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Angular Measurement. Session 2. Angular Measurement. Circles are divided into 360 equal parts, each being a degree. Each of these degrees can be evenly divided into 60 equal parts. These parts are called minutes.

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angular measurement2
Angular Measurement
  • Circles are divided into 360 equal parts, each being a degree.
  • Each of these degrees can be evenly divided into 60 equal parts. These parts are called minutes.
  • These minutes can be evenly divided into 60 equal parts. These parts are called minutes.
angular measurement3
Angular Measurement
  • 1 Circle = 360 Degrees ( 360° )
  • 1 Degree ( 1° ) = 1/360th of a Circle
  • 1 Degree ( 1°) = 60 Minutes ( 60\' )
  • 1 Minute ( 1\' ) = 1/60th of a Degree
  • 1 Minute ( 1\') = 60 Seconds ( 60" )
  • 1 Second ( 1" ) = 1/60th of a Minute
angular measurement4
Angular Measurement
  • The unit of degree can also be divided into either decimal or fractional parts and is referred to as decimal degrees or fractional degrees respectively.
  • 1½ Degree = 1.5 Degree ( 1.5°)
  • 87¼ Degrees = 87.25 Degrees ( 87.25° )
angular measurement5
Angular Measurement
  • Minutes and seconds can each be expressed as decimal or fractional degrees.
  • 1 Minute ( 1\' ) = 1/60th of a Degree = 0.01667°
  • 1 Second ( 1" ) = 1/60th of a Minute = 0.01667\'
angular measurement6
Angular Measurement

Change 5°25\' to decimal degrees

Divide the minutes by 60

25 divided by 60 = 0.4167

Add 0.4167 to 5 = 5.4167°

5°25\' = 5.4167°

angular measurement7
Angular Measurement

Change 27°52\'35" to decimal degrees

Divide the seconds by 60, add to minutes

35 divided by 60 = 0.5833

Added to the 52 minutes, it becomes 52.5833\'

Divide the minutes by 60, add to degrees

52.5833 divided by 60 = .8764

Added to the 27 degrees, it becomes 27.8764°

27°52\'35" = 27.8764°

angular measurement8
Angular Measurement

Change 47.75° to degrees, minutes, and seconds

Multiply the decimal portion by 60

75 x 60 = 45

This decimal .75 becomes 45 minutes. Add this to the degrees.

Since there isn\'t any decimal portion after the 45, no further work is necessary.

47.75° = 47°45\'

angular measurement9
Angular Measurement

Change 82.3752° to Degrees, minutes, and seconds

Multiply the decimal portion by 60

0.3752 x 60 = 22.512 (the 22 becomes the minutes) Now add this to the degrees

82.3752° = 82°22.512\'

Multiply the decimal minutes by 60

0.512 x 60 = 30.72 Now add this to the degrees and minutes to become seconds.

82.3752° = 82°22\'30.72"

angular measurement11
Angular Measurement
  • Most common tools
    • Simple Protractor
    • Multi-Use Gage
    • Combination Set
    • Universal bevel protractor
    • Sine bar
    • Sine plate
protractor13
Protractor

Whole degree increments

multi use gage
Multi-Use Gage

Pre-set positions for 45 and 90 degrees, 59 degree drill point angle, and whole degree increments.

multi use gage15
Multi-Use Gage

Pre-set position for 90 degrees.

multi use gage16
Multi-Use Gage

Pre-set position for 45 degrees.

multi use gage17
Multi-Use Gage

Measuring 59 degree drill point angle.

combination set protractor
Combination Set Protractor

Whole degree increments

protractor head
Protractor Head

Whole degree increments

protractor21
Protractor

Built-in Spirit Level

protractor22
Protractor

Angular Measure with Protractor Head

universal bevel protractor
Universal Bevel Protractor
  • Precision angles to within 5\' (0.083º)
  • Consist of base
    • Vernier scale
    • Protractor dial
    • Sliding blade
    • Dial clamp nut
vernier protractor
Vernier Protractor
  • Used to measure obtuse angle (90º-180º)
  • Acute-angle attachment fastened to protractor to measure angles less than 90º
  • Main scale divided intotwo arcs of 180º
    • Scale divided into 12 spaces on each side of 0
    • If zero on vernier scalecoincides with line on main: reading in degrees
reading a vernier protractor

Fourth

Reading a Vernier Protractor
  • Note number of whole degrees between zero on main scale and zero on vernier scale
  • Proceeding in same direction, note which vernier line coincides with main scale line
  • Multiply number by 5\' and add to degrees on protractor dial

50º

4 x 5\'= 20\'

Reading =

50º 20\'

sine bars
Sine Bars
  • Used when accuracy of angle must be checked to less than 5 minutes
  • Consists of steel bar with two cylinders of equal diameter fastened near ends
    • Centers of cylinders exactly 90º to edge
    • Distance between centers usually 5 or 10 inches and 100 or 200 millimeters.
  • Made of stabilized tool hardened steel
sine bars30
Sine Bars
  • Used on surface plates and any angle by raising one end of bar with gage blocks
  • Made 5 inch or in multiples of 5 or 100 millimeters or multiple of 100
    • Distance between lapped cylinders.
  • Face accurate to within .00005 in. in 5 inches or 0.001 mm in 100 mm.
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