Doomsday

How East and West calculated their chances in the Cold War.

IJzebrand Schuitema describes in his book "The Slide Rule – a Technical Cultural Heritage"[1]   a Radiac slide rule made by Blundell Rules Ltd. (Figure 1). You can use this slide rule to calculate how much radiation you would receive from radioactive fallout after an explosion of an atomic bomb. Linear Radiac calculators are less well known than their disk-shaped equivalents, which are typically made of soft plastic and packaged in a green plastic wrapper with a characteristic smell (Figure 2). The circular Radiac has elegantly curved lines, which can not be found on the linear one.

What is the relation between the Radiac slide rule and the Radiac disk calculator?

Figure 1: Radiac slide rule-of Blundell Rules Ltd.

   Figure 2: Radiac-calculator

The formulas for the slide rule are[2] 

Formula (1) gives the radiation intensity at a chosen time, if the radiation intensity at another time is known. Formula (2), the integral of formula (1) from  t  to eternity, gives the total radiation dose received, depending on the time after the explosion at which the exposure starts. In most slide rules, the shortest time between explosion and the start of irradiation is 15 minutes. If the observer would need a shorter time period, he has other things to worry about.

A more general version of formula (2), which contains a starting as well as an ending time of the exposure, can also be derived from formula (1):

(3)

At first sight, these formulas are strange. When you think of radioactivity, you think of exponential decay:

  I(t) = I(0) 2-t/T½                                      (4)

where T½ is the radioactive half life, and t is in the exponent, but the slide rules use a power of t.

What is going on here?

Formula (4) applies to an ideal radiation source: a radioactive isotope which decays into a stable isotope. The fallout from a nuclear bomb is far from ideal: it will contain some 300 different radioactive isotopes with very different half-lives, and their radiation can activate other isotopes. Therefore, for fallout the empirical formula (1) is used, with x estimated between 0.2 and 2.0. This value depends a.o. on the type of bomb, the height of the explosion and the type of surface over which the explosion takes place.[2,4,5]  In theory, x should be determined experimentally for each explosion. In practice, an estimate of x = 1.2 is used. This value is valid from about 30 minutes up to 200 days after the explosion. Eternity is therefore limited to 200 days, which seems optimistic to me in the event of a nuclear war.

Formula (1) with x = 1.2 is known as the Kaufmann formula, or the 7:10 rule: after 7 hours 1/10 of the radiation is left (because 7-1.2 = 0.1).  In Figure 3 the theoretical radiation curve and the x = 1.2-fit are given.[4]  The Radiac slide rule has a scale on the back with x = 1.3 for use at sea, in order to account for the influence of the Na24-isotope formed by neutron capture.

The round Radiacs have double-sided rotating disks: one for land-side explosions, the other for marine explosions, corresponding to the two sides of the slide of the linear Radiac slide rule. The disks use the same x values as the rule: x = 1.2 for land and x = 1.3  for sea. Unlike the slide rule the disks do not indicate these values, but I have them checked by measurement.

Blundell Rules Ltd. has also made disk calculators. They can have a Röntgen-scale or a Gray-scale. The scale on the outer disk has a dual function: it is used for both the radiant intensity (in R/h, or Gy/h) and dose (R or Gy).

Figure 3: the calculated and fitted curves for explosions over land[5] 

For formula (1), use the scale on the outer disk as radition intensity scale, in combination with the time scale on the intermediate disk: turn the intermediate disk so that the time of radiation measurement aligns with the measured radiation intensity, and read the radiation intensity expected at another time on the outer scale at a the desired time on the intermediate scale.

The linear slide rule can only calculate D(t,∞), equation (2), but the disks can calculate D(t1,t2), equation (3), for any two times without further ado. Align t1 on the central disk at the "start exposure" arrow on the holding disk, look up t2 on the central disk, follow the curve to the edge of the intermediate disk, and read the dose on the outer disk.

To determine D(t1, t2) with the linear slide rule would require the determinaton D(t1,∞) and D(t2,∞) and calculating the difference by hand. The disks can also calculate D(t,∞): the central disk contains a marker for t = ∞. Besides, this is a "gauge mark" that is missing in Venetsianos Panagiotis' Pocketbook of the Gauge marks...

Nestler has made a similar device, the 1962 ABL Radiation Commanders Guide, on which the beautiful curves have been replaced by ugly colored blocks.

The M-2 Radiation Calculator (Wade Products Inc. For the New York State Civil Defense Commission) has no collection of curves or blocks. The intermediate disk of this calculator has an auxiliary scale that abuts against the central disk. This scale corresponds to the scale at the outer edge of the intermediate disk. Instead of following a curve, the user has to read an auxiliary value aligned with the time t1 scale on the central disk, and look up this auxiliary value on the outer scale of the intermediate disk, and read the corresponding dose value on the outer disk. The M-2 illustrates the principle by two sample lines (Figure 4). These lines are similar to the lines on the more typical Radiacs disks.

In a series of patents granted to the State of the Netherlands[8] a different solution is described. It uses a combination of a slide rule and a slide chart (figure 5). It works as follows: set the window "hours after the explosion" at the start of irradiation t1, and a look for a window that corresponds to the irradiation period (t2-t1). This window shows a number, which is the dose factor. Remember this number. Align the arrow of the dose factor scale against the radiation intensity (measured at the start time) on the outer disk. This usually causes the start time to disappear from the "hours after the explosion" window. Locate the memorized dose factor on the dose factor "scale and read at the corresponding value on the outer disk the received dose. This last action is simply the multiplication of the dose factor with the measured radiation intensity. According to the patent, this calculator is more accurate than the Radiacs. The accuracy of the approach is indicated by the color of the numbers below the dose factor windows. The deviation from reality is in most cases less than 6.5%, but sometimes it is more than 15%. Traditional Radiacs would have even greater deviations.

Figure 4: part of the M-2 Radiation Calculator, with auxillary scale C and two sample lines.


Figure 5: Dutch Radiac, from U.S. Patent 4117315, see also an image  of the real thing, made by ALRO.

               Try an online simulation.

Behind the wall

The East German Rechenscheibe LS-67 (Figure 6) contains a Radiac calculator for land explosions. It also contains tables and a rotating data charts for other characteristics and consequences of a nuclear explosion, such as the diameter of the fireball, the size of the crater, the radius of the area where all the buildings will be destroyed (neatly distinguishing concrete, masonry and wood). The LS-67 also indicates how much protection against radiation is offered by various types of buildings or vehicles. This information is also briefly shown on back of the American M1A1 Radiac Calculator ABC.[7]  In the west, separate disk calculators where used for the material consequences, such as the Nuclear Bomb Effects Computer by the Lovelace Foundation/ Blundell Rules Ltd. and the RAND Bomb Damage Effects Computer.[6] 

The LS-67 also gives information about the direct impact on people from the nuclear explosion, according to the size of the areas in which persons are injured or suffer from burns, in three weight categories. This information is presented in a rotating table.

A Russian Radiac combines the "Radiac" scales with a table which gives, for a wind speed of 50 km/h and different explosion strengths, the radiation intensity as a function of distance from the explosion (Figure 7). This calculator is made of base metal and comes with a manual in a leatherette folder. The design of the scales looks like that of the American Radiacs, but the calculator is somewhat smaller: the outer scale has a diameter of 7 cm while the American one measures 10.5 cm.

The big difference between the Western disk calculators and those from the Eastern Block is that the radiation intensity scales in Eastern Europe run from 0.1 to 10,000 R/h, while those in the West run from 0.01 to 1000 R/h. Apparently it was expected that the soldiers in Eastern Europe could be faced with a higher amount of radiation.

Figure 6: Detail of the Rechenscheibe LS-67

Figure 7: Front and back of a Russian Radiac.

Life after the bomb

All these calculators do not give a clear answer to a crucial question: do I survive the fallout? Fortunately, I have a former-East German booklet called "Auswertung der Kernstrahlungslage".[9] The one I have was published in February 1989(!) and replaces a booklet from 1976. It is a loose-leaf edition, and comes with instructions how to add or replace future corrections and additions. One might assume that these instructions were never applied... The book contains a table for the calculation of the received dose. This calculation could also be done with the Radiacs. The booklet continues with a table which shows, per dose received and for different start and end times of the irradiation with respect to the explosion time, the loss of "combat or labor power" as a function of time. An extra column shows the death rate. The table stops at a survival time of 30 days. Apparently, the long term radiation damage was not interesting. The dose ranges from 1 Gy (little effect) to 6 Gy (everybody dead within 30 days). The sinister thing is that this table is very detailed. It takes six A5-pages and values are given with 1% accuracy. As if human suffering can be calculated exactly.

References

A Dutch version of this paper was published in MIR 54, October 2010.