High School Mathematics-Physics SMILE Meeting
09 October 2001
Notes Prepared by Porter Johnson

David Dunlop (Great Lakes Space Sport Foundation; Telephone Number: 708 - 848-6605)
Guest Presentation on Rocketry
[See http://www.rocketryonline.com/]
He described an outgrowth of the the Wisconsin Rockets for Schools http://www.rockets4schools.org/ educational program based upon rocket launches, which was begun in Sheboygan WI (a city on Lake Michigan 100 km North of Milwaukee and 300 km North of Chicago) in 1991, receiving initial support from the State of Wisconsin and Michigan Technological University in Houghton (UP) MI.  A parallel program, Michigan Rockets for Schools http://www.phy.mtu.edu/rocket/, has been operating out of Muskegon [UP] MI since 1997.  This launch site was used for Meteorological Rockets, such as the Super Loki rocket http://www.phy.mtu.edu/rocket/superlok.html, that rose up to a height of 50 km, had a maximum speed of about 1500 meters/second [about Mach 5], and produced a maximum thrust of about 110 g's.  Meteorological rockets are no longer used in meteorology http://www.phy.mtu.edu/rocket/superlok.html, their role in determining upper air wind velocities being replaced by detection of dispersion of signals from orbiting weather satellites.

The educational program rocket launch is held annually during the third week of May on the pier in downtown Sheboygan, about 60 meters into Lake Michigan. The rockets are accelerated to a speed of about 250 meters/second using a motor that produces about 600 Newton-seconds of impulse. They rise over the lake to a height of about 700 meters, and are retrieved by recovery teams --- 95 % of them fall into the lake, and 5 % onto the nearby shore. The rockets employ standard "low explosive" motors that are inserted by professionals, who also launch them.

They use the standard rocket propellant, Ammonium Perchlorate, NH4Cl04, [http://en.wikipedia.org/wiki/Ammonium_perchlorate_composite_propellant] with a category I rocket motor.  According to FAA Classifications, A, B, C, D, E, F, G are "model rocket" categories, whereas H, I, J, K are strictly licensed "high powered rocket" categories.   David said that they do additional launches with more powerful rockets [ie, K] on that date---one recently launched rocket went up around 3 km and drifted inland under prevailing winds, and landed in a K-Mart parking lot on the other side of town! David also described balloon launches, which may rise to a height of 30 km before the balloon bursts, a parachute opens, and the payload drifts to a "soft landing" somewhere on earth.

Student groups may enter the contest by ordering a rocket kit, which consists of a phenolic-impregnated cardboard tube about 2 meters long, assorted vanes, a payload bay about 50 cm long, etc. The rocket superstructure has a mass of about 2 kg, the rocket motor [attached onto the rocket at launch by professionals] is about 0.5 kg, and a rocket payload can be as much as 2 kg. The rocket automatically depressurizes at apogee, and a parachute opens to keep the payload from crashing down. There are speedboat recovery teams to fetch the payload, as well as teaching teams to answer questions about rocketry.

The payload, can be virtually anything that fits inside the tube, and is limited only by expense and durability. Students have put in accelerometers, anemometers, CPL devices, GPS sensors and transmitters, etc. It is important that the payload be waterproof, since the landing usually occurs over water. Many groups collaborate with local Amateur Radio Clubs, since those groups are good scroungers, are knowledgeable about electronics, and usually quite interested in the project. Each team makes an oral presentation after their launch.

David described a sport rocketry program that is based upon sound educational principles. The goal is to produce the excitement and enthusiasm of a sporting event, while maintaining a strong educational mission.  For additional details about the program you may call David Dunlop at (708) 848-6605.

The rocket launches in the 1958 by future NASA Rocket Engineer Homer Hickam [http://www.homerhickam.com/new1.htm] and his fellow students in Coalwood WVa are beautifully described in the book [ http://www.homerhickam.com/ (look under 'Books' for "Rocket Boys")] and film October Sky. Their home-made rocket engines were comparable in thrust to the "high powered rocket" categories I - K, and students would certainly not be allowed to build such rocket engines from scratch today. Lower category "model rocket" engines are available at hobby stores today for use under strict supervision.

Fred Schaal (Lane Tech HS, Mathematics) Conversion from Bat to Human Frequencies
Fred handed out and discussed the following exercise:

The range of a human's voice frequency, h (all in Hz), is 85 £ H £ 1100. The range of a human's hearing frequency, H, is about 20 £H £20,000.
  1. The relationship between a human's voice frequency h and a bat's voice frequency, b, is given as

    h = 85 + (b - 10000) ´ 203 ¸ 22000.
    Find the range of the bat's voice frequency.
  2. The relationship between a human's hearing frequency and a bat's hearing frequency is given to be

    H = 20 + (B - 1000) ´ 999 ¸ 5950.
    Find the range of the bat's hearing frequency.
  3. If a bat flies into your room and you scream, will it hear you? If you scare it and it screams, will you hear it? Explain.
The numbers for bats come out to be
Voice:      10000 £ b £ 110,000
Hearing:        1400 £ B £ 1,200,000  

It seems that you should hear the bats (if you are young enough), but the bats cannot hear you.  Alas, your screams (blood-curdling though they may happen to be) are wasted on them!

Porter Johnson remarked that bats and other small animals tend to produce and detect sounds of higher frequency, because their vocal chambers and  hearing receptors are smaller.  The lowest sound produced by humans, about 85 Hz, corresponds to a wavelength of about 4 meters.  For quarter-wave resonance, the length of the vocal cavity should be about 1 meter.  This sound of a Basso Profundo must come from deep within the lungs! The ratio of maximum to minimum frequency for human voice is 1100 ¸85 » 13, corresponding to 3.7 octaves.  The ratio for human hearing is 22000 ¸20 »1100, corresponding to 9.7 octaves.  Thus, we can hear every note on the piano [88 ¸ 12 » 7.3 octaves], but we cannot sing that full range!  Trained voices can roughly be categorized by the following types, in order of increasing frequency:

Although the vocal range can be extended through extensive training, to a great extent it is determined naturally. It is said that the popular singer Whitney Houston  [http://www.infoplease.com/ipea/A0154789.html] and Mariah Carey [http://mrshowbiz.go.com/celebrities/people/mariahcarey/bio.html] are said to have vocal ranges of 5 octaves, achieved without classical voice training.

For bats the ratios of maximum to minimum frequencies are similar:

Voice:      110,000 ¸10,000 » 11
Hearing:        1,200,000 ¸1400 » 860

Bats are rather intelligent mammals that use ultra-sound sonar (as well as their eyes; they are not blind) to guide their flight, and to track the flight of other things in their air space. Because of the webbed wings attached to their limbs, their pattern of flight is distinctively jerky, rather than smooth as in birds with feathered wings. Bats are nocturnal animals, and eat vast quantities of  insects. They hang by their limbs and sleep upside down  in caves, high in trees, or inside abandoned buildings. They make a high-pitched, audible sound.

Marilynn Stone (Lane Tech HS, Physics) Home Made System to Illustrate Circuits
Marilynn showed us a system consisting of a 4-plug convenience outlet box, with cord to house current, and two different bulbs {#1 and #2) screwed into plug sockets.  When the bulbs were plugged into the back two plugs, they both lit, with #1 being brighter than #2.  When the two bulbs were plugged into the front two plugs, then #2 is brighter than #1 How come?  As an additional hint for the wiring impaired, she unscrewed bulb #2 in the latter case, and we noted that #1 also went out.  By contrast, with bulbs in the back two sockets, #1 was lit, whether or not #2 had been unscrewed.  The group drew the following conclusions:

Can you explain everything that was seen under these assumptions?? Materials for assembly were estimated to cost $10 - $15.  However, it is important to practice safe science, and to label this device as a piece of laboratory equipment, and not an ordinary box extension cord.

Very nice, Marilynn!.

Notes taken by Porter Johnson