Sunday, June 1, 2008

Ballistic Missiles and their ineffectiveness

The Threat

Today the PLA has around 1100 SRBMs facing Taiwan. The Chinese Internet Brigades (CIBs) believe that this is enough to shut down all of ROC's important bases, disable their SAMs and do all sort of other fantastic things, and thus achieve the air superiority needed for an amphibious invasion. (Note that SRBMs don’t come cheap. An estimate puts the cost for an M-9 at $0.9 mil for a unitary variant, and $1 mil for the sub-munition variant, according to a RAND study on airbase vulnerability. If the current inventory of SRBMs were adequate and they are so effective, it makes for an interesting question as to why China is continuing its buildup of SRBMs which are less cost effective than aircraft) People like me say that that's BS because we know that the missiles simply aren't accurate enough and that historical evidence show how difficult it is to keep an airbase closed, with attacked Iraqi runways during ODS repaired in as little as 4 to 6 hours (remember, these attacks were carried out with dedicated runway attack munitions, and runway repairs were conducted under Allied aerial superiority).

Despite these facts, nobody on either side of the fence can truly say how many missiles are needed - if one cannot give a number which is required, how can one say with authority that the number of SRBMs China possesses is adequate/inadequate to disable ROC's airbases? The problem is that to calculate that golden number requires one to have the requisite skills in Operations Research. Which kind of stops the whole thing dead in its tracks, most of the time.

Which brings me to this post. I found a very interesting study in my harddrive (never had the time to read it until just a few days ago), titled 'Bringing Prithvi Down to Earth: The Capabilities and Potential Effectiveness of India's Prithvi missile" by by Z. Mian, A. H. Nayyar and M. V. Ramana.

In it is a detailed methodology (including the equations) used to determine the effectiveness of the Prithvi in doing to Pakistan exactly what the CIBs always claim the PLA's SRBMs are able to do to Taiwan - disable airbases by destroying runways as well as disabling radars and other important infrastructure like command and control centers. It is highly recommended you take the time to read through the study and familiarize yourself with the concepts used now before continuing. But for ease of reference, here’s the list of equations we’ll be using.

Equation 1 - P(damage) = P(launch) x P(survive flight) x P(penetrate defense) x (P(kill)
Equation 2 - N(missiles/strip with P(confidence)) = log(1-P(confidence))/log(1-P(damage))

Equation 1 gets us P(damage) which is required in Equation 2. P(launch) is the probability of successful launch of a SRBM, P(survive flight) is the probability of the SRBM surviving flight and P(penetrate defense) is the probability of surviving any encountered anti-ballistic missile (ABM) defense. Equation 2 gets us the number of missiles required to destroy a strip with a level of confidence P(confidence). For a better description of what each component means, refer to the Prithvi study. In the Taiwan scenario, the P(launch) x P(survive flight) is assumed to be 0.85 as opposed to 0.8 as used in the Prithvi study, based on the better reliability that solid fueled missiles bring, but tempered by lower Chinese production quality. On the other hand, note that P(penetrate defenses) should not be assumed to be unity as in the Prithvi study since the ROC has ABM defenses unlike Pakistan. For the sake of clarity though, we’ll first calculate the number of SRBMs required without taking into account ABMs, and take ABMs into account in the Caveat section.

Applying the study to the Taiwan scenario

Because this is a study focused on the Prithvi and the Indian-Pakistani scenario, we have to make some adjustments to apply it on the China-Taiwan scenario. Fortunately, the study varies the accuracy versus number of missiles required to take out specified targets. We can get open source information on the accuracy of the PLA SRBMs, with the DF-15 (M-9, CSS-6) having a CEP of 150~500m, and 30~50m on the later guided variants (taken to mean MMW radar + GPS. Note that there is no evidence MMW radar is in use for DF-15 yet), while the DF-11/A (M-11, CSS-7) has a CEP of 500~600m for the DF-11 and <200m for the DF-11A guided (GPS) variant.

I will use a CEP of 50m for the DF-15 (M-9, CSS-6), and a CEP of 150m for the DF-11/A (M-11, CSS-7).

Another important piece of information needed is the number of launchers the PLA possesses. Very often people assume 1100 missiles mean they can be shot off all at once and thus overwhelm the ROC air defense system. Of course, that’s not true. Each wave of missiles is limited by the number of launchers available for each type of missile, and the PLA does not have one launcher per missile. For the required information we look at the Annual Report to Congress “Military Power of the People’s Republic of China 2008”.

In it is given the estimate:

Missile Missile inventory Launchers Range
CSS-6 315-355 90-110 600 km
CSS-7 675-715 120-140 300 km

Thus we can see that only up to a max of 250 missiles can be launched in 1 wave.

Unfortunately the study uses a warhead or payload of 1000kg as compared to the 500kg warhead as used on the M-9 and M-11, which will inflate the P(kill) of PLA’s SRBMs. This means that in the Taiwan scenario, the number of SRBMs required in all three anti-runway, anti-radar and anti-bunker scenarios is actually increased as compared to what’s reflected in the study. Note, however, that in the analysis sub-munitions are used as the ordnance of choice in both the anti-runway and anti-radar scenarios, with the unitary warhead used only in the anti-bunker scenario.

I will attempt to calculate the number of unitary warhead equipped SRBMs required to take out ROC’s major runways.

Next is the length of runway strip required for fighter plane takeoff. The study uses a minimum strip of 400m x 10m as the minimum required based on a study of wing loading and undercarriage width. To be even more generous, I’m assuming a 500m x 20m strip is required, with any damage turning that airstrip unusable. The only exceptions here are the runways of Pingdong and Pingdong South, which E-2Ts will use. Minimum take off distance of the E-2 is 564m with a landing distance of 439m, so we’ll take the runway strip required as 600m x 40m. For ease of use we will term the 400m x 20m strips as fighter strips and the 600m x 40m strips as Hawkeye strips.

These are the runways I’m taking into account, with their length listed. Note that military runways have a width of about 45m, while commercial airports (some of which are connected to military airbases like the Zhongzhen airport to Taoyuan airbase) have runway widths of 60m. To make my life easier I will assume a width of 40m for all. The number of usable strips per runway will be in brackets.

List 1

Cha San - 2500m (10)
Hualien - 2700m (10)
Hsinchu - 3600m (14)
Taoyuan - 3600m (14)
Zhongzhen - 3300m (12) and 3600m (14)
QingQuanGang - 3600m (14)
Taichng - 1500m (6)
Chiayi - 3000m (12)
Tainan - 3000m (12) and 3000m (12)
Pingdong - 2300m (3) *
Pingdong South - 2300m (3) *
Taidong - 3300m (12)

* E-2 runway strips considered to be 600m x 40m.

(Information gained through GoogleEarth)

As can be seen, the total number of strips available for use is 142 fighter strips + 6 Hawkeye strips. Keep this in mind.

Now we have to find the Probability of hitting each strip for each SRBM, or the P(kill) component in equation 1 of the Prithvi study. The equation required isn’t found in the Prithvi study so I had to find it, and I believe the proper equation to use would be the Single-Shot Accuracy against Aligned Rectilinear Target using Polya-Williams Approximation.

Basically, upon calculation the P(kill) for the DF-15 is 0.18624 and the P(kill) for the DF-11/A is 0.0598 for the fighter strip, while for the Hawkeye strip, the P(kill) for the DF-15 is 0.3629, and the P(kill) for the DF-11/A is 0.1229.

Plugging the results above into Equation 1 followed by Equation 2, we get a stunning requirement of 17 DF-15s/strip or 57 DF-11As/strip for fighter strips, and a requirement of 8 DF-15s/strip or 27 DF-11As/strip for Hawkeye strips. Now multiply that by the figures shown above in List 1 and that gives us 2,462 DF-15s or 8,256 DF-11As required to take down all the runways listed above! Put another way, with 355 DF-15s and 715 DF-11As, they can only take out 32 fighter strips, or equivalently 3 runways in total. If we take into account the limitations imposed by number of Tactical Erector Launchers (TELs), then each wave can only take out 10 strips, or equivalently less than or equal to 1 runway at a time, assuming all TELs are focused on that 1 runway.

Even if we assume that all of the DF-15s and DF-11s utilize sub-munitions, then using the Prithvi study, approximately 12 DF-15s/strip or 32 DF-11As/strip will be required. Which in turn requires (when using 400m x 50m strip size, meaning 92 strips) at least 1104 DF-15s or 2944 DF-11As.

One last point. Remember, we are using a 95% confidence value when assessing the probability of destruction per strip. This means that even assuming 17 DF-15s were used against each strip for a runway containing 10 strips, there is a 40% chance that at least one strip will still remain intact for use. You are invited to try calculating based on a 99% confidence value. I’m lazy to do the calculations for all, but for the unitary DF-15 case, the missiles required per strip will increase from 17 to 26.

Now if this doesn’t disprove the notion that PLA can achieve aerial superiority through SRBMs, then I don’t know what can.


As in any study, we should always look out for the caveats in the analysis.

1. This analysis only takes into account the airbases that are used for fighters and the E-2T Hawkeyes. It does not take into account other airbases despite the possibility that ROC might base wing support assets in other bases so as to maximise operational effectiveness under an SRBM threat which they have already identified. It also does not take into account emergency highway strips as well as taxiway strips that could be used.

2. This study does not take into account the effect of Patriot PAC-3 missiles (and Tien Kung 2s which are claimed to have an anti-ballistic missile capability as well). Remember that while the attacking side has the choice of choosing the targets for its SRBMs, the defending side has the choice of choosing which SRBMs to engage. This results in a value for the P(penetrate defense) in Equation 1 as given in the Prithvi study. Even a value of 0.8 (which assumes that 8 out of every 10 SRBMs survive the defenses, be it because they were not engaged or because the PAC-3/Tien Kung 2 missile missed), the result is very significant. To give an idea, the DF-15s required per strip will increase from 17 to 22 with a P(penetrate defense) of just 0.8.

3. Specialised anti-runway submunitions are assumed to exist for PLA’s SRBMs, if you intend to utilize the Prithvi study’s numbers for anti-runway attacks with sub-munition equipped warheads. We have no evidence that these exist. Normal submunitions will only do superficial damage against runways and require just a clearing of debris and matting to reopen the runway, something which will require far less than 4 hours.

4. All SRBMs are assumed to be guided. That is very unlikely. The unguided versions are almost worthless, with their statistical ability to hit even airstrips being close to zero.

5. GPS is available for PRC use. There are 2 situations where this may not hold true. The US may choose to impose Selective Availability over the Taiwan Straits area, thus denying GPS-level accuracy to PRC forces while letting ROC forces maintain access to GPS by providing them with codes required for unscrambling the signals. ROC forces may also use GPS jamming to disrupt GPS availability to the SRBMs. China’s Beidou accuracy isn’t up to par with the GPS at 10m accuracy, and it is still jammable.

6. Numbers of SRBMs may be inflated slightly because of the possibility that an SRBM aimed at one strip may impact the adjacent strip. It would be unlikely, however, for this possibility to affect the results significantly, especially considering how the other important factors listed above which would increase the number of SRBMs required in actuality.

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