How much is enough?

By Austin Long

According to the Times of India and Pakistan’s Daily Times, India’s Army chief, Deepak Kapoor, chided Pakistan on Wednesday for overkill in its nuclear arsenal. The Times of India quotes him as saying:

There is a difference between having a degree deterrence, which is required for protection, and going beyond that. If the news reports of (Pakistan) having 70 to 90 atomic bombs are correct, then I think they are going well beyond the requirement of deterrence.” 

This statement raises two questions. First, if Pakistan’s arsenal is too large, what does that say about India’s arsenal? A 2008 assessment in The Bulletin of Atomic Scientists puts the number at around 70, with the expectation that it will grow in the coming years. If accurate, this would indicate rough parity in arsenals. Of course, the Indians might argue that their arsenal must be big enough to deter both China and Pakistan, while the Pakistanis need only deter India.

Second, and more difficult to assess is the question of is this enough for deterrence? The United States sought to grapple with this issue throughout the Cold War, though it was perhaps most acute during the early years of the Cold War. One assessment by the U.S. Navy in 1957 argued “[t]he first 10 delivered weapons would produce a major disaster with fully a quarter as many casualties as the first hundred.” In contrast, a subsequent assessment under Secretary of Defense Robert McNamara put the threshold of diminishing returns for additional warheads against the Soviet Union at roughly 1,000.

This latter estimate achieved the destruction of roughly 25 percent of the Soviet population and 60 percent of its industrial capability.  As long as the United States had high confidence that this many warheads would survive a Soviet first strike, it was deemed to have “assured destruction.”

Holding aside for a moment whether these numbers are right, does Pakistan have sufficient nuclear warheads to inflict this level of damage? This requires Strangelovian mathematics but unfortunately my copy of the indispensable tome of nuclear analysts, Samuel Glasstone’s Effects of Nuclear Weapons, is in transit so the following assessment is really, really back of the envelope. First, let’s assume that each warhead in Pakistan’s arsenal is roughly 50 kilotons (kt), roughly three times the size of the Hiroshima bomb. It claims to have tested a weapon in this range in its 1998 series of tests, though independent observers think the yield was much lower based on seismic data. But for the sake of argument, let’s give it to them, bearing in mind that actual yields and therefore lethal effects may be significantly less. A 50 kt weapon will produce lethal effects (mostly from prompt radiation and thermal effects) at a range of one to two miles from ground zero. Let’s call it a mile and a half — this means each weapon will cause immediate lethal effects over roughly seven square miles or eighteen square kilometers (km).

To cover all of Mumbai, with an area of about 600 square km, with this level of lethal effect would require about 33 weapons. However, there will be secondary fires and other effects from each explosion that would kill more people, so let’s cut the requirement in half, to about 15 weapons. This would kill the entire population of Mumbai — about 14 million. Delhi is more spread out with an area of about 1,480 square km. Covering it with lethal effects would require about 82 weapons, halved to about 40 weapons. This would kill the population of Delhi, another roughly 14 million. Bangalore, with an area of about 740 square km, would require about 20 weapons using the same math, killing about 6 million more. Thus with 75 warheads, Pakistan could expect to destroy India’s three largest cities, killing a total population of 34 million. This is gruesome, but represents only 3 percent of India’s population.

As a proxy for industrial destruction, 2008 estimates indicate that the three cities contribute roughly 15 percent of India’s GDP.

Of course, this is just immediate lethal effects. Radioactive fall-out would kill more people and wreak more economic damage. But this would be limited if each weapon were airburst (that is detonated several thousand feet above the ground) in order to achieve maximum immediate effect. Even if the fallout effects tripled the lethality and economic effect (highly unlikely) Pakistan would still fail to achieve the criteria considered essential for the Pentagon in the early 1960s. Of course, some would argue the Pentagon was out to lunch with this assessment but it does provide at least a benchmark assessment.

The Pakistani military, rightly or wrongly, are at least as fearful of India as the United States was of the Soviet Union in the 1960s so using a similar benchmark seems plausible.

It is also important to note that this is 75 warheads that survive any initial Indian attack and also assumes that each warhead and delivery system is perfectly reliable. In reality, a reliability rate of 90 percent would be good and would mean Pakistan would need to launch about 83 warheads to have 75 actually reach the target and detonate. If the Pakistani’s assume that an Indian first strike might destroy even 20 percent of their warheads, they would need to deploy about 105 warheads to have 83 survive. I am also assuming Pakistan’s weapons can reach these targets, which is not a given as it does not appear to have operationally deployed 75 of its longer range Ghauri and Shaheen-II missiles. This means it likely has to rely to some degree on the shorter range Shaheen/M11 as well as aircraft to deliver some of these warheads, both of which are more vulnerable to Indian attack or air defense.

Finally, the same macabre math applies to the Indian arsenal. Killing the roughly 20 million people of metro Karachi, which sprawls across 3,500 square km, would require nearly 100 of the 50 kt warheads. However, this would represent over 10 percent of Pakistan’s population and 20 percent of its GDP, closer to the assured destruction criteria.

Pakistan and India at present have nuclear arsenals of modest but significant size, capable of inflicting substantial damage on the other. They have helped keep the peace through several crises. However, neither is so large that it could be said to definitively exceed the requirements for deterrence.

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