Reference Handbook. 9.0 Version for Computer-Based Testing

Transcription

1 Referece Hdbook 9.0 Verso for Computer-Bsed Testg

2 CONVERSIONS AND OTHER USEFUL RELATIONSHIPS * U.S. survey foot = m * tertol foot = m *. = 5.4 mm (tertol) mle = km * cre = 43,560 ft = 0 squre chs * h = 0,000 m =.4704 cres * rd = 80 kg =.046 lb L = 0.64 gl ft 3 = 7.48 gl gl of wter weghs 8.34 lb ft 3 of wter weghs 6.4 lb tm = 9.9. Hg = ps Grvty ccelerto (g) = m/s = 3.74 ft/sec Speed of lght vcuum (c) = 99,79,458 m/s = 86,8 mles/sec C = (F 3)/.8 m of lttude () utcl mle utcl mle = 6,076 ft Me rdus of the erth 0,906,000 ft 6,37,000 m * Deotes exct vlue. All others correct to fgures show. METRIC PREFIXES METRIC PREFIXES Multple Prefx Symbol Multple Prefx Symbol tto femto pco o mcro mll cet dec f p m c d dek hecto klo meg gg ter pet ex d h k M G T P E QUADRATIC EQUATION x + bx + c = 0 Roots b b 4c

3 OBLIQUE TRIANGLES A Lw of ses b c s A s B s C Lw of coses b c bccosa or b c cos A bc Are = bs C sbsc Are = sa b b c Are = ss sb s c where s = ( + b + c)/ SPHERICAL TRIANGLES c A C Lw of ses s s b s c s A s B s C Lw of coses cos = cos b cos c + s b s c cos A Are of sphere 4R 4 3 Volumeof sphere R 3 Sphercl excess sec = bc s A R where R = me rdus of the erth C B B PROBABILITY AND STATISTICS (x x) v = stdrd devto (sometmes referred to s stdrd error) v = sum of the squres of the resduls (devto from the me) = umber of observtos x = me of the observtos (dvdul mesuremets x ) sum seres me product b x xy xy y where the couterclockwse t gle from the x xs xy x y Reltve weghts re versely proportol to vrces, or: W Weghted me: M w WM W M w = weghted me WM = sum of dvdul weghts tmes ther mesuremets W = sum of the weghts

4 HORIZONTAL CIRCULAR CURVES D = Degree of curve, rc defto L = Legth of curve from P.C. to P.T. c = Legth of sub-chord l = Legth of rc for sub-chord d = Cetrl gle for sub-chord P.C. c T P.I. E M Ι L.C T P.T. 5,79.58 D R T = R t I/ I L RI D LC = R s I/ c = R s d/ d D /00 M = R cosi/ E = R cos(i/) RL R I Are of sector 360 R I R si Are of segmet 360 R T L/ Are betwee curve d tgets R d NOT TO SCALE Ι/ D I Ι/ R b B +b A b C R b R R AC s b 3

5 VERTICAL CURVE FORMULAS BACK TANGENT g PVC TANGENT OFFSET x Y PVC y L PVI E PVT FORWARD TANGENT g ASTRONOMY N φ P 90 φ LHA(t) 90 δ E Z 90 h MERIDIAN S δ h EARTH EQUATOR So DATUM VERTICAL CURVE FORMULAS NOT TO SCALE W HORIZON L = Legth of curve (horzotl) PVC = Pot of vertcl curvture PVI = Pot of vertcl tersecto PVT = Pot of vertcl tgecy g = Grde of bck tget g = Grde of forwrd tget x = Horzotl dstce from PVC (or pot of tgecy) to pot o curve = Prbol costt y = Tget offset E = Tget offset t PVI r = Rte of chge of grde Tget elevto = Y PVC + g x d = Y PVI + g (x L/) Curve elevto = Y PVC + g x + x = Y PVC + g x + [(g g )/(L)]x y x ; g g ; L L E= ; g_ g r = L Horzotl dstce to m/mx elevto o curve, g gl x m = g g Cos (Az) (s s sh) / cos cos h (lttude method) T (Az) s(lha) / (cos t s cos (LHA) (hour gle method) S h s s cos cos cos LHA t = LHA or 360 LHA Horzotl crcle correcto for su's semdmeter = SD/cos h Equtos ccurte for Polrs oly: h = + p cos LHA Az = (p s LHA)/cos h Az = Azmuth (from orth) to su/str δ = Declto = Lttude h = Alttude of su/str LHA = Locl hour gle (sometmes referred to s "t" or "hour gle") SD = Arc legth of su's sem-dmeter p = Polr dstce of Polrs 4

6 PHOTOGRAMMETRY b f Scle vertcl photogrph AB H h rh Relef dsplcemet = vertcl photogrph H Prllx equtos: p x x X xb p yb Y p fb h H p (p p ) h h (Hh ) p f = Focl legth h = Heght bove dtum H = Flyg heght bove dtum r = Rdl dstce from prcpl pot p = Prllx mesured o stereo pr B = Arbse of stereo pr x, y = Coordtes mesured o left photo x = Coordte mesured o rght photo X, Y = Groud coordtes PHYSICS Les equto: o f o = Object dstce = Imge dstce f = Focl legth Sell lws: s = s = Refrctve dex = Agle of cdece Curvture d refrcto: (c + r) = 0.006M (c + r) = Combed effect of curvture d refrcto feet M = Dstce thousds of feet 5 s t s = Dstce trveled strtg from zero velocty = Costt ccelerto t = Tme of trvel GEODESY Ellpsod = semmjor xs b = semmor xs b Fltteg, f usully publshed s /f b Eccetrcty, e e Rdus merd, M 3 e s Rdus prme vertcl, N e s Agulr covergece of merds dt e s rd Ler covergece of merds e s dt = Lttude d = Dstce log prllel t lttude = Legth log merds seprted by d Ellpsod deftos: GRS80: = 6,378,37.0 m /f = Clrk 866: = 6,378,06.4 m /f = Orthometrc correcto: Correcto = shrc = lttude t strtg pot h = dtum elevto meters or feet t strtg pot = chge lttude mutes betwee the two pots (+ the drecto of cresg lttude or towrds the pole) N S b

7 STATE PLANE COORDINATES Scle fctor = Grd dstce/geodetc (ellpsodl) dstce Elevto fctor = R/(R + H +N) R = Ellpsod rdus H = Orthometrc heght N = Geod heght For precso less th /00,000: R = 0,906,000 ft H = Elevto bove se level N = 0 ELECTRONIC DISTANCE MEASUREMENT V c/ V/f md D V = Velocty of lght through the tmosphere (m/s) c = Velocty of lght vcuum = Idex of refrcto = Wve legth (m) f = Modulted frequecy hertz (cycles/sec) D = Dstce mesured m = Iteger umber of full wvelegths d = Frctol prt of the wvelegth ATMOSPHERIC CORRECTION A 0C temperture chge or pressure dfferece of. of mercury produces dstce correcto of pproxmtely 0 prts per mllo (ppm). AREA FORMULAS Are bycoordtes where s pot order closed polygo. Are XY XY Trpezodl Rule h h Are w h h h h Smpso's/3 Rule 3 4 Are wh hodds 4 heves h /3 6 EARTHWORK FORMULAS Averge ed re formul Volume = L(A + A )/ Prsmodl formul Volume = L(A + 4A m + A )/6 Pyrmd or coe Volume = h(are of Bse)/3 TAPE CORRECTION FORMULAS Correcto for temperture C t = (T T s )L Correcto for teso C p = (P P s )L/(AE) Correcto for sg C s = (w 3) / (4P ) T = Temperture of tpe durg mesuremet, F T s = Temperture of tpe durg clbrto, F L = Dstce mesured, ft P = Pull ppled durg mesuremet, lb P s = Pull ppled durg clbrto, lb A = Cross-sectol re of tpe, E = Modulus of elstcty of tpe, ps w = Weght of tpe, lb/ft = Legth of usupported sp, ft STADIA Horzotl dstce = KS cos Vertcl dstce = KS s cos K = Std tervl fctor (usully 00) S = Rod tercept = Slope gle mesured from horzotl

8 UNIT NORMAL DISTRIBUTION TABLE x f(x) F(x) R(x) R(x) W(x) Frctles

9 t-distribution TABLE VALUES OF t, = 0.0 = 0.05 = 0.05 = 0.0 =

10 CRITICAL VALUES OF THE F DISTRIBUTION TABLE For prtculr combto of umertor d deomtor degrees of freedom, etry represets the crtcl vlues of F correspodg to specfed upper tl re (α). Deomtor df Numertor df

11 ECONOMICS Fctor Nme Coverts Symbol Formul Sgle Pymet Compoud Amout to F gve P (F/P, %, ) ( + ) Sgle Pymet Preset Worth Uform Seres Skg Fud to P gve F (P/F, %, ) ( + ) to A gve F (A/F, %, ) Cptl Recovery to A gve P (A/P, %, ) Uform Seres Compoud Amout Uform Seres Preset Worth Uform Grdet Preset Worth Uform Grdet Future Worth Uform Grdet Uform Seres to F gve A (F/A, %, ) to P gve A (P/A, %, ) to P gve G (P/G, %, ) to F gve G (F/G, %, ) to A gve G (A/G, %, ) Nomeclture d Deftos A Uform mout per terest perod B Beeft BV Book Vlue C Cost d Combed terest rte per terest perod D j Deprecto yer j F Future worth, vlue, or mout f Geerl flto rte per terest perod G Uform grdet mout per terest perod Iterest rte per terest perod e Aul effectve terest rte m Number of compoudg perods per yer Number of compoudg perods; or the expected lfe of sset P Preset worth, vlue, or mout r Noml ul terest rte Expected slvge vlue yer S Subscrpts j t tme j t tme F/G = (F/A )/ = (F/A) (A/G) 0

12 Noul Compoudg e r m m Book Vlue BV = Itl cost D j Deprecto C S Strght le D j = Accelerted Cost Recovery System (ACRS) D j = (fctor from tble below) C Yer MODIFIED ACRS FACTORS Recovery Perod (Yers) Recovery Rte (%) Cptlzed Costs Cptlzed costs re preset worth vlues usg ssumed perpetul perod of tme. Cptlzed costs = P = A