Surveying Formulas

Measurement Corrections measure too long add too short subtract Due to temperature: C = αL(T2 − T1 ) E = 0.6745√ (P2 − P1 )L EA (add/subtract); measured length w L C= 24P 2 Proportionalities of weight, w: Due to slope: C =S −h 2 2 𝑤∝ Normal Tension: PN = 0.204W√AE √PN − P 1 𝑑 𝑤∝𝑛 h = h2 + = √ΣL2 + ΣD2 L (g + g 2 ) 8 1 = D = d + (f + c) 𝑓 D = ( )s+C 𝑖 D = Ks + C L 2 ( 2) x = L y H 1 1 acre = 4047 m2 CD MD = R R+h error/setup = −eBS + eFS 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 Reduction to Sea Level Inclined Upward: Simpson’s 1/3 Rule: Relative Error/Precision: D2 (h − h2 ) − 0.067D1 D2 D1 + D2 1 Elev𝐵 = Elev𝐴 + 𝐵𝑆 − 𝐹𝑆 d A = [h1 + hn + 2Σh] 2 Error of Closure: Azimuth from South Leveling Trapezoidal Rule: Lat = L cos α Dep = L sin α Symmetrical: 2 𝑤∝ hcr = 0.067K 2 Area of Closed Traverse Area of Irregular Boundaries Parabolic Curves H= 1 𝐸2 E=error; d=distance; n=no. of trials (subtract only); measured length e ) TL Effect of Curvature & Refraction Horizontal: ∑(x − x) Em = = 0.6745√ n(n − 1) √n 2 3 e ) TL Stadia Measurement E (subtract only); unsupported length 2 ∑(x − x) n−1 Probable Error (mean): Due to sag: CD = MD (1 + CD = MD (1 − Probable Error (single): Due to pull: too long too short Probable Errors (add/subtract); measured length C= lay-out subtract add 2A = Σ(DMD ∙ Dep) Note: n must be odd Simple, Compound & Reverse Curves Spiral Curve Unsymmetrical: H= L1 L 2 (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 I T = R tan 2 2 Ve = L (A + A 2 ) 2 1 I Lc = RI ∙ L (c − c2 )(d1 − d2 ) 12 1 Volume (Truncated): Σh VT = A Base ∙ Have = A ( VT = π v2 2g(f ± G) a = g(f ± G) (deceleration) v (breaking time) tb = g(f ± G) f (100) Eff = fave S = vt + v → speed in m/s t → perception-reaction time f → coefficient of friction G → grade/slope of road L< S A(S)2 200(√h1 + √h2 ) L = 2(S) − 0.0079k 2 R D L = DC L s e= Parabolic Sag Curve L>S 2 200(√h1 + √h2 ) A L → length of summit curve S → sight distance h1 → height of driver’s eye h1 = 1.143 m or 3.75 ft h2 → height of object h2 = 0 15 m or 0 50 ft 0.036k 3 R Ls = Parabolic Summit Curve L= L5 40R2 Ls 2 I Ls + (R + p) tan 2 2 I Es = (R + p) sec − R 2 ) L>S L3 6RLs Ts = n 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: VP = Ve − Cp 2 L = 2R sin 2 L VP = (A1 + 4A m + A2 ) 6 CP = I m = R [1 − cos ] Volume (Prismoidal): L2 180° ∙ π 2RLs i= I E = R [sec − 1] Volume (End Area): θ= 2 L= L< S A(S)2 122 + 3. 5S L = 2(S ) − 122 + 3.5S A A → algebraic difference of grades, in percent L → length of sag curve S → sight distance Underpass Sight Distance L>S L= L< S A(S)2 800H L = 2(S ) − H = C− 800H A h1 + h2 2 A → algebraic difference of grades, in percent L → length of sag curve A(K)2 For passengers comfort, where K is speed in KPH 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 Horizontal Curve L>S R= L< S R= S2 8M L(2S − L) 8M L → length of horizontal curve S → sight distance R → radius of the curve M → clearance from the centerline of the road