## Launch-o-Rocket

School, from our house as the crow flies, is 5.73 km. If we neglect air resistance and deal strictly with ballistic flight then we can materialize a wonderful fantasy. Starting in the backyard, extending over the top of the house, is a launch-o-rocket, a rail-like launcher that accelerates the school-bound student until he or she can cruise over the city and arrive without bother of traffic. Our charter is to find the acceleration of the student from the launch-o-rocket.

## Finding the Initial Velocity

We rely on the well-known fact that the maximum distance in a throw occurs when the departure angle is 45°. The vertical speed and the horizontal speed are equal. We denote these two identical speeds as $s$. Since distance is time multiplied by speed, the distance from home to school $d$ is
$$d = t\cdot s.$$

We know the distance $d =$ 5.73 km.

Turning to the vertical speed, the student departs the launch-o-rocket with vertical speed $s$, but is immediately subject to gravitational acceleration. Since the student’s upward flight is exactly matched by his or her downward flight. Because the flight is matched, the student spends $t/2$ time rising and $t/2$ time descending. Since the student has no vertical speed at the top, we know that his or her speed is
$$s = g\frac{t}{2},$$

where $g$ is the gravitational acceleration 9.8 m/s2.

Now, we have a system of equations

$$d = t\cdot s$$
$$s = g\frac{t}{2}.$$
The system looks like it has a many variables, but really there are only two, $s$ and $t$. We know $g$ and $d$. To solve the system we substitute for $s$ in the first equation with the second to get

$$d = tg\frac{t}{2} = g\frac{t^2}{2}$$
Solve for $t$
$$t = \sqrt{\frac{2d}{g}} = \sqrt{\frac{2\cdot 5.73\,\text{m}}{9.8\,\text{m/s}^2}} \approx 34.2\,\text{s}.$$
Not a bad commute, a little over half a minute.

With $t$ in hand, we can find the magnitude of the initial velocity. Remember that the initial velocity is $s$ in the horizontal direction and $s$ in the vertical direction, so the speed when leaving the launcher is
$$\left| \mathbf{v}_0\right| = \sqrt{s^2 + s^2} = \sqrt{2s^2} = s\sqrt{2}.$$
The initial speed the student must attain is given by the very first equation, $d = s\cdot t$. Solving for $s$ with the value of $t$ we found, we get

$$s = \frac{5.73\,\text{km}}{34.2\,\text{s}} = 168\,\text{m/s}.$$

## Finding the Acceleration

The ramp lives on a footprint that is about 80 ft, or 24.4 m. It is also 24.4 m tall, so special zoning is surely required! The rail of the launch-o-rocket is the hypotenuse of a triangle, and that triangle has sides 24.4 m, and a total length of $\sqrt{2}\cdot 24.4\,\text{m} = 34.5\,\text{m}$.

The formula for position after a period of acceleration is
$$p = \frac{1}{2}a\tau^2.$$
For our system, we also know that the acceleration is the change in speed divided by the change in time. Our speed goes from zero to 168 m/s in $\tau$. Again, we have a system of equations,

$$34.5\, \text{m} = \frac{1}{2}a\tau^2$$
$$a = \frac{168\,\text{m/s}}{\tau}.$$

Solve for $a$ by first solving the second equation for $\tau$, and then substituting that result into the first equation to get

$$34.5\, \text{m} = \frac{1}{2}a\left(\frac{168\,\text{m/s}}{a}\right)^2$$

$$a = \frac{\left( 168\, \text{m/s}\right)^2}{2 \cdot 34.5\,\text{m}} = 407\, \text{m/s}^2 = 41.5\, g.$$

The typical onset of death occurs when acceleration exceeds about $10g$, so unfortunately, the launch-o-rocket is a single try system.

## 300 Million Years Ago

This weekend my family came with me to hunt fossils in the Jemez mountains of New Mexico. We hunted fossils along Route 4, where I understand collecting is legal and ethical. The fossils we were looking for are quite common, mainly brachiopods (similar to clams), and crinoids (a kind of anemone). These fossils are common in the Pennsylvanian group, especially in the Madera subgroup. These strata were laid down in the Late Carboniferous period from about 323 to 299 million years ago.

I had excellent fun assembling our fossil hunting map. I used the grand open source QGIS geographic information system software, importing the road layers from the Open Street Map project through QGIS’ built-in plug in. The topographic information came from the USGS 1 m digital elevation model, which I traced at 25 meter intervals. The New Mexico Geological Survey provided a very detailed geological map of the Jemez Springs area, from which I selected the Pennsylvanian Madera sections. The total map is assembled in the following graphic.

My daughter found a crinoid calyx, or at least I believe that is what it is.

You can see the fan-like structure at the top of the crinoid tapering to one end where the frond-like structures joined the stem.

My son found a brachiopod, which was nearly completely isolated from the surrounding matrix, and it is nearly flawless without preparation.

I composited three perspectives of the same fossil to show all angles.

I found a collection of small sesame-seed sized bumps, which I believe are fusilinids. These are shells deposited by single-cell animals, which makes them gigantic as single-cell animals go. I’d like to cross-section one, since some fusilinids have really complex structures.

We also found an assortment of random bits piled together. It seems like a story of the past, I just can’t read. I don’t know what all the elements are, but I recognize sundry crinoid stem segments and shell pieces. I don’t know what the long stem-like structure is left of center, but it has a fascinating look.

We had fun, found far more fossils than I expected, of far more types. Next, I want to learn some amateur fossil preparation. So amazing to hold the remains of something that lived 300 million years ago in your hand.

## Hot Soup!

My kids blow on soup to cool it down. Sometimes they blow like a tornado and most of the soup exits the spoon rather than entering the child. I always tell them to blow gently—it will cool just as fast.

Well, we put the theory to the test. For cleanliness, we simulated a broth soup with hot water. Viscous soups, like cream soups, might be different.

For apparatus we mounted a spoon in a third hand tool. A thermistor temperature sensor was affixed to have the sensor at the lowest point in the spoon’s bowl. We had a small hand-held anemometer to measure the air speed at the spoon. We transferred hot—nearly boiling—water into the spoon with the turkey baster. The data logger, my own design, recorded the temperature.

Each of three test subjects blew on the soup to cool it. Each person blew lightly or strongly. We attempted to calibrate the airspeed at the spoon during an exhale. The picture below shows the first test subject (Dear Daughter) measuring the air speed. The anemometer is aligned with the spoon. Each subject attempts to hold their head in the same position.

Each subject blew on the spoon until the thermistor reading fell below 30°C. We recorded the start time and the stop time as indicated by the data logger. The start and stop time became cut points in the data processing.

We did all the experiments over about an hour, and left the data logger running the whole time. The plot of temperature is shown next. The spikes correspond to times when we recharged the spoon with hot water. The drops at the bottom of each trough correspond to our evacuation of the remaining water from the spoon.

A cut portion of the timeline, corresponding to each experiment, is fitted to an exponential function of the form Temp = A×exp(time×B). The time constant for these fits is –1/B. The time constant corresponds to the amount of time for the temperature to drop 73% of the way to the ambient temperature.

The time constants from each trial also describe a curve as a function of the air speed. I fitted these data with another exponential function, and although the fit is not exact, it is satisfying close to the data.

Each point color in the graph represents one person’s attempt. The dark blue point in the upper left is the a control where nobody blew on the spoon. The red point in the lower right corner corresponds to my son’s fastest effort, which removed about half the soup from the spoon.

To summarize the results, faster air speed does cool the soup considerably faster—meaning that I was not correct. My recommendation, based on the data, is to blow as fast as possible provided the soup is not sloshing out. You are welcome to use this data next time you’re trying to convince a young child to cool their soup properly. Your mileage may vary.

I love ribs, and I love the way they come out of my Masterbuilt electric smoker. Actually, it’s my dad’s smoker but I keep it safely at my house. The problem with ribs is the time. The late-night clean up, after cleaning and rubbing the ribs the night before and cooking six hours, is almost too much. The worst thing to clean is the racks. The chromed welded-mesh racks (picture below) sit in the smoker like oven racks. The racks’ many textures make them difficult to clean. My best success is to spray them with cooking spray before using, then soak them in the sink for an hour or two, followed by a brushing, and then often steel wool. They don’t get clean enough in the dishwasher.

My friend Scott owns the same kind of smoker, and provided the first piece of wise council. Instead of lining the water pan and drip pan with foil, put a disposable pan aluminum pan in place of the water pan. I also hang aluminum foil skirts on the sides of the smoker to keep from having to clean the sides as shown below. I use a 10.5×13 inch disposable pan purchased at Costco. I deform the pans a little to fit better.

To dispense with cleaning the racks demands an alternative. I built a hanger to suspend the ribs from near the ceiling. Then, I bent cheap stainless skewers into a shape that holds the ribs along their length. One skewer is native, unbent. The other has the end bent up and then into a loop. Then the two skewers interlock. String tied at the top holds the ribs in.

Each pair of skewers holds a half rack of ribs, squeezed. My design keeps the ribs upright with minimal risk of falling.

I align the loops at the top of the skewers so that they are both held.

I built a hanger out of piece of brass angle iron. I drilled and tapped along the length, and ran 2-inch 8-32 screws through, leaving plenty of length to hang the holders from. The rack fits snuggly inside the smoker, in fact too snuggly. However, the idea of the design seems sound. The angle iron rests on the wire slides Masterbuilt included. I use a steel clip. If I redo this, I’ll probably use a threaded hole on the inside of the wire slide, and a fender washer to hold the angle iron on.

To load the smoker, I hang the ribs from the screws.

To sauce the ribs, I use tongs to pull a whole rack out. The large rings in the skewer make them easy to take off for a saucing.

The skewers’ simple geometry makes them a breeze to clean. They came off the ribs without damaging the crust we work so hard to get. In addition to the easy clean-up, the method causes the fat to drip off the ribs and into a pan, rather than onto the rack of ribs below. The angle-iron hanger rack also works to hang chicken halves with a steel s-hook or a string, also with easy clean-up.

## Lawn Irrigation in the Desert

In central New Mexico there is not enough rainfall to grow a lawn. Water is precious—and expensive. A responsible homeowner maintains his lawn with no more water than required. But how much is required?

You can calculate the amount. Guide H-504 from the New Mexico State University cooperative extension How to Water Your Lawn shows how to calculate water usage, but it is confusing. To make this easier, I approach the problem from the point of view of a homeowner. A homeowner controls two things in an established lawn:

Watering frequency
Duration of each watering

The duration of each watering depends on how much water the soil can hold down to the root depth, how much water is in the soil when watering starts, and how fast the sprinklers deliver the water. The watering frequency depends on the rate water leaves the soil.

Water enters the lawn mainly from irrigation, but it leaves the lawn into the earth through seepage and into the air through transpiration and evaporation. Water leaves both up and down, but most of the loss is upward through transpiration and I will neglect downward loss.

Of the two controls, the watering duration requires knowing the how fast the sprinklers deliver water, and how much water is needed to soak the ground to the root depth. First, the speed at which the sprinklers deliver water. I measured this by putting eleven tuna cans distributed over the surface of the lawn, and letting the sprinklers run for 25 minutes. I measured the amount of water in each can, and calculated the average flow rate and the standard deviation over the surface of the lawn. My sprinklers deliver 0.75 ±0.28 inches per hour. A standard deviation of almost 30% is fairly uneven coverage, so the best strategy for me is to assume the low end of the range, about 0.5 inches per hour.

The next question is how much water is needed to soak the ground. The amount of water depends on the rooting depth—how deep the water has to go, and on the amount of water the soil can hold, both properties of the soil. The grass’ rooting depth depends on the grass type. Turf grass types in New Mexico are classified as cool season or warm season. Warm season grasses will stay brown longer into the spring, tolerate less foot traffic, and use less water over the year than cool season grasses. My lawn includes a section of grass with short leaves that grows long runners. It stays brown until the middle of May and turns brown in November. I’ve always called it Bermuda grass because it looks like the Bermuda grass I see in San Diego, but I’m no botanist. The majority of my small lawn is cool season, it stays green throughout the year, though it is not vibrant through the winter. Kentucky bluegrass and tall fescue are cool season grasses. According to New Mexico State University’s Circular 660, cool season grass has a rooting depth of about 18 inches.

The soil type governs three important parameters: the water holding capacity, the infiltration rate, and the management allowed depletion. The infiltration rate is only important to control puddling, and I have never been able to form puddles on my lawn with a sprinkler. The other parameters, however, are important. Therefore I set out to measure my soil’s type.

Soils are defined by a three-element mixture model; that is, a soil is defined by what fraction is clay, sand, or silt. One way to measure the soil content is to make a suspension and measure the layers that precipitate. I put about three quarters of a liter of soil in a jar, filled it with water, and shook it. The jar resulted in three layers.

 Clay 15% Silt 49% Sand 36%

Purdue defines soil type by a mixture model and also shows a technique for determining soil type based on mud plasticity. I used the layer thickness in the photo along with the ternary plot from Purdue to determine that my soil is a medium loam. I estimated the parameters of the soil and used Purdue’s soil model ternary plot to estimate the soil type.

With my soil type, medium loam, I looked up the soil properties in Circular 660 to get infiltration rate (0.75 in/hr), available water (1.5 in/ft), and management allowed depletion (50%). Management allowed depletion is the fraction of the soil’s water capacity that can be lost before plants are stressed.

 Infiltration Rate 0.75 in/hour Available Water 1.4 in/foot Allowable Depletion 50%

I believe my measurement overestimates the clay content, and that my soil’s behavior is more sand-like. To address this I use a water capacity margin factor to reduce the assumed available water content by half.

The amount of water to apply during a cycle is the amount needed to increase the soil moisture from its management allowed depletion up to capacity. In formula it is

Water to Apply [in] =

(Available Water [in/ft]) × (MAD [%]) × (Root Depth [ft])

To calculate the duration of the sprinkler run, just divide the
applied water by the sprinkler rate

Duration [min] = (Sprinkler Rate [in/min]) × (Water to Apply [in])

I calculate that an irrigation should last 67 minutes, the
necessary time to get 0.5 inches.

Finally, I need to determine the frequency of watering. Frequency of watering depends mainly on the rate water leaves the soil. In turn, the rate water leaves depends on the climate. The following schematic shows the process. The transpiration depletes the soil of moisture. The rate of moisture loss is, probably, non-linear in general but approximately linear at first.

The evaporation and transpiration rates are estimated in Circular 660
for Albuquerque. The following figure shows the data, and shows
that the peak rate of loss is in the first or second week of June.

By using the assumption of linearity, I can calculate the days between
watering. If ET is the evaporation and transpiration rate, then the
days between watering can be estimated as

Watering Interval [day] = (Water to Apply [in]) × (ET [in/day])

My watering interval, in the following figure, shows the variation over the course of the year. Albuquerque public works recommends  watering three times a week at the peak of the season. My calculations suggest watering only twice a week. Albuquerque’s recommendations
conspicuously lack a recommended time, or amount of water. Perhaps my calculation recommends a longer time than the Albuquerque.

## The Electric Henhouse

This spring three lovely chicks joined our family, Betty, Penny, and Ginger. Ginger discovered her inner rooster in due time, and was rehomed—we are not zoned for the crowing half of the species. To protect the birds from freezing during our winter travels, and to let them out at the sunrise, they have been housed in the electric henhouse. At dawn and dusk the hens are released or secured by a linear actuator, locking in heat, wind and potential predators locked out.

Betty watching the installation of the electric henhouse.

The heart of the electric henhouse is a bare-chip variant of the Arduino. It connects to a realtime clock with battery backup to get the time. The time, in turn, is used with calculated sunrise and sunset so the door opens at sunrise and closes shortly after sunset when the birds have settled down for the night. The ATMega runs at 5 volts, and so a dual H-bridge is used to provide the linear actuator with the power it needs.

The overall code architecture is straightforward, every second the processor checks the time. If the time is between the sunrise and sunset, tell the motor to open, otherwise close. The motor module maintains a state so that it won’t try to open an open door. The linear actuator is cleverly designed, it won’t strain to open when it is always open and it won’t close when all the way closed.

The only code module with much complexity is the sunrise and sunset calculation, which is an approximation based on a US Naval Observatory code, with only minor modifications. I tested it by running the calculation over a series of days throughout the year and comparing with published almanac.

I purchased two separate FTDI USB-to-serial chips to program the bare ATMega chip, and was unable to get either of them working. I followed programming instructions similar to those here, and those worked every time.

The linear actuator is visible at the top. It slides the door (currently open).

You can get the code on GitHub.

## Ear Tips for Noise Canceling Headphones

Most people have never tried in-ear headphones. They get ear wax on them, so to don’t share well. Wearing them on stage, musicians can hear their own instruments without going deaf. Since musicians use them for performance in-ear headphones are also called monitors, just like the speakers that point toward the band from the front of the stage.

Distraction, from airplane noise, office noise, maybe your own keyboard, annoys. Three headphones solve the problem. Most famously, Bose’s active noise canceling Quiet Comfort line and similar products by other makers. Passive noise reduction from sealed over-ear headphones is about 10 dB. In-ear monitors offer passive isolation between 20 and 30 dB.

I demoed the Bose phones years ago, and they hissed with the noise cancellation on. The sound quality was neither exceptional nor awful, but was poor for a \$300 price. World-class sound quality is available from makers like Etymotic and Westone with in-ear monitors that provide as much isolation as active noise canceling models.

But in-ear monitors have one major drawback, they go in your ear canal. That means that they can get gross with ear wax, can be painful or itchy, and they can wear out. In my nine years using in-ear monitors I only ever found the foam tips from the manufacturer comfortable. The three-flange silicon tips isolate amazingly, but itch like fire after twenty minutes and hurt like a drill after sixty. The foam tips are comfortable, almost as isolating as the three-flange tips, but cannot be fully cleaned and wear out after three months.

The most recent time I wore out a pair of foam tips, I decided it was time to look at the alternatives. I hoped to find, ideally, a comfortable silicon tip with the isolation of the foam tips or an inexpensively replaceable foam tip. It seems to be sort of a niche market, and I failed to find any useful comparisons on the web. So, I did my own.

I purchased a sizing kit from Westone, another from Monster, and a pack of the universally-liked Comply foam tips. Testing included a few leftover tips from the headphone’s original purchase, and I included those in the comparison.

I evaluated each tip for fit, seal, pain, itching, sound quality, isolation, and microphonics. Fit, seal, sound quality, and isolation are all related. With in-ear phones a poor seal means poor isolation and poor bass response and poor sound quality. Good fit depends on having the correct size tip for your ear. Medium tips from most manufacturers fit my ears well. The calipers in the picture below show a base diameter around 0.465 in (1.18 cm).

Most of the tip designs are old. Grubby among my grandfather’s shooting supplies, foam and triple flange tips were familiar to me twenty-five years ago. Recently Westone introduced a single-flange tip focusing on good seal and comfort. These, along with other single-flange tips, suffer from awful microphonics. When cables rub against anything, like your arm as you move the mouse, the motion travels along the cables and makes loud popping noises. Single-flange tips have the worst microphonics.

The best overall tips for me are Comply’s T-100 PLT medium foam tip. They cause no pain or itching, seal great and offer very good isolation, have low microphonics, and sound very good. Like all foam tips, they will wear out in three months and get waxy and gross. And they are neither the most isolating nor the quietest.

The best sounding tips are the Westone silicone three-flange tips, which offer by far the best isolation and by a small margin the best sound. After twenty minutes they also offer crushing pain and infernal itching. The three-flange tips have a place in my kit, but I don’t use them long.

Westone’s single flange tips are silicone, and are comfortable. My notes describe the itching from Westone’s silicone three-flange tip as extreme. After that, finding any silicone tip bearable was a surprise. The Westone Star tip is comfortable. It has poor microphonics, and poor isolation; it has no place on an airplane or a noisy office. On the other hand, Star Tips are cleanable and provide some isolation, so they are candidates for the gym. These also have a place in my kit.

The rest of the tips are unsurprising. Everything from Monster had poor isolation and had distracting microphonics due to a poor design. All of the other fitting foam tips are acceptable, but none are as good as Comply’s. All the other silicone tips are unacceptable for me, too painful, too itchy, too microphonic, and sound too poor. The results for all tips that fit reasonably well are in the table at the end.

I tested these tips with an hour-long playlist from mixed genre, seven songs in all. It starts with D. Barenboim/Berliner Staatskapelle recording of Beethoven’s Symphony 9, included to show dynamic range of symphonic instrumentation. The next two songs have typical mid-pitch-heavy pop songs including Adele’s One and Only off her album 21, and Erica Badu’s Four Leaf Clover from Baduism. Next, Erica Badu’s Rimshot shows the performance with an extreme deep bass opening line. Sweet Jane from the Cowboy Junkies is more typical pop. A mid-heavy but delicate sound and detailed sound from Miloš Karadaglić’s album Mediterráneo with his performance of Granados’ Danzas españolas, Op.-No. 2 Oriental. Finally, a very detailed song from Rush, The Necromancer off their album Caress of Steel has shown the weaknesses of many sound systems. I chose an hour-long playlist because in my experience in-ear monitors often lead to such itching and pain in the ears that I want to claw them out of ears screaming after forty minutes.

Monster produced the only foam tips I avoid. To fit my earphones you put the tiny red rubber rings around the earphone and then slide the tip over the top. The result was poor isolation and poor microphonics.

 Tip Size Fit Seal Sound Iso. Mic. Pain Itch Westone Classic Foam Med G G G G G G G Westone Silicone White 3-flange — G E E E G M VP Comply Foam T-100 PLT Med G G VG VG VG VG VG Westone Star Silicone Black 1-flange Med G G VG P P VG VG Westone Classic Foam Med-Long G G G G G VG G Westone Truefit+ Foam Med G G G G G G VG Westone Silicone Black 1-flange Med G G G G P G G Westone Star Silicon Black 1-flange Med-Long G G VG P P P G Weston Truefit+ Foam Med-Long G VG G VG G G G Westone Silicone Clear 1-flange Med G P P P P P G Westone Classic Foam Small-Long G P P P G VG G Monster Foam Med G G G P P G G

My wife put me onto Bloglovin for those who follow with an aggregator. If you like, Follow my blog with Bloglovin. Finally, I have had no contact with the makers of these products, and I wasn’t compensated or paid in any way. Quite the contrary, I bought all the equipment reviewed here.

## Some Curious Micrographs

We have an old microscope and a camera adapter for it. Occasionally we dig it out, and light some small stuff up. Several weeks ago my son’s science workbook had a multiple choice question, roughly “which of these would look different under a microscope”

• salt in water
• sugar in water
• pollen in water

An experiment seemed in order. After exploring those boring solutions we explored other things. The first is the tip of a technical pen. I believe the narrow diameter part is the wire, and the large diameter is the tube. I suppose the fillet is a meniscus of ink.

Rotring Technical Pen Tip

The feather is cool enough to look at, but within the feather is a single fiber from a blue yarn that my wife was crocheting with.

A Feather and a Colored Thread

At the request of my son, I plucked one of my precious head hairs. I had hoped to see the surface structure of the hair, a tiny scaled surface. It is visible, but not clearly. Still, pretty cool.

A Hair at the Root

We looked at paper, too. But paper was not that interesting until we compared three different types. Notebook paper, a Kleenex, and slice of technical drawing paper (like vellum). The difference between the fibers is amazing.

A Tissue and a Strip of Technical Drawing Paper

My son wanted to look at candle wax too, but the toothpick we used to get it is far more interesting.

Toothpick with Candle Wax

You think that milk has been homogenized and so it should look like a smooth, uniform material. I was fascinated to observe a sandy or granular structure under an optical microscope. The microscope cannot really resolve the individual particles, but it can show that the particles are there.

Milk

The final picture is shows the microchip inside a slow-fade RGB LED. This LED fades through the gamut of colors, and macroscopically looks identical to any other LED. The picture is blurry because it is imaged through the acrylic body of the LED. Nevertheless, the microchip structure is visible. At the bottom you can see four solder joints, one for ground (or Vcc) and red, green, and blue components.