# Chapter 11: Tacheometric Surveying¶

### section 11.7 , pg 413, problem 1¶

In [1]:
from __future__ import division
import math

retiftoi=100
fplusd=0.15
s1=2.450-1.150
thetha1=5+(20/60)
v1=(100*1300*math.sin(10+(40/60))/2)+(0.15*math.sin(5+(20/60)));
s2=1.5
thetha2=8+(12/60)
V2=21.197
d2=147.097
RL=750.500+1.8+12.045
RLD=RL+V2-1.5
print "RL of instrument axis=",RL,"m"
print "RL of D=", RLD,"m"
print "Distance of CD=147.097m"

RL of instrument axis= 764.345 m
RL of D= 784.042 m
Distance of CD=147.097m


### section 11.7, pg 415, problem 2¶

In [2]:
from __future__ import division
import math

v1=7.534
v2=16.871
v3=15.326
RLatp=255.750+v1+1.825
RLofA=265.109+v2-1.6
RLatB=280.380+v3+2.315
RLofB=298.021-1.450
D3=118.009
print "RL of axis when isnt. at P=", RLatp
print "RL of A=", RLofA
print "RL at B=", RLatB
print "RL of B=", RLofB
print "Distance between A and B=", D3

RL of axis when isnt. at P= 265.109
RL of A= 280.38
RL at B= 298.021
RL of B= 296.571
Distance between A and B= 118.009


### section 11.7 , pg 413, problem 1¶

In [3]:
from __future__ import division
import math

v1=10.494
d1=108.989
V2=24.807
d2=176.514
v3=25.652
d3=145.477
RL=450.500+1.455+v1
RLofA=462.449-1.345
RLofB=462.449+24.807-1.655
RLatB=487.151
RLofC=RLofB+v3-2.250+1.53
print v1
print "RL of axis when isnt. at A=", RL
print "RL of A=", RLofA
print "RL at B=", RLatB
print "RL of B=", RLofB
print "RL of C", RLofC

10.494
RL of axis when isnt. at A= 462.449
RL of A= 461.104
RL at B= 487.151
RL of B= 485.601
RL of C 510.533


### ch-11 page 416 pb-4¶

In [4]:
from __future__ import division

import math

c=100;
h=1.55;
rlo=150;
ra1=1.155;ra2=1.755;ra3=2.355;
rb1=1.250;rb2=2;rb3=2.750;
t1=30.5;t2=75.5;
a1=4.5;a2=10.25;

print('in 1st observation')
v1=c*(ra3-ra1)*(math.sin(9*(math.pi/180)));
v1=v1/2;
d1=c*(ra3-ra1)*(math.cos(a1*(math.pi/180)))*(math.cos(a1*(math.pi/180)));
print('v1,d1=',v1,d1);

print('in 2nd observation');

v2=c*(rb3-rb1)*(math.sin(20.5*(math.pi/180)));
v2=v2/2;
d2=c*(rb3-rb1)*(math.cos(a2*(math.pi/180)))*(math.cos(a2*(math.pi/180)));
print('v2,d2=',v2,d2);

rl=rlo+h;
rla=rl+v1-ra2;
rlb=rl+v2-rb2;

print('RL of A=',rla);
print('RL of B=',rlb);

t=t2-t1;
AB=math.sqrt((d1*d1+d2*d2)-2*(d1*d2*(math.cos(t*(math.pi/180)))));
print('difference of level AB=',AB,'meters');

dab=rlb-rla;
gab=AB/dab;
print('gradient of AB is 1 in',gab);

in 1st observation
('v1,d1=', 9.386067902413853, 119.26130043570826)
in 2nd observation
('v2,d2=', 26.26555359446006, 145.25041419362984)
('RL of A=', 159.18106790241387)
('RL of B=', 175.81555359446008)
('difference of level AB=', 104.0330138511747, 'meters')
('gradient of AB is 1 in', 6.254056529136824)


### ch-11 page 418 pb-5¶

In [5]:
from __future__ import division

import math

h=1.5;
a1=10;a2=12;
c=100;
ra1=1.150;ra2=2.050;ra3=2.950;
rb1=0.855;rb2=1.605;rb3=2.355;
rlp=450.5;

v1=c*(ra3-ra1)*(math.sin(a1*(math.pi/180)));

v2=c*(rb3-rb1)*(math.sin(a2*(math.pi/180)));

h1=ra2*(math.cos(a1*(math.pi/180)));
h2=rb2*(math.cos(a2*(math.pi/180)));

print('v1,v2=',v1,v2);
print('h1,h2=',h1,h2);

rlai=rlp+h;

rla=rlai-v1-h1;
rlb=rlai-v2-h2;

print('RL of A=',rla);
print('RL of B=',rlb);

d1=c*(ra3-ra1)*(math.cos(a1*(math.pi/180)))-ra2*(math.sin(a1*(math.pi/180)));
d2=c*(rb3-rb1)*(math.cos(a2*(math.pi/180)))-rb2*(math.sin(a2*(math.pi/180)));

dab=d1+d2;
print('distance between A an B is',dab);
gpa=d1/(rlp-rla);
gpb=d2/(rlp-rlb);

print('gradient of PA is 1 in ',gpa);
print('gradient of PB is 1 in ',gpb);

('v1,v2=', 31.256671980047464, 31.1867536226639)
('h1,h2=', 2.0188558936750263, 1.5699268991777582)
('RL of A=', 418.7244721262775)
('RL of B=', 419.24331947815836)
('distance between A an B is', 323.2978586242886)
('gradient of PA is 1 in ', 5.567473732648181)
('gradient of PB is 1 in ', 4.68342893110529)


### ch-11 page 419 pb-6¶

In [6]:
from __future__ import division

import math

c=100;
ra1=1.25;ra2=1.75;ra3=2.25;
rb1=0.95;rb2=1.75;rb3=2.55;
rc1=1.55;rc2=2.15;rc3=2.75;
a1=10;a2=5;a3=8;

ab=c*(ra3-ra1)*(math.cos(a1*(math.pi/180)))*(math.cos(a1*(math.pi/180)));
bc=c*(rb3-rb1)*(math.cos(a2*(math.pi/180)))*(math.cos(a2*(math.pi/180)));
cd=c*(rc3-rc1)*(math.cos(a3*(math.pi/180)))*(math.cos(a3*(math.pi/180)));

print(ab,bc,cd);

lab=ab*(math.cos(30.5*(math.pi/180)));
lbc=-bc*(math.cos(40*(math.pi/180)));
lcd=-cd*(math.cos(45*(math.pi/180)));
print('latitudes of AB,BC,CD=',lab,lbc,lcd);

dab=ab*(math.sin(30.5*(math.pi/180)));
dbc=bc*(math.sin(40*(math.pi/180)));
dcd=-cd*(math.sin(45*(math.pi/180)));
print('depatures of AB,BC,CD ',dab,dbc,dcd);

lc=-(lab+lbc+lcd);
ls=-(dab+dbc+dcd);

print(lc,ls)
k=-ls/lc;
t=math.atan(k);
t=t*(180/(math.pi));

print('Bearing of DA=',t);
DA=math.sqrt(lc*lc+ls*ls);
print('length DA=',DA);

(96.98463103929541, 158.78462024097664, 117.67570175629913)
('latitudes of AB,BC,CD=', 83.56478621811925, -121.63607598835735, -83.20928669276485)
('depatures of AB,BC,CD ', 49.22342087003188, 102.06478649968226, -83.20928669276483)
(121.28057646300294, -68.07892067694931)
('Bearing of DA=', 29.30698225670086)
('length DA=', 139.08169422226874)


### ch-11 page 419 pb-7¶

In [7]:
from __future__ import division

import math

h1=1.48;h2=1.42;c=100;
ra1=0.77;ra2=1.60;ra3=2.43;
rb1=0.86;rb2=1.84;rb3=2.82;
a1=12.166;a2=10.5;
la=112.82;da=106.4;
lb=198.5;db=292.6;
ac=c*(ra3-ra1)*(math.cos(a1*(math.pi/180)))*(math.cos(a1*(math.pi/180)));
bd=c*(rb3-rb1)*(math.cos(a2*(math.pi/180)))*(math.cos(a2*(math.pi/180)));

print('Distance AC=',ac);
print('Distance BD=',bd);
lac=-ac*(math.cos(53.5*(math.pi/180)));
tlc=la+lac;
print('total latitude of C=',tlc);

dac=ac*(math.sin(53.5*(math.pi/180)));
da=-da;
tdc=da+dac;
print('total depature of C=',tdc);

lbd=-bd*(math.cos(4.75*(math.pi/180)));
tld=lb+lbd;
print('total latitude of D=',tld);

db=-db;
ddb=-bd*(math.sin(4.75*(math.pi/180)));
tdd=-(db+ddb);
print(ddb)
print('total depature of D=',tdd);

dx=tdc+tdd;
cx=tlc-tld;

CD=math.sqrt(dx*dx+cx*cx);
print('length CD=',CD,'meters');

('Distance AC=', 158.62738402665204)
('Distance BD=', 189.49088179672577)
('total latitude of C=', 18.46481737819161)
('total depature of C=', 21.113710931586226)
('total latitude of D=', 9.659924163502069)
-15.6914002615
('total depature of D=', 308.2914002614939)
('length CD=', 329.52276617048415, 'meters')


### chapter 11, section 11.8, pg 422, example 1¶

In [8]:
from __future__ import division

import math

c=600
fplusd=0.5
s=3
n=6.860
distance= (c*s/n)+ fplusd
print "distance =",distance

distance = 262.890670554


### chapter 11, section 11.8, pg423, eg2¶

In [9]:
from __future__ import division

import math

d=65.340
x=4.5
y= math.tan(x)
v=5.142
RLofA=255.500+v-0.950
print v
print "RL of A=", RLofA

5.142
RL of A= 259.692


### chapter 11, section 11.8, pg423, eg2¶

In [10]:
from __future__ import division

import math

s1=2
h1=0.655
v1=6.578
RL=v1+h1+510.5
v2=1.085
d2=12.396
h2=1.25
RLofB=RL-v2-h2
d=37.31+12.396
print "distance between B and BM=",d
print "RL of B=", RLofB

distance between B and BM= 49.706
RL of B= 515.398


### chapter 11, section 11.8, pg423, eg2¶

In [11]:
from __future__ import division

import math

d=124.45
c=1000
s=2
fplusd=0.3
thetha=(5+(6/30))
n=1980/d
print "n=",n

n= 15.9100040177