The Prospects for SuccessfulAir-Defense Against Chemically-Armed Tactical Ballistic Missile

Attacks on Urban Areas

THEODORE A. POSTOL

March 1991

DEFENSE AND ARMS CONTROL STUDIES PROGRAM

ItCenter for International Studies

Massachusetts Institute of Technology292 Main Street, Cambridge, Massachusetts 02139

The Prospects for SuccessfulAir-Defense Against Chemically-Armed Tactical Ballistic Missile

Attacks on Urban Areas

THEODORE A. POSTOL

March 1991

The Prospects for Successful Air-Defense AgainstChemically-Armed Tactical Ballistic Missile

Attacks on Urban Areas

THEODORE A. POSTOLProfessor of Science, Technology and National Security Policy

March 1991

A DACS Working Paper

Defense and Arms Control Studies ProgramCenter for International Studies

Massachusetts Institute of Technology

WP 91-1

This technical note examines the possible effects of attempts to interceptchemically armed tactical ballistic missiles with air defense missiles that make interceptsat high tropospheric altitudes ( 10 km) or low stratospheric altitudes ( 20 km). Theexamination is further limited to interceptors that destroy tactical ballistic missiletargets using non-nuclear fragmentation warheads or by direct impact with a target.PATRIOT and HAWK are examples of such air defenses and the Soviet SCUD (SS-1A,SS-1B and other variants) is an example of a tactical ballistic missile that couldpotentially be used for delivery of chemicals. The tentative conclusions of thispreliminary analysis are as follows:

1. A successful PATRIOT or HAWK intercept of a SCUD at high altitudewhich results in the destruction and catastrophic breakup of the chemicalwarhead could well result in significant and possibly lethal concentrations ofnerve agents on the ground at several miles distance from the point abovethe ground where the intercept occurs.

An intercept at an altitude of 10 km, for instance, could result in lethallevels of nerve agent on the ground 15 to 60 minutes after an intercept. Fortypical wind conditions, the area of contamination could be several tenths ofkilometers in width and several kilometers in length, perhaps 5 to 10 milesdownwind from the actual point above the ground where an interceptoccurs.

2. If these initial estimates of chemical dispersal behavior are correct, it suggeststhat a defense of urban areas against chemical SCUD attacks which utilizesnon-nuclear hit-to-kill missiles or fragmentation warheads at hightropospheric altitudes might only alter the pattern of chemicals thatultimately fall to the ground, rather than stopping the delivery of suchchemicals.

3. This conclusion is, however, highly tentative, and requires an assessment ofhow the size distribution of chemical aerosols created at high altitudes,where air temperatures may be as low as -70 F, differs from that at lowaltitudes, where air temperatures might be of order 50* F.

For example, a cloud of very widely different particle sizes created at highaltitudes by a successful intercept could potentially become so dispersed asit falls that the biological hazard from it would be greatly reduced by thetime it reached the ground. This analysis suggests that such a desirabledispersal of such chemical clouds is unlikely. However, this is a preliminaryanalysis of a very complex problem, and a more detailed assessment ofaerosol formation at high altitudes is needed to confirm this tentativeconclusion. Such a more detailed analysis should also include anassessment of the effects of upper atmospheric turbulence and wind shearon the rate of aerosol cloud dispersal.

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Analytical Basis for the Tentative Conclusions Presented Above

When a ballistic missile like a SCUD is used to deliver a chemical agentagainst a target, it is likely that the large aerodynamic forces at the release point, thetemperature of the surrounding air, and the thermophysical properties of the chemicalagent mixture, all play a role in determining the nature of the chemical dispersalpattern. The objective of the chemical release is to create a cloud of tiny droplets ofhighly toxic chemical agent that will fall to the earth under the influence of gravity,aerodynamic drag, and wind motion -- creating a lethal environment on the ground.Such a cloud of droplets (or particles) is called an aerosol cloud.

The shape and extent of the contaminated area created on the ground bysuch an attack depends on the height of release of the chemicals, the rate of fall ofaerosol particles, the local wind conditions, and the lethality of the chemicals. Figure 1(taken from page 74 of the 1986 edition of Soviet Military Power) shows an estimate ofthe contaminated region that might occur from a SCUD attack, assuming a height ofchemical release between 1.4 and 1.5 km and an unusually low wind speed of .9 m/sec(about 2 mph). The contours of the pattern presumably show regions of variouslethality. The size of this region is plausible, if one assumes a chemical nerve agent likeVX. An unprotected human breathing normally in an aerosol cloud of VX of density 30milligrams per cubic meter (mg/m3) will receive a lethal dose of this agent within oneminute.

As will be demonstrated shortly, the droplet fall rates implied by the windspeed, height of burst, and dimensions of the contaminated area associated with figure 1suggests that the aerosol cloud created by the SCUD release consists of droplets withdiameters roughly between 100 and 300 microns (pm). If droplets of similar size werecreated at altitudes of 10 to 20 kilometers, rather than at 1.5 km, they would initially fallat a rate that is larger by a factor of three to five.

However, since the air temperature at higher altitudes can be as low as -70°

Fahrenheit, it is likely that dispersal of chemicals at these altitudes would result in theformation of considerably larger aerosol particles that would fall at still higher rates.These particles would initially be frozen (rather than being a liquid that suffersevaporation as at lower altitudes) until they drop below about 2 kilometers altitude.Since the cloud of large particles (of diameters perhaps of thousands of Am) would fallquite fast (perhaps 10 or more m/sec), it would likely be distributed in a column of airof only a few kilometers altitude. In a wind field of .9 m/sec, such a cloud could deposita large fraction of its total chemical content on the ground over a downwind distance ofseveral kilometers. The net effect of a high altitude intercept could therefore be thecreation of a contaminated area quite comparable in size and lethality to the region thatwould otherwise be created by a SCUD releasing its chemicals at an optimum altitude.

As a result, it is possible that high altitude intercepts of tactical ballisticmissiles intended to protect urban populations from chemical attack might only alter theexact pattern of damage. If this is the case, such defenses would have little or no netmitigating effect on the overall levels of damage. In addition, the fall of toxic chemicalmaterials from high altitude intercepts might considerably decrease the predictability ofcontamination patterns, forcing responsive civil defense and monitoring efforts to bemade over much larger areas of an urban target area.

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The probable method for creating aerosol clouds with ballistic missiles is byrapid release of chemicals stored in a container that is quickly cut open with explosivecutting chords. When the explosive cutting chords open the chemical container at apredetermined release height, the chemicals are acted upon by large aerodynamicforces. The chemical agent then "pancakes" against the atmosphere and shortlythereafter breaks up into droplets.

In order to verify that the fluid will be stopped quickly by the air, and tounderstand how the particle size distribution of chemical aerosol can be controlled by anattacker, consider the expression below for the dynamic pressure of air acting on thefront of the missile,

dynaic pv 2dynamic 2

where PdnaiC is the dynamic pressureJue to the flow of air at high speed

p is the density of the flowing airand

v is the velocity of the flowing air

At sea-level, the value of p is about .00237 slugs/ft3 . Assuming a missile arriving atMach 5 to Mach 8, the value of v is roughly equal to 5000 to 8000 ft/sec, leading tovalues of the dynamic pressure Pdyn ic of between 30,000 and 75,000 pounds per squarefoot (200 to 525 pounds per square mch). As a result of this high dynamic pressureacting on the chemical at release, the chemical violently "pancakes" against theatmosphere in a manner that is probably similar to that which would occur if the fluidhit a wall.

As the thin layer of fluid spreads, the internal vapor pressure of the chemical agenttends to cause the layer to break up into filaments of fluid and then droplets. Thesedroplets are "held together" by a balance of forces created by the internal pressure ofthe chemical agent, the external pressure of the atmosphere, and by surface tension. Ifthe chemical agent has been designed so that it contains dissolved agents with a vaporpressure that is comparable to that of the surrounding atmosphere at the plannedrelease height, the high vapor pressure will create forces that overcome those of thesurrounding atmosphere and surface tension for all droplet sizes larger than a fewhundred microns. Thus, a careful choice of solvent can make it possible to create anaerosol cloud with droplet diameters that will fall to the ground at the desired rate. Theend result of such careful attention to detail is that aerosol clouds of very high lethalitycan be generated over large areas of the ground below a release point.

In order to demonstrate the role of surface tension and internal vapor pressure incontrolling the size distribution of the droplets formed in a chemical attack, consider aplane passing through the center of spherical droplet with internal pressure P h, andsurface tension ay. The surface tension on each side of that plane creates a cohesiveforce at the surface of the droplet along a line of length 2r. The net force of surfacetension thereby acts on each half of the droplet, tending to hold it together. Thus thesurface tension force holding the droplet together is,

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Fsurface = 2rry

where y is the surface tension in dynes/cmand

r is the radius of the droplet

Acting against the surface tension force is the force due to the net total pressure on thedroplet. The net total pressure on the droplet is the difference between the internalliquid vapor pressure and the external atmospheric pressure. The net force frompressure is therefore equal to the total pressure times the cross sectional area of thedroplet,

vapor = chem atm)

where Pchem is the total partial pressure ofthe fluid comprising the chemical droplet

Patm is the atmospheric pressure at thealtitude of the chemical droplet

andr is the radius of the droplet

For a stable droplet in equilibrium, the net force due to pressure balances against thecohesive force from surface tension. These considerations lead to an expression for themaximum allowable radius of a chemical droplet.

r 2-Pchem Patm

For a given set of conditions (atmospheric pressure Patm, chemical vapor pressure Pchem'and surface tension ), smaller stable droplets are energetically possible, but larger onesare not. Since the surface tension and vapor pressure of liquid Pchem in the droplets isa strong function of temperature, and the atmospheric temperature T and pressure Patmare strong functions of altitude, it is clear that the size distribution of chemical dropletswill be substantially altered as a function of altitude.

Since y increases dramatically with T while PChem decreases dramatically with T, andPtm decreases only slowly with altitude (and hence T), one expects that a high altitudechemical dispersal will result in particles of considerably larger size relative to thosecreated in a dispersal event at lower altitudes. As a result, frozen particles created athigh altitude could well to fall to low altitudes at a high rate suffering little dispersal.When these particles reach the lower warmer altitudes, they might then melt formingunstable large droplets that break up, forming a relatively localized and highly toxicaerosol cloud of nerve agent that will then shortly reach the ground.

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For the particular case of a SCUD attack with the characteristics andconsequences of that shown in figure 1, it is straightforward to estimate the fall rate ofthe created aerosol cloud, which is perhaps .3 to 1.5 meters per second. This suggeststhat a very large fraction of the droplets created during dispersal are of diameterbetween 100 and 300 pm.

In order to see that this is the case, consider a spherical droplet fallingunder the competing influences of gravity and aerodynamic drag. The force of gravityacting on this droplet is simply its weight, which is,

3 Pchem go

where Pchem is the mass density of the dropletr is the radius of the droplet

andgo is the acceleration of gravity at the

earth's surface

and the aerodynamic drag on the particle is,

Fdrag = Pair V 2 CDA

where Pair is the density of the airsurrounding the droplet

v is the droplet's velocity in airCD is the Reynolds number dependent

drag coefficient for a sphereand

A is the cross sectional area of thedroplet of radius r (A= rr2)

The droplet falls at a uniform speed when the drag and gravitational forces are equal.That is, when

W = Fdrag

Thus, to compute the terminal velocity of a particle of given radius, all that is needed isthe value of the drag coefficient CD.

However, for such small particles which drop at such low speeds the drag coefficent CDis a strong function of the Reynolds Number, which is defined as

p. DvRe = air

Y/

and D =2r

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For values of the Reynolds number less than one, CD is given by the famous Stoke'sexpression,

24D Re

where Re is the Reynolds Number

When this expression is used in the aerodynamic equation for the drag force, theexpression for Fdrag reduces to the Stoke's Law expression for the drag force on aparticle of radius r,

F = 6irrrvdrag

where r is the viscosity of the airsurrounding the droplet

r is the radius of the dropletand

v is the droplet's velocity in air

However, for an important range of particle sizes of interest here, the particle size andfall rates are such that Reynolds numbers of order one thousand or more occur. In thisregion of Reynolds numbers the drag coefficient varies strongly with the Reynoldsnumbers but does not behave according to Stoke's Law.

At sea-level, typical values that can be used for calculating fall rates and the otherphysical quantities relevant to this problem are as follows:

Pair = .0012 gm/cm3

Pchem = 1 gm/cm3= 1.771x10l 4 gm/(cm-sec)

go = 980 cm/sec 2

To estimate the above quantities at high altitude it is useful to note that theviscosity of air is independent of density and varies as the square root of the absolutetemperature. It is also useful to note that the density of air decreases exponentially witha scale height of about 10 miles. Thus, the density of air at 10 km altitude is roughly25% of that at sea-level and at 20 km the density is about 10% of that at sea-level.

Figure 2 shows the drag coefficient for spheres at low Mach numbers as afunction of the Reynolds number (Re) for values of Re between 1 and 1x107. Asalready mentioned, the values of Re of interest for aeorosol sizes being considered herelie between values of Re from less than 1 to greater than 1000. In this range of flowregimes, the drag coefficient is a very strong function of Re.

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Figure 3 shows the fall rate in centimeters per second (cm/sec) of dropletsranging in diameter from 0 to 500 pm. The assumed wind speed of .9 meters per sec(m/sec) shown for the chemical dispersal pattern shown in figure 1 suggests fall rates ofbetween 25 and 150 cm/sec are needed to achieve the shown dispersal pattern. Thus,the droplet diameters appear to be roughly between 100 and 300 0m.

Figure 5 shows that if the droplets are as large as 2000 Am, they would fallat a very high rate, comparable to that of raindrops during light rain.

Figure 6 shows that droplets of comparable size fall at much higher rates ataltitudes of 10 and 20 km. The reason for this is shown in figures 7 and 8. At higheraltitudes the density of air is lower by a factor of 4 at 10 km altitude and by 10 at 20 km.As a result, the drag at a given fall rate is lower and the particle falls faster. Since theparticle falls faster, the flow field around it is at a higher Reynolds number Re, whichresults in a lower drag coefficient CD, which in turn results in still a higher fall rate.

As can be seen from figure 7, these particles will fall through quite cold airuntil they arrive at an altitude of 2 km, where the air temperature is on the averagebelow that of freezing. At this point, significant evaporation of particles may begin asthey continue falling towards the earth surface.

I believe that this preliminary examination of the issues associated withchemical dispersal from SCUDs intercepted at high altitudes leads to the conclusionthat a detailed analysis of the consequences of such intercepts is needed as part of anassessment of the utility of such defensive actions. Such an assessment should alsoinclude a larger and very detailed review of our now substantial experience from theGulf War. That larger assessment should examine the estimated damage that couldhave occurred if SCUDs were not intercepted relative to damage that occurred fromfalling intact missile warheads, debris, and perhaps occasional unexploded PATRIOTinterceptors. Comments on this highly preliminary analysis would be most welcome, asthese exploratory calculations raise as many questions as they answer.

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-11-

Fall Rate of Spherically Symmetric Particlesat Sea-Level

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Drag Coefficients ofTerminal Velocity Spherical Droplets

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THEODORE A. POSTOL

Theodore A. Postol is Professor of Science, Technology and National Secu-rity Policy in the Program in Science, Technology, and Society at the Massa-chusetts Institute of Technology. He did his undergraduate work in Physicsand his graduate work in Nuclear Engineering at MIT. After receiving hisPhD, Dr. Postol joined the staff of Argonne National Laboratory, where heused neutron, x-ray and light scattering, along with computer moleculardynamics techniques, to study the microscopic dynamics and structure ofliquids and disordered solids. Subsequently he went to the CongressionalOffice of Technology Assessment to study methods of basing the MX Missile,and later worked as a scientific adviser to the Chief of Naval Operations.After leaving the Pentagon, Dr. Postol helped to build a program at StanfordUniversity to train mid-career scientists to study developments in weaponstechnology of relevance to defense and arms control policy. In 1990 Dr.Postol received the Leo Szilard Award from the American Physical Society.