Fremling Field Notebook 1967 - 1968

R

. ,,',

t

+; r

SIOE t

DmsTANCES FROM SIDE STAKES FOR CROSS-SECTIONaN SLOPE I TO 1. ROADWAY OF ANY WIDTH 0 0.00 1.00 2.00 3.00 4.00 6.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00 13.00 14.00 16.00 16.00 17.00 18.00 19.00 20.00 21.00 2 22.00 23 23.00 24.00 26 35.00 26 26.00 27 27.00 S28.00 29.00 40 30.00 31 31.00 32 32.00 33 33.00 34 34.00 35 35.00 36 36 00 37.00 37 38 38.00 39 39.00 40 40.00 41 41.00 42 42.00 43 43.00 44 44.00 145 45.00 46 46.00 47 47.00 48 48.00 49.00 49 .0 60.00 0 4 2 3 4 5 6 7 8 9 10 11 12 13 14 16 16 1O i1 19 23

.1

.2

0.10 1.10 2.10 3.10 4.10 5.10 6.10 7.10 8.10 9.10 10.10 11.10 12.10 13.10 14.10 15.10 16.10 17.10 18.10 19.10 20.10 21.10 22.10 23.10 24.10 25.10 26.10 27.10 28.10 29.10 30.10 31.10 32.10 33.10 34.10 35 10 36.10 37.10 38.10 39.10 40.10 41.10 42.10 43.10 44.10 45.10 46.10 47.10 48.10 49.10 50.10

0.20 1.20 2.20 3.20 4.20 5.20 6.20 7.20 8.20 9.20 10.20 11.20 12.20 13.20 14.20 16.20 16.20 17.20 18.20 19.20 20.20 21.20 22.20 23.20 24.20 25.20 26.20 27.20 28.20 29.20 30.20 31.20 32.20 33.20 34 20 35.20 36.20 37.20 38.20 39.20 40.20 41.20 42.20 43.20 44.20 45.20 46.20 47.20 48.20 49.20 60.20

.3

.4

.5

.6

.7

0.30 1.30 2.30 3.30 4.30 6.30 6.30 7.30 8.30 9.30 10.30 11.30 12.30 13.30 14.30 15.30 16.30 17.30 18.30 19.30 20.30 21.30 22.30 23.30 24.30 25.30 26.30 27.30 28.30 29.30 30.30 31.30 32.30 33.30 34.30 35.30 36.30 37.30 38.30 39.30 40,30 41.30 42.30 43.30 44.30 45.30 46.30 47.30 48.30 49.30 50.30

0.40 1.40 2.40 3.40 4.40 5.40 6.40 7.40 8.40 9.40 10.40 11.40 12.40 13.40 14.40 16.40 16.40 17.40 18.40 19.40 20.40 21.40 22.40 23.40 24.40 25.40 26.40 27.40 28.40 29.40 30.40 31.40 32.40 33.40 34.40 35.40 36.40 37.40 38.40 39.40 40.40 41.40 42.40 43.40 44.40 45.40 46.40 47.40 48.40 49.40 50.40

0.50 1.50 2.50 3.50 4.50 6.50 6.50 7.50 18.50 9.50 10.50 11.50 12.50 13.50 14.50 16.50 16.50 17.50 18.50 19.50 20.50 21.50 22.50 23.50 24.50 25.50 26.50 27.50 28.50 29.50 30.50 31.50 32.10 33.50 34.60 35.50 36.60 37.50 38.50 39.50 40.60 41.50 42.50 43.50 44.60 45.50 46.50 47.60 48.50 49.50 50.50

0.60 1.60 2.60 3.60 4.60 6.60 6.60 7.60 8.60 9.60 10.60 11.60 12.60 13.60 14.60 15.60 16.60 17.60 18.60 19.60 20.60 21.60 23.60 23.60 24.60 25.60 26.60 27.60 28.60 29.60 30.60 31.60 32.60 33.60 34.60 35.60 36.60 37.60 38.60 39.60 40.60 41.60 42.60 43.60 44.60 46.60 46.60 47.60 48.60 49.60 50.60

0.70 1.70 2.70 3.70 4.70 6.70 6.70 7.70 8.70 9.70 10.70 11.70 12.70 13.70 14.70 15.70 16.70 17.70 18.70 19.70 20.70 21.70 22.70 23.70 24.70 25.70 26.70 27.70 28.70 29.70 30.70 31.70 32.70 33.70 34.70 35.70 36.70 37.70 .38.70 39.70 40.70 41.70 42.70 43.70 44.70 45.70 46.70 47.70 48.70 49.70 50.70

*

.8" 0.80 1.80 2.80 3.80 4.80 6.80 6.80 7.80 8.80 9.80 10.80 11.80 12.80 13.80 14.80 15.80 16.80 17.80 18.80 19.80 20.80 21.80 22.80 23.80 24.80 25.80 26.80 27.80 28.80 29.80 30.80 31.80 32.80 33.80 34.80 35.80 36.80 37.80 38.80 39.80 40.80 41.80 42.80 43.80 44.80 46.80 46.80 47.80 48.80 49.80 60.80

9 0.90 1.90 2.90 3.90 4.90 5.90 6.90 7.90 8.90 9.90 10.90 11.90 12.90 13.90 14.90 15.90 16.90 17.90 18.90 19.90 20.90 21.90 22.90 23.90 24.90 26.90 26.90 27.90 28.90 29.90 30.90 31.90 32.90 33.90 4.90 35.90 36.90 37.90 38.90 39.90 40.90 41.90 42.90 43.90 44.90 45.90 46.90 47.90 48.90 49.90 50.90

0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 36 37 38 39 40 41 42 43 44 45 46 47 48 49 60

Distance of slope stake from side or shoulder stake for any width roadway, slope 1 to i. It ground is nearly level the cut or fill at side stake is located by the double entry method in left column and top row. The number in body of table in same row and column gives distance from side stake to slope stake. It ground is not level estimate the difference in elevation between the side stake and slope stake, lower target by this amount if out, elevate if fill. Add this amount to cut or fill and find distance in table. Set up rod at this point, and line of sight should cut target if it does not make the slight adjustment necessary.

nB ,~':c"

i(i3/& Q

F' n -lcc

LSi'

s-s"r- 7 1 L~n~ccnc/L~ ~

et

IMPROVED

TABLES

AND

INFORMATION

DIRECTIONS FOR USE OF TABLES TABLE No. XIV Distance of slope stake from side or shoulder stake for any width roadway, slope 1Y~ to 1.

If ground is nearly level, the cut or fill at side stake is located by the double entry method in left column and top row. The number in body of table in same row and column gives distance from side stake to slope stake. If ground is not level estimate the difference in elevation between the side stake and slope stake, lower target by this amount if cut, elevate if fill. Add this amount to cut or fill and find distance in table.

Set up rod at this point, and line of sight should cut target. If it does not make the slight adjustment necessary.

TABLE No. VIII To find Tangent and External for curve of any other degree, divide by degree of curve and add correction found in column of corrections.

Degree of curve with a given I may be found by dividing tangent, (or external). opposite I by given tangent, (or external).

The distance from a point on the tangent to the curve is very nearly the square of the tangent length divided by twice the radius.

TABLE II

TRIGONOMETRIC FORMULE. LA = LMOP LB =LPON = LOPL R= OB= c= 1 sin A .

.

c .b sos A= c tan A= cot A =

sec A= -2 csc A =

aa

MQ MQ

NT

NT

ON

1

OM

2O 1

OT

OT

b

OM

ON LM vers A = -= OP covers A

1 b 1

-=

I

= a = sos B= LP b = sin B = OL

MQ 1

MQ -- cot B = MQ

= NT = tan B = NT

OQ= csc B

=

OQ

= OT = sec B = OT

LM = covers B 1

OP-LP

OP

OP-LP = vers B

exsec A = PQ = coexsec B coexsec A = PT = exsec B S/ 1-Cos A sin l/s A= 2

l-Cos A

cos 1/2 A 2 sin 2 A = 2 sin A cos A cos 2 A = cos' A--sin' A sin B sin C1 sin A Law of Lines a B C Law of Cosines c2=a 2+b*-2 ab cos C Law of Tangentsa-b = tan /s(A+B) a--b tan 'I (A-B)

TABLE II - Continued TRIGONOMETRIC FORMULJE (continued) in any triangle: Given a, b, C; to find c, B, A. Use Law of Lines.

Given A, B, c; to find a, b, C. Use Law of Lines.

Given a, b, c; to find A, B, C. Let+b+ =s, / (s-a) (s-b) (s-c) r

Mid. Deg.

00

Radius

10' 34377.5

Ord.

.038

.

'i

II .

RI

.;

VI TANGENTS, COTANGENTS TABLE

/sin

tan jsin tan sin- tan 20' 30' 30' 40' 40' 50'

tan 50'

b

c

TABLE VI (continued)

SINES, COSINES, TANGENTS, COTANOENTS (continued) i '

sin 0'

tan

sin

ten

sin

tan sin

tan sin

tan

sin

tan t

0'

10'

10'

20'

20'

30' 40'

40'

50'

50'

30'

46 7193 1.0355 7214 1.0416 7234 1.0477 7254 1.0533 7274 1.0509 7294 1.0661 43 412 .1041 42 47 314 .0124 333 .0786 353 .0850 373 .0913 392 .0977 48 431 .1106 451 .1171 470 .1237 490 .1303 509 .1369 528 .1436 41 49 547 .1504 566 .1571 585 .1640 604 .1708 623 .1778 642 .1847 40 50 660 1.1918 7679 1.1988 7698 1.2059 7716 1.2131 7735 51 771 .2349 790 .2423 808 .249 826 .2572 844 52 880 .2799 898 .2876 916 .2954 934 .3032 951 53 986 .3270 8004 .3351 8021 .3452 8039 .3514 8056 158 54 8090 .3764 107 .3848 124 .3934 141 .4019 55 192 .4281 208 .4370 225 .4460 241 .4550 258 355 56 290 .4826 307 .4919 323 .5013 339 .5108 450 57 387 .5399 403 .5497 418 .5597 434 .5697 .6319 542 .6212 526 496 .6107 511 58 480 .6003 59 572 .6643 587 .6753 601 .6864 616 .6977 631

1.2203 7753 1.276 39 .2647 862 .2723 38 .3111 969 .319037 .3597 8073 .3680 36 .4106 175 .4193 35 .4641 274 .4733 34 .5204 371 .5301 33 .5795 465 .5900 32 .6426 557 .6534 31 .7090 646 .7205 30

60 660 1.7321 8675 1.7437 8689 1.7556 8704 1.7675 8718 1.7797 61 746 .8040 760 .8165 74 .8291 788 .8418 802 .8546 62 829 .8807 843 .8940 857 .9074 870 .9210 884 .9347 63 910 .9626 923 .9768 936 .9912 949 2.0057 962 2.0204 64 9063 988 2.0503 .0965 90382 .2113 .1123 65 .1445 9001 075 2.0655 .1609 9013 088 2.0809 .1775 9026 100 .1943 66 135 .2460 147 .2637 159 .2817 171 .2998 182 67 205 .3559 216 .3750 228 .3945 239 .4142 250 .3183 .4342 68 272 .4751 283 .4960 293 .5172 304 .5386 315 .5605 69 336 .6051 346 .6279 356 .6511 367 .6746 377 .6985

8732 1.7917 29 816 .8676 28 897 .9486 27 975 2.0353 26 9051 124 ,1283 .2286 25 24 194 .3369 261 .4545 23 22 325 387

.5826 21 .7228 20

TABLE VII Degree of Curve

Radius

Defleetions for Sub Chords for Short Radius Curves.

50 sin. I def.ang.

193.18 181.39 171.01 161.80 153.58 146.19 139.52 133.47 127.97 122.92

1 12.5 Ft. 10 5

I '

10 59' 20 06' 20 13' 20 20' 20 27'

20 341 20

41'

20 48'

20o55

R

I def.

angle

Lengt

15 Ft.

20 Ft.

25 Ft.

20 17' 20 25 20 331 1 20 4 20 49

20 58'

3 43'

30 to' 30 So 21 eix'

4' 12"

o0 57'I 20

3o 05 t

3

30 58'

'3

30 131

3

44'

30

55'

4

18'

40 54 508' 22 22'

102.06

So

5036

291

40 5g

30 46

50

3 54

50

3 22' 3029'

40 02'

30 35'

40

I'

5 23'

5 34 18'

R = Tc

ii:

ec

I

5 44

DI

5

50'

6

31' I'

60 04

0'

'

10or1.15 101.33 101.48

1oi.66

30 2I' 3

of arc for 100 ft.

4026' 401

30333'

30 38'

118.31 I14.o6 IIO.II io6.5o 101.14

sub chord = sin of

7

60 571 I 70

o101.85 102.29 102.53 102.76 103.00 103.24 o103.54 103.84 o104.14 10o4.-43 o104.72

Chord def. = chord'

R

)I

I ft.

;NALS TO A 10 CURVE. =20o0

T

E

1=300

1061.9 97.577 210 10' 1070.6 99.155 + 20' 1079.2 100.75 C. 30' 1087.8 102.35 5 C. T 40' 1096.4 103.97 T 50' 1.105.1 105.60 .10 .06 1113.7 107.24 .013 220 .0

+

0

TABLE VIII TANGENTS AND EXTERNALS TO A 1 CURVE I 81o 10' 20'

T

E

1589.0

216.3

1598.0 1606.9

nA1 1G

A

I=.40

218.7 °+ 221.1 5 C. n7

T

I 41°

T

E

2142.2

387.4

10' 2151.7 20' 2161.2 1A,

t7

Q

1=500

390.7 + 394.1 5C. n

A

T

1 51

10' 20' nn

T

E

2732.9

618.4

2743.1 2753.4 M

7

f

I=too

622.8 627.2 5oC. +t

-,

o ND EXTERNALS TO A 10 CURVE.

T

E

I=800

)86.9 1308.2 )99.5 1315.6 + 112.11322.9 124.8 1330.3 5 0C. T 137.4 1337.7 150.1 1345.1 .30

162.8 1352.6

1

I o1 10' 20' 30' 40' 50'

82

E

T 4893.6 4908.0 4922.5 4937.0 4951.5 4966.1

I=900

1805.3 1814.7 + 1824.1 1833.6 5° C. T 1843.1 1852.6 .36

4980.7 1

. 149

TABLE VIII I

T

5830.5 5847.5 5864.6 5881.7 5898.8 5916.0

TANGENTS AND EXTERNALS TO A t o CURVE hE

I

101 10' 20' 5 C. T 30' .43 40' E 50' .200 102 10' 20' 30' 40' 50' 0-t-

T'

6950.6 6971.3 6992.0 7012.7 7033.6 7054.5

t

110 3278.1 + 3294.1 10' 3310.1 5 C. 20' 30' 3326.1 T 3342.3 .51 40' E 3358.5 50' .268 3374.9 1120 10' 3391.2 20' 3407.7 3424.3 30' 40' 50'

T

8336.7 8362.7 8388.9 8415.1 8441.5

8468.0

8494.6 8521.3 8548.1 8575.0

E

1-12

4386.1 4407.6 + 4429.2 S C. 4450.9 T 4472.7 .62 4494.6 E 4516.6 .360 4538.8 4561.1 4583.4 4606.0 4628.6 1* C. toot.

TABLE IX MIDDLE ORDINATES OF RAILS Length of Rail (feet) o'

ReC 3

8 126

24 22 20 C R 30

Fet

Inch Inch Ine h Inch

0-20 17189

.08 .07 .06 .05 .16 .14 .12 .10 .24 .20 .18 .15 .31 .27 .23 .20 .39 .34 .29 .25 .47 .41 .35 .30 .55 .48 .41 .35 .63 .55 .47 .40 .45 .71 .62 .53 .78 .68 .59 .50 .86 .75 .65 .55 .94 .82 .71 .60 1.02 .89 .77 .65 1.10 .96 .83 .70 1.18 1.03 .. 89 75 1.41 1.23 1.06 .90 1.65 1.44 1.24 1.05

0-40 1-0 1-20 1-40 2-0 2-20 2-40 3-0 3-20 3-40 4-0 4-20 4-40 5 6 7

8594 5730 4297 3438 2865 2456 2149 1910 1719 1563 1433 1323 1228 1146 955.3 819.0

Feet

.041 .03

.08 .13 .17 .21 .25 .29 .33 .38 .42 .46 .50 .55 .59 .63 .76 .89

.07 .10 .13 .17 .20 .23 .27 .31 .35 .38 .42 .45 .48 .52 .62 .73

8 9 10 11 12 13 14 15 16 17 18 19 20 22 24 26

h

716.8 637.3 573.7 521.7 478.3 441.7 410.3 383.1 359.3 338.3 319.6 302.9 287.9 262.0 240.5 222.3

1.88 2.12 2.36 2.59 3.83 3.05 3.30 3.54 3.76 4.00 4.21 4.45 4.70 5.16 5.64 6.07

28

26

24

22

1.64 1.84 2.05 2.26 2.47 2.66 2.87 3.08 3.28 3.48 3.67 3.89 4.09 4.44 4.92 5.29

1.42 1.60 1.78 1.95 2.15 2.30 2.48 2.68 2.83 3.02 3.18 3.36 3.55 3.84 4.20 4.58

1.20 1.35 1.50 1.65 1.81 1.96 2.10 2.26 2.40 2.57 2.70 2.86 3.00 3.30 3.59 3.88

1.01 1.14 1.27 1.39 1.54 1.66 1.78 1.91 2.04 2.16 2.28 2.41 2.54 2:80 3.04 3.29

nch

nch Inch Inch

20 .84 .94 1.04 1.15 1.26 1.36 1.46 1.57 1.67 1.78 1.87 1.98 2.09 2.29 2.50 2.70

TABLE X

SHORT RADIUS CURVES Radius Feet

Chord Feet

Central Angle

Deflection Angle

Deflection for 1 Foot

35 45 50 60 75 100 120 150 190 200 225 240 250 275 288 300 350 376 400 410

10 10 15 15 15 20 20 20 25 25 25 25 25 25 50 50 50 50 50 50

16-26 12-46 17-16 14-22 11- 30 11-30 9-34 7-39 7-32 7-10 6-25 5 58 5 44 5 -12 9-58 9 -32 8-12 '-40 7-10 7-00

8-13 6-23 8-38 7-11 5-45 5-45 4-47 3-49 3-46 3-35.

3-12 2-59 2-52 2-36 4-59 4-46 .4-06 3-50 3-35 3-30

49.3 38.3 34.5 28.8 23.0 17.3 14.3 11.5 9.15 8.6 7.7 7.2 6.9 6.2 6.0 5.7 4.9 4.6 4.3 4.2

To find length of curve divide antle from P. C. to P. T. by central angle of chord, and multiply by length of chord.

TABLE XI INCLINED DISTANCE OF 100 FT. REDUCED TO HORIZONTAL Slope

0000'

15' 30' 45' 1 00 15 30 45 2 00 15 30 45 3 00 15 30 45 4 00 15 30 45 5 00 15 30 45 6 00 15 30 45 7 00 15 30 45

Hrizntal Correction HrDistance 100.000 99.999 99.996 99.991 99.985 99.976 99.966 99.953 99.939 99.923 99.905 99.885 99.863 99.839 99.813 99.786 99.756 99.725 99.692 99.657 99.619 99.580 99.540 99.497 99.452 99.406 '99.357 99.307 99.255 99.200 99.144 99.087

0.000 0.001 0.004 0.009 0.015 0.024 0.034 0.047 0.061 0.077 0.095 0.115 0.137 0.161 0.187 0.214 0.244 0.275 0.308 0.343 0.381 0.420 0.460 0.503 0.548 0.594 0.643 0.693 0.745 0.800 0.856 0.913

nta Correction HDistance

Rise

Slope

0.000 0.004 0.009 0.013 0.017 0.022 0.026 0.031 0.035 0.039 0.044 0.048 0.052 0.057 0.061 0.065 0.070 0.074 0.078 0.083 0.087 0.092 0.096 0.100 0.105 0.109 0.113 0.118 0.122 0.126 0.131 0.135

800Q' 15' 30' 45' 9 00 15 30 45 10 00 15 30 45 11 00 15 30 45 1200 15 30 45 13 00 15 30 45 14 00 15 30 45 15 00 15 30 45

99.027 98.965 98.902 98.836 98.769 98.700 98.629 98.556 98.481 98.404 98.325 98.245 98.163 98.079 97.992 97.905 97.815 97.723 97.630 97.534 97.437 97.338 97.237 97.134 97.030 96.923 96.815 96.705 96.593 96.479 96.363 96.246

0.973 1.035 1.098 1.164 1.231 1.300 1.371 1.444 1.519 1.596 1.675 1.755 1.837 1.921 2.008 2.095 2.185 2.277 2.370 2.466 2.563 2.662 2.763 2.866 2.970 3.077 3.185 3.295 3.407 3.521 3.637 3.754

Rise 0.139 0.143 0.148 0.152 0.156 0.161 0.166 0.169 0.174 0.178 0.182 0.18.

0.191 0.195 0.199 0.204 0.208 0.212 0.216 0.221 0.225 0.229 0.233 0.238 0.242 0.246 0.250 0.255 0.259 0.263 0.267 0.271

For each foot take one one-hundredth of each reading.

TABLE XII MINUTES IN DECIMALS OF A DEGREE. 0'30" 100 30 200 30 3 00 30 4 00 30

5 00

30 6 00 30 7 00 30 8 00 30 9 00 30 1000

.00833 10'30" .01667 1100 .0500 30 .03333 1200 .04167 30 .05000 1300 .05833 30 .06667114 00 .07500 30

.17500 .18333 .19167 .20000 .2183 .21667 .22 22500 .23333 .24167

20'30" .34167 30'30" .50833 21 00 .35000 31 00 .51667 30.3833 30.52500 2200 .36667 3200 .53333 30 .37500 30 .54167 2300 .38333133 00 .55000 30 .39167 30 .55833 2400 .400003400 .56667 30 .40833 30 .57500

40'30" 41 00 30 4200 30 43 00 30 44 00 30

.67500 68333 .69167 .70000 .7083 .71667 .72500 .73333 .74167

.09167 .1000016 .10833 .11667 17 .12500 .13333 18 .14167 .15000 19 .15833 .16667 20

.25833 .26667 .27500 .28333 .29167 .30000 .30833 .31667 .32500 .33333

30 2600 30 27 00 30 2800 30 29 00 30 3000

30 46 00 30 47 00 30 48 00 30 49 00 30 50,00

.75833 30 .76667 56 00 .77500 30 .78333 57 00 .79167 30 .80000 58 00 .80833 30 .81667 59 00 .82500 30 .83333 6000

.0833315 00

30 00 30 00 30

00 30 00 30 00

.250002500

50'30" 5100 30 5200 30 53 00 30 54 00 30

.41667 35 00 .58333 45 00 .75000 5500 .42500 .43333 .44167 .45000 .45833 .46667 .47500 .48333 .49167 .50000

30 36 00 30 37 00 30 3800 30 39 00 30 40 00

.59167 .60000 .60833 .61667 .62500 .63333 .64167 .65000 .65833 .66667

.84167 .85000 .85833 .86667 .87500 .88333 .89167 .90000 .90833

.91667 .92500 .93333 .94167 .95000 .95833 .96667 .97500 .98333 .99167 1.00000

TABLE XIII--CORRECTIONS FOR TANGENTS AND EXTERNALS These corrections are to be added to the approximate values, found by dividing the tangent, or external,for a 10 curve (Table V III) by the degree of curve, in order to obtain the true tangents, or externals. Intermediate values may be obtained by interpolation.

FOR TANGENTS ADD Daonas or Cunva

Central Angle

S S

10

°

15

03 .06 04 10 06 .13 .08 16

10 150 0°

26

°

20

°

25

°

30

°

35

°

°

40

45

09 13 16 19 .22 .25 14 19 24 .29 .34 .39 19 .26 .32 .39 .45 .51 24 .33 40 49 .58 67

°

°

50

.28 .4 .58 .75

55

°

60

°

°

65

70

.31 .34 38 42 .51 .53 58 .63 .65 .72 79 .84 .83 90 .99 1.06

°

.46 .68 .90 1.14

10 19 .29 39 49 .59 .69 79 .89 .99 1.09 1.20 1.29 1.39 11 22 .34 47 .58 .69 ,70 .81 .921.041.291.421.541.66 13 .26 .40 .53 .67 .80 .93 1.06 1.201.

34 1.49 1.64 1.79 1.94 15 .30 44 60 76 91 1.06 1.211.37 1.521.70 1.872.042.21

80S 85o° 40 465 60s°

17 19 .21 23

5o °

60 66

°

t0 °

.51 .57 .63 .69

.34 38 42 46

.68 76 .84 .93

25 .51 76 1.02 .27 .56 .831.12 30 .61 .911.22 33 66 1.00 1.33

7s °

80 850

.85 1.02 1.19 1.36 .951.141.321.52 1.05 1.271.49 1.71 1.16 1 40 1.64 1.88

1.54 1.72 1.94 2.13

1.28 1.54 1.40 1.69 1.531.84 1.68 2.02

2.332.602.883.163.44 3.72 2.57 2.87 3.16 3.473.784.09 2 78 3.10 3.44 3.78 4.12 4.46 3.05 3.403.774.144.554 8$

1.80 1.98 2.15 2.36

2.06 2.27 2.46 27

86 .72 1.09 1.45 1.83 2.20 2.57 2.94 3.32 39 791.19 1.552.002.40 2.80 3.20 3.61 .43 .86 1.30 1.74 2.18 2.62 3.06 3.50 3.95 51 1.03 1.56 2.08 2..61 3.143.67 4.214 76

90 s° 100 110 °

1.72 1.92 2.17 2.38

1.912.10 2.29 2.48 2.14 2.35 2.56 2.77 2.38 2.602.833.07 2.63 2.88 3.13 3.39

3.70 4.10 4.50 4.02 4.40 4.98 4.40 4.88 5.37 5.315 86 6.43

4.91 5.32 5.38 5.83 5.856.34 7 01 7 60

62 1.25 1 93 2.52 3.16 3.814 45 5.11 5.77 6 44 7 12 7.80 8.50 9 22

1.0

FOR EXTERNALS ADD OF CURvz

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Central Angle 5o

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55

600

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35

40

.009 .027 .038 .065

.011 .029 .045 .074

.012 .032 .051 .083

.014 .035 .057 .093

.015 .017 .018 .020 .039 .043 .047 .051 .063 .070 .076 .083 .106 120 127 135

50

10 16 20 $5s

.001 .003 .004 .006 .007 .008 .003 .007 1.010.014 .018 .023 .006 .011 .017 .022 .028 .034 .009 .018 .027 036 .046 .056

80W 835 ° 40 480

.013 .025 .018 .035 .023 .046 .030 .060

.038 .054 .070 .093

.051 .072 .093 .119

.065 .086 .117 .153

.078 .109 .141 .184

.090 .131 .172 .216

.103 .153 .203 .254

.116 .175 .234 .289

.129 .197 .265 .325

.149 .213 .277 .351

.170 .230 .290 .378.

00° 88 00 660

.037 .075 .046.093 .056 .112 .067 .135

.116 .142 .168 .204

.151 .188 .225 .273

.189 .236 .283 .343

.227 .283 .340 .412

.266 .332 .398 .483

.305 .381 .457 .554

.345 .420 .516 .625

.384 .479 .575 .697

.425 .530 .636 .711

.467 . .550 .582 .641 .700 .697 .774 .851 .845 .922 1.01

70° To 800° 85

°

.080 .159 .095.182 .110.220 .128 .259

.240 .286 .332 .391

.321 .383 .445 .524

.403 .480 .558 .657

.485 .578 .671 .790

.568 .678 .787 .926

.652 .735 .777 .877 .9031.02 1.06 1.20

.819 .977 1.13 1.34

.906 1.07 1.25 1.47

.994 1.18 1.38 1.62

1.08 1.29 1.50 1.76

1.17 1.39 1.62 1.91

9W° 95 1000 1100

.149 .299 .174.350 .200.401 .268 .36

.450 .603 .756 .522 .706 .985 .604 .809 1.01 .806 1.08 1.35

.910 1.06 1.22 1.63

1.22 1.43 1.64 2.20

1.54 1.80 2.06 2.76

1.70 1.99 2.28 3.05

1.87 2.18 2.50 3.35

2.03 2.38 2.73 3.66

2.20 2.58 2.96 3.96

110

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.360.72 !1.08

1.07 1.25 1.43 1.91

1.38 '1.62 1.85 2.48

.179 .247 .315 .411

1.45 1.82 2.19 2.57 2.95 3.33 3.72 4.11 4.50 4.91

.188 .264 .341 .445

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KSTP-AM-FM-TV

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TELEVISION

3415 UNIVERSITY AVE. * MINNEAPOLIS 55414 * ST. PAUL 55114 * MINNESOTA

yAffiliate

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May 21, 1969

Professor Calvin R. Fremling State of Minnesota Winona State College Winona, Minnesota Dear Professor Fremling: Concerning your letter requesting information on the mayfly invasion aired Sunday, May 18.

The mayfly invasion we spoke of occured July 12, 1954 and was run as a "nostalgia" piece on our Sunday news May 18. Some added information that you may be interested in is that the invasion occured during a period of some highly warm temperatures in downtown St. Paul.

If I may be of any more assistance to you, please do not hesitate to contact me.

Sine

y,

Thomas

. Aaker

Associate Director of News Operations KSTP NEWS TNA:ne

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DISTANCES FROM SIDE STAKES FOR CRO1 SLOPE 1'1/ TO 1. ROADWAY OF ANY ' 0

0.00 1.50 3.00 4.50 6.00 7.50 9.00 10.50 12.00 13.50 15.00 16.50 18.00 19.50 21.00 22.50 24.00 25.50 27.00 28.50 30.00 31.50 33.00 34.50 36.00 37.50 39.00 40.50 42.00 43.50 45.00 46.50 48.00 49.50 51.00 52.50 54.00 55.50 57.00 58.50 60.00 61. 50 63.00 64.50 66.00 67.50 69.00 70.50 72.00 73.50 75.00

.

0.15 1.65 3.15 4.65 6.15 7.65 9.15 10.65 12.15 13.65 15.15 16.65 18.15 19.65 21.15 22.65 24.15 25.65 27.15 28.65 30.15 31.65 33.15 34.65 36.15 37.65 39.15 40.65 42.15 43.65 45.15 46.65 48.15 49.65 51.15 52.65 54.15 55.65 57.15 58.65 60.15 61,65 63.15 64.65 66.15 67.65 69.15 70.65 72.15 73.65 75.15

.2

0.30 1.80 3.30 4.80 6.30 7.80 9.30 10.80 12.30 13.80 15.30 16.80 18.30 19.80 21.30 22.80 24.30 25.80 27.30 28.80 30.30 31.80 33.30 34.80 36.30 37.80 39.30 40.80 42.30 43.80 45.30 46.80 48.30 49.80 $1 30 52.80 54.30 55.80 57.30 58.80 60.30 61.80 63.30 64.80 66.30 67.80 69.30 70.80 72.30 73.80 75.30

.3

0.45 1.95 3.45 4.95 6.45 '7.95 9.45 10.95 12,45 13.95 15.45 16.95 18.45 19.95 21.45 22.95 24.45 25.95 27.45 28.95 30.45 31.95 33.45 34.95 36.45 37.95 39.45 40.95 42.45 43.95 45.45 46.95 48.45 49.95 51.45 52.95 54.45 .5.95 57.45 58.95 0.45 61.95 63.45 64.95 66.45 67.95 69.45 70.95 72.45 73.956 75.459

THE NATIONAL HOLYOKE NEW YORK

.4

4.60 2.10 3.60 5.10 6.60 8.10 9.60 11.10 12.60 14.10 15.60 17.10 18.60 20.10 21.60 23.10 24.60 26.10 27.60 29,10 30.60 32.10 33.60 35.10 36.60 38.10 39.60 41.10 42.60 44.10 45.60 47.10 48.60 50.10 51.60 53.10 54.60 56.10 57.60 59.10 60.60 62.10 63.60 65.10 66.60 68.10 69.60 71.10 72.60 74.10 75.60

.5

BLANK

CHICAGO

.6

0.75 2.25 3.75 5.25 6.75 8.25 9.75 11.25 12.75 14.25 15.75 17.25 18.75 20.25 21.75 23.25 24.75 26.25 27.75 29.25 30.75 32.25 33.75 35.25 36.75 38.25 39.75 41.25 42.75: 44.25 45.75 47.25 48.75 50.25 51.75 53.25 54.75 56.25 57.75 59.25 60.75 62.25 63.75 65.25 66.75 68.25 69.75 71.20 72.75 74.25 75.75

0.90 2.40 3.90 5.40 6.90 8.40 9.90 11.40 12.90 14.40 15.90 17.40 18.90 20.40 21.90 23.40 24.90 26.40 27.90 29.40 30.90 32.40 33.90 35.40 36.90 38.40 39.90 41.40 42.90 44.40 45.90 47.40 48.90 50.40 51.90 53.40 54.90 56.40 57.90 59.40 60.90 62.40 63.90 65.40 66.90 68.40 69.90 71.40 72.90 74.40 75.90

1.05 2.55 4.05 5.55 7.05 8.55 10.05 11.55 13.05 14.55 16.05 17.55 19.05 20.55 22.05 23.55 25.05 26.55 28.05 29.55 31.05 32.55 34.05 35.55 37.05 38.55 40.05 41.55 43.05 44.55 46.05 47.55 49.05 50.55 52.05 53.55 55.05 56.55 58.05 59.55 61.05 62.55 64.05 65.55 67.05 68.55 70.05 71.55 73.05 74.55 76.05

1.20 2.70 4.20 5.70 7.20 8.70 10.20 11.70 13.20 14.70 16.20 17.70 19.20 20.70 22.20 23.70 25.20 26.70 28.20.

29.70 31.20 32.70 34.20 35.70 37.20 38.70 40.20 41.70 43.20 44.70 46.20 47.70 49.20 50.70 52.20 53.70 55.20 56.70 58.20 59.70 61.20 62.70 64.20 65.70 67.20 68.70 70.20 71.70 73.20 74.70 76.20

BOOK COMPANY MASSACHUSETTS

BOSTON

SAN FRANCISCO

1.35 2.85 4.35 5.85 7.35

-8.85

10.35 11.85 13.35 14.85 16.35 17.85 19.35 20.85 22.35 23.85 25.35 26.85 28.35 29.85 31.35 32.85 34.35 35.85 37.35 38.85 40.35 41.85 43.35 44.85 46.35 47.85 49.35 50.85 52.35 53.85 55.35 56.85 58.35 59.85 61.35 62.85 64.35 65.85 67.35 68.85 70.35 71.85 73.35 74.85 76.35

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