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Challenge Questions

Stop in and exercise your brain. Talk about this month's Challenge from Specs & Techs or similar puzzles.

So do you have a Challenge Question that could stump the community? Then submit the question with the "correct" answer and we'll post it. If it's really good, we may even roll it up to Specs & Techs. You'll be famous!

Answers to Challenge Questions appear by the last Tuesday of the month.

Mystical Magnetic Fields: Newsletter Challenge (October 2017)

Posted September 30, 2017 5:01 PM

This month's Challenge Question: Specs & Techs from GlobalSpec:

As you know, the direction of the Earth’s magnetic field changes with time, as does “North” on a compass. Some researchers have used old paintings, such the murals in the old Vatican Library (Bibliotheca Apostolica Vaticana), or ancient clay kilns to find compass directions for specific times in the past. How is this possible?

And the answer is:

The clay in the walls of ancient kilns contains the iron oxide magnets magnetite and hematite. These materials contain individual grains in which there are “ domains”—regions in which the magnetic fields of the material are uniform.

When the clay is heated to hundreds of degrees Celsius as the kiln is used, the domains already aligned with the Earth’s field increase in size while the others shrink. When the kiln cools after using the arrangement of the domains—and also the magnetic field of the clay—is retained. This is a well-known phenomenon called thermoremanent magnetism (TRM).

Many mural paintings—including the murals of the Vatican Library—contain hematite suspended in the liquid pigment of the paint. When the pigment is applied to the wall each hematite grain rotates in the liquid until it is aligned with the Earth’s magnetic field. When the paint dries the orientation of the grains is locked in place, and therefore indicate the direction of the Earth’s magnetic field at the time of the painting.

Researchers have several methods to determine the orientation of the grains in a kiln or in the mural at any time.

13 comments; last comment on 10/10/2017
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Turbofan Tips: Newsletter Challenge (September 2017)

Posted August 31, 2017 5:01 PM
Pathfinder Tags: challenge question turbofan

This month's Challenge Question: Specs & Techs from GlobalSpec:

The low-pressure rotor of a PW100G-JM turbofan engine spins at a maximum rpm of 10,047. At what speed are the fan blade tips travelling at this rpm, and what (if any) noise concerns would this generate?

And the answer is:

Turbofan engines take advantage of momentum transfer efficiencies by moving large masses of air. A larger diameter turbofan moves more air, but must spin slower due to prevent the blade tips from reaching very high velocities.

The tip of a fan blade travels a greater distance than the section near the center for each revolution of the fan. For the same fan rotation speed (revolutions per minute), the tip of a fan blade will move at a higher speed (m/s) than the base of the blade. As fan diameter increases, the longer blades can cause blade tips to travel at very high speeds.

To calculate the blade tip speed, the fan diameter and fan rotational speed are needed. The Airbus A320neo is powered by the PW1100G-JM, which has a fan diameter of 81 inches. The maximum rotation speed of its low pressure rotor is 10,047 rpm. Since there is a gear train with a ratio of 1:3.0625 between the low pressure rotor and the fan, the maximum rotational speed of the fan is 10,047 / 3.0625 = 3,281 rpm.

Blade tip speed = π x D x S


D is fan diameter, and

S is fan rotation speed

So the maximum blade tip speed of the PW1100G-JM is 353 m/s. [ π x (81 in) x (3,281 rpm) = 83,4912 x (0.0254 m/in) x (1 min / 60 sec) = 353 m/s ]

The speed of sound is 343 m/s, so the blade tips are travelling at supersonic speeds at maximum rpm. For a simple, straight-bladed propeller operating in free air, supersonic motion would cause shock waves to form, generating a large amount of noise. But in turbofan engines like the PW1100G-JM, the fan blades are shrouded by the casing around the engine. The casing or nacelle helps guide the airflow into the compression stage of the engine, minimizing shock waves. In addition, the casing has noise-reducing liners.

19 comments; last comment on 09/07/2017
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Mystery of the Part-time Stud Finder: Newsletter Challenge (August 2017)

Posted July 31, 2017 5:01 PM
Pathfinder Tags: challenge question Screen

This month's Challenge Question: Specs & Techs from GlobalSpec:

Steve recently moved into a new apartment and wants to use his father’s stud finder to help put up a TV mount. It’s a nice summer day, so Steve doesn’t mind driving to his parents’ house. After retrieving it he went back to his apartment and turned it on but the screen remained blank. He changed the batteries and still it didn’t work. Steve ended up guessing where the studs were. When he finished working he tried the stud finder again and this time it turned on. Why didn’t it work the first time?

And the answer is:

It’s a nice summer day, so it is sunny. When Steve drove to his parents’ house to get the stud finder he was wearing polarized sunglasses. The stud finder had an LCD screen, so the light coming from it was polarized. Steve forgot to take off his sunglasses when he went into his apartment. When he turned on the stud finder, his glasses blocked the polarized light from the screen and the display looked unchanged, thus he thought the battery had died. When the battery change didn’t work he assumed it was broken. Later, when he checked it again he had been in the house a while and taken off his polarized sunglasses, so it worked.

30 comments; last comment on 09/05/2017
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Tricky Tubes: Newsletter Challenge (July 2017)

Posted June 30, 2017 5:01 PM
Pathfinder Tags: challenge question CRT tv

This month's Challenge Question: Specs & Techs from GlobalSpec:

You are watching TV on an old television set with a cathode ray tube. It’s well-known that TV CRT’s produce x-rays as well as images. To measure the radiation dose coming from the TV set, where should you point the x-ray detector?

And the answer is:

When electrons strike the CRT they stop and produce x-rays, but they are always surrounded by an electric field (see first image below) even when they move. If an electron is brought to a sudden stop, its electric field will not completely stop or disappear. The part of the field near the electron will stop first, but the part of the field “behind” the electron does not yet know about the stop, so it continues moving toward the CRT. At the point of contact with the CRT, a “kink” or “twist” is produced in the electric field (see second image), forcing the x-rays to move sideways at an angle of 90 degrees with respect to the direction of the electron beam. There, if you want to measure the maximum available radiation, align your detector with the surface of the TV set.

36 comments; last comment on 07/21/2017
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Satellite Struggle: Newsletter Challenge (June 2017)

Posted May 31, 2017 5:01 PM
Pathfinder Tags: challenge question satellite

This month's Challenge Question: Specs & Techs from GlobalSpec:

Column 54 through 61 of a TLE set for the IRIDIUM 20 satellite has a value of -21027-4. What is this number’s meaning, and what are the physical implications of its negative value?

And the answer is:

Simplified perturbation models (SGP4 in particular) are used to determine a satellite’s orbital path. They use a standard data source known as two-line element sets (TLE). TLE sets are made available to the public by the North American Aerospace Defense Command (NORAD) for non-classified objects orbiting Earth. These data sets consist of two 69-character lines that contain all of the parameters necessary to calculate a satellite’s orbital position and velocity for a period of time around the TLE “epoch” (the moment in time corresponding to the TLE data points).

The number in the challenge question (-21027-4) represents the term of the TLE known as B* (Bstar), the ballistic drag coefficient that indicates aerodynamic drag on a satellite in the SGP4 orbit model. In aerodynamics, the ballistic drag coefficient B = CD (A/m) where CD is an object’s coefficient of drag, A is its cross-sectional area, and m is its mass. When B is modified by a reference value for atmospheric density, ρo, B* is obtained: B* = Bo /2). B* represents an object’s susceptibility to drag.

Negative B* values occasionally show up in TLE sets, indicating erroneously that energy is somehow being added to the system. This is not the physical reality of drag acting on a satellite, of course. It is instead a consequence of the way SGP4 models forces with respect to the actual dynamic environment. From Revisiting Spacetrack Report #3 [PDF], we know that “SGP4 uses power density functions that require a term that encapsulates the ballistic coefficient, B*. Simplified force modeling and the batch-least-squares processing of observational data often yield a B* that has “soaked up” force model errors.”

The full TLE set for this challenge question was:

IRIDIUM 20 [+]

1 25577U 98074A 17107.88627323 -.00000039 00000-0 -21027-4 0 9999

2 25577 86.3914 280.5847 0002046 90.5751 269.5679 14.34214463145187

For more detail on the two-line element set format used for satellite tracking, see T.S. Kelso’s FAQ on the topic.

3 comments; last comment on 05/31/2017
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