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Chapter 6: Coordinate and Vector Systems


 Date

Entry Task

Activity

Assignment/Homework*

10/27
What two pieces of information are needed to define a course from one airport to another?
Chapter 6 Introduction (Pg. 347).

Play Polar Tic-Tac-Toe (see Pg. 348).

See an actual RADAR screen and how a RADAR screen is set up in ATC for a person to use.

JR:  Explain two different (common) ways direction can be displayed in polar graphing.
Pg. 353 #1 (graph and label).

Note: test correction sessions tomorrow before and after school.
10/28
Trillian and her pet bird decided to race to her friend's house.  Trillian rode her bike at five miles per hour 0.3 miles to the east and 0.1 miles to the south.  Her bird flew straight there at four miles per hour.  How far and in what direction did the bird travel?  Who arrived first?
Polar Coordinates activity (pp. 349-352).  Refining the meaning of polar graphing and converting between polar and rectangular coordinates.

JR:  Explain in simple language two ways how angles measured in "azimuth" (measured with a navigation compass) differ from those measured in polar form (measured with a protractor).
Graph the sun transit data (for 31 October 2014) on polar graph paper.

Note: test correction sessions TODAY before and after school.




10/29
The latitude and longitude of Boston are 42 degrees 19' and 71 degrees 5' respectively.  Boston is in the Eastern time zone, which is three hours different from Seattle.  List the similarities and differences between the graphs of the Sun transit data if done for Boston and Seattle for the same day of the year. Graph Boston's sun transit data (for 31 October 2014) on the polar graph paper you used for Seattle's.  Make Boston's marks in a different pigment!

Explain the similarities and differences between the plots.

JR:  Explain in simple language why the sun transit plots for Seattle and Boston are different.  Be specific!
Pg. 358 #16.  Graph on polar graph paper.
10/31
Pg. 357 #14.  Graph on Graph on a new sheet of polar graph paper. Compare the ET graph to a recent sounding.  List the similarities and differences between the hodographs in your homework notebook.

JR:  List the domain and range of sin–1, cos–1, and tan–1.
Pgs. 355-356 #9, 13.
11/3
Create three arbitrary non-collinear vectors: a, b, and c.  Sketch how to perform the vector sum a – (b + c).  Explain the process in simple language. The Algebra of Vectors activity (Pgs 384-387).

JR:  Explain in simple language what happens to a vector if you multiply it by a number (such as “2”).  Include a reason the number is referred to as a “scalar.”
Pg. 388 #2, 4.
11/4
What are the local forecast winds aloft at 9000'?

GEG 2215-05 2929-06 2930-10 2938-25 3043-36 317248 SEA 2522 2519-01 2624-04 2730-09 2943-23 3076-31 800544 YKM 9900 2821+01 2829-04 2727-08 2839-23 3165-32 810144
Of Course activity.

Click HERE for an answer to Scenario #2 (wait until you have completed the problem before checking!!!).

JR:  How far off course will the airplane be from its destination in today’s Scenario #1 if the heading is off by 1 degree?
Compute heading, ground speed, and ETE for a flight plan from Boeing Field Airport (KBFI) to Astoria (KAST) assuming an airspeed of 120 KTS and current winds.  Use vectors for airspeed and wind speed to confirm the ground speed and course (remember to convert the azimuths to polar then to rectangular coordinates, then convert back to polar then azimuths).

Get your own electronic copy of the North and South Seattle Sectional Charts (note: the originals are here!).
11/5
Why can a vector be described in BOTH polar and rectangular coordinates? Compute heading, ground speed, and ETE for a flight plan from Boeing Field Airport (KBFI) to Walla Walla (KALW).  Assume an airspeed of 128 KTS and the same winds you used for yesterday's homework.

JR:  Explain the difference between True and Magnetic North then explain how to determine the correction for a specific location.  Give detail!
Compute heading, ground speed, and ETE for a flight plan between airports of your choosing, as long as the enroute distance is at least 150 NM. Assume an airspeed of 135 KTS and current winds.  Include the day and time you obtained the winds.
11/7
Convert the vector (3, 200 degrees) to rectangular coordinates using trig.  Convert the result to polar coordinates using trig.  What happened and why?
Compute heading, ground speed, and ETE for a flight from Bellingham International Airport (KBLI) to Pullman/Moscow Regional Airport (KPUW).  Use an airspeed of 118 KTS and use the current winds aloft.  Record the latitude and longitude of each airport.

JR:  Explain in simple language the advantage of adding vectors algebraically even if the answer must be in polar form.
Determine the number of minutes of latitude KPUW is East of KBLI.  Determine the number of minutes of longitude KPUW is South of KBLI.  Use the number of minutes of latitude and longitude as legs of a right triangle and compute the hypotenuse.  Convert this measure into nautical miles (this represents the distance from Bellingham Airport to Pullman Airport).  Give two reasons why this distance is different from the one you measured on the chart today in class.
11/10
Explain the advantage of performing all vector operations in rectangular coordinates.  What disadvantages are there? Quiz 6.1 (flight plan).  You may use YOUR calculator and a 3 x 5 note card* along with any measurement devices you brought

*Note cards may not be mechanically reproduced (no photo copies, word processing, etc.).

JR:  Explain in simple language how to convert angles measured in "azimuth" (measured with a navigation compass) to those measured in polar form (measured with a protractor)
Compute heading, ground speed, and ETE for a flight plan from Boeing Field Airport (KBFI) to Quillayute (KUIL).  Assume an airspeed of 138 KTS and the current winds aloft.  Include the day and time you obtained the winds.

11/12
A projectile is launched at a 40 degree angle.  Explain in simple language how the horizontal component of the projectile's velocity changes over the projectile's flight if its speed is low enough for air resistance to be negligible. Parametric Equations.

Graphing rectangular coordinates when X and Y are derived from functions (parametric equations--see Example 10, p. 398).
 
It’s About Time activity.

JR:  Summarize with simple parametric equations an object launched at 35 degrees with an initial velocity of 42 feet per second.  Provide the "graphing Window" that will show the path of the object.
Pgs. 403-404 #11, 12.
11/14
Explain how the game "Battleship" would work if played in 3-d. 3-d graphing.

Play Sky Wars.

JR:  Explain a strategy for success in playing Sky Wars.
Pgs. 420-421 #12, 13.
11/17
Draw a three-dimensional coordinate system on your paper. Vector Equations in Three Dimensions (Activity 6.6, Pgs. 406-410).  Isometric graph paper is needed.  Use the following links to download either of the full-page isometric dot papers:
JR: Describe an aerospace application of 3-d vectors.
Draw the vector <3, 4, 5> making sure you show the vector <3, 4> in the x-y plane.  Calculate the length of each vector (hint: use the Pythagorean Theorem twice).
11/18
Write parametric equations for a golf ball struck at 101 ft/s with a club angle of 22 degrees.  Determine how far, horizontally, will the ball travel. Activity 6.7 Pgs. 410-412 (up to Vectors In Space).

How could you tell by a pair of 3-d vectors' "rectangular coordinates" they are perpendicular?

JR:  Explain the extent to which adding a third dimension contributes to the difficulty of working with vectors.  Connect this to the difference between driving a car and flying an airplane.
Pg. 421 #14.

Check out THIS Website that offers help with spherical coordinates (thanks to Lauren Crom for the link).
11/19 Feflog's golf ball is located 145 yards from the center of the green on a level fairway.  There is a 51' tree 30 yards from the ball in the direction of the green.  She selects a club with a 36 degree loft and will strike the ball at 123 feet per second.  analyze the outcome of the shot.
Obtain a copy of the Parametric POGIL activity.  Read through the first page.

Parametric POGIL
activity.

JR:  What is the purpose of today's activity?  List some "new understandings" you gained today.
The World's newest golfing sensation is Doow Regit, who is from Elbonia.  While playing The British Open, she hits the ball so far off the first tee it lands in a "fairway bunker" (a deep sand trap).  Although only 45 yards from the center of the green, the ball is only two feet away from the "lip" of the bunker that extends upward two feet.  Further, the green is four feet above the fairway and the sand in the bunker is two feet below the fairway.  She selects her 56 degrees sand wedge and will strike the ball at 85 feet per second.   Note: 1 yard = 3 feet.

1.    Sketch the situation, including all relevant facts.
2.    Write parametric equations for this situation.  "Identify the variables!"
3.    Determine if Doow's shot will make it to the green.  Explain how you know!
11/21
Why is there a -16T2 in the Y equation for golf ball flight?
Quiz 6.3 (writing parametric equations to address a scenario--it will be a golf problem!).  You may use YOUR calculator and a 3 x 5 note card* along with any measurement devices you brought.  Materials will NOT be loaned during class.

*Note cards may not be mechanically reproduced (no photo copies, word processing, etc.).

JR:   Create an isometric diagram depicting the sum of vectors <1, 2, 3> and <2, 4, 1>.  Give the value of the vector sum and show it (in a contrasting color, if possible) on your diagram.
Pg. 418 #4.
11/24
Solve for WCA, TH, MH, GS, ad ETE for a flight from Everett (KPAE) to Ellensburg (KELN).  Assume an airspeed of 110 KTS.
Debrief ET.

Solve for WCA, TH, MH, GS, and ETE for a flight from Avey State at Laurier (69S) to Copalis State (S16).  Assume an airspeed of 110 KTS.

JR:  Explain how do convert TH to MH using information from an aeronautical chart.
Prepare for tomorrow's test.
11/25
Get ready for the test!  Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people. Test 6.2.  You may use YOUR calculator and a 3 x 5 note card* (writing on both sides is permitted).  Measurement devices (e.g. ruler and protractor) are also allowed.  No materials will be loaned during class!  Expect a question on
  • Flight planning (solving for WCA, TH, MH, GS, ETE).
*Note cards may not be mechanically reproduced (no photo copies, word processing, etc.).

JR:  What were the hardest parts of Chapter 6 for you?  What were the easiest parts?
Take a break but remain current.  :-)
*Unless otherwise noted, homework is due the next class day.