1) ()
-
()(transition curve)
-
()(compound curve)
-
()(reverse curve)
2) ()
;
R(m) (100ft )θ° , R(m) θ

3) R=15.24 cosec θ 2 (m)
(2) (:circular curve )
- () , (
) . R=800
() .( 13)
2) ()
- AP BP
- R (IA) () TL P
A, B TL C, D (BC), (EC)

- C D ∠ACO = ∠PCO =∠BDO = ∠PDO=
(90 ) .
∠θ+ ∠CPD = 360 - 2 x 90 = 180
180 ∠IA + ∠CPD = 180
∴ ∠θ = ∠IA
TL = R x tan IA 2
CL = 2πR x IA 360

3) ( )
- , P TL
(B C) .
- BC , 180
() .
- (δ) δ , B C
L(5M 10M) A . A
L 2δ B .
, (Curve Setting) .

ABO
- θ 2 = 90 - θ
( )= 2πR x θ 360
θ( )= x 360 2πR
δ1( )= 90 - γ(BC ,
. ∴ ∠OAA′ = 90° )
δ1 = 90 - (90 - θ 2 ) = 90 - 90 +
θ 2 =
θ 2
= ( 360 2πR
() () ( :mm )
R 100 m 200 m 250 m 300 m
5 m 1 0 0 0
10 m 4 1 1 0.5
20 m 33 8 5 4
4) (Curve Setting)
() R = 247.395 ΙA = 18° 28′ 00″ 18.46667°
ΙA (STA) = 2k 898.273 (m) : 10m
TL = 247.395 x tan 18.46667
2 = 40.2169 40.217 (m)
360 = 79.7467 79.747 (m)
= 2k 858.056 (m)
= 2k 937.803 (m)
R

δ = 28.64789° R
(STA) (L) () (δ )
B C 2k 858.056 1.944 1.944 0.22511 0 - 13 - 30
860.000 10.000 11.944 1.38309 1 - 22 - 59
870.000 10.000 21.944 2.54108 2 - 32 - 28
880.000 10.000 31.944 3.69906 3 - 41 - 57 890.000 10.000 41.944 4.85703 4 - 51 - 25 900.000
10.000 51.944 6.01502 6 - 00 - 54 910.000
10.000 61.944 7.17300 7 - 10 - 23 920.000
10.000 71.944 8.33098 8 - 19 - 52 930.000
7.803 79.747 9.23455 9 - 14 - 04 E C 937.803
(3) (Transition Curve)
1) () ()
- , ()
() () .
- 0 , R=250 20m
( 1 ) 2°17′31″ ,
, .
-
( ) .
2)
() : ( 1 R ) ,
.
- = 0 / ∞ = 0
( : ) : 1 (L= 20m)
- = 0°
- R=800m = 28.64789°x R = 28.64789°x20/800 =0.7162°=0°42°58″
- R=400m = 28.64789°x 20/400 = 1.4324°= 1°25′56.62″
- R=250m = 28.64789°x 20/250 =2.2918°= 2°17′30.59″
3)
- ,
( 0 ) , ( )
( )
(clothoid curve)( )
( )
(lemniscate spiral) :
4 , 3 ,AREA ,
; , 2
4)
- (2.5m) 3
() .
-
.(AREA 31.75mm/sec)
: L = 8.75 CV (L= ,C=cant, V= (/hr)
- .
- ( )
, .
-

c= n=
1 2 3 4
- : 600
-
-


3, 4 .
250 m 200 m
:80 m
3
- , 4 1
3 .
25mm .
÷ =2500÷25=100
n = 600 ( :450 )
∴ (S)=600 ÷ 100 = 6
( ) n=450 : 2,500÷450=5.6mm
(S) =25 ÷ 5.6 = 4.46 (25-5.6=19 mm )
5) (Clothoid)
- ()
, () .
- , α
(Clothoid)
.

- t β = t× α
(BTC) ∞ , (BCC)
() .
.
L = A² R L : (BTC )
( )
L = 100×100 250
0 = ∞
R8(L= 40m) = 10000
40 = 250 (m)
A² , R , L .
, ( A²) (L) (R) , (R)
(L) .
6) (Clothoid)
(3,4 ) 3 (1,2 ) BTC:Beginning Transition Curve SP:Straight Parabola
BCC:Beginning Circular Curve PC:Parabola Curve ECC:End Circular Curve CP:Curve Parabola
ETC:End Transition Curve PS:Parabola Straight
*
- Curve : ,
- Parabola : ()
P: () ΙA: () G: BC H: EC
f: ( R Ro )
Xm: BC BTC
x: BTC BCC
y : BTC BCC L:
Ιo : BC BCC O:
R: Ro: (R-f)
AP BP R (IA) (TL) G,H BC EC
.
- C′( 0 ~ 100)
(L)= 600 C ( 450 )
(f) = L² 24R

(f) AP′ BP′
R f Ro
(x) = L(1 - L² 40Ro²
)
(1- L²
)
′ΙA′= ΙA - 2 x Ιo
- OJD′ OD = Ro, KD′ Ro
∠OD′J = 90°
HJK OH=R KH R
∠OHK = ∠JHK = 90° ∴ .
∠OJD′= ∠HJK = 90 - Ιo ( )
∴ ∠JKH = ∠JOD′= Ιo
Xm = X - Ro sin Ιo BTC
BTC(STA) = BC (STA) - Xm
BCC(STA) = BTC + L
360 )
7) ( )
() R = 248 m (Rc-D/2 = 250-2.0) n( ) = 600
Rc = 250 m( ), D=4.0m( , )
IA = 32°20′40″= 32.34444°
IP (STA) = 2k 900.000 (m)
TL = 248 x tan 32.34444
2 °= 71.920 m
360 = 140.018 m
(BC) = 2k 900.000 -71.920 = 2k 828.080 (m)
(EC) = 2k 828.080 + 140.018 = 2k 968.098 (m)
(C)= 11.8 x V² R - C′( V = 55km/H, C′= 45 mm)
C = 11.8 x 55² 248
- 45 = 98.931 100mm
L ( ) = n x C = 600 x 100 = 60 m
f ( ) = L² 24×R
= 60×60 24×248
Ro ( ) = R -f = 248 - 0.605 = 247.395 m
A²( ) = L x Ro = 60 x 247.395 = 14,843.70
X ( ) = L(1 - L² 40Ro²
) = 60(1 - 60² 40×247.395²
)
(1- L² 56Ro²
) = 3600 6 247.395
)
IA′= IA - 2xIo = 32.34444 - 2x6.93884 = 18.46676 = 18°28′00″
C( ) = 2 x 3.142 x 247.395 x 18.46676 ÷ 360 = 79.747 m
Xm ( BC BTC ) = X - Ro sin Io
= 59.912 - 247.395 ×sin 6.93884 = 59.912 - 29.888 = 30.024 m
BTC(STA) = BC(STA)- Xm = 2k 828.080 - 30.024 = 2k 798.056
BCC(STA) = BTC(STA)+L= 2k 798.056 + 60.000 = 2k 858.056
ECC(STA) = BCC(STA)+C= 2k 858.056+79.747 = 2k 937.803
ETC(STA) = ECC(STA) +L = 2k 937.803 + 60.000 = 2k 997.803
- (STAx)
(Xo)
(Yo)
798.056 1.944 1.944 7,635.648 1.944 0 0 0 0 800.000
5.000 6.944 2,137.630 6.944 0.004 0.03300 0-01-59 0.00001 805.000
5.000 11.944 1,242.775 11.944 0.019 0.09114 0-05-28 0.00009 810.000
5.000 16.944 876.045 16.944 0.055 0.18598 0-11-10 0.00037815.000 5.000 21.944 676.435 21.943 0.119 0.31072 0-18-39 0.00105
820.000 5.000 26.944 550.909 26.942 0.220 0.46785 0-28-04 0.00239825.000 5.000 31.944 464.679 31.940 0.366 0.65652 0-39-23 0.00473
830.000 5.000 36.944 401.789 36.936 0.566 0.8792 0-52-41 0.00845835.000 5.000 41.944 353.893 41.929 0.828 1.13131 1-07-53 0.01405
840.000 5.000 46.944 316.200 46.918 1.161 1.41751 1-25-03 0.02204
845.000 5.000 51.944 285.764 51.901 1.573 1.73597 1-44-10 0.03304
850.000 5.000 56.944 260.672 56.876 2.071 2.08536 2-05-07 0.04772
855.000 3.056 60.000 247.395 59.912 2.423 2.31593 2-18-57 0.05882
BCC 858.056 1.944
A²( ) = 247.395 x 60 = 14,843.70
L² R²
40 Rx 2 )
yo = Lx 2
56Rx 2 )
tan -1
1)
,
( ) , () ()
() () .

≥ 1200 R R: (m)
1. 3 2 R=600m
(3,4 ).
) R×R R - R
1200 ∴ 600×R 600-R
1200
R400m ∴ 400m
2 : 3 R=600
) 600R≥-1200R+7200, 1800R≥7200, ∴R≥400m )400m
3. 3 2 600m

1) R 600m ... R×R R - R
1200 ∴ 600×R 600-R
1200
600R720000-1200R 1800R720000 R400m
2) R 600m ... R×R R - R
1200 ∴ R×600 R- 600
1200
600R 1200R- 720000 600R720000 R 1200m
400 R 1200
4. V= 90/h, C´ F R 1200 .
R×R R - R
1200 G×V² C .g
G×V² 1,200.g
g×C G
9.8×0.076 1,435
V² R
90² 1,200
P g
60,000 400
Ι =
Ι =
TL = R TL = R
P = (IP) ΙA = (I)
- C
D E ,
ADCO BECO
ADCO
∠D = 360 - 2 x 90 -Ι = 180 - Ι
∠PDC = 180 - (180 - Ι ) =180 -180 + Ι = Ι
BECO
∠E = 360 - 2 x 90 -Ι = 180 - Ι
∠PDC = 180 - (180 - Ι ) =180 -180 + Ι = Ι
DPE

- C R B
PB DE .
- PB DE , d , C
R A PA
QF .
- QFPA , d .
TL1
ADEO 360°
∠CO E = 360 - 2x 90 - (180 - Ι ) - Ι
= 360 - 180 -180 + Ι - Ι
= Ι - Ι = ( Ι + Ι ) - Ι = Ι
- d = R -(R - R ) cosΙ - R
= R -(R cosΙ - R cosΙ )- R
= R -R cosΙ + R cosΙ - R
= R ( 1- cosΙ ) - R ( 1 -cosΙ )
= R VersΙ - R VersΙ
------------------------------
sin (α-β)= sinαcosβ - cosαsinβ
= 0 x cos Ι - (-1)sin Ι = sin Ι
- AE () S
S = R sin ( I + I) 2
x 2
= 2R sin I 2 ------------------------------------
- ADE
= 180-(180-Ι )÷2
∴AD = 2R sin I/2× sin I/2 sin (180 - I)
= 2R sin ²I/2 sin I
= 2R×
= RVersI
sin I ----------------------------------
:
cos 2α= cos(α+α)= cosαcosα- sinαsinα
= cos²α- sin²α = (1- sin²α) - sin²α
( sin²α + cos²α = 1 )
= 1 - 2sin²α
()
I 2
∴ sin² I 2 =
+ ( R - R)VersI sin I
= RVersI + ( R -R )VersI sin I
-------------------
FQCO 360°
∠CO F = 360 - 2x 90 - (180 - Ι ) - Ι
= 360 - 180 -180 + Ι - Ι
= Ι - Ι = ( Ι + Ι ) - Ι = Ι
- d = R -(R - R ) cosΙ - R
= R - (R cosΙ - R cosΙ )- R
= R - R cosΙ + R cosΙ - R
= R ( 1- cosΙ ) - R ( 1 -cosΙ )
= R VersΙ - R VersΙ
= ( R - R ) VersΙ -----------------------
d sin∠Q
sin (α-β)= sinαcosβ - cosαsinβ
= 0 x cosΙ - (-1)sin Ι = sin Ι
- AE () S′
S′= R sin ( I + I) 2
x 2
= 2R sin I 2 ---------------------------------
- FQB
S'
sin(180-I) =
QB
I 2
sin I
= 2R×
= RVersI sin I
------------------------------------
cos 2α= cos(α+α)= cosαcosα- sinαsinα
= cos²α- sin²α
= (1- sin²α) - sin²α ( sin²α + cos²α = 1 )
= 1 - 2 sin²α
α I 2
()
I 2 )
2sin² I 2 = 1 - cos Ι
∴ sin² I 2 =
= RVersI + ( R -R )VersI
sin I --------------
1)
- ()

.
- 5‰
.( 18)
2)
-
-
-
-
∠ACO = 90
BCO
R²= BC²+ CO²= BC²+ (R-M)²
R²= ( L 2 )²+R²-2MR+ M²= L²
4 +R²+M²-2RM
R²- R²+2RM = L² 4 + M²
2RM = L² 4 + M²
M = L²
M² 2R
= L² 8R
+ M² 2R
M 3
2R 5 0.1mm .
R=250 M=50mm M=0.05m
M = l² 2R
∴ : M = L² 8R
1. R = 250m 10m ?
) M = l² 8R
= 10×10 8×200
×1000 = 62.5mm
2. R = 400m 10m -4mm ?
) M = l² 8R
= 10×10 8×400
×1000 = 31mm ∴ 31 - 4 = 27mm
3. R = 500 10m 28mm . ?
) M = l² 8R
= 10×10 8×500
χ y
M = L² 8R
M = (2χ)² 8R
= 4χ² 8R
= χ² 2R


5)
m: M 1000
L : R
y = χ² 2R
n = +10‰ m = - 20‰
BC (STA) = 0 k 170 - 45 = 0 k 125
EC (STA) = 0 k 125 + 90 (2 L) = 0 k 215
y . y = χ² 2R
y (B C, E C ) = 0² 2×3000
= 0 (m)
= 0.0375 0.038 (m)
= 0.3375 0.338 (m)
= 0.204 (m)
= 0.0375 0.038 (m)
R L( ) : R L - y
- 0k 100 = 7.000
- 0k 120 = 0K 100 R L + L(=20) x n 1000
= 7.000 + 20 x 10 1000
= 7.000 + 0.200 = 7.200
- 0k 140 = 7.400 - 0.038 = 7.362
- 0k 160 = 7.600 - 0.204 = 7.396
- 0k 170 = 7.700 - 0.338 = 7.362
- 0k 180 = 7.500 - 0.204 = 7.296
- 0k 200 = 7.100 - 0.038 = 7.062
- 0k 215 = STA 0K 170 R L - (215-170) x 20 1000
= 7.700-0.900 = 6.800
- 0k 220 = STA 0K 170 R L - (220-170) x 20
1000 = 7.700-1.000
= 7.700 - 1.400 = 6.300
(6) (Reverse curve)
1) :

2)
( 1.5 )
- 1 : 70m 150×{1000/3600}×1.5 = 62.5
- 2 : 50m 120×{1000/3600}×1.5 = 50
- 3 : 30m 80×{1000/3600}×1.5 = 33.3
- 4 : 30m 70×{1000/3600}×1.5 = 29.2
1.
) 1.3 , 1.5 1.5

2) 2 : 120×1000
60×60 ×1.5 = 50 m
2. V=100/h 1.5 .
) 100()×1,000
3)
-
-
( )
1. 3 .
500m .
) 3.4
R×R R - R
1200 ∴ 500R
500-R 1200
∴ R 600,000/1,700 = 352.9 360m
4) 2
- 3.4
R1×R2 R1-R2
1. () curve
(1) () ()
(2) (:circular curve )
(3) (Transition Curve)
(4) ()(compound curve)