes time. If you adjust the valve a little bit, it only applies a little bit of force. That's why it's slow and why temporarily adjusting the valve much more would make it change speed faster.

Yes, your system is probably better, since digital stuff is pretty cheap these days, and it would be able to correct for differences in input temperature.

But, I don't think an initial burst system needs to be digital.

Here's one way it could possibly work:

You have something that measures flow, producing its output as the movement of some physical element.

You also have a human input. The human input moves a different element.

You connect these two elements to a third element, which moves according to the difference between these two.

You have a valve, controlled by movement of the third element. The valve can accommodate input far beyond the zero-to full range (and still produces zero or full if beyond these). It produces an intermediate restriction of the flow only if the difference between the human input and the flow measurement is quite small. It also needs to have low momentum relative to the force either the flow meter and human input produce.

You would also need a smaller bypass separately connected to the human input to prevent full shutoff except when the valve is actually supposed to be shut off.

There's probably much more elegant ways to do it, and there's probably flaws in my way, but I'm just trying to show it can be done without being super complicated.

Simon said...

Actually, I think instead of having the human input control a parallel bypass, it would be easier to make the parallel bypass be built in and always open, and have the human input control a shut-off in series with the rest of the valve.

Simon said...

I retract my retraction. I earlier assumed that the pipes stay the same diameter between the valve and shower head with no restriction at the shower head. The trick is, the pipes need to stay fat up to the shower head, where they get thin (or limited holes in the shower head supply the thinness). I had realized that the pipes needed to be fat up to the valve, just not that this could be extended up to the shower head.

Momentum is not affected by area of the pipes, but applied force is proportional to area. Effective speed should be proportional to the ratio of the area of the pipes leading to the shower head to the area at the shower head. Another way to think of it is in terms of energy - kinetic energy is proportional to the square of the speed times mass, so doubling the size of the pipe halves the total kinetic energy and the input power is proportional to force times speed, which stays constant as area changes. The energy associated with pressure should be negligible in comparison as water is nearly incompressible.

Of course, there's a tradeoff in that the bigger the pipes, the longer it takes to get the initial flow of water to arrive and reach a temperature equilibrium.