BRAE 237: Useful Formulas and Math

basic formula for the accumulation of random errors

'the expected error per occasion times the square root of the number of occasions'

For survey adjustments:

(1) address instrument errors first (averaging) and then make geometrical adjustments (balancing) (2) Most survey adjustments are linear based on a specific metrix

1 square chain

(66' x 66') = 1/10 acre

Allowable error =

0.0014 x square root of the distance in ft (distance is sum of LOSDs)

1 acre

10 square chains

1 cubic yard

27 cubic feet

1 meter

3.28083333 ft

1 acre

43,560 square feet

10 square chains

43,560 square ft

1 chain

66ft

1 mile

80 chains

20 seconds of arc

approximately 0.01' in 100'

1 minute of arc

approximately 0.03' in 100ft

L

arc length

2pi radians

in one circle

D

internal angle at radius point from BC to EC

R

radius

For difference in elevation use

the cosine of the vertical angle times the slope distance

To reduce to level use

the sine of the vertical angle times the slope distance

3mm

~ 0.01'

1cm

~0.03'