Fibonacci Sequence In The Hiding…

Ceramics: Aluminum Nitride

First synthesized in the late 1800s, aluminum nitride’s potential wasn’t realized until a hundred years later in the late 1900s. AlN is a ceramic with high thermal conductivity but is an electrical insulator. It is classified as a covalent compound, the only stable compound in the binary Al-N system. 

AlN is similar in properties to beryllium oxide (BeO), but is cheaper and has less of a potential to be toxic. In addition to the properties mentioned above, this ceramic also has high chemical resistance and exhibits piezoelectric properties. 

Thanks to its thermal and electrical conductivity properties, AlN is useful in microelectronics. It is used in microelectronic packaging, surface acoustic wave sensors, in RF filters, as a crucible for the growth of gallium arsenide crystals, in piezoelectric MEMs applications, and many more. In addition, the wurtzite phase of aluminum nitride, w-AlN, is a wide band gap semiconductor material, with potential applications in deep ultraviolet optoelectronics. 

Because AlN is a covalent compound, high pressures or sintering aids are required to assist densification during production. Typical additives include rare-earth or alkaline-earth oxides, such as yttrium compounds. The additives and sintering conditions used can alter the properties of commercially available grades of AlN.

Sources: ( 1 ) ( 2 - images 2 and 3 ) ( 3 - images 1 and 4 ) ( 4 )

On the direction of the cross product of vectors

One of my math professors always told me:

Understand the concept and not the definition

A lot of times I have fallen into this pitfall where I seem to completely understand how to methodically do something without actually comprehending what it means.

And only after several years after I first encountered the notion of cross products did I actually understand what they really meant. When I did, it was purely ecstatic!

Why on earth is the direction of cross product orthogonal ? Like seriously…

I mean this is one of the burning questions regarding the cross product and yet for some reason, textbooks don’t get to the bottom of this. One way to think about this is :

It is modeling a real life scenario!!

The scenario being :

When you try to twist a screw (clockwise screws being the convention) inside a block in the clockwise direction like so, the nail moves down and vice versa.

i.e When you move from the screw from u to v, then the direction of the cross product denotes the direction the screw will move..

That’s why the direction of the cross product is orthogonal. It’s really that simple!

Another perspective

Now that you get a physical feel for the direction of the cross product, there is another way of looking at the direction too:

Displacement is a vector. Velocity is a vector. Acceleration is a vector. As you might expect, angular displacement, angular velocity, and angular acceleration are all vectors, too.

But which way do they point ?

Let’s take a rolling tire. The velocity vector of every point in the tire is pointed in every other direction.

BUT every point on a rolling tire has to have the same angular velocity – Magnitude and Direction.

How can we possibly assign a direction to the angular velocity ?

Well, the only way to ensure that the direction of the angular velocity is the same for every point is to make the direction of the angular velocity perpendicular to the plane of the tire.

Problem solved!

Looping thunderstorm gifs by Mike Hollingshead

Dissecting Iron Man Suit - An Engineering Analysis

Structural, energy, and thermal analysis of Iron Man Suits specifically Mark I to Mark XLVI which have the following capabilities in common: external armor, supersonic flight, hovering, weaponry, and decoy flares.

1. STRUCTURAL ANALYSIS 

Wear Resistant and Shock Absorbent Exoskeleton  The physical protective value of exoskeleton is its ability to resist any penetrative loads as well as any shock loads. However, the whole thickness of exoskeleton panels should not be too hard because it will pass on the external impact load into the suit’s internal hardware, or even the human body inside it. All of this can be achieved by combining more than one materials; a hard material on the outside and the soft material on the inside

Hard Outer Layer for Penetrative Loads The materials needed for the exoskeleton’s outer layer should be hard and tactile. Titanium Alloy would be an ideal choice. Fiber glass has good tensile strength but not good shear strength, while titanium has both .Titanium Alloy is not only much stronger, but is also lighter than steel, which will provide more fluidity of movement compared to any heavy material counterparts.

Ductile Inner Layer for Shock Loads There should be a soft inner linings behind titanium panels to serve as shock absorbent. Sorbothane is a material that is extremely soft and has the ability to convert shock loads into heat transfer at a molecular level. It is a proprietary, visco-elastic polymer. Visco-elastic means that a material exhibits properties of both liquids (viscous solutions) and solids (elastic materials).

Sorbothane is a thermoset, polyether-based, polyurethane material. Sorbothane combines shock absorption, good memory, vibration isolation and vibration damping characteristics. In addition, Sorbothane is a very effective acoustic damper and absorber. Even if one drops an egg from the top of a building into a bed of sorbothane, this remarkable material is soft enough to cushion the impact and would not allow the egg to break.

This technique of having a hard material on the outside and the soft material on the inside is not new. It has been used for centuries in Japan for making samurai swords. The hardness of its outer layer give the swords its cutting edge and penetrative power, and its ductility allows it to absorb shock loads when it strikes or struck. 

2. ENERGY ANALYSIS : Hovering Capability

Hovering using thrusters (aka repulsors) requires tremendous amount of energy, particularly when the suit is used for a long duration. Energy usage for hovering is dependent upon the hovering methods

Magnetic Levitation requires no energy at all, but is limited to the presence of magnetic field.

Ducted and Open Propellers (helicopter blades). Several human powered helicopters have been made overtime that have achieved flight. It has been experimentally recorded that a 78 kg person in a 58 kg copter requires only 1.1 kW to climb using helicopter blades, and only 60 Watts to maintain altitude.

Jet Thrust is the least energy-efficient method. Because thrust-to-weight ratio needs to be greater than 1 to achieve lift-off, a Jet-pack requires over 1KN of thrust force, depending on the weight of the jet and the person. If wings are attached to the jet-pack, horizontal flight can be achieved with thrust to weight ratio lower than 1, thus improving the duration of the flight and its range.There have been jet-packs made in the past, most iconic display of it was in 1994 Olympics opening ceremony. The fuel used in the jet-pack was mostly hydrogen peroxide. It provides thrust at low temperature compared to other fuels. However, it has low energy density of 810 Wh/kg, giving the jet-packs up to only 30 seconds of flight-time. Jet’s flight time is limited even by using energy-rich fossil fuel. Yves Rossy (aka Jet Man) has successfully used kerosene oil in his flight, but the thruster jets have to be pushed away from the body for safety. His suit allows only several minutes of flight. In addition, if a heavier suit (greater than 25 kg) is used, hydraulics are needed, which would require additional energy and slow down mobility. The Iron Monger suit was an example of hydraulic-driven mobility suit.

3. POWER SOURCE

Tony Stark manages the suit’s energy requirements, including thermal management and artificial intelligence system, through the fictional arc reactor. The reactor is able to provides almost limitless clean energy despite being a very small device. In real life, the only thing that has an energy density comparable to the arc reactor, and would meet all the energy requirements of the suit would be nuclear power. Uranium (fission) energy density is 80.620.000 MJ/kg. However, nuclear power is not suitable to be harnessed in a manned suit, since it generates a tremendous amount of heat.

A more practical solution would be a battery energy-storage. If lithium batteries are used on propeller blades, minutes-long flight time can be achieved. Furthermore, these batteries can readily power suit’s electrical devices / electronics requirements. Lithium ion battery has energy density of 150 Wh/kg (0.5 MJ/kg). Fossil fuel, on the other hand, have a much higher energy density than batteries, but would require a clunky generator to power the suit’s electrical requirements.

Lithium sulfur batteries have 5 times more energy density compared to lithium ion batteries. Lithium sulfur packs had already powered the longest unmanned flight for more than 30 hours. Unless we discover something like an arc-reactor, lithium sulfur batteries could be just the thing to power up the suit. The downside is, it requires hours of charging for just minutes of usage.

There is an alternative option, though not a ‘reactor’ proper. A compact and high-output generator (standard car alternators crank out 50-70 amps at 12 volts for years, and some can go as high as 150 amps) could be spun by a small and strong output electric motor (all alternators have to do is spin). That motor can be powered by a high density battery like used for electric bikes in the 1500w to 2500w range at 20 something volts. This would power a strong and small motor at 3500 to 4000 rpm for hours. That’s more than enough to create power for a number of systems, if they’re built to take advantage of the amperage. And with new constructions of carbon arrays coming out every day, one or more of those could bring a meaningful electric output increase in an otherwise standard generator, even above what we have in cars now.

4. THERMAL MANAGEMENT 

The suit cannot be hermetically sealed. Human body heat evaporates water from the skin. Therefore, air ventilation is a must to remove them. It is also needed to maintain a good supply of oxygen. So, there must be a structure inside the exoskeleton that allows air flow. This would prevent any internal condensation to settle and will also remove buildup of body heat. The layer of sorbothene would act both as a thermal and an electrical insulator. This means that extreme external temperature would not be transferred to the inner layer. The suit would not get too hot or too cold from the outer environment. There should be small fans to draw and pull air from the ambient in controlled amount, and should be able to exchange hot air. With the technology available today, the thermal management of the suit is easily manageable. There are also solid state devices such as thermal pads and thermoelectric generators. Thermoelectric generators can surfaces hot or cold depending on the polarity of the electric current and thus can be an integral component of the suit for controlling the internal temperature.

Source (x)

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Concrete vs. Cement

Concrete and cement are (mostly) two different materials. Why mostly? Because concrete is made using cement. Though cement can (technically) be used on its own, concrete cannot be made without first making cement.

Classified as a ceramic, cement starts as a powder, a mixture of limestone and other minerals, which is heated and mixed with gypsum to form what we know of as cement. Still a powder in this form, once water is added and mixed the cement then hardens. 

Portland cement, probably the most well known and commonly used cement, is classified as a hydraulic cement. This essentially means that once water has been added the chemical reaction, called hydration, that hardens the cement is not dependent on how much water is added. Hydraulic cements can harden underwater and remain strong even in wet conditions. As a side note, Portland cement is not a brand name, but a particular type of cement.

On the other hand, concrete is composed of cement, aggregate, and water, and is thus classified as a composite. Composites are defined as consisting of a matrix or binder that has a reinforcement within it. In the case of concrete, the cement water mixture is the matrix in which the reinforcement, or aggregate exists. 

The aggregate is typically comprised of stones, rocks, and sand and its addition increases the durability of the concrete. The amount of the aggregate or the size of the aggregate added can also effect the water-to-cement ratio required to harden the material, strengthening the final product. The hardening process continues for years, meaning that concrete only gets stronger with age.

Though most concretes are lime-based, asphalt concrete uses asphalt as the cement material and polymer concretes also exist. Another common type of concrete is reinforced concrete, in which rebar, or reinforcing bars, are embedded within to add to the strength of the concrete.

Sources: ( 1 ) ( 2 ) ( 3 ) ( 4 ) ( 5 )

Does one of these LEGO men look bigger than the other? They’re actually the exact same size, but are in an Ames room - a false-perspective illusion room that tricks your brain into thinking things are smaller, or larger, than they really are.

You can make one of these models to try this for yourself. Download our free template from here. And it even works in full size, if you can make one large enough!

We started looking at fluctuating loads last time - that is, loads that feature some combination of non-zero mean and alternating stresses - and how to account for them using a Goodman diagram. Let’s re-examine the bracket design problem we did earlier. This time, instead of a fully-reversed load, we’ll assume a fluctuating load with a mean force of 200 lbs, a minimum force of 50 lbs, and a maximum force of 350 lbs. We’ll say the dimensions of the bracket are those we calculated earlier that could handle the fully reversed load. (Problem adapted from Machine Design: An Integrated Approach, 4th Ed., by Robert L. Norton.)

Most of the calculations we did earlier will still hold. We won’t need to recalculate the endurance limit or stress concentration factors. The only new things we need to do are calculate the mean and alternating stresses and the new safety factors.

First step is to calculate the mean and alternating force.

From here, we get the mean and alternating moment.

We’re dealing with a situation of simple bending, so we can calculate mean and alternating stress using the basic bending stress equation.

The geometry of the part hasn’t changed, so we’ll apply the same stress concentration factors that we used before.

Great. We’ve got our new stresses. Now we need to figure out safety factors. As we mentioned earlier, this is now a slightly more complicated proposition. Which safety factor is appropriate will depend on how the alternating and mean stress behave in relation to each other. The possible failure states are shown as points A, B, C, and D on the Goodman diagram for this situation.

We’ll step through all the possible situations one by one using the new stresses we calculated and the endurance limit we got earlier.

Case 1: Constant alternating stress, variable mean stress.

Case 2: Variable alternating stress, constant mean stress.

Case 3: Alternating and mean stress are proportional to each other.

Case 4: Alternating and mean stress vary independently.

We take the worse case, with the failure state F being as close as possible to the current stress situation.

Our design will survive all four cases. Note that Case 4 is always the most conservative case - if you don’t know what your stresses are going to do, this is the one to go with.

Due to the Mandela Effect, we remember things that didn’t happen or exist. Get the answer and why in our NEW VID: https://youtu.be/hvu4D1jngCY

The fifth conic section - Straight line

Although many textbooks regard the straight line to be a specific case of the hyperbola and proclaim only four conic sections, it is something worth noting that the straight line is also a conic section.

The ocean is where the aliens live.

Transcript under the cut.

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