f. Exercises.—Solve graphically(1) y=x2 y—x=0 (2) 4y—x=0 y-x=0 (0,0); (4,4) Answer. (3) y=x2+2 y-x=4 (4) 4y—15=22 22—3=y (3,6); (-3,6) Answer. SECTION VI ANGULAR MEASUREMENT Paragraph Purpose------Angle and units of angular measurement. Course, heading, drift.-Miscellaneous exercises- 37. Purpose.—The purpose of this section is to familiarize the student airman with angular measurements and how they are used in determining directions in the U. S. Army Air Forces. 38. Angle and units of angular measurement.-a. Consider a circle. The circumference, or any part of that circumference which is called an arc, is divided into units called degrees. There are 360 degrees in a complete circumference (or one revolution). For more accurate measurements a degree is divided into 60 equal parts called minutes and a minute is divided into 60 equal parts called seconds. The following table of angular measurement shows the symbols used for these units of angular measurement: 360° (degrees)=1 circumference part of a circumference ----- 10 60' (minutes)=1° 60" (seconds)=1' Only the degree is used in this manual. b. An angle is the figure formed by drawing two straight lines outward from a common point. The common point is called the vertex of the angle and the straight lines are called the sides of the angle. In figure 38, O is the vertex and NO and PO are the sides of the angle NOP. Another definition of an angle is the amount of rotation or turning necessary to rotate NO to the new position PO. The air navigation system of measuring and naming directions consists of designating directions by measuring them in degrees clockwise from the north through 360°. This angle is sometimes referred to as azimuth. VERTEX ANGLE FIGURE 38. C. The instrument for measuring angles is the protractor. To. measure an angle with a protractor, place the protractor on the angle to be measured (see fig. 39) so that either half of the side AB will fall upon one side of the angle and the point 0 on the vertex. The reading on the scale where the other side of the angle crosses it is the measure of the angle in degrees. : d. Exercise.—Measure each of the angles in figures 40, 41, 42, and 43. e. To construct an angle with a protractor.-Draw one side of the angle and locate the vertex. Place side AB of the protractor on the side drawn with point 0 of the protractor on the vertex. Locate the reading of the value of the angle required on the scale of the protractor and connect this with the vertex. Measure the angle by starting at the north line. (1) Example: Lay off an angle of 115o. Solution: First draw the north line, then follow the instructions in c above (see fig. 44). (2) Exercise.—Use a protractor and lay off angles of 30°, 135°, 180°, 240°, and 315o. NORTH LINE FIGURE 44. f. Angles of elevation and depression. The angle of elevation or angle of depression of any given object is the angle made by the line to that object and a horizontal line at the eye level in the same vertical plane. In figure 45 the angle made with the two airplanes is the angle of elevation while the angle made with the power lines is the angle of depression. POINT OF O FIGURE 45. 39. Course, heading, drift.-a. True course (C)—Direction over the surface of the earth expressed as an angle with respect to true north in which an aircraft intends to fly. It is the direction as laid out on a map or chart. 6. True heading (H).—Angular direction of the longitudinal (front to rear) axis of the aircraft with respect to true north. C. Drift (D)-Angle between the true heading and the true course. It is right drift if the true course is greater than the true heading. If the true course is less than the true heading, it is left drift. d. Wind direction.—Wind is designated by the direction from which it blows (see fig. 48). e. In determining true heading when true course is given, subtract right drift from true course. Add left drift to true course to obtain true heading. 40. Miscellaneous exercises.—a. Determine the direction (north, south, east, west, etc.) in each of the following cases: (1) True course 180°. True course west. Answer. Wind from northwest. Answer. (5) Wind from 135o. (6) Wind from 0°. Wind from north. Answer. (7) True heading 45°. (8) True heading 90°. True heading east. Answer. 6. Determine the true heading in each of the following cases: . (1) True course=90°, right drift=6o. Solution: COURSE = HEADING + RIGHT DRIFT 90° = HEADING + 6° FIGURE 49. Answer. - Answer. (5) True course=0°, left drift=15°. |