Chapter 5: Levelling

ch-5 page 151, pb-1

In [1]:
from __future__ import division

import math

a=150;
b=100;
ar=2.525;
br=1.755;

sc=1000;
d=(a*a)/(sc*sc);

A=0.0673*d*d;

fa=ar-A;

print('correct reading on A =',fa,'meters');


d=(b*b)/(sc*sc);

B=0.0673*d*d;
fb=br-B;

print('correct reading of B =',fb,'meters');

AB=fa-fb;
print('true difference is',AB,'meters');

('correct reading on A =', 2.524965929375, 'meters')
('correct reading of B =', 1.75499327, 'meters')
('true difference is', 0.769972659375, 'meters')

ch-5 page 152, pb-2

In [2]:
from __future__ import division

import math


d=30;
sc=1000;

h=0.0673*d*d;

print('heigght of lighthouse is',h,'meters');

('heigght of lighthouse is', 60.57000000000001, 'meters')

ch-5 page 152, pb-3

In [3]:
from __future__ import division

import math

h=50;

d=math.sqrt(h/0.0673);
print('D=',d);

r=6370;
dip=d/r;
print('dimp  of horizon',dip,'degrees');

dip1=dip*((180*60)/math.pi)
print('dimp  of horizon',dip1,'minutes');

('D=', 27.25696334003587)
('dimp  of horizon', 0.0042789581381531975, 'degrees')
('dimp  of horizon', 14.709974521760092, 'minutes')

ch-5 page 152,153, pb-4

In [4]:
from __future__ import division

import math

h1=50;
h2=10;
c=0.0673;

d1=math.sqrt(h1/c);

d2=math.sqrt(h2/c);

dis=d1+d2;

print('distance between man and object is',dis,'meters');

('distance between man and object is', 39.44664791774385, 'meters')

ch-5 page-153, pb-5

In [5]:
from __future__ import division

import math

h1=10;
c=0.0673
d1=math.sqrt(h1/c);

d2=d1-80;               #since d1+d2=80;
h2=c*d2*d2;

print('height of the hill is ',h2,'meters');

('height of the hill is ', 309.46147646724046, 'meters')

ch-5 page-153,154 pb-6

In [6]:
from __future__ import division

import math

h1=100;
h2=150;

r2=12880;
c=(6/7)*(1000/r2);
d1=math.sqrt(h1/c)
d2=math.sqrt(h2/c)

d=d1+d2;
print('distance AB =',d,'meters');

('distance AB =', 86.24055457549457, 'meters')

ch-5 page-154 pb-7

In [7]:
from __future__ import division

import math

r1=2.550;
r2=2.500;

s=r1-r2;
d=0.002;
D=100;
n=5;
r=(n*d*D/s);

print('R=',r);

alp=(s/(n*D))*206265;

print('sensitiveness of bubble is ',alp,'seconds');

('R=', 20.00000000000007)
('sensitiveness of bubble is ', 20.626499999999925, 'seconds')

ch-5 page-154,155 pb-8

In [8]:
from __future__ import division

import math

n=2;
D=100;
alp=20;


s=(alp*n*D)/206265;

print('error is ',s,'meters');

('error is ', 0.01939252902819189, 'meters')

ch-5 page-156, pb-1

In [9]:
from __future__ import division

import math

a=2.245;
b=3.375;
AB=b-a;

ap=1.955;
bp=3.055;

dAB=bp-ap;

tl=(AB+dAB)/2;
print('true level of difference is',tl,'meters')
rla=125.55;
rlb=rla-tl;


print('RL of B =',rlb,'meters');

('true level of difference is', 1.115, 'meters')
('RL of B =', 124.435, 'meters')

ch-5 page 157, pb-2

In [10]:
from __future__ import division

import math

aa=1.155;
ab=2.595;
ba=0.985;
bb=2.415;

td=((ab-aa)+(bb-ba))/2

rla=525.5;
rlb=rla-td;
dab=500;
print('true RL of B',rlb,'meters');

dab1=dab/1000;

correct=0.0673*dab1*dab1;
print('combined corrction for 500m=',correct,'meters');

sc=100;
a=1.155;
e=-(0.0118*sc)/(dab);


print('collimation error per 100m=',e,'meters')

('true RL of B', 524.065, 'meters')
('combined corrction for 500m=', 0.016825, 'meters')
('collimation error per 100m=', -0.0023599999999999997, 'meters')

ch-5 page 157,158, pb-3

In [11]:
from __future__ import division

import math

aa=1.725;
ab=1.370;
ba=1.560;
bb=1.235;

A=aa-ab;
B=ba-bb;

AB=(A+B)/2;

print('true difference between A and B is ',AB,'meters');

CB=bb;
CA=CB+AB;

OCA=1.560;
e=OCA-CA;

print('amount of collimation error =',e,'meters');

('true difference between A and B is ', 0.33999999999999997, 'meters')
('amount of collimation error =', -0.015000000000000124, 'meters')

ch-5 page 158,159, pb-4

In [12]:
from __future__ import division

import math

aa=1.725;
ab=2.245;
ba=2.145;
bb=3.045;

AB=200;
rla=450;


aAB=ab-aa;

print('apparent difference of level between A and B is',aAB,'meters');

dB=bb-ba

print('apparent difference of level at B',dB,'meters')

td=(aAB+dB)/2;

print('true differece of level=',td);

CB=bb;

CA=CB-td;

e=ba-CA;

print('correction to be applied at A is =',e)

rlb=rla-td;

print('RL of B=',rlb,'meters')

('apparent difference of level between A and B is', 0.52, 'meters')
('apparent difference of level at B', 0.8999999999999999, 'meters')
('true differece of level=', 0.71)
('correction to be applied at A is =', -0.18999999999999995)
('RL of B=', 449.29, 'meters')

ch-5 page 185,186 pb-1

In [13]:
from __future__ import division

import math

aa=1.725;
ab=2.245;
ba=2.145;
bb=3.045;
dAB=200;
rla=450.0;
AB=ab-aa;
print(AB)
adif=bb-ba

print('apparent difference of level =',adif,'meters');

#a
td=(AB+adif)/2;
print('true difference of level=',td,'meters')
#b

tb=bb;
ta=bb-td;

print('true reading on A=',ta,'meters');

#c

e=ba-ta;

print('collimation error =',e,'meters');

#d

rlb=rla-td;
print('RL of B=',rlb,'meters');

0.52
('apparent difference of level =', 0.8999999999999999, 'meters')
('true difference of level=', 0.71, 'meters')
('true reading on A=', 2.335, 'meters')
('collimation error =', -0.18999999999999995, 'meters')
('RL of B=', 449.29, 'meters')

ch-5 page 186,187 pb-2

In [14]:
from __future__ import division
import math

ma=1.585;
mb=1.225;
aa=1.425;
ab=1.150;

dAB=100;

#a
td=ma-mb;
B=aa-td;

print('correct staff reading on B should be =',B,'meters');

#c


e=ab-B;
print('collimation error is ',e,'meters')

('correct staff reading on B should be =', 1.0650000000000002, 'meters')
('collimation error is ', 0.08499999999999974, 'meters')

ch-5 page 187 pb-3

In [15]:
#ch-5 page 187  pb-3

from __future__ import division
import math

dAB=100;

aa=1.875;
ab=1.790;

le=10;

ba=1.630;
bb=1.560;


td=aa-ab;

apd=ba-bb;
print('first setting')
print('true difference is',td,'meters');
print('apparent difference of level =',apd,'meters');

print('second setting');

A=ba-td;

e1=bb-A

cA=(le/dAB)*e1
cB=((le+dAB)/dAB)*e1
print('collimation error is',e1,'meters')
print('correction at A=',cA,'meters')
print('correction at B=',cB,'meters')

first setting
('true difference is', 0.08499999999999996, 'meters')
('apparent difference of level =', 0.06999999999999984, 'meters')
second setting
('collimation error is', 0.015000000000000124, 'meters')
('correction at A=', 0.0015000000000000126, 'meters')
('correction at B=', 0.01650000000000014, 'meters')

ch-5 page 163 pb-1

In [16]:
from __future__ import division
import math

bs1=2.375;bs2=2.835;bs3=0.435;
is1=1.730;is2=0.615;is3=2.070;is4=1.835;is5=1.630;
is6=2.255;
fs1=3.450;fs2=0.985;fs3=3.630;

sbs=bs1+bs2+bs3;
sis=is1+is2+is3+is4+is5+is6;
sfs=fs1+fs2+fs3;

r1=bs1-is1;
r2=is1-is2;
r3=bs2-is3;
r4=is3-is4;
r5=is4-fs2;
sr=r1+r2+r3+r4+r5;
print(r1,r2,r3,r4,r5,sr);


f1=bs2;
f2=is5-bs3;
f3=fs3-is6;
f4=is6-is5
sf=f1+f2+f3+f4;
print(f1,f2,f4,f3,sf);

k=sbs-sfs
print('k=',k);
k1=sr-sf
print('k1=',k1);

(0.645, 1.115, 0.7650000000000001, 0.23499999999999988, 0.85, 3.6100000000000003)
(2.835, 1.1949999999999998, 0.625, 1.375, 6.029999999999999)
('k=', -2.4200000000000017)
('k1=', -2.419999999999999)

ch-5 page 163,164 pb-2

In [17]:
from __future__ import division
import math

bs1=3.150;bs2=3.860;bs3=0.470;
is1=2.245;is2=2.125;is3=0.760;is4=1.935;is5=3.225;
fs1=1.125;fs2=2.235;fs3=3.890;

sbs=bs1+bs2+bs3;
sis=is1+is2+is3+is4+is5;
sfs=fs1+fs2+fs3;

r1=bs1-is1;
r2=is1-fs1;
r3=bs2-is2;
r4=is2-is3;

sr=r1+r2+r3+r4;
print(r1,r2,r3,r4,sr);


f1=fs2-is3;
f2=is4-bs3;
f3=is5-is4;
f4=fs3-is5;
sf=f1+f2+f3+f4;
print(f1,f2,f4,f3,sf);

k=sbs-sfs
print('k=',k);
k1=sr-sf
print('k1=',k1);

(0.9049999999999998, 1.12, 1.7349999999999999, 1.365, 5.125)
(1.4749999999999999, 1.465, 0.665, 1.29, 4.8950000000000005)
('k=', 0.22999999999999954)
('k1=', 0.22999999999999954)