# Chapter 1 : Buoyancy and Stability¶

### Example 1.4.1 Page no : 5¶

In [1]:

#initialisation of variables
ws= 64. 			#lbf/ft**3
wi= 57. 			#lbf/ft**3

#CALCULATIONS
vabyvb= (ws/wi)-1
vtbyva= (1./vabyvb)+1
vabyvt= (1./vtbyva)*100

#RESULTS
print  'percentage of total volume extended above the surface= %.1f per cent'%(vabyvt)

percentage of total volume extended above the surface= 10.9 per cent


### Example 1.4.2 page no :5¶

In [1]:
import math
#initialisation of variables
p= 20. 			#lbf/in**2
d1= 4. 			#in
d2= 18. 			#in
d3= 0.5 			#in
sw= 62.3 			#lbf/ft**3

#CALCULATIONS
Fa= p*(math.pi/4)*d3**2
Fb= (4/d2)*3.92
V= 1.5*(Fb/sw)*1728
r= (0.75*(V/math.pi))**(1/3.)
d= 2*r

#RESULTS
print  'diameter of the float= %.2f in'%(d)

diameter of the float= 4.11 in


### Example 1.6.1 page no : 12¶

In [2]:
import math

#initialisation of variables
delta_W= 4. 			#tonf
x= 30. 			#ft
W= 2000. 			#tonf
O1=(0.015)
O2= -0.015

#CALCULATIONS
O = O1-O2
GM = (delta_W*x)/(W*O)

#RESULTS
print  'metacentric height= %.f ft'%(GM)

metacentric height= 2 ft


### Example 1.6.2 page no : 12¶

In [3]:

#initialisation of variables
ws= 1./35 			#tonf/ft**3
A= 10500. 			#ft**2
wf= 1/36. 			#tonf/ft**3
Wo= 7000. 			#tonf
Wf= 6950.			#tonf
li= 300. 			#ft
lh= 400. 			#ft
l= 7200. 			#ft
l1=50. 			    #ft
l2= 10. 			#ft
l3= 250. 			#ft
l4= 40. 			#ft

#CALCULATIONS
Dod= (1./A)*((Wo/wf)-(Wf/ws))  #decrease of draught(ft)
x= (l1*l2+l3*l4)/(l+l3-l1*l2)
do= (x/lh)*li

#RESULTS
print  'change of draught= %.3f ft'%(Dod)
print  '  change of trim=%.1f ft'%(do)

change of draught= 0.833 ft
change of trim=1.1 ft


### Example 1.6.3 page no : 14¶

In [4]:
#initialisation of variables

M= 500. 			#tonf ft/in
D= 32. 			    #tonf/in
l= 200. 			#ft
L= 380. 			#ft

#CALCULATIONS
x= l+(M/D)*(L/l)

#RESULTS
print  'length= %.1f ft aft'%(x)

length= 229.7 ft aft


### Example 1.7.2 page no : 19¶

In [7]:
#initialisation of variables
import math
a= 6.
b= -6.
c= 1.

#CALCULATIONS
s1= (-b+math.sqrt(b**2-4*a*c))/(2*a)
s2= (-b-math.sqrt(b**2-4*a*c))/(2*a)

#RESULTS
print  'upper limit for specific gravity s= %.3f '%(s1)
print  'lower limit for specific gravity s=%.3f tonf'%(s2)

upper limit for specific gravity s= 0.789
lower limit for specific gravity s=0.211 tonf


### Example 1.7.3 page no : 21¶

In [8]:
#initialisation of variables
b= 350. 			#ft
d= 12. 			#ft
L= 46. 			#ft
Ac1= 500.*80*12 			#ft**3
Ac2= 350.*12*9 			#ft**3

#CALCULATIONS
Ic= (b*d**3)/12.
A= b*d
Io= Ic+A*L**2.
I= 2*Io
V= Ac1+2*Ac2
BM= I/V

#RESULTS
print  'print lacement of body= %.1f ft'%(BM)

print lacement of body= 32.2 ft


### Example 1.8.1 page no : 23¶

In [11]:
#initialisation of variables
W= 4500. 		#tonf
b= 20. 			#length(ft)
s= 0.83         #specific gravity

#CALCULATIONS
I= int(b*d**3/12.)
r= 3*s*I/(36*W)
inc = r * 12      # inch

#RESULTS
print  'Reduction caused by three compartments= %.3f in.'%(inc)

Reduction caused by three compartments= 0.157 in.


### Example 1.9.1 page no : 25¶

In [10]:
#initialisation of variables

import math
Kg= 12. 			#ft
g= 32.2 			#ft/s**2
GM= 2. 			#ft

#CALCULATIONS
T= 2.*math.pi*math.sqrt(Kg**2/(g*GM))

#RESULTS
print  'periodic time of rolling of the ship= %.1f sec'%(T)

periodic time of rolling of the ship= 9.4 sec