Second Agni-III test-2

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ramana
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Post by ramana »

Op-Ed in Pioneer, 14 April, 2007
Fire in the sky

The Pioneer Edit Desk

Agni-III multiplies India's strike force

After a long dry spell during which it was pilloried for tardy progress in the implementation of various projects, the Defence Research and Development Organisation has reason to celebrate. The spectacular launch of Agni-III, an intermediate range ballistic missile, on Thursday is not only a feather in the DRDO's cap, but also marks an important milestone in India's missile programme. With Agni-III, India has acquired the capacity to strike as far as 3,000 km - which includes China's major cities like Beijing and Shanghai - with both conventional and nuclear warheads. Of course, it would be silly to suggest that an IRBM of Agni-III's capacity has added to India's conventional might; it was necessary to develop this missile as a deep-strike delivery system for nuclear warheads and thus make India's nuclear deterrence that much more credible. It would be equally silly to suggest, as has been done in the past by peaceniks and Lenin's lost children, that with Agni-III in its arsenal - it will take some time for this to become a reality - India will indulge in sabre-rattling with its northern neighbour or that mutually assured destruction will pave the way for mutually assured distrust. That's balderdash: China's missile capacity is many times more than that of India and the nuclear arsenal of the two countries (or, for that matter, their strategies and doctrines) are not comparable, at least for the moment. What, however, is important to note is that Thursday's successful test demonstrates that India has neither abandoned its nuclear doctrine nor diluted its commitment to develop indigenous technology to carry Pokhran-II to its logical conclusion. With the UPA Government - and before that the NDA regime - dragging its feet on Agni-III and the first test on July 9, 2006 proving to be a failure, there was speculation over whether India would persist with its quest to develop IRBMs, especially in view of pressure brought about by the US and unstated conditions on which the Indo-American civil nuclear cooperation deal is predicated.

Hopefully, India's missile programme will now gain momentum. Both China and Pakistan have not allowed their respective missile programmes to flag. In the first three-and-a-half months of 2007, Pakistan has carried out five tests - two of long range cruise missiles and three of ballistic missiles. China's missile-testing has been more frenzied, akin to that of the USSR at the height of the Cold War. India, on the contrary, has been laid back in pushing the frontiers of indigenously developed missile technology. There is no merit in adopting such a minimalist posture when our neighbours are pursuing a missile programme that is both aggressive and maximalist. Hopefully, the DRDO's astonishing diffidence, as well as the not-so-surprising reluctance of the country's political leadership, has come to an end with Agni-III blazing a trail of glory. Pakistan's faux testing of gifted missiles that are renamed after Islamic invaders need not really bother us. But we cannot afford to ignore China's inexorable march towards economic and military superpowerdom.


This article is an example of the dual mind set of Indian elite vis a vis PRC. One part says PRC is the threat and so AIII is an answer. Another part says PRC has so much more in inventory that its not credible to think like that.
This begs the question that in case of nukes when small numbers offer enough deterrence as large numbers. So AIII with its range and accuracy provides a quantum leap with regard to PRC. PRC has to think twice as the escalation ladder in now in place.

It is another thing that PRC is only one of the threats at this time . In future it could be others.
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Post by rsingh »

Chinese on Agni tests.... it is against Pakistan and forthcoming longer range missiles are for Unkil :lol:
But according to the United States Department of Defense's "Defense News" reported that in addition to developing the "Agni-3" missile, India is developing a range of up to the farthest 12,000 km of the "Surya-2" missiles, will be available in future years. 。American nonproliferation experts Shibier that such a missile apparently from the United States.。Thus, the United States acquiescence India combustion "Agni", and perhaps one day this fire will burn his body. (王辉)★(Wang)

Guys, It is not the best translation but you get the essence. This shows what Chinese tell to the Chinese in Chinese language . Usually English websites of Xinhua "change" the contents to suit the readers.
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Post by Arun_S »

I use Google Earth for my distance thing, it gives the coordinates.

BTW 3000Km means it splashed 6 degress south of equator.
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Post by Arun_S »

For Agni-III to be able to plaster furtherest corner of China from any part of continental India, requires a range of 6,800 KM. So why the hell is the claimed 3000Km enough against China? Why will Indian stage Agni-III near Chinese border just so to push the 3000Km range to as much into China and not cover cover China from any of Indian choice to spread, conceal and attack the challenger?

That is the reason India needs Agni-3++ to be able to punch full 1,800 kg or more payload wherever Chinese want to stage their offensive weapons. So MOD needs to pronto double up and get the Agni-3++ in the arsenal.
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Post by mandrake »

Someone posted this in rediff,
"Listen carefully, I'm engineer. Range of a missile is not fixed parameter. Please note range of missile is function of payload weight and trajectory. New generation warheads designed by ISRO are fractional weight while giving greaster blast yield, practically putting ranges of upto 20,000 km even in Agni III parabolic reach, when not utilizing full 1,5 ton payload capability. The 3000 km range is worst case scenario, when using high payload (old 80's Indian nuke) and parabolic path. Modern nuke weighs only 100-300 kg. And don't forget there's always the orbital option for advanced space power like India, allowing missile to go via orbit rather than parabolic trajectory. Using orbital mechanics, even proven Agni II can deliver thermonuclear payload (myriads of times more powerful than Hiroshima blast) over ranges exceeding earth's diameter. Agni III engines are powerful enough to place a MIRV style bomb in TLI (Lunar orbit). One should ask, when you can reach satellite orbit of earth and space, what can stop you from reaching any place on earth? India is not signatory to SALT treaty and reserves right to use FOBS (fractional orbit), obviating most range constraints. Nuclear war is not a mere philosophy, it's a brutally crude form of self defence using the feasibility of laws of nature. What matters is that Indian rudimentary global deterrance for attack is there. Note our smart Indian leaders diplomatically say Agni 3 range is "more" than 3000. The exact number is calculable via orbital mechanics, and as I stated it is not limited for earth's small size. The wonders of using later / mature technology gives India's delayed &young missiles more range than believable. Believe it or not Agni III is a potent ICBM and Agni IV is standing in line right behind it eager to improve on that and lifting India's capability to desirable level. While range is no longer relevant, the more intelligent question is now, what is the payload capability of missile, for striking nuclear offenders. World should focus more on proliferators China and N.Korea that force India to undertake nuclear defence via servile/rogue states such as Pakistan/Iran. Thank you and kind regards, your respectful reader."
:wink:
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Post by Vriksh »

What is the probability that we can use A3 for satellite launch, or even for an ASAT role with adequate mods given it can place warheads in fractional orbits.
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Post by ShauryaT »

Arun_S wrote:That is the reason India needs Agni-3++ to be able to punch full 1,800 kg or more payload wherever Chinese want to stage their offensive weapons. So MOD needs to pronto double up and get the Agni-3++ in the arsenal.
Very smart reason Arun...ofcourse, we will not ask you on what will be the rage, if the same missile is fitted with a 250K TN weapon, what shall be its range? :wink:
Raju

Post by Raju »

ramana wrote:This article is an example of the dual mind set of Indian elite vis a vis PRC. One part says PRC is the threat and so AIII is an answer. Another part says PRC has so much more in inventory that its not credible to think like that.
Indian elite seems extremely casual and relaxed about the future. Whereas the Chinese seem to be frenzied.

I wonder what is the secret behind this casual countenance and relaxed cofidence ?? Do they see something in the future that we don't ?
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Post by SaiK »

Raju wrote:Do they see something in the future that we don't ?
FEAR!
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Post by Arun_S »

ShauryaT wrote:
Arun_S wrote:That is the reason India needs Agni-3++ to be able to punch full 1,800 kg or more payload wherever Chinese want to stage their offensive weapons. So MOD needs to pronto double up and get the Agni-3++ in the arsenal.
Very smart reason Arun...ofcourse, we will not ask you on what will be the rage, if the same missile is fitted with a 250K TN weapon, what shall be its range? :wink:
It is India's prerogative & choice to spend Rs.150 to plaster offensive weapon cluster hiding east of Mangolia, or spend 3X Rs101 each with a flower, because Indian Yindu missile do not have the muscle?
India chooses what is economical and/or required for robust defense.

Same reason why France has full range MIRV missiels with 8000Km range.

Zimple onleeee.
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Post by Vick »

Awesomeness! "Plans are proceeding as I have forseen them..."
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Post by svinayak »

Raju wrote:

Indian elite seems extremely casual and relaxed about the future. Whereas the Chinese seem to be frenzied.

I wonder what is the secret behind this casual countenance and relaxed cofidence ?? Do they see something in the future that we don't ?
Chinese know the threat to their govt and forces.
Totalitarian govt have insecurity which makes them alert.
Raju

Post by Raju »

I was connecting it to some other plan. There has to be a larger plan or else I would call their approach suicidal. Anyway within 2 yrs there is going to be a massive showdown on Iran.

How well prepared are we ?? How united is our citizenry ? Is Agni-3 to be fully operational within 2 yrs ?

btw IBN is reporting that MEA informed Indonesia atleast a week in advance on the Agni tests.
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Post by Austin »

Arun_S wrote: Austin please provide the link or in the quote pls provide name of the poster who posted link or said it.
Thread moving too fast.
Hi Arun , the link the above is this outlook report link

Agni-III will also be converted into a submarine-launched ballistic missile to open more second-strike options for the country, DRDO scientists told reporters during a briefing.
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Post by Rahul Shukla »

Gerard & Arun & Suraj Saa'r - Thank you for your replies. All gyan is appreciated. :)

Since you have been so kind, I decided to get some answers to one of your concerns - H1B. I actually met a US immigration attorney friend of mine for dinner and asked for a solution to the H1B woes of SDRE's. The answer is posted in the Indo-US thread.

Please click HERE to see...
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Post by Arun_S »

Rahul Shukla: You are welcome.
Pls see my reply there and a message from Bhishma Pitamah if Indian Strategic Thinkers.
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Post by SriSri »

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Post by p_saggu »

AFAIK we have had deterrance against the chinese with the agni 2 and A 2-AT versions for some time around. Why is this test sending raptures of orgasm through the people in the know.
My feel is that finally Our love 'n affection can be delivered to the stiff upper lips in the European region and the still reluctant Uranium peddlers south of the equator.
Everything that GOI's done here is downgraded by a factor of 2 - 3. Multiply range etc. with 3 and you get the real picture...
Nothing is what it seems :!:
Last edited by p_saggu on 14 Apr 2007 09:30, edited 3 times in total.
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Post by SriSri »

Btw those stiff upper lips are perceived as threats .. why? :-?
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Post by krishnan »

Top DRDO Scientists have revealed to PTI that a Submarine Launched Version of Agni III missile is going to be developed. They also revealed that Agni III range can be extended to up to 5,000 Kms but Government approval would be required for the same.
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Post by satyarthi »

Only decent picture yet of AGNI-III launch (from kakkaji's link above).

Image
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Post by Gaurav_S »

http://www.india-defence.com/reports/3035
For the first time, Chander said, DRDO had acted only as an integrating agency with the Agni-III, with most of the missile's components being made by private industry. A total of 258 private firms and 20 DRDO laboratories were involved in this venture.

"This is why there were no production delays and the next missile is being readied in parallel," he said.
258 private players is a whooping number... :eek: Maintaining co-ordination between them must have been a nightmare.

AFAIK, more involvement of private agencies will bolster the confidence to take down future defence projects.
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Post by mohanty »

Singha wrote: we are going to take the panda down off the tree and spank it soundly.
I can see Singha dragging Panda down by its leg off the bamboo tree and spanking. And Panda saying, 'Wahahohoho..wahahohoho'. :D
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Post by Singha »

the distance from balasore to the equator west of indonesia is around 2100km

the flight path from indonesia to KSA would pass just south of car nicobar
this is still some distance north of the probable impact area

so would indicate the two garuda planes saw the flaming RV very high above
them against the deep blue sky reentering the atmosphere perhaps around 200K-300K ft AGL

make me think the RV followed a relatively flattened end trajectory using
its onboard engine to test anti-ABM strategy
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Post by Singha »

dnaindia.com .... as the next installment of the "credible minimum deterrent" we have a new word - limited range ICBM (L-ICBM) :rotfl:

Limited range ICBMs appear on the horizon
Josy Joseph
Saturday, April 14, 2007 01:23 IST

NEW DELHI: Following the successful test of the Agni III intermediate-range ballistic missile, scientists handling the country’s missile programme say they can produce a limited-range intercontinental ballistic missile (ICBM) that can hit targets 5000km away in three years.

M Natarajan, chief of the Defence Research and Development Organisation (DRDO), said it would require just “three yearsâ€
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Post by kmc_chacko »

What is normal weight of ICBMs ?
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Post by kmc_chacko »

Increasing India's missile reach
http://www.hindu.com/2007/04/14/stories ... 271000.htm[/url]
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Post by SriSri »

gauravsurati wrote:http://www.india-defence.com/reports/3035
For the first time, Chander said, DRDO had acted only as an integrating agency with the Agni-III, with most of the missile's components being made by private industry. A total of 258 private firms and 20 DRDO laboratories were involved in this venture.

"This is why there were no production delays and the next missile is being readied in parallel," he said.
258 private players is a whooping number... :eek: Maintaining co-ordination between them must have been a nightmare.

AFAIK, more involvement of private agencies will bolster the confidence to take down future defence projects.
It is natural that there'd be so many private partners. No single private entity would've been developing a major component, and there'd be many developing small sub components without knowing what it would be for.

As for co-ordination .. they'd have to simply stick to the specifications. Standards aren't too hard to impose in engineering.
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Post by Singha »

the road mobile ones (less mirv) tend to be 25-40T with Topol-M 48T being a
upper end, the railway models can be heavier in general (40-60T). the biggest silo based ones like SS-18 (10xmirv and massive range) tip the scale off the radar at a MTOW of 200tons and a payload of immense 5.5 Tons!!

ideally a 3-stage, 1.5T (3xMirv) projectile with 7500km range for SLBM and a 2mts longer version with 12000km range for land use is pretty decent goal to shoot for. a 500kg payload will take both way past the 14000km range barrier to NYC/LA which are farthest places from mainland india.
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Post by Austin »

Singha wrote:the road mobile ones (less mirv) tend to be 25-40T with Topol-M 48T being a
upper end, the railway models can be heavier in general (40-60T). the biggest silo based ones like SS-18 (10xmirv and massive range) tip the scale off the radar at a MTOW of 200tons and a payload of immense 5.5 Tons!!

ideally a 3-stage, 1.5T (3xMirv) projectile with 7500km range for SLBM and a 2mts longer version with 12000km range for land use is pretty decent goal to shoot for. a 500kg payload will take both way past the 14000km range barrier to NYC/LA which are farthest places from mainland india.
Singha , We will have to design a new TEL vehical for A 3 , which can accomodate a larger gross weight ( 48.3 T ) , Infact I have yet too see any compact vehical ( like prithivi TEL ) for Agni series , Designing one for A 3 would require some very heavy trucks like those used by Russi.

Add a 1m 3rd stage and the Gross weight goes to 50+ tons , we should also look at some Land Based Silo for the Agni 3 plus.

BTW the SS-18 Mod 5/6 has a payload of 8.8 Tons per START declaration , In reality they can carry around ~ 9.5 tons :twisted:
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Post by kmc_chacko »

Why Indian R&D organisations make overweight equipements ? :-?
Arjun 55+tons now Agni III 45+ tones compared to ther having around 30+ with more range :oops: . Will DRDO scale down the size so that they can be moved quickly. :cry: :wink: :D
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Post by Shankar »

The single-warhead RT-2UTTH Topol-M is an advanced version of the silo-based and mobile Topol intercontinental ballistic missile. While the SS-25 Topol is generally similar to the American Minuteman-2, the more sophisticated SS-27 Topol-M is comparable to the American Minuteman-3. The Topol-M is 22.7 meters (75 feet) long and has a diameter of 1.95 meters (6 feet 3 inches). The missile weighs 47.2 metric tons and has a range of 11,000 kilometers (6,900 miles).
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Post by p_saggu »

SriSri wrote:Btw those stiff upper lips are perceived as threats .. why? :-?
Who said anything about perceiving anyone as a threat. We are onlee talking about spreading Love 'n Affection. Bear Hugs, massive - crushing types onlee - very persuasive, mellows da tougher nuts... :wink:
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Post by Arun_S »

Singha wrote:the distance from balasore to the equator west of indonesia is around 2100km

the flight path from indonesia to KSA would pass just south of car nicobar
this is still some distance north of the probable impact area

so would indicate the two garuda planes saw the flaming RV very high above
them against the deep blue sky reentering the atmosphere perhaps around 200K-300K ft AGL

make me think the RV followed a relatively flattened end trajectory using
its onboard engine to test anti-ABM strategy
I think what they saw was debris of First/second/inter stage or the payload adapter. The second stage & payload adapter in particular will be flaming due to re-entry energy
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Post by Arun_S »

Singha wrote:dnaindia.com .... as the next installment of the "credible minimum deterrent" we have a new word - limited range ICBM (L-ICBM) :rotfl:

Limited range ICBMs appear on the horizon
Josy Joseph
Saturday, April 14, 2007 01:23 IST
Call it Yindu ICBM or Snake Charmers ICBM or PC Sorkar ICBM, its reach and knock is vicious and fearful to those on the wrong end of the RV. :P
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Post by Arun_S »

Austin wrote:we should also look at some Land Based Silo for the Agni 3 plus.
What makes Silo of any use to India given the precision of modern missiles that Serpent etc etc have?

Silos are destabilizing because they invite first strike. During alert time, moving them around is critical IMHO.
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Post by Shankar »

Trying to collaborate Aruns calculation on agni 3 range actual (not the down graded crap given out in official handouts stumbles on this article which I edited some what and may be an interesting read


he question frequently arises as to the difficulty or ease
of extending the range of a ballistic missile from the
common Scud B of perhaps 300 km range to a range of 9000 km
or 10,000 km.
ne way to answer this question is simply to point to the
various missiles that exist in the inventory of the various
nations, to show that ICBM range is indeed possible and
conventional. But this conceals the very substantial
difference between the technology of a short-range ballistic
missile or medium-range ballistic missile and that of an
ICBM.
Another approach is to go back to first principles-- namely,
the rocket equation-- to see what is involved actually in
reaching such range for a ballistic missile. The reader
should bear with us while we explain some simple concepts,
probably familiar to just about everybody.

A "ballistic missile" is a vehicle or object that continues
on its path under the force of the Earth's gravity. It
continues because of Newton's laws of motion. More
specifically, it exchanges its kinetic energy of radial
motion for potential energy as it rises to apogee and then
recovers kinetic energy as it loses potential energy as it
comes closer to the center of the earth. That applies to a
rock just as well as it does to an ICBM.
A given rocket stage operates ordinarily at constant chamber
pressure. Hot gas is produced by the combustion of liquid
or solid fuel, exchanging chemical energy for thermal
energy. The hot gas creates some chamber pressure in the
combustion chamber, which is connected to space by the
throat of a rocket nozzle. If there were just an aperture
in the combustion chamber, one would still have a rocket,
but the gas would be emitted from that aperture in a
hemisphere, rather than in a directed stream. So the
momentum associated with the thermal energy would be lower
than if all the gas went in the same direction.
In fact, the function of the rocket nozzle is to expand the
combustion gas in such a fashion that it cools and
constitutes a largely uni0directional jet. At the throat,
one has hot gas with the molecules going in every direction.
As the gas expands in the rocket nozzle, it repeatedly
pushes on the material of the nozzle (except in the
direction of the exit circle), and as the rocket nozzle
diameter increases with distance from the throat, the gas
expands and cools itself. So in the rocket jet that is
ejected into space, the gas is quite cold, but moving
extremely rapidly. The best that can be done in obtaining
exhaust velocity is to convert all of the thermal energy of
the fuel into kinetic energy of the exhaust (leaving nothing
left over for internal thermal energy of the exhaust plume).
For rocket exhaust into space (above the atmosphere), that
condition is closely approached. Certainly billions of
dollars have gone into wringing the last bit of performance
out of rocket nozzles. Eventually one gets to a point at
which the size and mass of additional nozzle outweighs the
small benefit that can be obtained by reducing the already
small residual thermal energy in the exhaust plume.
For exhaust into the atmosphere in the boost phase of a
rocket, such large expansion ratios are not available,
because the atmospheric density and pressure is finite. So
first-stage rocket nozzles lack the long skirt of a
deep-space nozzle.
For instance, it is a simple matter to follow the trajectory
of a specific choice of rocket design, launched at a
specific angle to the horizontal; one can determine the
entire course of propulsion, burnout, and the range to
impact. One would, of course, like to know the elevation
angle corresponding to maximum range, which is a simple
problem for a flat Earth (the result is 45 deg, without
taking into account gravity loss or atmospheric drag), but
even that could be obtained through multiple computer
trials.
Quantitatively one can have an excellent approximation to
rocket performance by the assumption that all of the thermal
energy of the fuel emerges as uni-directional kinetic energy
of the exhaust. Then Newton's third law states that for
every action there is an equal and opposite reaction. This
means that in a coordinate frame centered on the rocket at
any given time, the momentum associated with the exhaust
emitted in a very short interval (say, one second), is
countered by the momentum given to the remaining rocket plus
un-exhausted fuel. So one has an equation relating the two,
and specifically giving the rate of increase of rocket
momentum as determined by the rate m (in grams/second) at
which mass is exhausted, together with the velocity Ve of
the exhausted mass.

Eq. 1: mVe = M dV/dt

In this Equation, m is the mass ejected per second in the
rocket plume; Ve is the exhaust velocity of the jet; M is
the remaining mass of the rocket (decreasing with time); V
is the instantaneous velocity of the rocket, and t is the
time.

This equation has a simple solution which can be written as:

Eq. 2: Mf/Mo = e**-(Vg/Ve)

Here Mf is the final mass of the rocket stage-- the payload
plus the dry weight of the rocket; M0 is the gross launch
overall weight (GLOW); Vg is the velocity gain overall; and
Ve is again the rocket exhaust speed. The reader is asked
to pardon the rather gross appearance of the simple
mathematics; expedience may be worth more than elegance.
"**" stands for exponentiation; "r x s" or "r*s" is the
product of r and s, as is "r s".
It is quite remarkable that large liquid-fuel space
boosters, for instance, have an excess acceleration of only
about 0.3 g, so that most (1.0/1.3) of their thrust and
their initial fuel expenditure simply replaces the upward
thrust of the launch stand. Ballistic missiles as weapons,
however, typically have a larger initial thrust and have in
this way less "gravity loss" associated with their burn
rate.
That is, we
know how for a single stage to relate the GLOW, the fuel
mass, the dry weight, and the payload. There is a direct
trade-off between dry weight (structure, fuel tanks, rocket
nozzle, pumps, etc.) on the one hand, and payload on the
other. Indeed, because there is a maximum speed even with
zero payload, and because some of that dry weight is
associated with the initial thrust and the initial nozzle,
there is benefit or even necessity to "staging" rocket
propulsion.

For a given technology level, the idea is to throw away as
much of the inert mass as possible as the fuel is being
expended, and to end up with a smaller rocket, with unburned
fuel, as the second "stage". The trick can be repeated, so
that in principle a given level of technology could
accelerate a second stage to a certain velocity, which would
then burn and separate from the third stage, which would
then burn and separate from the fourth stage, etc.
If one sketches the optimum trajectory for a stone to go the
greatest distance for given initial speed (or a baseball
hit) one finds that the optimum launch angle is 45 degrees
from the horizontal, and one can obtain the range simply by
noting the time required for the vertical velocity Vz to
reverse. During flight without thrust or drag, the rocket's
horizontal velocity Vh is constant. So we have the set of
equations:

Voz = Vo/sr2

(For brevity, I write "sr2" for the square root of two).

T = 2Voz/g; R = VhT = (2/g)(Vo/sr2)(Vo/sr2) = Vo**2/g

g = 9.8
m/s**2 R = 300 km Vo = sr(gR) = sr(9.8x3x10**5) =1.7146 km/s.

Vo km/s R km(Flat Earth) Mo/Mb Reality
1.7146 300 2.140 2.69 Scud B
2.425 600 2.933 3.80 Al Hussein
3.1305 1000 4.01
9.900 10,000 80.82

(Round Earth)
7.1 10,000 23.33
Table 1 required initial velocity Vo for range R in the
flat, non-rotating Earth approximation. Mo is the initial
launch weight and Mb is the burn-out mass of the rocket.

It should be noted that an exhaust velocity Ve = 2.254 km/s
corresponds to a "specific impulse" (Isp) of 230 sec = Ve/g.
The specific impulse is a time that characterizes the energy
per unit mass of the propellant. Equipped with an
appropriate nozzle, it is equal to the time that an initial
mass of propellant could provide a thrust equal to the
Earth's gravitational force on that initial mass.
If one wants to have a greater range than 1200 km, even with
zero payload, one must either change the technology or go to
a rocket with more than one stage. First we consider adding
a second stage. By "technology" we mean here only two
things-- the structural weight of the rocket and the motors
(the dry weight or structural fraction SF) and the Isp.

First we consider the use of staging for a given technology,
taking Isp = 230 s and a structural fraction of 22% (SF).
We assume that the SF is constant for a payload less than or
equal to the SF, assuming that not much structure is
required to support the payload.

Then we have:

c Eq. 3: V2 = Ve ln M2/(M2*SF +PL)

wherefore the second stage, we have written the burnout
c weight explicitly as (M2*SF + PL), where PL is the payload
c in kg. By "ln" we mean the base-e logarithm.

And for the first stage we have

Eq. 4: V1 = Ve ln M1/(M1*SF + M2)
The entire mass of the second stage rocket-- fuel and all--
is the payload of the first stage.

Now we want to minimize M1 for a given total velocity gain
(V1+V2):

(V1+V2)/Ve = ln M1/(M1*SF+M2) + ln M2/(M2*SF+PL)

e**(V1+V2)/Ve = M1 x M2/(M1*SF+M2)x(M2*SF+PL)

Eq. 5: e**Vg/Ve = 1/(SF+M2/M1)(SF+PL/M2)

Let PL' = PL/(SF*M2) SR = M2/(SF*M1), where we have
introduced the "staging ratio" SR.

Eq. 6: e**(V1+V2)/Ve = (SF)**-2 /(1+SR)(1+PL') =
constant

Note that for a given M1

Vg is maximized for the minimum of Q = (1+SR)(1+PL') with
respect to M2. So


c dQ/dM2 = 0 for -PL*SF*M1 = PL*M2 + M2**2(SF+PL/M2) = 0

or

-PL*SF*M1 + M2**2 SF = 0

or M1*PL = M2**2.

Therefore M2 = sr(M1*PL). This means that the velocity gain
is the same for each stage of the multi-stage rocket with
the same technology for each stage.

We can now solve for M1 to obtain

(SF + sr(M1*PL)/M1)(SF + PL/sr(M1*PL)) = e**-Vg/Ve

(SF + sr(PL/M1))(SF + sr(PL/M1)) = e**-Vg/Ve

or

(SF + sr(PL/M1)) = e**-(Vg/2)/Ve
Now take the Vg = 7.1 km/s; Vg/2 = 3.55 km/s;
Ve = 2.254 km/s

sr(PL/M1) = e**-(Vg/2)/Ve - SF

Eq. 7: (M1/PL) = 1/(e**(-Vg/2)Ve - SF)**2 = 1/(0.2070-0.22)**2




PAGE 8


Unfortunately, this denominator is negative, and there is no
launch mass that will propel even a two-stage rocket with Al
Hussein technology to a range of 10,000 km on a round Earth.
e should have noted that the launch velocity requirements
for a round Earth are less than those for a flat Earth at
long range simply because the Earth falls away from the
rocket as it travels-- a phenomenon noted by Newton in his
comparison between the speed of a falling apple and the
speed of the falling moon. For instance, for a range beyond
20,000 km, there is no additional velocity requirement,
since the rocket has gone into orbit and can have any range
with no additional velocity.
So maybe one wants to go to better technology rather than to
a third stage. For instance, we could imagine a structural
fraction SF = 0.15 instead of the structural fraction of
0.22.

Better structural fraction can be obtained by use of higher
strength materials, by chemical milling or other tailoring
of parts, and so on. Assuming a 30% reduction in SF (to
0.15), the denominator in the previous equation is
D = 0.2070 - 0.15 = 0.0570, and the launch mass of a
two-stage rocket would be given by M1/PL = (1/D)**2 = 308.
So for a payload of 300 kg , this would be a launch weight
of 90 tons.

If this seems high, and we want a 30 ton launch weight for
600 kg payload; (M1/PL) = 50, then we need D = 0.1414. So
that SF = 0.2070 - 0.1414 = 0.0656. This is an
astonishingly low structural fraction compared with the
0.22.

Another option is to move to higher Isp-- for instance 300
seconds. Then Ve = 2.94 km/s and e**(-Vg/2Ve) = 0.271. So
we would have the desired denominator of D = 0.1414 for a
structural fraction SF = 0.130, allowing a 30 ton launch
weight for a 600 kg payload. Or we could use three stages.
http://www.fas.org/rlg/980327-range.htm
shyamd
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Post by shyamd »

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Nayak
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India is just doing what great powers do

Post by Nayak »

India is just doing what great powers do
It wants to play with the Big Five, and playing the great-power game means you end up playing the nuclear-war game, too.
By Gwynne Dyer
Independent
More articles by this columnist
(Apr 14, 2007)

The test would hardly have made the news outside of India if the local air-traffic controllers had posted a warning in advance, but when an Indonesian airliner had to turn around in Indian airspace on Thursday and return to Jakarta to avoid flying into the missile's path, it was bound to draw attention. So now the whole world knows India has test-fired a nuclear-capable missile that can hit Shanghai and Beijing, and a few people (especially in China) may be asking: Why?

The Agni-III missile failed its first flight test last July, but this one seems to have gone off very well. The missile, which reportedly can carry a 300-kiloton nuclear warhead, was not tested at its full range of more than 3,000 km on this occasion, but that is the number that gets people's attention. India's main potential enemy is Pakistan, which is right next door, and it already has missiles that can strike anywhere there. The Agni-III gives India the range to strike the Middle East (but it has no enemies there) or southern Russia and Central Asia (likewise) -- or China.

China is not India's enemy, either, but there is a worrisome drift in Asian affairs, and the Agni-III is just the tip of the iceberg. To be fair, China has had missiles that could strike Indian cities for more than 30 years now (though they were actually built to reach American cities), so there is no monopoly of blame here. And neither China nor India is planning to attack the other. They're just doing what comes naturally for great powers.

Why is India doing this now, 30 years after China built its missiles? Because India, with U.S. encouragement, has finally decided, after a half-century of "nonalignment," that it wants to play the great-power game too. It has the resources these days, and it's just too galling to be left out when the Big Five get together to sort out the world. Even if playing the great-power game means you end up playing the nuclear-war game, too.

There's more. American strategists do not think that China intends to attack the United States, but they know that China is going to be the second-biggest economy in the world in 10 or 15 years' time. China is therefore a potential challenger to America's position as the world's sole superpower, and as such it must be "contained." So for the past five or six years Washington has been busy renewing old military ties and forging new ones with countries all around China's borders.

Of those countries, the two most powerful by far are Japan (already an American ally) and India. Japanese right-wing politicians are tired of being a special country that has foresworn the use of force in its international relations (in the constitution that the United States wrote for it after the Second World War). They want to be a "normal" country -- well, a normal great power, really -- so Prime Minister Shintaro Abe has pledged to rewrite the constitution in order to remove those unreasonable restrictions on sending Japanese troops overseas and so on.

And since India is now a "normal" great power, too, it is doing the things that normal great powers do, such as making alliances with other great powers. Specifically, with the United States, with which New Delhi signed a 10-year military co-operation agreement in 2005. (No, it's not officially called an alliance. It doesn't need to be.)

When you go to Beijing and ask Chinese officials (off the record) how they feel about all this, they swear that they are not going to panic. They understand that this sort of thing is just the reflexive way that great powers have always behaved, and that they know it doesn't mean that America, Japan and India are planning to attack them. Quite right, too, and as long as they hang on to that thought no harm will come of all this.

But if they do panic at some point -- maybe over some crisis in the Taiwan Strait or the disputed seabed between China and Japan or some stupid incident like the American spy-plane that collided with a Chinese fighter in 2001 -- then all the pieces are already in place for an Asian Cold War. Which would be a serious waste of half the world's time at best and a mortal peril to the whole planet at worst.

But they're all just doing what comes naturally to great powers. History doesn't repeat itself, as Mark Twain remarked, but it does rhyme.

Gwynne Dyer is a London-based independent journalist whose articles are published in 45 countries.
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