Sunday, November 20, 2005

China's Ballistic Missiles

According to the 2005 report "The Military Power of the People's Republic of China":
China has deployed some 650-730 mobile CSS-6 and CSS-7 short-range ballistic missiles (SRBMs) to garrisons opposite Taiwan. Deployment of these systems is increasing at a rate of about 100 missiles per year. Newer versions of these missiles feature improved range and accuracy. [4]

These missiles often come up in conversations about China employing force upon Taiwan. It is worth taking the time to do the math and figure out what exactly 700 missiles (plus or minus) could accomplish.

Quantity of Missiles
China has about 700 SRBMs, but how many of those would actually be used? Strategist and Nobel laureate Thomas Schelling points out the value of the threat of force relative to its employment:
To be coercive, violence has to be anticipated... It is the expectation of more violence that gets the wanted behavior, if the power to hurt can get it at all. [Arms and Influence, 2-3]

Thus it would appear that China would want to hold a substantial missile capability in reserve to maximize its influence. This is logical because, were China to shoot all of its missiles without Taiwan capitulating, it would have little remaining leverage (short of an invasion or blockade). While it is anyone's guess how many missiles China would calculate that it should hold in reserve, I've heard from a few different military types that one-third or more is the standard formula. If that is the case, that would mean that China could employ about 467 of its 700 and maintain a reserve of roughly 233.

Mechanical Malfunctions
Chinese SRBMs were designed to be improved SCUD missiles. Thus it would seem to be fair to use estimates for the probability of mechanical malfunction in flight used for the older Soviet tactical missiles. The probability of a missile surviving its flight (not accounting for missile defenses) ranges from 70% to 90% for such Soviet missiles. Assuming the Chinese missiles are on the more reliable end of the estimates, 10% (or 47 missiles) are still lost to mechanical malfunctions. That leaves 420 missiles headed for Taiwan.

Missile Defenses
Currently Taiwan's missile defenses are meager. Taiwan fields 200 Patriot-2 Plus (PAC-2 Plus) missiles for its three Patriot batteries. Were it to acquire the Patriot missiles under consideration for purchase from America, Taiwan's Patriot inventory would increase to almost 600 with the majority being Patriot-3s (PAC-3). Both generations of Patriots are untested under combat conditions and thus it is unclear how many incoming missiles Taiwan's missile batteries could be expected to destroy with or without the new PAC-3s. Estimates for the success of earlier generation of Patriots in the first Gulf War vary too much to be helpful.

I personally would guess that the Patriots would have a 50% kill rate, but to be honest I have no data to back that estimate up. Based on my estimates, Taiwan could kill 100 missiles before they reach their targets (with their current Patriot capabilities), bringing the number that would cause damage down to 320. If more Patriots are acquired the number reaching Taiwan would be further reduced.

One problem with this analysis is that China may have already found a way to improve their SRBM's survivability against Patriot missiles. (Hat Tip: Michael Turton)
Mr. [Richard] Fisher... believes the PLA used illicit Patriot data to improve M-9 [CSS-6] short-range missiles aimed at Taiwan, which China views as a breakaway republic and has vowed to reincorporate with the mainland -- by force if necessary. "They used the information from the Patriot for the M-9 to be able to evade Patriot interception," Mr. Fisher said. [source]

CSS-6s have a circular error probability (CEP) of 280 meters. CSS-7s have a CEP of 200 meters. With this accuracy, and assuming that the targets are not hardened and the target location is precisely known to the Chinese, China would have a 3% probability of destroying a building with a CSS-6 or a 6% probability of destruction with a CSS-7. With this limited degree of accuracy, it would take 44 CSS-6s or 23 CSS-7s to destroy a target with 75% certainty.* Thus, if China's missile batteries are composed equally of CSS-6s and CSS-7s, China could expect to destroy ten buildings with 75% certainty using all of its missiles (except the 233 it has held in reserve). If no missiles were held in reserve and thus 530 missiles reach their targets, 15 buildings could be destroyed with the same degree of certainty.

GPS Upgrades
The most recent models of both SRBMs may be equipped with global positioning system (GPS) guidance systems which improves their accuracy to a CEP of 30-45 meters. With such an accuracy, the missiles could be expected to achieve a one shot, one kill accuracy with 87% confidence. This would completely change the accuracy section of analysis above and allow China to be relatively confident of its ability to kill one target with each missile. With GPS upgrades, China could reasonably expect to destroy 240 targets with its 320 missiles that reach their targets or 461 targets if no missiles were held in reserve.

The above analysis assumes that China has a specific list of targets that it deems most important to destroying Taiwan's will to defend itself, such as the Presidential Palace, the Ministry of Defense building, command and control facilities, and Taipei 101. This may not, however, be the case.
That’s the lesson that Saddam taught us, that ballistic missiles may have little military value but do have great terror potential. [GEN Charles Horner]

If China were to target populated areas instead of specific targets, it would be able to create great destruction. No longer would China be launching 20 or more missiles at one target, and it could send all of its missiles toward Taiwan's residential and commercial areas with the greatest population density. This would be a direct attack on national will--as would any missile attack. China could not take any ground with missiles, only boots on the ground can do that, but China may hope to convince Taiwan to surrender because of the vast destruction and threat of more destruction (see the importance of reserves).

National Will
When attacking national will, missiles are no different than saturation bombing. The same munitions, delivered by different platforms (planes instead of missiles) were seen on both fronts in World War II and numerous times since. Bombing cities in order to sway the population was first tried in the Battle of Britain and served only to strengthen the resolve of the Brits to fight and win the war. It has never had the decisive negative effect on national will that the air forces of the world often attribute to it.
[I]n more than thirty major strategic air campaigns that have thus far been waged, air power has never driven the masses into the streets to demand anything. [Bombing to Win, 68]

Simply put, the combined warhead capacity of 467 CSS-6 and CSS-7 SRBMs (1,100 pounds each) is the equivalent of only 9.5 Vietnam era B-52 sorties (54,000 pounds each). Even if all 700 SRBMs were used and all reached their targets, it would only equal 14 sorties. To look at it another way, the 700 SRBMs would only total 385 tons of high explosives, compared with the hundreds of thousands of tons dropped on Vietnam, for example.

Any prediction as to what level of bombing would cause Taiwan to surrender is nothing but a guess, but if Taiwan surrendered as a result of such a minimal attack, it would be "history's statistical outlier," as one of my professors characterized such unlikely events. Many nations, including the ROC during the shelling of Kinmen and Matsu Island, have survived much worse.

Other Options
Another strategic bombing possibility is that the missiles would be aimed at command and control (C2) installations or strategic resources such as oil reserves. The goal would be to undermine the country's ability to wage war and thus encourage capitulation. In either case, such missile strikes would only be decisive if combined with other military action. Degrading C2 would only be beneficial if coupled with an invasion and oil is easily replaced unless a blockade is put into place.

Further Reading: After a significant amount of research, I found this analysis (PDF) of India's Prithvi missile to be the best analysis of the potential effectiveness of a conventionally-armed missile. My calculations have focused on the destruction of soft targets or semi-hardened buildings. If anyone is interested in calculating the effect China's SRBMs would have on Taiwan's airfields, the math is explained therein.

*This analysis is based on numerous assumptions. For simplicity of analysis, I assume that the lethal radius of each missile is 60 meters, as would be the case with a high explosive warhead (the most logical for the destruction of buildings). Other warhead types (prefragmentation, incendiary, or cluster) would differ. Additionally, I assume that if the missile lands within the blast radius of the center of the building, the structure is destroyed. The totality of destruction will vary with the size and hardness of the building, but I find this to be a fair simplification.

Update: An article in the Christian Science Monitor also looks at China's missile capabilities and comes to the same conclusion.
Then there are those 600-800 Chinese missiles aimed at Taiwan from Fujian province in China. US commanders, Taiwanese politicians, and journalists often describe these missiles as if they are a decisive military threat. In fact, they are more likely symbolic. As a munitions expert told the Monitor, 700 missiles is "nothing. For a military attack that is supposed to incapacitate and paralyze a country, it is not impressive."