PS Reference Handbook Revised September 20, 2018 The following pages have been changed in this version of the PS Reference Handbook: p. iii, Copyright page p. 1, Abbreviations and Acronyms p. 15, MACRS section This document may be printed from the NCEES website for your personal use, but NCEES material may not be copied, reproduced, distributed electronically or in print, or posted online without the express written permission of NCEES. Contact [email protected] for more information. PS REFERENCE HANDBOOK Copyright ©2019 by NCEES®. All rights reserved. All NCEES material is copyrighted under the laws of the United States. Except for U.S. government material in the public domain, no part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means without the prior written permission of NCEES. Requests for permissions should be addressed in writing to [email protected]. PO Box 1686 Clemson, SC 29633 800-250-3196 www.ncees.org Printed in the United States of America Second posting January 2019 Edition 1.1 About the Handbook The Principles and Practice of Surveying (PS) exam is computer-based, and the PS Reference Handbook is the only resource material you may use during the exam. Reviewing it before exam day will help you become familiar with the charts, formulas, tables, and other reference information provided. You won't be allowed to bring your personal copy of the Handbook into the exam room. Instead, the computer-based exam will include a PDF version of the Handbook for your use. No printed copies of the Handbook will be allowed in the exam room. The PDF version of the PS Reference Handbook that you use on exam day will be very similar to this one. Pages not needed to solve exam questions—such as the cover and introductory material—will not be included in the exam-day PDF. In addition, NCEES will periodically revise and update the Handbook, and each PS exam will be administered using the version of the Handbook in effect on the date the exam is given. The PS Reference Handbook does not contain all the information required to answer every question on the exam. Basic theories, conversions, formulas, and definitions examinees are expected to know have not been included. Special material required for the solution of a particular exam question will be included in the question itself. Updates on exam content and procedures NCEES.org is our home on the Web. Visit us there for updates on everything exam-related, including specifications, exam-day policies, scoring, and practice tests. Errata To report errata in this book, send your correction using our chat feature on NCEES.org. We will also post errata on the website. Examinees are not penalized for any errors in the Handbook that affect an exam question. CONTENTS Abbreviations and Acronyms .................................................................................................... 1 Conversions and Other Useful Relationships ........................................................................... 2 Metric Prefixes .......................................................................................................................... 2 Quadratic Equation ................................................................................................................... 2 Oblique Triangles ...................................................................................................................... 3 Spherical Triangles.................................................................................................................... 3 Probability and Statistics ........................................................................................................... 3 Confidence Intervals ................................................................................................................. 4 Horizontal Circular Curves ....................................................................................................... 5 Horizontal Spiral Curves ........................................................................................................... 6 Vertical Curve Formulas ........................................................................................................... 7 Photogrammetry ........................................................................................................................ 7 Physics ...................................................................................................................................... 8 Curvature and Refraction .......................................................................................................... 8 Geodesy ..................................................................................................................................... 8 State Plane Coordinates............................................................................................................. 9 Electronic Distance Measurement............................................................................................. 9 Atmospheric Correction ............................................................................................................ 9 Area Formulas ........................................................................................................................... 9 Earthwork Formulas .................................................................................................................. 9 Tape Correction Formulas ...................................................................................................... 10 Stadia ....................................................................................................................................... 10 Unit Normal Distribution Table .............................................................................................. 11 t-Distribution Table ................................................................................................................. 12 Critical Values of the F Distribution Table ............................................................................ 13 Economics ............................................................................................................................... 14 Minimum Standard Detail Requirements for ALTA/NSPS Land Title Surveys .................... 17 United States National Map Accuracy Standards ................................................................... 27 FGCS Specifications and Procedures to Incorporate Electronic Digital/Bar-Code Leveling Systems .................................................................................................................... 28 FEMA Elevation Certificate and Instructions ......................................................................... 33 Geospatial Positioning Accuracy Standards Part 1: Reporting Methodology ......................................................................................... 48 Part 2: Standards for Geodetic Networks .......................................................................... 60 Part 3: National Standard for Spatial Data Accuracy........................................................ 69 Part 4: Standards for Architecture, Engineering, Construction (A/E/C) and Facility Management .................................................................................................. 97 Part 5: Standards for Nautical Charting Hydrographic Surveys ..................................... 120 ABBREVIATIONS AND ACRONYMS ALTA American Land Title Association ALTA/NSPS ALTA/NSPS Land Title Surveys. Formerly, ALTA/ACSM BLM Bureau of Land Management CADD computer-aided design and drafting DOD Department of Defense DOI Department of the Interior DOT Department of Transportation DTM digital terrain modeling EDM electronic distance measurement EPA Environmental Protection Agency FEMA Federal Emergency Management Agency FGCS Federal Geodetic Control Subcommittee GIS geographic information system GLO General Land Office GNSS Global Navigation Satellite Systems GPS global positioning system NAVD North American Vertical Datum NGVD National Geodetic Vertical Datum NGS National Geodetic Survey NOAA National Oceanic and Atmospheric Administration NSPS National Society of Professional Surveyors, successor organization to the American Congress on Surveying and Mapping (ACSM) PLSS Public Land Survey System PPP precise point positioning RTK real-time kinematic RTK GPS real-time kinematic global positioning system USGS United States Geological Survey 1 CONVERSIONS AND OTHER USEFUL RELATIONSHIPS 12 * 1 U.S. survey foot = m 39.37 * 1 international foot = 0.3048 m * 1 in. = 25.4 mm (international) 1 mile = 1.60935 km * 1 acre = 43,560 ft2 = 10 square chains * 1 ha = 10,000 m2 = 2.47104 acres  180 * 1 rad = π 1 kg = 2.2046 lb 1 L = 0.2624 gal 1 ft3 = 7.481 gal 1 gal of water weighs 8.34 lb 1 ft3 of water weighs 62.4 lb 1 atm = 29.92 in. Hg = 14.696 psi Gravity acceleration (g) = 9.807 m/s2 = 32.174 ft/sec2 Speed of light in a vacuum (c) = 299,792,458 m/s = 186,282 miles/sec °C = (°F – 32)/1.8 1 min of latitude (φ) ≅ 1 nautical mile 1 nautical mile = 6,076 ft Mean radius of the earth ≅ 20,906,000 ft ≅ 6,372,000 m * Denotes exact value. All others correct to figures shown. METRIC PREFIXES METRIC PREFIXES Multiple Prefix Symbol Multiple Prefix Symbol 10–18 atto a 101 deka da 10–15 femto f 102 hecto h 10–12 pico p 103 kilo k 10–9 nano n 106 mega M 10–6 micro μ 109 giga G 10–3 milli m 1012 tera T 10–2 centi c 1015 peta P 10–1 deci d 1018 exa E QUADRATIC EQUATION ax2 + bx + c = 0 −b± b2 −4ac Roots= 2a 2 OBLIQUE TRIANGLES PROBABILITY AND STATISTICS B (x −x)2 v2 σ= i = c n−1 n−1 a where: A σ = Standard deviation (sometimes b C referred to as standard error) Law of sines v2= Sum of the squares of the residuals a b c = = (deviation from the mean) sinA sinB sinC n = Number of observations x = Mean of the observations (individual Law of cosines measurements x) i a2 = b2 +c2 −2bccosA or σ = σ2 +σ2 ++σ2 b2 +c2 −a2 sum 1 2 n cosA = 2bc σ = σ n series absinC Area = σ 2 σ = mean a2sinBsinC n Area = 2sinA σ = Α2σ2 +Β2σ2 ( )( )( ) product b a Area = s s−a s−b s−c σ2 σ  where s = (a + b + c)/2  = σx σx2y  xy y  SPHERICAL TRIANGLES c 2σ whereθ=thecounterclockwise A tan 2θ= xy σ2 −σ2 anglefromthexaxis x y B b a Relative weights are inversely proportional to variances, or: 1 C W ∝ a σ2 Law of sines a Weighted mean: sina sinb sinc = = sinA sinB sinC WM M = w W Law of cosines where: cos a = cos b cos c + sin b sin c cos A M = Weighted mean w Areaofsphere=4πR2 WM = Sum of individual weights times 4 Volumeofsphere= πR3 their measurements 3 bcsin A W = Sum of the weights Spherical excess in sec = 9.7×10−6R2 where R = Mean radius of the earth 3 CONFIDENCE INTERVALS Confidence Interval for the Mean μ of a Normal Distribution (A) Standard deviation σ is known σ σ X −Zα/2 ≤μ≤ X + Zα/2 n n (B) Standard deviation σ is known s s X −tα/2 ≤μ≤ X +tα/2 n n where tα/2 corresponds to n–1 degrees of freedom. Confidence Interval for the Mean σ2 of a Normal Distribution (n−1)s2 (n−1)s2 ≤σ2 ≤ 2 2 x x α/2,n−1 1−α/2,n−1 Confidence Interval for the Ratio of Two Normal Distribution Variances S2 σ2 S2 1 ≤ 1 ≤ 1 S2 F σ2 S2 F 2 α/2,n1−1,n2−1 2 2 α/2,n2−1,n1−1 Values of Zα/2 Confidence Interval Zα/2 80% 1.2816 90% 1.6449 95% 1.9600 96% 2.0537 98% 2.3263 99% 2.5758 4 HORIZONTAL CIRCULAR CURVES D = Degree of curve, arc definition P.I. I (OR Δ) D = Degree of curve, chord definition c L = Length of curve from P.C. to P.T. E T c = Length of sub-chord T 100.00 ℓ = Length of arc for sub-chord d = Central angle for sub-chord M P.C. c L.C P.T. I or Δ = Angle of interior or delta 5,729.58 D= I/2 I/2 R D 50 d Radiusbychorddefinition,R = R sin1/2D R I (OR Δ) ( ) T = R tan I/2 π I ( ) NOT TO SCALE L=RI = 100 180 D ( ) LC = 2R sin I/2 ( ) c = 2R sin d/2 d =D/100 ( ) M = R 1 −cos I/2     1  E = R −1    cos(I/2)  B a+b b RL πR2I A a b C Areaofsector = = 2 360 πR2I R2sinI Areaofsegment = − 360 2 ( ) R R Area between curve and tangents =R T−L/2 2b 2a AC R = ( ) 2 sin a+b 2 2 2 Equation of a circle, X + Y = R 5