Surveying Formulas PDF

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Formulas used in Surveying...

Description

Measurement Corrections

measure too long add too short subtract

Due to temperature: (add/subtract); measured length

C = αL(T2 − T1 ) Due to pull:

(P2 − P1 )L C= EA

(add/subtract); measured length

(subtract only); unsupported length

w 2 L3 24P 2

∑(x − x) n−1

(subtract only); measured length

C 2 = S 2 − h2

∑(x − x) Em = = 0.6745√ n(n − 1) √n

√PN − P

1 𝑑

E=error; d=distance; n=no. of trials

Normal Tension:

0.204W√AE

1 𝐸2

𝑤∝

𝑤∝𝑛

Area of Closed Traverse

Symmetrical:

L H = (g 1 + g 2 ) 8 L x 2 ( 2) = L y H 1 2

Reduction to Sea Level

CD MD = R R+h

error/setup = −eBS + eFS Inclined Upward:

Subtense Bar

error/setup = +eBS − eFS Inclined Downward:

D = cot

eT = error/setup ∙ no. of setups Total Error:

Inclined:

D = Ks cos θ + C H = D cos θ V = D sin θ

θ 2

Double Meridian Distance Method DMD

DMD𝑓𝑖𝑟𝑠𝑡 = Dep𝑓𝑖𝑟𝑠𝑡 DMD𝑛 = DMD𝑛−1 + Dep𝑛−1 + Dep𝑛 DMD𝑙𝑎𝑠𝑡 = −Dep𝑙𝑎𝑠𝑡 2A = Σ(DMD ∙ Lat)

Double Parallel Distance Method DPD

DPD𝑓𝑖𝑟𝑠𝑡 = Lat𝑓𝑖𝑟𝑠𝑡 DPD𝑛 = DPD𝑛−1 + Lat 𝑛−1 + Lat 𝑛 DPD𝑙𝑎𝑠𝑡 = −Lat 𝑙𝑎𝑠𝑡

d A = [h1 + hn + 2Σh𝑜𝑑𝑑 + 4Σh𝑒𝑣𝑒𝑛 ] 3

Error of Closure Perimeter

1 acre = 4047 m2

D = d + (f + c ) 𝑓 D = ( )s+C 𝑖 D = Ks + C

Simpson’s 1/3 Rule:

Relative Error/Precision:

D2 (h − h2 ) − 0.067D1D2 D1 + D2 1

Elev𝐵 = Elev𝐴 + 𝐵𝑆 − 𝐹𝑆

d A = [h1 + hn + 2Σh] 2

= √ΣL2 + ΣD2

Azimuth from South

Leveling

Trapezoidal Rule:

Lat = L cos α Dep = L sin α

=

h = h2 +

Area of Irregular Boundaries

Error of Closure:

Parabolic Curves

hcr = 0.067K 2

Horizontal:

E

𝑤∝

e ) TL

Effect of Curvature & Refraction

Stadia Measurement

Proportionalities of weight, w:

Due to slope:

PN =

CD = MD (1 −

Probable Error (single):

E = 0.6745√

e CD = MD (1 + ) TL too long

too short

Probable Errors

Probable Error (mean):

Due to sag:

C=

lay-out subtract add

2A = Σ(DMD ∙ Dep)

Note: n must be odd

Simple, Compound & Reverse Curves

Spiral Curve

Unsymmetrical:

H=

L1 L2 (g + g 2 ) 2(L1 +L2 ) 1

g 3 (L1 +L2 ) = g1 L1 + g 2 L2 Note: Consider signs.

Earthworks

𝑑𝐿 0 𝑑𝑅 ±𝑓𝐿 ±𝑓 ±𝑓𝑅

f w A = (dL + dR) + (fL + fR ) 4 2

T = R tan

2

L Ve = (A1 + A 2 ) 2

L = 2R sin

Volume (Prismoidal):

L (A + 4A m + A2 ) 6 1

Lc = RI ∙

L (c − c2 )(d1 − d2 ) 12 1

VP = Ve − Cp

Σh = A( ) n

Volume (Truncated):

VT = ABase ∙ Have

VT =

2

2

π

v2 S = vt + 2g(f ± G)

(deceleration)

L= LS

L3 6RLs

Ts =

A (Σh1 + 2Σh2 + 3Σh3 + 4Σh4 ) n

Stopping Sight Distance

x=

Ls 2 θ ; p= 24R 3

Y=L−

180° 20 2πR = 360° D 1145.916 R= D

Prismoidal Correction:

CP =

I

m = R [1 − cos ] I

L2 180° ∙ π 2RLs

i=

I

E = R [sec − 1]

Volume (End Area):

VP =

I

2

θ=

Parabolic Sag Curve

Underpass Sight Distance

Horizontal Curve

A(S)2 L= 122 + 3. 5S

L>S

A(S)2 L= 800H

L>S

L>S

2

200(√h1 + √h2 )

LT → long tangent ST → short tangent R → radius of simple curve L → length of spiral from TS to any point along the spiral Ls → length of spiral I → angle of intersection I c → angle of intersection of the simple curve p → length of throw or the distance from tangent that the circular curve has been offset x → offset distance (right angle distance) from tangent to any point on the spiral xc → offset distance (right angle distance) from tangent to SC Ec → external distance of the simple curve θ → spiral angle from tangent to any point on the spiral θS → spiral angle from tangent to SC i → deflection angle from TS to any point on the spiral is → deflection angle from TS to SC y → distance from TS along the tangent to any point on the spiral

L...