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I'm a 2-decade subscriber to Consumer Reports, but sometimes they just get their science (engineering) completely wrong.

A force doesn't bend an object. A moment does. That is, the propensity to bend is not proportional to the force applied. It's proportional to the force times the lever arm. i.e. A 90 pound force applied to one point on an object may not bend it, while applied to a different point it can easily bend it. So the bigger (longer) phones were actually resisting greater moments, even though the force was the same.

Another problem is the test they came up with supported the phone at both ends, while pressing down in the middle. Basically a simply supported beam. The important thing to note here is that in such a config, both sides of the phone are resisting the bending moment. If it took 90 pounds of force applied to the middle, then the left side was resisting 45 pounds, the right side 45 pounds.

When a phone in your pocket is bent, it is in a cantilever configuration. One end of the phone is held rigidly, while the other end is free-floating. If the phone reached sufficient deflection to permanently bend in a simply supported config at 90 pounds, it will reach the same deflection at just 45 pounds in an equivalent cantilever (more precisely, 45 pounds pushing one way at one end, while your body weight holds the other end of the phone in place). You can try it in the calculators I've linked. Give both the same load, make the cantilever half the length, and you'll see the cantilever has twice the deflection. Make the load on the cantilever half that of the simply supported beam, and they have the same deflection.

(The actual force and moment diagram when you're sitting on your phone is a lot more complicated, since the force is distributed along the phone instead of all at one point. Integrating this is trivial for anyone who's taken a structural engineering course, but explaining it is beyond the scope of a forum post.)

I'm a 2-decade subscriber to Consumer Reports, but sometimes they just get their science (engineering) completely wrong.

A force doesn't bend an object. A moment does. That is, the propensity to bend is not proportional to the force applied. It's proportional to the force times the lever arm. i.e. A 90 pound force applied to one point on an object may not bend it, while applied to a different point it can easily bend it. So the bigger (longer) phones were actually resisting greater moments, even though the force was the same.

Another problem is the test they came up with supported the phone at both ends, while pressing down in the middle. Basically a simply supported beam. The important thing to note here is that in such a config, both sides of the phone are resisting the bending moment. If it took 90 pounds of force applied to the middle, then the left side was resisting 45 pounds, the right side 45 pounds.

When a phone in your pocket is bent, it is in a cantilever configuration. One end of the phone is held rigidly, while the other end is free-floating. If the phone reached sufficient deflection to permanently bend in a simply supported config at 90 pounds, it will reach the same deflection at just 45 pounds in an equivalent cantilever (more precisely, 45 pounds pushing one way at one end, while your body weight holds the other end of the phone in place). You can try it in the calculators I've linked. Give both the same load, make the cantilever half the length, and you'll see the cantilever has twice the deflection. Make the load on the cantilever half that of the simply supported beam, and they have the same deflection.

(The actual force and moment diagram when you're sitting on your phone is a lot more complicated, since the force is distributed along the phone instead of all at one point. Integrating this is trivial for anyone who's taken a structural engineering course, but explaining it is beyond the scope of a forum post.)

A ball inside a ball-bearing race typically fails by "spalling": a tiny flake breaks off of the surface of the ball.

As it rolls around the race, the ball makes a periodic "tick" sound whose frequency is related to its rotation.

So... if you record the sound coming from an engine, and you have an index mark input (when the flywheel reaches TDC, for instance) and you know the gearing ratios of all the shafts, the inner race and outer race diameter of the ball bearing races, and the number of balls &c you can relate the frequency to a particular bearing which is going bad before it fails.

You can do the same thing for the races: the inner and outer races rotate with a particular speed relative to the balls, so a crack or spall on a race will also make a sound at a particular frequency.

Essentially, look for energy in the particular frequency that a particular failure in a particular bearing would make based on the engine RPM, and repeat for all races. If you find enough energy (ie - audio volume), you know which bearing is going bad and the nature of the problem.

A bad gear typically starts with a broken tooth: a crack forms at the base of the tooth, resulting in a tooth which doesn't push as hard against the mating tooth in the next gear. This causes the driving shaft to speed up slightly as the cracked tooth mates, and slow down for the next tooth due to inertia.

If you continuously monitor an accelerometer attached to one of the engine shafts you can see this speedup/slowdown signature, and if you know the gearing ratio you can figure out which gear is going bad within the engine. The crack tends to mature over time, so an individual tooth will first become "wobbly" before complete failure.

A Journal Bearing typically wears when the "hole" becomes bigger than the shaft (the oil and mating shaft grind the hole bigger over time). When this happens, the mating shaft and attached mechanics will "wobble" within the hole, causing a noticeable shift in the mass of the engine.

If you continuously monitor an accelerometer attached to the engine block, you can index this wobble to the shaft speed based on the engine RPM and tell if any bearings are failing and how bad they are.

In all cases you can determine the nature and extent of the damage while it is relatively minor - before it damages other parts of the engine (scored shafts, pieces breaking off, catastrophic failure in flight, &c.)

At the time this was figured out the technology was expensive to implement, so it was only appropriate in select situations - aircraft maintenance, for instance.

Nowadays with the rise of high-power microprocessors and personal phone displays, perhaps some enterprising hobbyist will figure out a way to implement this for automobile maintenance.

1 edison = 100 amperes

A mechanical engineer should know that most structures fail due to buckling, not a lack of tensile strength.

That L ^2 term in the denominator bites hard.

http://www.efunda.com/formulae/solid_mechanics/columns/columns.cfm

Hey he was talking about spending money :). It'll still be faster, and you don't have to use 100x the water - just recirculate it.

This calculator seems to give a heat transfer change of about 10x every time you speed/slow the fluid by 100x

http://www.efunda.com/formulae/heat_transfer/convection_forced/calc_lamflow_isothermalplate.cfm#calc

You have to fill in the water characteristics yourself though. I used 0.001, 0.010 and 0.100 metres per sec. plate at 4 C, fluid at 60 C

So say at 10cm per second you get 1200 watts transfer, at 0.1cm per sec you get 120 watts transfer. Seems significant enough to me, assuming the calculator works for that range, and I put in the right values :).

They are probably these.

While it's true that some portion of your customers are going to lie when they say there has been no water intrusion, including, at extra cost a device aimed at proving that your customer is lying on every device is unfair. Let alone close to the external extremedies of the device.

The cost for these detectors is pennies a phone.

Consumer devices need to be built to withstand the normal environments they will be used in. Surprise, people sometimes come into a warm building from the cold outside.

Quite simply; put the phone in a warmer spot like a pants pocket for a few minutes before going inside. Keep the phone in a purse for a few minutes so it can warm up gradually.

This is how the indicators work. Get them slightly damp by condensation enough time and they may indicate water. That is enough moisture to damage electronics. The Indicators are not failing; they are working as designed.

There are no contacts involved in this process. Look at this this. It is basically a compound that changes colour when exposed to enough water. No electricity involved.

Didn't early airplanes use either paper or silk for the skin, rather than metal? All they had to do to make characteristics of the medium more desirable (weatherproof, taught) was to "dope" the medium...

It also rots. My neighbour had a Pacer whose fabric rotted out and he had to get the wing recovered.

Silk is still an extremely attractive (oops, no pun intended) medium for composites...

Silk is often referred to as "stronger than steel". That may be true per unit density (strength/weight), it really doesn't matter because silk is useless as a structural due to it's low stiffness. Young's modulus is around 100 or 200 MPA, whereas aluminum is about 70,000 and steel is 200,000.

But, with any of those modern materials used in composites, the tensile strength is one thing, but torsional stiffness is nonexistent...

There is no such thing as the torsional strength of a material. Structures have torsional strength, not materials. Materials have shear strength, and the shear strength of even the very very best polymers are negligible compared to common structural materials. The shear strength of common high-performance epoxies used in aircraft composites are maybe 5 ksi when you account for moisture absorption and service temperature, whereas 2024 aluminum is maybe 30 ksi.

Resin by itself has extremely good torsional strength, but very little tensile strength and is very brittle...

Resin doesn't have good "torsional" (shear) strength, it has bad shear strength. Ditto for the tensile strength. Again, compared to most structural materials, most polymers (resins) have high elongation to failure but that varies widely depending on the amount of crosslinking of the hydrocarbon chains. Within the epoxies, you can formulate ones that have low crosslinking and stretch like bubblegum, or you can crosslink the bejeepers out of them and create glass. It depends on the chemistry.

Carbon fibre is protected from UV, water, and abrasion by the epoxy (and usually a additional layer of protection using acrylic, lacquer, or other coating - in other words paint)...

Actually, the resin together with the fibers forms a microstructure that becomes a material continuum from the macro perspective. That is, the composite is actually a structure on a microscopic scale, but from an engineering point of view it is viewed as a material with properties derived using classical lamination theory. So the purpose of the matrix (resin) is structural, you could say to support the fibers that carry the actual load. The paint is required to protect the matrix from UV and moisture as most polymers are susceptible to both.

...and the resin provides torsional stiffness by itself AND by bonding several layers of the cloth together, which utilizes the tensile strength of each composite to further increase torsional strength without becoming brittle.

The resin doesn't provide any of the stiffness, the fibers do all that, the resin (matrix) supports the fibers so they can do their job. The shear stiffness and strength of the laminate stack come from plies at 45 degrees to the load application direction. Mohr's circle for pure shear tells us that you get pure tension and compression in the 45 degree directions, which the fibers can carry. It's quite clever and is the classic example of structural tailoring.

Why should paper be any different?

A million reasons. How resistant the material is to delamination would be my first question. Hidden delamination and it's effect on compression strength was carbon/epoxy's Achilles heel for a long time. Getting the matrix (epoxy?)

Didn't early airplanes use either paper or silk for the skin, rather than metal? All they had to do to make characteristics of the medium more desirable (weatherproof, taught) was to "dope" the medium...

It also rots. My neighbour had a Pacer whose fabric rotted out and he had to get the wing recovered.

Silk is still an extremely attractive (oops, no pun intended) medium for composites...

Silk is often referred to as "stronger than steel". That may be true per unit density (strength/weight), it really doesn't matter because silk is useless as a structural due to it's low stiffness. Young's modulus is around 100 or 200 MPA, whereas aluminum is about 70,000 and steel is 200,000.

But, with any of those modern materials used in composites, the tensile strength is one thing, but torsional stiffness is nonexistent...

There is no such thing as the torsional strength of a material. Structures have torsional strength, not materials. Materials have shear strength, and the shear strength of even the very very best polymers are negligible compared to common structural materials. The shear strength of common high-performance epoxies used in aircraft composites are maybe 5 ksi when you account for moisture absorption and service temperature, whereas 2024 aluminum is maybe 30 ksi.

Resin by itself has extremely good torsional strength, but very little tensile strength and is very brittle...

Resin doesn't have good "torsional" (shear) strength, it has bad shear strength. Ditto for the tensile strength. Again, compared to most structural materials, most polymers (resins) have high elongation to failure but that varies widely depending on the amount of crosslinking of the hydrocarbon chains. Within the epoxies, you can formulate ones that have low crosslinking and stretch like bubblegum, or you can crosslink the bejeepers out of them and create glass. It depends on the chemistry.

Carbon fibre is protected from UV, water, and abrasion by the epoxy (and usually a additional layer of protection using acrylic, lacquer, or other coating - in other words paint)...

Actually, the resin together with the fibers forms a microstructure that becomes a material continuum from the macro perspective. That is, the composite is actually a structure on a microscopic scale, but from an engineering point of view it is viewed as a material with properties derived using classical lamination theory. So the purpose of the matrix (resin) is structural, you could say to support the fibers that carry the actual load. The paint is required to protect the matrix from UV and moisture as most polymers are susceptible to both.

...and the resin provides torsional stiffness by itself AND by bonding several layers of the cloth together, which utilizes the tensile strength of each composite to further increase torsional strength without becoming brittle.

The resin doesn't provide any of the stiffness, the fibers do all that, the resin (matrix) supports the fibers so they can do their job. The shear stiffness and strength of the laminate stack come from plies at 45 degrees to the load application direction. Mohr's circle for pure shear tells us that you get pure tension and compression in the 45 degree directions, which the fibers can carry. It's quite clever and is the classic example of structural tailoring.

Why should paper be any different?

A million reasons. How resistant the material is to delamination would be my first question. Hidden delamination and it's effect on compression strength was carbon/epoxy's Achilles heel for a long time. Getting the matrix (epoxy?)

See steam tables.

At 1100 PSI, the boiling point of water is about 291C.

The average human can hear frequencies between 20Hz and 20KHz. The reason for the 44KHz sampling rate is explained here.

Explanation is here, and here and more in google

To be clear - the value of the SI prefixes do NOT change, no matter what you happen to be measuring. Thats the entire point of the SI system, for crying out loud!

I think you're both right. Go here for example:
http://www.efunda.com/units/si_prefixes.cfm

The IEC came up with Kibi etc to avoid confusion where the SI units when used for computer storage were set to 2^10, etc.

Here's another quote:

The IEEE Standards Board decided that IEEE standards will be using the conventional, internationally adopted, definitions of the base-ten SI prefixes, except that the base-two definition may be used if such usage is explicitly pointed out on a case-by-case basis.

Higher sampling rates do capture more accurate detail particularly on the phase accuracy.

No, you get EXACT reproduction without having to use higher sampling rates.

In fact, if sampling a 1kHz sine wave at 2kHz, one has to sample at the peaks or get a magnitude error. If the samples happen at the zero crossing (out of phase sample), one gets no signal samples at all:

That's because you mistakenly think Nyquist's theorem is Fn = 2Fmax. Nyquist's theorem is Fn > 2Fmax. So what you're seeing is aliasing when Fn = 2Fmax. This causes an attenuation in the amplitude proportional to cosine of the phase difference between the sampling frequency and the signal. If you have Fn < 2Fmax then you get a "beating volume" effect as the phase difference shifts over time.

Don't get all excited. You haven't proven Nyquist wrong. You just didn't understand what Nyquist said.

Check out the Nyquist Sampling Frequency.

It explains how a xHz signal needs to be sampled at 2xHz to reproduce it perfectly, but explains how sounds that can't be properly sampled (above xHz) interfere and therefore, need to be filtered before sampling.

As for the accuracy, mathg mathematicians better than myself say that it can... Not that it proves anything.

So no, digital will never perfectly reproduce all analog signals, but then neither will analog gear. The material used to make records (for instance) can only be formed into features so small before the grain of the material interferes (like grainy photos) and before the needle destroys the feature as it reads it.

If you assume that a record's diameter is 11" (?), this gives just under a meter (work with me) per second of material to hold features which describe the media.

If you assume that the detail in the record is a perfect minature of the 22kHz sine wave we'll use, then the peaks are 1/22,000th of a meter apart, or 1/22nd millimeter apart. This feature needs to be smooth enough the needle can glide over it, and strong enough it won't be sheared off by the diamond needle.

And that's only CD quality, it gets worse if you assume that because "analog is perfect" that it can record 50kHz sounds.

Anyways, it's somewhat accademic because you get much more noise in reproduction than even the worst (mostly) storage format/media introduces.

the company has to taylor it[emphasis mine]

What have Taylor series got to do with it? Oh, wait... I bet you meant tailor . ;-P

For those who are number-impaired, here's one reason that's so funny. Enter 10 into the calculator and then scroll down to the base-12 number on the resultant page. :)

Well played!

The sampling theorem is considered to have been articulated by Nyquist in 1928 and mathematically proven by Shannon in 1949. Some books use the term "Nyquist Sampling Theorem", and others use "Shannon Sampling Theorem". They are in fact the same sampling theorem.

the guy who developed the Uniform Sampling Theorem [wolfram.com] was Nyquist, not Shannon.

Nyquist conjectured it in 1928; Shannon proved it in 1949. Many texts split the credit, calling it the "Nyquist-Shannon sampling theorem."

http://www.efunda.com/math/reliability/reliability .cfm

But the real issue here is deducing something about a group of units, based on one unit's MBTF. Some discussion towards the bottom of this doc: http://www.hardwaregroup.com/faq/gen_mtbf.htm

Yes solving non-linear PDE such as the physically based Navier Stokes Equation are difficult. Genetally there are no closed form solutions for such equations with complicated boundary conditions and initial conditions. You can make numerical approximations to arbitrary precision given detailed enough data and a big enough computer. Many non-linear solvers exist. But I doubt that is what is going on here. My guess is they are not solving a fully coupled set of physiclly based PDEs. Instead they are probably solving a set of empircal equations modelling energy fluxes and mass balances for all large climatological drivers. Additionally I doubt they are trying to model the temperatue at 8:12pm on Jun 12 2462 AD in fiji. Rather then are probably looking for long term trends. This seems much more plausible.