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International Network of Engineers and Scientists Against Proliferation |
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One purpose of arms control is to prevent the world from war, especially from nuclear war. During the long way of seeking effective measures to reach the purpose, western scholars have developed strategic stability theory. The theory was established during cold war times, but it still plays an important role in the practice of arms control in the post-cold war era. According to this theory, nuclear first strike is deterred by possible nuclear retaliation. Once the nuclear deterring forces of one side are insufficient to prevent the other from igniting nuclear war, a first strike may occur. So the effectiveness of the nuclear deterrent force is significantly important to strategic stability.
Since there is no point to prevent first strike if the deterrent force can not survive a first strike, survivability of nuclear deterrent forces is one of the basic requirements ensuring effective deterrence. Therefore, once the nuclear retaliation capability is threatened, measures are taken to eliminate or reduce the threat. An effective way to achieve this purpose is to improve the nuclear arsenal both in quantity and in quality. This may result in a new round of the arms race.
A lot of research has been done on the survivability of nuclear force under nuclear attack, since conventional forces are thought to be too weak to be taken into account. However, conventional technology advances so quickly, that it is now time for us to ask a question: are conventional weapons now possible to threaten the survivability of nuclear weapons? We will discuss this possibility in this paper: First, we are going to review the improvements of conventional weapons in accuracy and versatility, then calculate the survivability of nuclear weapons; finally, we will discuss the impact on strategic stability.
The rapid advances of conventional weapons technology in lethality foreshadow a quantum leap in the role of non-nuclear forces in regional and international deterrence. This was graphically illustrated by the impressive performance of U.S. conventional technology during the Gulf War.[2] The improvements concentrate on accuracy, versatility, range and stealth. To be specific, we take the US Tomahawk cruise missile as an example to illustrate the improvement of accuracy, and take earth penetrating warheads (EPWs) as an example to illustrate the advance of versatility.
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| Figure 1: Tomahawk (BGM-109C) land attack cruise missile | |
| Length: 6.25m |
Body diameter: 0.52m
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| Warhead: 454 kg |
HE Guidance: Inertial, TERCOM, DSMAC
and GPS
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| Accuracy: 10m CEP |
Range: more than 1,300 km
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A great deal of effort has been put into improving the guidance of cruise missiles to enable very low CEP (circular error probable). The increased accuracy is due to further improvement in inertial guidance, stellar and satellite midcourse updates and terminal guidance. We can see the quick improvement in accuracy through the development of the US Tomahawk cruise missile (see figure 1[3]).
In 1976, General Dynamics (now Hughes Missile Systems) won the contract to develop the surface-launched cruise missile for US navy. Seven years later, BGM-109 Tomahawk entered into service. Originally there were three versions of the ship- and submarine-launched cruise missile: BGM-109A, a nuclear warhead missile; BGM-109B, a conventional HE warhead anti-ship missile; and BGM-109C, a conventional HE warhead land attack missile (LAM). A fourth version, BGM-109D, still a conventional LAM, entered service in 1989.
In BGM-109C versions, inertial navigation and terrain contour matching (TERCOM) midcourse guidance are used with Digital Scene Matching Area Correlation (DSMAC) for terminal guidance. The terminal matching area correlation system uses a stored digital representation of a target area, and compares this with the scene viewed below the missile by a TV camera. This system is claimed to be extremely accurate for attacking land targets, and a CEP of 10m has been reported.
However, there are some drawbacks that decrease the accuracy. DSMAC terminal guidance system is just an assistant-guidance system.[4] It can not track and identify targets automatically like radar and infrared seekers do. Further, DSMAC is a system controlled by an onboard computer. This computer can not process real time guiding data in time. So DSMAC, which begins to work about 12 kilometers away from the target, modifies the inertial guidance system only two times discontinuously during the entire end course flight. These drawbacks greatly reduce the hit accuracy.
Therefore, the Tomahawk block III upgrade program was proposed to improve the guidance system. The program includes a GPS receiver, improved guidance computer and propulsion system. In 1992, Tomahawk Block III was manufactured. One year later, it entered service with a total of 176 new missiles and 401 missiles remanufactured to upgraded standard. A CEP error of 6m is expected to be achieved under this program.[5]
The pace of achieving low CEP did not stop here. A block IV upgrade program was planned for Tomahawk since the statistic CEP of Tomahawks fired during Gulf War in 1991 was 18m, much higher than expected. This might incorporate laser radar and synthetic radar and other technology. The new version will be deployed at the end of this century. A CEP error is claimed to be 3m for this version.
From the development of Tomahawk, we can see that the accuracy of Tomahawk has been improved from 10m to 3m in just a few years. This accuracy has greatly improved its lethality, and makes Tomahawk possible to attack any point targets or to perform any surgical attacks.
Another area of development of conventional weapons is versatility. Specialized conventional warheads aimed at specific targets are developed or under development.
In other words, conventional weapons are more professional than they were. For instance, earth penetrating warheads (EPWs) are particularly effective against hardened underground targets. Studies show that a warhead detonated at a depth of 65 feet has yield effectiveness more than 25 times greater than an equivalent surface burst.[6]
Research on EPWs was initiated in the US in the late 1960s. Intensive research on EPWs at Los Alamos and Lawrence Livermore began in the 1980s. Reports show that EPWs now can penetrate theoretically a depth of 6-8m in concrete, and over 30m in earth.[7] DoD was reported, in June 1987, to commencing a major project study on highly accurate EPWs against Russian hardened underground command and control centers.[8] The superhard silos will be destroyed easily if the project succeeds. The Tomahawk Block IV was also planed to use penetrating warheads against the reinforced concrete targets, such as the silo covers of ICBMs.
EPWs have already been put into use against hardened targets. During the Gulf War in 1991, an air force base of Iraq in northern Baghdad was destroyed by EPWs on 27 February.
In general, the rapid advances of conventional weapons in accuracy and versatility, as well as other aspects, are improving lethality of conventional weapons. It makes conventional weapons more destructive. Among all the aspects, advance on accuracy has contributed much to improve the capacity of attacking hardened point targets. To determine the lethality of conventional weapons to nuclear weapons in terms of accuracy, the survivability of nuclear weapons under attack by precision strike conventional weapons has been calculated.
Conventional weapons cause damage usually by overpressure or/and dynamic pressure. In some special cases, it is by other effects. For example, a superhard silo[9] is destroyed only by crater. Within the crater, the silo is destroyed not by air-blast, but rather by ground motion during the formation of the crater. In our calculation, only overpressure is considered.[10]
A huge amount of energy is released in a conventional explosion. This energy forms a fireball of high temperature and high pressure, which compress the ambient air drastically and spread everything around rapidly. Then an air shock wave comes into being.
An air shock wave consists of the expansion region where the pressure is lower than atmospheric pressure and the compression region where the pressure is much higher than atmospheric pressure. The compression region is followed by the expansion region. Its forward boundary is a shock front. The main characteristics of the compression region is 1) the pressure exceeds atmospheric pressure; and 2) the air moves forward. The pressure exceeding the atmospheric pressure is overpressure. The pressure generated by flowing air (wind) is dynamic pressure. Both overpressure and dynamic pressure reach their maxima at the shock front. They are called peak overpressure and peak dynamic pressure respectively.
For a conventional explosion of yield Y, the dependence of peak overpressure in the shock wave on the distance r (in meters) from the explosion center can be approximated by equation (1):
where p0 is atmospheric pressure[11]. The so-called scaled distance rsc contains correction factors for air density on the ground — ambient air density — and explosive yield Y (in 1kg TNT):
We take Tomahawk III as an example to calculate peak overpressure, which uses 454kg HE conventional warhead. The results are shown in figure 2.
Figure 2: Peak overpressure of Tomahawk Block III cruise missile versus distance r from center. Both axes are in logarithmic scale.
Lethal Distance and Survivability
The destructive effect of explosion decreases with the distance from the center of explosion according to a known law. Often, the amount of effect needed to destroy a target is known as damage pressure (see Table 1). It is assumed that every target is destroyed if the threshold is exceeded, while targets stay intact if the weapon effect remains below the threshold. Thus the explosion is destructive in a certain distance from the explosion center. This destructive distance is lethal range (RL). For the explosion of the Tomahawk warhead, the lethal ranges of different targets are shown in Table 1 according to Figure 2.
If we assumed that the probability distribution of the actual warheads' impact points around the target is governed by a Gaussian function, the survival probability is
where n is number of warheads;[13] CEP, the "circular error probable," is the radius of a circle within which a warhead will land with probability 50%.
We further assume that the possibility of pre-launch survival, launch success rate, possibility of defense penetration, and warhead ignition rate are 100%. Survivability of different targets related to nuclear weapons under attack of Tomahawk block III are calculated according to formula (3) and damage overpressure in Table 1. The results are shown in Table 2. For mobile systems, the positioning error is ignored.[14]
From the calculation results, we know that:
1) Parked aircraft (such as US B-52, B-2 bombers) with nuclear weapons, trucks mounted nuclear warheads (such as Russian SS-25 Road mobile ICBM), as well as air defense radars, are destroyed easily if they are not sheltered. They don't have any survivability under the attack of one warhead;
2) Aircraft, land mobile systems and air defense radar have only 10% chance of coming out of this situation and have almost no possibility of survival under strikes by two warheads, if they are put into shelters;
3) US Minuteman II and Minuteman III silos may survive one-warhead strike with about 90% and 95% probability respectively. But they may be destroyed by more strikes. So, the hardened ICBM silos are not robust enough to stand against conventional strikes;
4) The so-called superhard silos, US MX and Russia SS-18 silos, for instance, are hard enough against these strikes.
Further, if accuracy is improved by using a laser radar and IR seeker, the threat of conventional weapons to nuclear forces will increase immensely. For instance, Minuteman III silos (about 3.6m in diameters) will be destroyed with 50% possibility by Tomahawk Block IV (CEP 3m) carrying EPWs.
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Targets
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Damage overpressure [12] (kilopascal) |
RL (m) |
| Parked aircraft |
20
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30
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| Air defense radar, road and rail mobile systems |
100 |
18
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| Reinforced concrete structures (aircraft shelter, command bunker) |
300
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11
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| Minuteman II silos |
7.000
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2,5
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| Minuteman III silos |
14.000
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1,5
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| MX silos |
35.000
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/
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| SS-18 silos |
40.000
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/
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Table 1:Criteria of damage overpressure for different targets and lethal range of the Tomahawk Block III cruise missile for different targets.
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Number of Warheads
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Damage overpressure needed for different targets (kilopascal) |
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20
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100
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300
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7.000
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14.000
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1
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0.0000
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0.0020
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0.0973
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0.8866
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0.9576
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2
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0.0000
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0.0000
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0.0095
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0.7861
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0.9170
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3
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0.0000
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0.0000
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0.0009
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0.6970
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0.8781
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4
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0.0000
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0.0000
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0.0001
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0.6179
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0.8409
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5
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0.0000
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0.0000
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0.0000
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0.5479
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0.8052
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6
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0.0000
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0.0000
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0.0000
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0.4848
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0.7711
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7
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0.0000
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0.0000
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0.0000
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0.4307
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0.7384
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8
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0.0000
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0.0000
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0.0000
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0.3819
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0.7071
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9
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0.0000
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0.0000
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0.0000
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0.3386
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0.6771
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10
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0.0000
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0.0000
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0.0000
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0.3002
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0.6484
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Table 2: Survival Probability of Different Targets under Attack of Tomahawk Block III
We can draw a conclusion from the calculation, that conventional weapons do possess a capacity of attacking nuclear forces. Therefore, nuclear retaliation capability is threatened not only by nuclear forces, but also by conventional forces. Since the rapid development of conventional technology is primarily available only to some states (US, for instance) because of their technological lead and wealth, it may impair the strategic stability and induce a new round of the nuclear arms race. So, conventional force should be taken into account for the strategic balance as the nuclear disarmament process proceeds to a certain degree, and it should be limited to a certain degree.
Lots of questions related to security issues and disarmament have risen since the role of conventional forces in strategic stability has varied. These questions need to be studied carefully before answers come out. For example:
1) What is a first strike? Supposing that one country launches conventional strikes against nuclear forces of its adversary, is it a first strike?
2) How can we distinguish a conventional warhead from a nuclear warhead in flight?
3) When shall we take conventional weapons into consideration for the nuclear disarmament process? In the bilateral stage of START, or in further multilateral stages? And
4) How to protect a facility related to nuclear weapons from being damaged by conventional strikes if conventional technology is inferior to that of the adversary?
1. This study is directed by He Yingbo. M.V. Ramana generously gave the author some helpful suggestions to improve this paper during 11th Summer Symposium in Shanghai, July 28- August 8, 1999
2. Bruce G. Blair, The Logic of Accidental Nuclear War, The Brookings Institution,1993, p.270
3. Taken from http://210.79.226.9:81/report/s-weapon/missle/bgm-109-1.htm
4. DSMAC system in tomahawk provides inertial guidance system with updated guidance data to improve guidance performance. It can not independently fulfil the terminal guidance task.
5. For more detailed information on the development of the Tomahawk cruise missile, see "Jane's Strategic Weapon Systems", 1994, USA: Offensive Weapons.
6. Paul Rogers, "Guide to Nuclear Weapons", New York, Bradford Peace Studies Papers: New Series No. 2. Page 11.
7. "The Research and Development of EPWs in U.S.", JIA Hao and FENG Xiaohui, 1993.
8. See"The Future of Land-based Strategic Missiles", part V, chapter 11, Art Hobson, Survivability of superhard silos, page 274.
9. Its damage overpressure is a few hundred megapascal.
10. In this sense, the results are conservative.
11. There are many experimental formulas which can be used to estimate overpressure in conventional explosion, and their results agree with each other quit well. We choose this one from Jürgen Altmann"SDI for Europe?" Frankfurt 1998, pages 37-38
12. See "SDI for Europe? ", Jürgen Altmann, page 38; "The Future of Land-based Strategic Missiles ", Part V Chapter 11, Survivability of superhard silos, page 267; "Minuteman ICBM", ZHANG Zongmei, page 447; and "the Survivability of Land-based Strategic Ballistic Missiles", QIN Zhigao, page 30.
13. In the case of N warheads attacking the same target, the survival probability is statistically correct by formula 3. But the effects are not independent. Because a subsequent warhead approaches to its target through the blast and dust of the foregoing warheads' explosion, it decreases the accuracy and reliability of the later warhead. This phenomenon is known as "fratricide". We ignore it in our calculation.
14. Although the mobile systems are very vunerable according to our calculation, the positioning error is the most important factor that determines kill possibility of conventional weapons.
Author's address: Institute of Structural Mechanics, China Academy of Engineering Physics (CAEP), P.O. Box 919-411, Mianyang, 621900, Sichuan, P.R. China; email: qiuyong223@163.net.
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