Spiral Curves Made Simple

SPIRAL CURVES MADE SIMPLE

August 2009 Revised 2013

Jim Crume P.L.S., M.S., CfedS A New Math-Series of books with useful formulas, helpful hints and easy to follow step by step instructions.

Digital and Printed Editions Math-Series Training and Reference Books. Designed and written by Surveyors for Surveyors, Land Surveyors in Training, Engineers, Engineers in Training and aspiring Students. Printed - Digital - Apps Many Titles to choose from. http://www.cc4w.net/ Join our “Mailing List” for new Book and App releases by www.facebook.com/ surveyingmathematics clicking the button to the right. Spiral Curves Made Simple

 HISTORY

 Spiral curves were originally designed for the Railroads to smooth the transition from a tangent line into simple curves. They helped to minimize the wear and tear on the tracks. Spiral curves were implemented at a later date on highways to provide a smooth transition from the tangent line into simple curves. The highway engineers later determined that most drivers will naturally make that spiral transition with the vehicle; therefore, spiral curves are only used on highways in special cases today.

 Because they were used in the past and in special cases today, we need to know how to calculate them.

 From the surveyor’s perspective, the design of spiral curves has already been determined by the engineer and will be documented on existing R/W and As-built plans. All we have to do is use the information shown on these plans to fit the spiral curve within our surveyed alignment.

August 2009 Spiral Curves Made Simple

 REFERENCES

 There are many books available on spiral curves that can help you know and understand how the design process works. It can get complicated when you dive into the theory and design of spiral curves.

 My reference material includes the following books:

 Railroad Curves and Earthwork; by C. Frank Allen, S.B.

 Route Surveying and Design; by Carl F. Meyer & David W. Gibson

 Surveying Theory and Practice; by Davis, Foote & Kelly

August 2009 Spiral Curves Made Simple

 ADOT Roadway Guides for use in Office and Field 1986

 This guide has all of the formulas and tables that you will need to work with spiral curves. The formulas, for the most part, are the same formulas used by the Railroad.

 The Railroads use the 10 Chord spiral method for layout and have tables setup to divide the spiral into 10 equal chords. Highway spirals can be laid out with the 10 Chord method but are generally staked out by centerline stationing depending on the needs in the field.

 For R/W calculations we only need to be concerned with the full spiral length.

 The tables that will be used the most are D-55.10 (Full Transition Spiral) and D-57.05 through D-57.95 (Transitional Spiral Tables).

 On rare occasions you may also need D-55.30 (Spiral Transition Compound Curves).

August 2009 Spiral Curves Made Simple

 COURSE OBJECTIVE

 This course is intended to introduce you to Spiral Curve calculations along centerline alignments.

 It is assumed that you already now how to calculate simple curves and generate coordinates from one point to another using a bearing and distance.

 Offsets to Spiral Curves and intersections of lines with Spiral Curves will not be discussed in this lesson. These types of calculations will be addressed in a future lesson.

 You can check your calculations using the online Spiral Calculator at:

 http://www.cc4w.net/spiral/index.aspx

August 2009 Spiral Curves Made Simple

 EXAMPLE SPIRAL

 Included are two example spiral curves from ADOT projects. The one that we will be calculating contains Equal Spirals for the Entrance and Exit on both sides of the main curve.

 The second example contains Unequal Spirals for the Entrance and Exit and a Transitional Spiral between two main curves with different radii. We will look at the process used to calculate this example but we will not be doing any calculations.

 The example spiral that we will be calculating is from the ADOT project along S.R. 64 as shown on sheet RS-17 of the Results of Survey.

 We will walk through each step to calculate this spiral.

 Note: My career started 30 plus years ago, before GPS and computers. I did all my calculations by hand and I teach my staff to do the calculations by hand so that they will have a thorough understanding of the mathematical process. I am a big advocate of technology and use it exclusively. I also have a passion for the art of surveying mathematics, therefore I feel that everyone should know how to do it manually. I feel that my staff has a better appreciation for technology by having done the calculations manually, at least once, before they rely on a computer to do it for them.

August 2009 Spiral Curves Made Simple

 No. 1

 Gather your known information for the spiral curve.

August 2009 Spiral Curves Made Simple

 Look for the spiral curve and main curve information

 The key information needed is the Degree of Curvature and the Spiral length.

 D=2º00’00” and Ls=200.00’ August 2009 Spiral Curves Made Simple

 No. 2

 Your tangent lines should be defined either by survey or record information. Sketch your tangent lines and Point of Intersection. Add the bearings for the tangent lines and calculate the deflection at the P.I. As shown below, the deflection is 36º29’16”.

 13º14’11” + 23º15’05” = 36º29’16”

August 2009 Spiral Curves Made Simple

 No. 3

 The following are spiral formulas that have been derived from several reference materials for spiral calculations that will be utilized for this lesson.

August 2009 Spiral Curves Made Simple

 No. 3 – continued

 Next we will calculate the tangent distance (Ts) from the T.S. to the P.I.

 Use the following formulas to calculate Ts.

 Delta(t) = 36-29-16(dms) ~ 36.48777777(ddd)

 D = 2-00-00(dms) ~ 2.0000(ddd)

 Ls = 200.00’

 R = 5729.578 / D = 5729.578 / 2.0000 = 2864.789’

 a = (D * 100) / Ls = (2.0000 * 100) / 200.00 = 1.00 (Checks with record data)

 “o” = 0.0727 * a * ((Ls / 100)^3)

 “o” = 0.0727 * 1 * ((200.00 / 100)^3) = 0.5816

 “t” = (50 * Ls / 100) – (0.000127 * a^2 * (Ls / 100)^5)

 “t” = (50 * 200.00/100) – (0.000127 * 1^2 * (200.00 / 100)^5 = 99.9959

 Ts = (Tan(Delta(t) / 2) * (R +”o”)) + “t”

 Ts = (Tan(36.48777777 / 2) * (2864.789 + 0.5816)) + 99.9959 = 1044.515’

August 2009 Spiral Curves Made Simple

 No. 3 – continued

 Calculate the Northing and Easting for the Tangent to Spiral (T.S.) & Spiral to Tangent (S.T.)

 Use coordinate geometry to calculate the Latitude and Departure for each course and add them to the Northing and Easting of the Point of Intersection (P.I.) to get the Northing and Easting for the T.S. and S.T.

August 2009 Spiral Curves Made Simple

 No. 4

 Calculate the spiral chord distance (Chord) and deflection angle (Def).

 Chord = (100 * Ls / 100) – (0.00034 * a^2 * (Ls / 100)^5)  Chord = (100 * 200.00 / 100) – (0.00034 * 1^2 * (200.00 / 100)^5) = 199.989’

 Def = (a * Ls^2) / 60000 = (1 * 200.00^2) / 60000 = 0.666666(ddd) ~ 0-40-00(dms)

 Calculate the chord bearing and Northing & Easting for the Spiral to Curve (S.C.) & Curve to Spiral (C.S.)

 Note: Substitute Ls for any length (L) along the spiral to calculate the sub-chord and Def angle to any point along the spiral from the T.S.

August 2009 Spiral Curves Made Simple

 No. 5

 Calculate the spiral delta and tangent distance to the Spiral Point of Intersection (SPI).

 Delta(s) = 0.005 * D * Ls = 0.005 * 2.0000 * 200.00 = 2.0000(ddd) ~ 2-00-00(dms)

 “u” = Chord * Sin(Delta(s) * 2 / 3) / Sin(Delta(s))

 “u” = 199.989 * Sin(2.0000 * 2 / 3) / Sin(2.0000) = 133.341’

 Calculate Northing and Easting of SPI.

August 2009 Spiral Curves Made Simple

 No. 6

 Calculate the radial line and radius point for the main curve.

 Calculate the back deflection from the S.C. to the SPI is as follows:

 Delta(s) – Def = Back Def

 2.0000 – 0.666666 = 1.333334(ddd) ~ 1-20-00(dms)

 Using the Back Def and chord bearing calculate the tangent bearing at the S.C. then perpendicular from the tangent line calculate the radial line. Do this for the C.S. as well. Calculate the Radius point from the S.C. and C.S. You should come up with the same coordinates. If not, then something is wrong. Recheck all of your calculations.

August 2009 Spiral Curves Made Simple

 No. 7

 Using the radial bearings calculate the Main Curve Delta of 32-29-16(dms) ~ 32.487777(dms)

 Now add the Spiral Delta as follows:

 Delta(t) = Delta(s) + Delta(m) + Delta(s)

 Delta(t) = 2-00-00 + 32-29-16 + 2-00-00 = 36-29-16 this should equal the deflection in Step 2.

 Calculate the arc length for Main Curve

 Lm = (Delta(m) * R * pi) / 180

 Lm = (32.487777 * 2864.789 * 3.141592654) / 180 = 1624.389’

August 2009 Spiral Curves Made Simple

 No. 8 – Almost done

 The final step is to calculate the stationing.

 Starting with the T.S. calculate each stationing along the curve.

 T.S. 2180+84.70 + 200.00 (Ls) = S.C. 2182+84.70

 S.C. 2182+84.70 + 1624.39 (Lm) = C.S. 2199+09.09

 C.S. 2199+09.09 + 200.00 (Ls) = S.T. 2201+09.09

 P.I. Stationing = T.S. Stationing + Ts

 T.S. 2180+84.70 + 1044.51 (Ts) = P.I. 2191+29.21

 Be aware that you may have some slight differences in the coordinates, distances and stationing due to rounding errors.

August 2009 Spiral Curves Made Simple

 Unequal Spiral information and Transitional Spirals

 The following example is an ADOT project along U.S. 60 west of Globe AZ.

 The 10 miles section of highway is almost completely composed of spiral curves. There is one area that contained an entrance spiral, then a curve, then a transitional spiral, then a curve, then a transitional spiral, then a curve and finally an exit spiral.

 The next slide shows the record information for this segment.

August 2009 Spiral Curves Made Simple

20 MicroStation tools and manual calculations were used to solve for curves 13, 14 & 15.

Table D-55.30 was used for the formulas needed to calculate the transitional spirals connecting the three main curves.

August 2009 Spiral Curves Made Simple

Sheet RS-8 is how this multi-curve segment was shown on the Results of Survey

August 2009 Spiral Curves Made Simple

Calculating spiral curves does not have to be complicated. Once you understand the elements needed and methodically step through the process, you will obtain consistent results and might even have fun while doing it.

I hope that this presentation will debunk some of the myths that spiral curves are complicated and difficult to work with and will not make your hair turn gray.

You can contact me at [email protected] if you have any questions.

The Appendix contains full size PDF sheets that you can printout for your reference material.

August 2009 Spiral Curves Made Simple

APPENDIX

August 2009 ? s s ?

. C . P

d R T S a e R S t T t n T n g c e e " e g n C t j n t h " o a o r T r P d

L " s f s o C L e " " C S D u " S

DEFINITIONS S X P I Y ?s = Spiral Delta T s s T ?m = Main Curve Delta Lm ?t = Total Curve Delta Ls = Length of Spiral Lm = Length of Main Curve Lt = Length of Total Curve Delta(t) = Delta(s) + Delta(m) + Delta(s) a = Rate of Change per 100' Delta(s) = 0.005 * D * Ls "o" = Radial Offset Lm = (Delta(m) * R * pi) / 180 "t" = Projected curve P.C. Lt = Ls + Lm + Ls R = Radius of Main Curve R = 5729.578 / D ?t D = Degree of Curve PI a = (D * 100) / Ls Def = Deflection from "o" = 0.0727 * a * ((Ls / 100)^3) Begin Spiral "t" = (50 * Ls / 100) - (0.000127 * a^2 * (Ls / 100)^5) Ts = Tangent Length Ts = (TAN(Delta(t) / 2) * (R + "o")) + "t" (In Degrees) of Total Curve Chord = (100 * Ls / 100) - (0.00034 * a^2 * (Ls / 100)^5) PI = Point of Intersection Def = (a * L^2 )/ 60000 of Total Curve X = Chord * Cos(Def) TS = Tangent to Spiral Y = Chord * Sin(Def) SPIRAL DIAGRAM SC = Spiral to Curve "u" = Chord * Sin(Delta(s) * 2 / 3) / Sin(Delta(s)) CS = Curve to Spiral ST = Spiral to Tangent

spiral.dgn

RESULTS OF SURVEY

3617

1/4 Cor. 3620

1/4 Cor. Fd. 3" GLO Cap 3619 Sec. Cor. 1/4 Cor. on 2 1/2" IP, 1.2 up, Fd. 3" GLO Cap Sec. Cor.

7 Not searched for Not searched for

3673 on 2 1/2" IP, .3 up, Fd. 3" GLO Cap 1916 1 4038

5 1/4 Cor.

1916 1

6 on 2 1/2" IP, .3 up,

1 1/4 Cor.

2 Fd. 3" GLO Cap .

3 1916 3

Fd. 3" GLO Cap O on 2 1/2" IP, 2.0 up,

C on 2 1/2" IP, 1.5 up,

In Mound of Stones 0

EXIST R/W \

In Mound of Stones,

1916 8 O

HOWARD LAKE CURVE DATA 1 1916

E N

E ' 4385 PI 2191+29.21 S

4518 3

0 C

C1/4 Cor. 7

T 5 TOTAL CURVE

Not searched for 6 .

2 C

E 9

?=3629’16" LT

Calculated 4

6 6

By Intersection 2 T=1044.51'

N0011’45"E L=2024.39'

2644.85'

4 N0011'45"E 2636.55' N0010'37"E 2640.76' N0010'37"E 2641.68'

7 4 N0010'47"E 5276.30'

0 MAIN CURVE 0

?=3229’16" LT

' HOWARD

5 8

. 3674 D=0200’00" 8

' 3618 4519 .

E 1 E 1/4 Cor. 4 C1/4 Cor.

MESA 6 1/4 Cor. C1/4 Cor. L=1624.39' 3

2 Fd. 3" GLO Cap, 6

0 SFNF Fd. 3" GLO Cap, SFNF 4388

6 2 EXIST R/W \ . .

' R=2864.79'

. on 2 1/2" IP, 2.3 up,

3 6 Position Not

on 2 1/2" IP, 9 A

RANCH Calculated .

2 E

1 CURVE DATA U 1916

" Calculated

.1 up, 1916 .

By Intersection Q

SPIRAL 3 SPIRAL

E 4

PI 2072+08.96 4375 PHASE 3 . '

D BASIS OF STATIONING

a=1.00 8 K a=1.00

2 H

E 4037 3839 5 B

?=1200’29" LT HOWARD MESA " Exist R/W Stationing from

UNIT 8 6 ?=0200’00" ?=0200’00" Sec. Cor.

9 1/4 Cor. 3

" 6

0 P.O.T. 2135+00.26 AHD to 8 7 D=0029’58"

' 2 2 Fd. 3" GLO Cap, Fd. 3" GLO Cap

. S

9 . L=200.00'

2 L=200.00' RANCH PHASE 3 P.T. 2240+54.74 BK is based 3

. BOOK 16 . 3

8 0

' T=1206.41' 5 on 2 1/2" IP, .5 up, on 2 1/2" IP, .1up, 5 0

8 on P.O.T. 2135+00.26 AHD as

T T SPI= 4391 SPI= 4392

9 + 0 PAGE 20 + 1916 1916

. 8 shown on R/W Strip Map 3-T-291. 3 L=2403.99' UNIT 3 5 1

S 3 See Detail "2" 3 4

8 1 4374 3656 BOOK 15 PAGE 89 1

S + 2 R=11470.46' 3632 2 8

9 . . 3 0

1 P.O.T. 2110+50.47 9 1 T T 0 3631 4465 . . 1 2

. 4467 8 O

O SPI 4528

0 . . . SPI 4531

4882 4394 +

3630 P T P 4470

7 4481 4378 . 0

9 0 O 7 9

5 7

. 4414 0

Exist 4471 . 0 2

R/ . W . \ . 4393

P 4

4 4529 2

9 8 9

4380 8 0 4382 0

2 . +

+ +

' T

3637 S03 0 1 4480 03 2 9 4

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9 9"W 49 0

47.19' 8 8 9 '

1 O

3 2 3629 1

3664 1 .

. 2 2

4526 2 2

0 7

104 3655 S.R P

. 6 4 7

2 .

0 .

501.23' 4883 5

6 S T 2 N0011'56"E S 3 C

4466 6 . . 3 . 4379 1 3669 .

3 4469 4472 4478 1407.91'

S 2638.74' T C S E 5" N0010’29"E N0019'15"E 2631.66' N0011'36"E 2640.58' N0012'13"E 489.89' '0 3 5 '

4 1

3 8

4 9 0

9 2650.96' 2639.71' 4527 23 0. See 6 4

2 3 S 3 4473 4530

4468 S 8 1 5 3 3663 14 Detail . 8 ' 11"W N0011’38"E 0 5 276 4395 4390 "3" . 0 7 3624 .12 2640.31' 7 '

3625 + 1

3626 3675 3676 See Detail "1" 7

Sec. Cor. 3

+ 1

1/4 Cor. 4 Sec. Cor. 1/4 Cor. 3 .

1 4386 Fd. 3" GLO Cap, 3671 9 5

1 '

Fd. 3" GLO Cap Fd. 3" GLO Cap, Fd. 3" GLO Cap, 3

on 2 1/2" IP, .5 up, 2 0

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on 2 1/2" IP, 3.0 up, 0

on 2 1/2" IP, .2 up, 4523 4387 4532 9 on 2 1/2" IP, 1.0 up, 1 C

1916 . 0 0

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1916 T 3665

1916 2 1916 P

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E SPI 4534

P Sec. Cor. 4389 SPI 4525 4

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2 Fd. 3" GLO Cap, C

HOWARD MESA .

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5 4524 4533 ' P

1 4479

on 2 1/2" IP, 2.5 up, 1 8

. + 4 1 RANCH PHASE 1 1916 6 2 5

. 7

9 4

6 1

6 0

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UNIT 5

2 .

E . EXIST R/W \ 4 2 . T

" B

8 6

1 BOOK 15 PAGE 61 . .

6 0

0 O

T CURVE DATA

2 .

' .

0 P EXIST R/W \ 4483 L .

4474 N0012’13"E 5 PI 2225+01.23 4184

9 4464 287.29' CURVE DATA " P

8 4461 4482 9 ?=1022’49" RT

5 4182 S 1/4 Cor. PI 2148+10.40 '

435 8 D=0019’59" 3633 Not

4383 0 ?=1010’22" RT DETAIL "3"

1 searched

9 T=1562.06'

3 4376 P.O.T. 2084+14.20 8 for D=0100’01" S L=3115.57' P.O.T. 2162+29.09 S8950’01"E

4 9 T=509.86' 66.58' R=17197.05' 4396

L=1017.04'

4377

9 P.O.T. 2165+24.04

R=5728.24' 4381 3636 4384

3682 4462 4463 4475 1/4 Cor. C1/4 Cor. 3635 Fd. 5/8" DETAIL "1" SFNF E

Rebar .4 up N

Position not I DETAIL "2" Added Tag 3683 L calculated PLS 19817

1/4 Cor.

Fd. 3" GLO Cap C

on 2 1/2" IP, .8 up, T

E A 0 250 500

8 N 1916

L Scale

H 064rw185_rs17.dgn

T ARIZONA DEPARTMENT OF TRANSPORTATION CHANGE ORDER REVISIONS DRAWING NO.

A D-03-T-694 INTERMODAL TRANSPORTATION DIVISION

M C.O. NO. DATE BY DESCRIPTION OF REVISIONS RIGHT OF WAY PLANS SECTION LEGEND SURVEY Aug 2008 DATA TABLE HIGHWAY NAME: PRELIMINARY NOT FOR DRAWN/DATE Jordan/Nov 08 WILLIAMS-GRAND CANYON-CAMERON 5 Calculated CONSTRUCTION 302 Set Monument 301 FEDERAL AID NO.: 6 position ADOT REVIEW Ken Richmond OR RECORDING UNASSIGNED --Created-- HUBBARD 480-892-3313 7/31/2009 300 Found Monument Existing ADOT R/W PROJECT NO.: Gilbert, AZ ENGINEERING 9:50:11 AM monument 064 CN 185 H7142 01R [email protected] Job # 08121 SFNF Seacherd For Not Found ROUTE NO.: LOCATION: S.R. 64 Jct. I-40 - Tusayan SHEET RS-17 .- -.

Ls =200.00' D =2-00-00 Controlling spiralcurvedata P.I.

3 6 2 9 ' 16 " Ls =200.00' D =2-00-00 Controlling spiralcurvedata

T . S .

E =622683.766192496 N =1630448.65338332

4 ' P.I. E =622444.605199428 N =1629431.88935962

T s 1 0 4 4 . 5 1 4 ' 3 6 2 9 ' 16 "

S . T . E =622856.942620664 N =1628472.20977166 199.989' Spiral Chord Ls =200.00' D =2-00-00 Controlling spiralcurvedata

T . S .

E =622683.766192496 N =1630448.65338332

1 0

E =622640.243104831 N =1630253.45761247 4

4 ' P.I. E =622780.137138348 N =1628656.86232649 E =622444.605199428 N =1629431.88935962

T s 1 0 4 4 . 5 1 4 ' 3 6 2 9 ' 16 "

S . T . 199.989' Spiral Chord E =622856.942620664 N =1628472.20977166 E =622683.76619 N =1630448.65338 E =622653.2352 N =1630318.8546 SPI 133.341' 199.989' Spiral Chord Ls =200.00' D =2-00-00 Controlling spiralcurvedata Spiral

T . S .

1 0

E =622640.24310 N =1630253.45761 4

4 ' P.I. E =622780.13713 N =1628656.86232 E =622444.60519 N =1629431.88935

T s 1 0 4 4 . 5 1 4 ' 3 6 2 9 ' 16 " Spiral

S . T . 199.989' Spiral Chord E =622856.94262 N =1628472.20977 E =622804.3042 N =1628594.7212 SPI 133.341' E =622683.76619 N =1630448.65338 E =622653.2352 N =1630318.8546 SPI Def 133.341' T.S. 199.989' Spiral Chord Ls =200.00' D =2-00-00 Controlling spiralcurvedata N.T.S. Detail Spiral S.C.

T . S . Back Def

S . C .

1 0

E =622640.24310 N =1630253.45761 4

4 ' E =625450.1188 N =1629695.2331 Radius Point P.I. E =622780.13713 N =1628656.86232 E =622444.60519 N =1629431.88935

T s 1 0 4 4 . 5 1 4 ' 3 6 2 9 ' 16 "

C . S . Spiral

S . T . 199.989' Spiral Chord E =622856.94262 N =1628472.20977 E =622804.3042 N =1628594.7212 SPI 133.341'

1435

1444

1335

ST 166+ 1340 43.12 1430 "

5 .

2 1338 1 "

' 4

2 . 1 5 1 ' 6 8 2 4

1332 1

a=1 2/3 A 0" 0. Ls=360.00' ' '0 5 3 2 24 ?=1048’00" 2 1 .

" 2 1 3 4 5 . 1429 1 35 = ' 0 C 4 S S 8. " ' 16 4 2 T " .0 4 +8 00 0 3. ' 12 21 6 55 1

1339

10 4 7 S ' 4 C 7 . 16 5 0 " " + 0 15 . .3 0 C 4 0 S ' 1251 8 1 1 5 2 9 0 4 + 0 48 3 5 K . ' 0 5 B 00 . 5 .9 3 1425 1 " 4 ' + 15 4 L.T.B. (in): N 34-24-16 E 0 4 4 . 1 5 D.O.C. Arc: 6-00-00 4 S T 2 Radius: 954.93 = 1337 Transitional Spiral S Delta Angle: 16-04-01 (LT) T (Table D-55.30) 1935 Tangent length: 134.78 0 317' a=1 2/3 Arc length: 267.78 59.1" 0 Ls=60.00' L.T.B. (out): N 18-20-15 E 0 1336 . ?=318’00" 5 7 + 3

4 1330 4 4 1428

1 3

. C . 8 1423 S 8 8

a=1 2/3 + +

Ls=360.00' 4 1

' ?=1048’00" 1 S

C 9

C . T S 2 S 4 14 6 = 5 = 0 4 S . T 9 3 '

1426 B K

Transitional Spiral 13 (Table D-55.30) 1331 a=1 2/3 Ls=60.00' 1427 ?=318’00"

L.T.B. (in): S 86-56-44 E D.O.C. Arc: 5-00-00 TS=3 25.14' A HD Radius: 1145.92 1249 1333 Delta Angle: 55-21-00 (LT) 1334 TS =642.91' Tangent length: 600.98 Arc length: 1107.00 1934 L.T.B. (in): S 58-50-44 E L.T.B. (out): N 37-42-16 E 1250 D.O.C. Arc: 6-00-00 Radius: 954.93 Delta Angle: 24-48-01 (LT) Tangent length: 209.96 Arc length: 413.34 L.T.B. (out): S 83-38-45 E RESULTS OF SURVEY

TONTO

4E. R.1 ** END U S. NEQUA MATC 1 L SP N H LI T. IRAL 0732 NE CUR '16"E VES 44.24' S 6 .T. 16 S 6+43. HEET 12 RS-9 EXIST R/W \ 7 CURVE DATA SPIRAL VAR IES 1340 VAR N 9 PI ------a=1.67 IES CTIO SE ?=1604’01" LT ?=1048’00" TY OUN * M A C D=600’00" L=360.00' GIL * A * D

T T=134.78' * SPI 1429 H E

A C "

S L=267.78' 6 H ' E 1

3 V '

2 1338 2 L R R=954.93' .

3 I U 7 C. 5 N C S. 2 7 * K 2 16 E 2 4 ' + 0 C C L L.T 83 4 I . = N A . A B. 12 N s 3 B N1 1 R EXIST R/W \ 5 8 E T T I 20 C P '1 E 6" 1339 S S E " S CURVE DATA SPIRAL T 0 S 0 L R . A C ' A PI ------NATIONAL N . a=1.67 S L 1499 0 * U I .T 16 4 ' T 0 Q I .B + 6 ?=2448’01" LT O 8 E ?=318’00" N . 1 6 5 N A N . 2 1501 L 3 3 U 4 4 D=600’00" L=60.00' S C P 2 * 4 . 4 N S IR ' 10 ' I 0 T=209.96' SPI 1428 L . A 15 ' 6 G 1 . L " 8 1904 T 1 E 6 E . 5 * EXIST R/W \ B 9 * B L=413.34' . + * 5 10 1251 N 5 0' SPIRAL 3 . 6 * R=954.93' 1332 3 CURVE DATA 7 3 0 4 * SPI=1905 0 4 K . a=1.67 2 E S B 1422 5 PI ------' " * 1 1498 K 1 5 6 H SPIRAL ' ' C " 1 C + E 4 4 I ?=1048’00" ' E A 0 4 4 ?=5521’00" LT =1921 2 N SPI 3 . B E 1 1524 1 1 a=1.67 5 E T L=360.00' T . 4 6 C D=500’00" E S 2 3 S . ?=318’00" S = N S T 1426 R SPI s 4 T=600.98' 1901 8 T S 1903 L=60.00' 1337 0 - 2 1527 ' L=1107.00' 5 7 4 SPI 1427 4 1525 " R=1145.92' 1335 E E "

2 * 1 0 4 1500 . * 6 0 4 . 7 ' * 1336 ' 5 0 E 1916 7 5 " 3 L + 5 SPI=1922 3 A . 8 4 3 4 E 1423 5 R 1526 3 4 ' 1 1 S 3 I " S 3 3 8 .

5 P 4 S C 3 8 + . . 4 E ' S E 6 4 * * C 8 B ' N 1935 1330 . T * 3 . 3 3 6 I 1 S + L B C ' T . 8

5 1 7 . A A

8 9 S . C L 4 N .

1900 4 SPI=1918 1 S 6 K

O 2 . . SPI=1902 8 I + 4 C 6 . B 6 S 6 T 8

. S I ' =

4 * . s T 1 S S .

C . T

4 1 N 8 B L .

. A 6

0 C 6 T 2 R . ' ' . T *

S 1913 4 L 3 4 3 " 8 EXIST R/W \ . E 1917 3 9 + CURVE DATA T SPI=1919 9 1 3 s 3 1 = S 4 1248 5 S C PI 133+46.70 . 0 E ' 1331 E * T 4 N . . T 9 I S 3 1531 E B C ' " A TOTAL CURVE SPI=1915 6 SPIRAL 0 1 C B 1528 6 K K . ' * .S 2 a=1.67 * U \ 1 ?=6208’30" RT 4 1914 2 /W 6 1333 R 3 T=758.58' ?=1048’00" ist N 1334 Ex L=1395.69' L=360.00' 3 0" FOREST '0 21 1249 Ts=325. SPI 1425 14' AHD** 58 MAIN CURVE S 8526'44 S8 "E 526'44"E 37 2 1934 T ?=4032’30" 4' s=642.91' 00" ** D=600’00" 1530 1250 L=675.69' 1529

R=954.93' 1421 SPI=1920

** RECORD DIST: ANNOTATION PER STRIP MAP 4-T-137

*** TRANSITIONAL SPIRAL CALCULATED USING FORMULAS AND 0 50 100 RELATIONSHIPS SHOWN ON PLAN NO. 55.30, REVISED * DENOTES A U.S.F.S. SPECIAL USE PERMIT DATED 6-22-49 WHICH DATE OF 1/82, OF 1986 ADOT ROADWAY GUIDES FOR USE Scale

INCLUDES A 132' RIGHT OF WAY WHEREIN THE ROAD WILL BE IN OFFICE AND FIELD. 060rw236_rs08.dgn PARAMOUNT, BUT, NO USE OR OCCUPANCY OTHER THAN FOR ARIZONA DEPARTMENT OF TRANSPORTATION CHANGE ORDER REVISIONS DRAWING NO. D-04-T-432 CONSTRUCTION AND MAINTENANCE OF THE ROAD IS AUTHORIZED INTERMODAL TRANSPORTATION DIVISION WITHOUT PERMIT FROM THE FOREST SERVICE, AND A 132' WIDE PERMIT LEGEND C.O. NO. DATE BY DESCRIPTION OF REVISIONS RIGHT OF WAY PLANS SECTION SURVEY April 2006 TO CONSTRUCT AND MAINTAIN A FENCE. WHERE THE FENCES ARE HIGHWAY NAME: CONSTRUCTED OUTSIDE OF THE 132' RIGHT OF WAY, NO IMPROVEMENTS DRAWN/DATE J Crume/2006 PHOENIX - GLOBE PRELIMINARY OTHER THAN THE FENCES SHALL BE CONSTRUCTED BY THE STATE Calculated NOT FOR 302 Set Monument 301 FEDERAL AID NO.: EXCEPT BY AGREEMENT WITH THE FOREST SUPERVISOR. position ADOT REVIEW C. Woodford CONSTRUCTION Unassigned A 400' WIDE SCENIC STRIP OF "SET BACK" WHEREIN NO CONSTRUCTION OR RECORDING HUBBARD 480-892-3313 300 Found Monument Existing R/W monument PROJECT NO.: --Created-- OTHER THAN THAT NECESSARY TO THE CONSTRUCTION OF THE HIGHWAY Gilbert, AZ ENGINEERING 8/14/2009 WILL BE ALLOWED, EXCEPT BY SPECIAL PERMIT FROM THE FOREST SERVICE. [email protected] Job # 26015 060 GI 236 H6140 01R 8:19:50 AM ROUTE NO.: LOCATION: U.S. 60 County Line - Pinto Valley SHEET RS-8 .- -.