Two vehicle system for Pakistani Missiles?

[thesameguy]

Jet vanes may be old but still being used by most maneuverable missiles such as s 400

 

[Mrc]

Shaheen 1 with satellite nav antennas
..
So saying pakistan does not have terminal guidance tech is also not correct

 

[shaheenmissile]

@The Deterrent in a previous discussion you said warhead slows down to around Mach 5 after re entey and becomes vulnerable to being shot be ABM like the one India is trying to buy, the S-400. But here is a video of Russian Bulav missile are entry. In addition to the shallow non vertical angle ,try to count the seconds between the first glow, which would be atmosphere entry and the impact. There is hardly a few seconds.

 

[The Deterrent]

@The Deterrent in a previous discussion you said warhead slows down to around Mach 5 after re entey and becomes vulnerable to being shot be ABM like the one India is trying to buy, the S-400. But here is a video of Russian Bulav missile are entry. In addition to the shallow non vertical angle ,try to count the seconds between the first glow, which would be atmosphere entry and the impact. There is hardly a few seconds.

Please search for authentic material on this matter instead of trying to estimate it from videos.

RVs possess a tremendous amount of kinetic energy, which must be dissipated during reentry as the vehicles decelerate to their impact or landing velocity. The RV reenters the Earth's atmosphere at velocities of up to Mach (M) 25. As the RV passes through the atmosphere, atmospheric friction decelerates it to below M 1, and converts its kinetic energy primarily into thermal energy (heat). Within the stagnation zone, an area immediately in front of the RV, an area of compressed, extremely hot, ionized and stagnant air is formed. Heat from the hot gas is transferred to the surface of the RV.

http://fas.org/nuke/intro/missile/basics.htm

 

[amardeep mishra]

@The Deterrent in a previous discussion you said warhead slows down to around Mach 5 after re entey and becomes vulnerable to being shot be ABM like the one India is trying to buy, the S-400. But here is a video of Russian Bulav missile are entry. In addition to the shallow non vertical angle ,try to count the seconds between the first glow, which would be atmosphere entry and the impact. There is hardly a few seconds.

hi @shaheenmissile
The flight time from the instance the warhead enters the atmosphere till it hits the surface depends on a lot of parameters- namely
1. Ballistic Coefficient (beta=W/Cd*A)
2. Lift to Drag Ratio L/D
3. Flight Path Angle at Entry

Any object falling through the viscous medium will eventually slow down because of the following equaitons-
mg-kv=mx''-------------(note that the second term in LHS is velocity dependent vicsous force)
taking laplace transform and solving the above equation will lead to-
x(t)=mg/k(1-exp(-kt/m))---------------1
v(t)=g*exp(-kt/m)-----------------2
from equation 2 you can see that velocity does decrease,-kindly note that i have not solved this differential equation taking everything into account,i have merely taken weight,opposing velocity dependent force and resultant acceleration thats all.My aim was to show that the velocity does decease during dense phase of atmosphere!

Now coming to the re-entry,there are mainly two types of re-entries depending on the direction of opposing force-
1)ballistic re-entry- the direction of opposing force is opposite to velocity of RV
2)lifting re-entry- perpendicular to RV
ICBMs follow the former i.e #1. I will restrict my analysis to #1,wherein the major role is played by ballistic coefficient beta as mentioned above.Older ICBMs had smaller values of beta which resulted in lesser deceleration and lesser heating but increased error,modern ICBMs on the other hand have higher beta value.
I will show you an example -
H=76200m
V=6858m/s
gamma=12degrees(flight path angle)
with beta values of 500,1000 and 5000 ,look how mach number,flight time vary

As you can clearly see, from the graphs above modern ICBMs with beta close to 5000,the mach number is close to 7 or 8 at point of impact and entry time close to 1minute(in older ICBMs of beta=500,this time was as much as 3 minutes!)

Please search for authentic material on this matter instead of trying to estimate it from videos.

http://fas.org/nuke/intro/missile/basics.htm

@The Deterrent
Only if beta=W/Cd*A~500(older ICBMs)
Where W= weight,Cd=drag coeffient,A=effective area,
Only then will the terminal velocity be subsonic,in case of higher beta~5000,the terminal velocity be still hypersonic(in range of 7-8M)

 

[The Deterrent]

@The Deterrent
Only if beta=W/Cd*A~500(older ICBMs)
Where W= weight,Cd=drag coeffient,A=effective area,
Only then will the terminal velocity be subsonic,in case of higher beta~5000,the terminal velocity be still hypersonic(in range of 7-8M)

Ahan, then what would be your approximate estimate on Pakistani Shaheen-II's (1500km max range) impact velocity?

 

[Mrc]

To around 4000m/sec from info available on internet

 

[milen]

wish You'll a better articles that can make another people live.

 

[amardeep mishra]

Ahan, then what would be your approximate estimate on Pakistani Shaheen-II's (1500km max range) impact velocity?

hi @The Deterrent
Sorry i was busy with my exams hence couldnt calculate impact velocity.Now if you can furnish Cd(drag coefficient),dimension of cone(for calculating effective area A) for shaheen-2 ,i will better be able to write a program in python to calculate and even plot the range/altitude graphs- so that you can better visualize.
It will be better to assume the mass of RV~1000kg

 

[amardeep mishra]

Ahan, then what would be your approximate estimate on Pakistani Shaheen-II's (1500km max range) impact velocity?

hi @The Deterrent
Here is my analysis -
I have written code in python to analyse the entry of a ICBM with beta=5000kg/ft^2,entry velocity of close to 7000m/s or 20mach and initial entry flight path angle of 12 degrees.
For Analysing the terminal velocity of shaheen we would need to know-
1)beta - which would require the knowledge of Cd from wind tunnel tests,because beta=W/Cd*A
2)flight path angle at the time of entering dense atmosphere(here i have assumed 12 degrees)
For finding the terminal velocity of shaheen just plug in the values of #1 and #2 in python code that i have written below and you will get your answers!


p, li { white-space: pre-wrap; }
# -*- coding: utf-8 -*-

"""
Created on Sat Nov 21 10:54:20 2015
@author: amardeep
"""
import scipy.integrate as sci
import numpy as nm
import matplotlib.pyplot as plt
def ICBM(y,h):
v=y[0]
gamma=y[1]
t=y[2]
r=y[3]
ge=9.81
beta=5000*4.88
Re=6378000
T0=288.15
p11=22632
M=.0289
R=8.31
g=(ge*(Re/(Re+h))**2)
if (h>25000):
T=(-131.21+.00299*h)+237.15
p=(2.488*((T+273.1)/216.6)**(-11.388))*1000
rho=p/(.2896*(T+273.1))
q=0.5*rho*v**2
elif (11000<h and h<25000):
T=216.65
rho=M*(p11*nm.exp((-g/R*T)*(h-11000)))/R*T
q=0.5*rho*v**2
elif (h<11000):
T=T0-(6.5/1000)*h
rho=101325*(.02896/(8.3*T))*((1-(.0065*h)/T0)**(g*.02896/8.3*.0065))
q=0.5*rho*v**2

f=[g*(((q/beta)-nm.sin(gamma))/(v*nm.sin(gamma))),nm.cos(gamma)*((-g+(v**2)/(Re+h))/v**2*nm.sin(gamma)),-1/(v*nm.sin(gamma)),-Re*nm.cos(gamma)/((Re+h)*nm.sin(gamma))]

return f

h=nm.linspace(76200,0,1000000)
y0=[6858,12*nm.pi/180,0,0]
solution=sci.odeint(ICBM,y0,h)
velocity=solution[:,0]
gamma=solution[:,1]
entry_time=solution[:,2]
range_missile=solution[:,3]
fig1 = plt.figure()
ax1 = fig1.add_subplot(111)
ax1.plot(h,velocity,'b-')
plt.xlabel('altitudein m')
plt.ylabel('velocity in m/s')
plt.grid()
fig2 = plt.figure()
ax2 = fig2.add_subplot(111)
ax2.plot(h,entry_time)
plt.xlabel('altitude in m')
plt.ylabel('entry time in second')
plt.grid()
fig3 = plt.figure()
ax3 = fig3.add_subplot(111)
ax3.plot(h,range_missile)
plt.xlabel('altitude in m')
plt.ylabel('range in m')
plt.grid()
plt.show()

 

[thesameguy]

So what is the answer?