Unit Standards

Meter – Definition of length changed 9 times over about 200 years 1 m = 3.280833 ft (12/39.37) 1790 - equal to the length of a pendulum with a half-

period of one second 1791 - 1 / 10,000,000 of the distance from the equator to

north pole 1870’s - defined by Meter Bar in Paris as part of unit

standardization Standardized in 1959 as 1/3.280733 = 0.3048006 m in

relation to wavelengths of krypton gas Currently considered the time it takes for light to travel

thru vacuum in 1/299,792,458 seconds

Global Positioning Systems

Uses precision timing of satellite signals to determine location of user

Comprised of three segments Space – 24 satellites the size of a car Control – 5 world-wide base stations that

monitor altitude, position and speed User – GPS receivers used by the

general public, surveyors and the military

Trigonometry Review

The cosine function (cos) Cos(A) = opposite (b) /

hypotenuse (c)The tangent function

(tan) Tan(A) = adjacent (a) /

hypotenuse (b) Sin / Cos

The sine function (sin) Sin(A) = opposite (a) /

adjacent (c)

Angle – Distance Relationship

L = R * ThetaIf an error of 1 minute is present, a surveyors

line will be off 1 foot in 3440 feet 1/3440 ratio of precision

Angular Error Angular Precision

5' 1/688

30" 1/6880

1" 1/206,000

Example

Terms

Meridian – fixed line of referenceAstronomic north – direction of a line passing

through the astronomic north and south poles Determined by solar or Polaris observations Used as the basis for many surveys

Geodetic north Mathematical approximation of earth

Magnetic meridian Direction the compass points Changes over time

Assumed meridian Arbitrary direction

Vernier Compass

• 138 degrees 45 minutes to the right, 221 degrees 15 minutes to the left

Definitions

Trigonometric Leveling