Last fall, the US Congress adopted the Missile Defense Act of 1991, which mandates the Secretary of Defense to "develop for deployment by the earliest date allowed by the availability of appropriate technology or by fiscal year 1996 a cost-effective, operationally effective, and ABM Treaty compliant" missile defense system, to consist of 100 interceptors based at a single site. This system is seen as the first step toward a multiple-site continental missile defense that would not comply with the ABM Treaty. Thus the Act calls for renegotiation of the ABM Treaty, and if renegotiation is not possible, the Act states the US will "consider the options available ... as now exist under the ABM Treaty," which includes withdrawing from the treaty with six months notice. The Act, however, explicitly states that it does not constitute a deployment decision, and that such a decision will require additional approval by Congress.

The Missile Defense Act was carefully worded to allow ABM Treaty supporters to vote for missile defenses in the aftermath of the Gulf War. However, a Treaty-compliant ABM system is not a viable compromise between missile defenses and the ABM Treaty: we show here that a Treaty-compliant system would protect only limited portions of the US even if the system worked flawlessly, leaving uncovered the east and west coasts and the southern US. Building a system that could even in principle adequately cover the coasts would violate the ABM Treaty.

Thus, Congressional supporters of the ABM Treaty should realize that making a deployment decision before renegotiating the Treaty implies a willingness either to spend large amounts of money on a treaty-limited system that even in principle can only be marginally effective, or to unilaterally abrogate the treaty, if mutually-agreeable changes cannot be negotiated. Although Russian President Boris Yeltsin has proposed developing joint US-Russian ground-based defenses, he has clearly stated that he will not relinquish the ABM Treaty if the US proceeds with unilateral development and deployment and that, in any case, he is opposed to deployment of space-based interceptors.¹

Of course, any reasoned support for missile defenses requires an assessment of the possible threats and alternative methods of dealing with them. Accidental or unauthorized nuclear attacks by the former Soviet republics would be more effectively addressed by deploying destruct-after-launch systems², and the CIA director recently asserted that there will be no long-range missile threats to the continental US from developing countries other than China for at least a decade.³

Coverage of a Battle-Management Radar at Grand Forks

Since there have been contradictory statements in recent months about the capabilities of a treaty-compliant ABM system, we describe below how to calculate the coverage of this system. Specifically, we consider the limits on the coverage provided by a ground-based ABM radar; other factors will further limit the capabilities of a treaty-compliant ABM system.⁴

We note that the assumptions made about the direction and apogee of the trajectories of incoming missiles are critical, and it is important to check the sensitivity of the results to variations in these assumptions. For example, coverage results presented in SDIO briefings often assume that missile attacks originate in central Russia, against which a site at Grand Forks has the best coverage, and that the missiles will be flown on standard "minimum-energy" trajectories. We show below that the defended area can change considerably if the trajectories are depressed slightly. Flying on such trajectories might degrade the accuracy of the missiles slightly, but flying existing missiles on such trajectories would not be difficult.⁵ Table 1 lists all relevant trajectory parameters for the cases we consider.

The ABM treaty allows deployment of 100 interceptors at a single site (chosen by the US to be at Grand Forks, ND), and requires that the ABM battle-management radars, which track incoming missiles and guide the interceptors to their targets, be located within 150 kilometers of the ABM site (Articles III, VI). The treaty restrictions on the location of ABM radars were formulated specifically to limit the capability of the ABM system to provide a nationwide defense, since this was a central objective of the treaty.

The distance at which a battle-management radar can see an incoming missile is limited by the inability of the radar to see around the curve of the earth.⁶ For this reason, a radar at Grand Forks would be unable to see missiles aimed at large portions of the US from a wide range of directions.⁷ This fundamental limit means that a treaty-compliant ABM system would be unable to defend the majority of the US population, regardless of the range or flight time of the ABM interceptors.

The radar coverage problem is illustrated in Figure 1. We assume a new radar capable of looking in all directions would replace the existing radar at Grand Forks left over from the Safeguard system, which looks only north. The bold line shows the lower limit of the radar field-of-view of an ABM radar at Grand Forks out to several thousand kilometers (the calculation of the radar field-of-view limit is discussed in the Appendix). The lighter lines show the flight paths of two SLBMs on standard (min-imum-energy) trajectories with ranges of 3000 and 7400 kilometers (km) launched from the Atlantic Ocean and targeted on Washington DC. The dashed line indicates the flight path of an SLBM on a 3000 km range depressed trajectory with an apogee of 150 km.

Figure 1. This figure shows the lower limit of the coverage of an ABM radar at Grand Forks, ND. The distance between Grand Forks and Washington DC is roughly 1900 km. (Washington DC, New York, Boston, San Francisco, and Los Angeles all lie 1900-2300 km from Grand Forks.) Also shown are the flight paths of two SLBMs launched from the Atlantic Ocean on standard (minimum-energy) trajec-tories with ranges of 3000 km and 7400 km; both stay below the region of radar coverage throughout their flights. The dashed line is the flight path of an SLBM on a 3000 km range depressed trajectory with an apogee of 150 km; such a trajectory could underfly the radar field-of-view to attack targets far inland.

As Figure 1 shows, the radar would be unable to see these missiles at any point during their flights, and thus would be unable to guide the interceptors to attack the missiles. As is also evident from the Figure, regions hundreds of kilometers inland from Washington would also not be covered by the radar. Similarly, a radar based at Grand Forks would never see SLBMs launched from most of the Atlantic and Pacific Oceans against the east and west coastal areas, and all of the southern US.⁸ Thus a Grand Forks ABM system could not protect those regions of the continental US containing most of the population from such an SLBM attack. (There would also, of course, be no coverage of Alaska or Hawaii.)

For a single-site system, the Grand Forks radar is nearly optimally located to detect missiles aimed at the continental US from the former Soviet republics, and could in theory provide coverage of the central US against such attacks. However, ICBMs launched from missile fields near Moscow on standard, or in some cases slightly depressed, trajectories could underfly the radar to attack New York and the northeast coastal areas, as could ICBMs launched against San Francisco and the northwest coastal areas from missile fields in the far eastern Russia. Yeltsin recently announced that Russia would no longer target the US, removing the possibility of an accidental attack. However, if Russia once again targets the US, it could be expected to reprogram its missiles to fly on slightly depressed trajectories to avoid US defenses if they were built, and thus the ABM radar would be unable to detect even an accidental launch of one of these missiles. Moreover, an unauthorized attack would presumably be targeted to avoid US defenses.

Similarly, missiles launched from China against San Francisco and the northwest coast of the US would never enter the ABM radar's field-of-view.

A radar at Grand Forks would also provide coverage of only a limited part of the US against hypothetical missile attacks from developing countries. If a country in the Middle East were able to acquire an ICBM in the future, the radar would not be able to see such a missile launched against Boston, New York, Washington or other targets on the east coast. Similarly, this system would not cover San Francisco and the northwest coast against a hypothetical future ICBM launched from North Korea. The radar could not see hypothetical missiles launched from countries in South or Central America or the Caribbean region against large portions of the continental US. Any country with only a few missiles would target cities, many of which would be left uncovered by the radar. In the case of a country with a small arsenal, partial coverage of the US is equivalent to no coverage.

Treaty Compliance Issues

The most obvious way to increase the coverage of an ABM system would be to build multiple ABM sites. Doing so is unambiguously prohibited by the treaty, as is deploying additional ABM radars outside of Grand Forks.

Cuing the Grand Forks ABM radar from early-warning radars or other sensors would not alleviate the radar coverage problem discussed above since we consider the extreme case in which the missile or RVs never enter the field-of-view of the radar.

Since in these cases the RV is never seen by the radar, extending the coverage of a single-site system to include missiles on these trajectories would require developing intelligent interceptors that could guide themselves to their target using onboard sensors after being cued by other sensors, such as satellites or ground-based sensors at other sites. However, any such approach would involve some sensor substituting for the ABM radar, and thus would be a clear violation of Agreed Statement D of the Treaty.

Appendix: Calculation of Radar Coverage

The radar field-of-view is assumed to extend down to inclination angles of 3^o above the local horizontal.⁹ Due to the decrease in atmospheric density with increasing altitude, radar waves bend toward the earth slightly as they propagate through the atmosphere. This effect was accounted for using the standard method of calculating the radar propagation in the absence of an atmosphere, but assuming the earth's radius is 4/3 its actual value.¹⁰ This refraction effect was included until the beam was above 100 km altitude; at higher altitudes atmospheric effects are negligible and the beam was extrapolated linearly.

Since in general the radar, target, and launch point will not lie in a plane (see Figure 2), we use the following method to determine whether a missile on a particular trajectory (with a given range and apogee) approaching a target from a particular direction can be seen by the radar. Given the relative location of the radar and target, and the particular trajectory of interest, we change the direction of the attack by increasing the angle f (see Figure 2) until the trajectory first intersects the radar field-of-view at f₀. Thus, the radar will never see a trajectory launched from a direction f that is less than f₀. This method actually overestimates the directions of attack that an ABM system would be able to defend against since our criteria is that the trajectory intersect the radar field-of-view at a single point, and the radar would actually have to see the RV for a longer period to be able to direct an interceptor to attack it.

Figure 2. This figure shows the direction of attack given by the angle f, as measured from the line connecting the Grand Forks radar and the target (in this case, Washington, DC).

Details of the Calculation

We choose the origin of our coordinate system to be at the center of the earth, with the z-axis pointing at the radar (assumed to be at Grand Forks, ND). The x-z plane contains the radar and the target (see Figure 3), and Y is the range angle between the radar and the target, defined as the range between them divided by the radius of the earth (Re).

Figure 3. This figure shows the coordinate system and angles used in the radar coverage calculation described in the Appendix. It shows a cross-sectional view of the earth, with the x-z plane containing the radar and the target. The y-axis points into the page.

In the region of interest for this calculation, we find that the net effect of the 3^o inclination angle and the bending in the atmosphere is to give a lower limit of the radar field-of-view that can be approximated by a plane perpendicular to the z-axis, defined by all points with z = Z_R ~~ R_e + 40 km.

We then consider the particular trajectory of interest (with specified range and apogee) lying in the x-z plane and terminating at the target, and choose a point P on this trajectory. P can be specified by its height h above the earth and its range angle q from the target, and has coordinates (x,y,z) = ((h+R_e)sin(Y+q), 0, (h+R_e)cos(Y+q)). A right-handed rotation of the trajectory by an angle f about the line from the center of the earth to the target can be performed by rotating P using the rotation matrix M:



where C_Y = cosY, S_Y = sinY, C_f = cosf, and S_f = sinf.

The rotated point P' = MP will intersect the radar's field-of-view when the z-component of P' equals Z_R. This will occur at a value of f given by:

By examining all points P on a trajectory using this method, one can determine the rotation angle f₀ for which the trajectory first intersects the radar field-of-view at a single point. A missile approaching the target on this trajectory along a direction given by f that is less than f₀ will never be seen by the radar. For each target, the orientation of the target relative to the radar must be taken into account, since the angle f given in Equation (2) is measured with respect to the line between the target and radar. We give our results for several launch points and targets in Table 1 below.

REFERENCES

¹Don Oberdorfer and R. Jeffrey Smith, "New Era of Nuclear Disarmament," Washington Post, 2 February 1992, p. A26, and Aerospace Daily, 4 February 1992, p. 183.

²Sherman Frankel, "Aborting Unauthorized Launches of Nuclear-Armed Through Post-Launch Destruction," Science and Global Security 2 (November 1990), p.1.

³Robert M. Gates, Hearing before the Senate Committee on Governmental Affairs, 15 January 1992. See also Lora Lumpe, Lisbeth Gronlund, and David C. Wright, "Third World Missiles Fall Short," The Bulletin of Atomic Scientists 48 (March 1992).

⁴See, for example, Anthony Fainberg, Arms Control Today (April 1989), pg. 17.

⁵See Lisbeth Gronlund and David C. Wright, "Short Time-of-Flight Nuclear Weapons," Physics and Society 20 (January 1991), p. 13, and "Depressed Trajectory SLBMs," Science and Global Security, to be published.

⁶Over-the-horizon backscatter (OTH-B) radars, which "bounce" radar energy off the ionosphere in order to see around the curvature of the earth, are unsuitable for ABM battle-management for a number of reasons, including their long wavelength and performance limitations imposed by their ionospheric propagation.

⁷Early-warning radars would detect incoming missiles, but are not capable of serving as ABM battle management radars.

⁸A radar at Grand Forks could detect Russian SLBMs launched from bastions north of Russia.

⁹Gen. John C. Toomay (ret.), "Warning and Assessment Sen-sors," in Managing Nuclear Operations, ed. A.B. Carter, J.D. Steinbruner, and C.A. Zraket (Washington, DC: Brookings Institu-tion, 1987), pg. 298.

¹⁰See J.L. Eaves and E.K. Reedy, Principles of Modern Radar (New York: Van Nostrand Reinhold, 1987), pg. 54. Refraction in the ionosphere, which is important for radio waves with frequencies less than 30-50 MHz (Eaves and Reedy, pg. 63), is ignored in our calculation since the frequencies of interest are several hundred MHz (Toomay, pg. 284).