Jamming and countermeasures calculators

The theory and practice of the Profession of Arms through the ages.
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Micael
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Joined: Thu Nov 17, 2022 10:50 am

Jamming and countermeasures calculators

Post by Micael »

I saw these posted elsewhere and I find them very beat, wouldn’t mind getting my hands on the at some point. However while the rectangular jamming calculator seems relatively straight forward to figure out how to use the circular countermeasures one seems a bit more complicated. Does anyone here know how it works, or can figure it out based on the formulas and such, and can elaborate a bit on that?
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Craiglxviii
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Re: Jamming and countermeasures calculators

Post by Craiglxviii »

Throw it into AI and you will probably get a printable template with instructions
Craiglxviii
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Re: Jamming and countermeasures calculators

Post by Craiglxviii »

I did. This is what it came up with.

Yes. The circular one is a purpose-built analogue radar/ECM slide rule, and the equations printed on its face tell us quite a lot about exactly what it was intended to do. It is not an electronic calculator at all: it is a set of concentric logarithmic scales and rotating plastic/card discs. I also found a clearer photograph of the reverse of the same GE device: it is marked “Copyright 1959, General Electric Co., Utica, New York” and “Slide-Chart by PERRYGRAF, Maywood, Ill.” Perrygraf specialised in exactly this sort of purpose-built circular slide chart.

The important point is that the circular one isn’t simply calculating “jamming” in the abstract. It is essentially a radar-versus-jammer / burn-through calculator. The three equations printed in the centre are the clue.

Reading the notation from the face, they are essentially:

Radar echo received at the radar:

S = Pr × Gr² × λ² × σ / [(4π)³ × R⁴]

Jamming power received by the radar:

J = Pj × Gj × Gr × λ² × Br / [(4π)² × R² × Bj]

and, combining those two and solving for range:

R = √[(1 / 4π) × (Pr / Pj) × (Gr / Gj) × (Bj / Br) × (J / S) × σ]

where the terms are approximately:

* Pr = radar transmitter power
* Pj = jammer transmitter power
* Gr = radar antenna gain
* Gj = jammer antenna gain in the radar’s direction
* Br = radar receiver bandwidth
* Bj = jammer bandwidth
* λ = wavelength
* σ = target radar cross-section
* R = radar-to-target/jammer range
* S = target echo power received at the radar
* J = jammer power received at the radar
* J/S = jammer-to-target-signal ratio.

That is a very recognisable classical electronic-warfare calculation. Modern EW references still define J/S in essentially the same way and use the point at which the target echo becomes detectable through the jamming as the burn-through range.

The clever bit is why there are two different range dependencies. The jammer transmission only has to make one journey from the aircraft to the radar, so its received power falls with approximately:

J ∝ 1 / R²

The radar signal, however, has to go radar → target → radar, so the target echo falls as:

S ∝ 1 / R⁴

Consequently, at long range the jammer can dominate the echo. As the target approaches the radar, however, the genuine radar echo rises much faster than the jammer signal. Eventually the radar “burns through” the jamming.

That is what the big R equation is calculating. You put in radar power and gain, jammer power and gain, the relative bandwidths, target radar cross-section and the J/S ratio considered necessary for effective jamming, and it gives you the range at which that condition exists.

There is a particularly nice piece of physics visible in the equation: λ disappears from the final burn-through equation. It occurs as λ² in both the radar echo and jammer received-power equations, so when J is divided by S it cancels. The circular rule has wavelength scales because it can calculate J and S separately, but it doesn’t need wavelength when directly solving the combined J/S range equation.

How the physical calculator works

The different coloured scales correspond to the three equations. The red scales/lines relate primarily to the radar echo S, the blue scales/lines to jammer power J, and the black scales to the combined R / J-to-S calculation. You can see the same red, blue and black references in the little ALIGNMENT GUIDE at the left side of the face.

Mechanically it is just logarithms turned into angular distance. On an ordinary slide rule,

log(A × B) = log A + log B

and

log(A / B) = log A – log B.

Rotating one disc relative to another therefore performs multiplication and division. The scale spacing also incorporates the powers appearing in the equations: R², R⁴, λ² and the square root. So the operator does not square, fourth-power or square-root anything manually; GE/Perrygraf built those factors into the scale graduation.

The prominent outer J/S (dB) scale is particularly telling. Rather than convert between a power ratio and decibels manually, the calculator allows the engineer to work directly with the J/S figure normally used by radar/ECM engineers. The various power, antenna-gain, bandwidth, wavelength, RCS and range scales are then aligned using the coloured index marks.

So a typical use would conceptually be:

“Given this radar, this target and this jammer, how strong is the jamming at the radar?”

or:

“At 20 nautical miles, what are J and S and therefore J/S?”

or probably most usefully:

“If I require, say, X dB of J/S for the jammer to remain effective, at what range will the radar burn through?”

The last one is almost certainly the principal reason for the big combined equation in the centre.

There are some assumptions buried in it. It appears to be aimed primarily at the classical self-screening case, where the jammer is on or effectively colocated with the radar target, because the same range R is used for both. It also assumes simple free-space propagation and a jammer whose power is distributed across bandwidth Bj, of which the radar receiver accepts only Br. The GE reverse side explicitly notes that antenna gains along the jammer–radar line of sight are to be used. A stand-off jammer at a substantially different distance would require a more complicated geometry.

Interestingly, the other side of this circular calculator is almost a miniature radar-engineering handbook. It contains a parabolic-antenna gain/beamwidth calculator, radar target-return power, approximate radar signal-to-noise calculations and related scales. The surviving GE pocket handbook shown with these devices even lists sections entitled “Radar Range Equation,” “Receiver Noise,” “Countermeasures Nomograms,” and “Gain and Beamwidth of Circular Parabolic Reflectors.”

So for a forum answer I would put it this way:

The round GE device is basically a 1959 analogue electronic-warfare computer. It is a circular logarithmic slide rule designed to solve the radar equation, jammer equation and their ratio. The red scales calculate target echo S, the blue scales jammer power J, and the black scales combine them to calculate J/S or the corresponding range. Because radar echo falls as 1/R⁴ while jammer power falls as 1/R², it can directly calculate the range at which a radar will “burn through” a jammer. The coloured index marks are simply alignment guides for the rotating logarithmic scales.

And yes — “very neat” is entirely justified. It is essentially a pocket analogue computer for doing 1950s radar/EW engineering without having to spend several minutes working the radar equations on a conventional slide rule. The rectangular one is much narrower in purpose; the circular one is considerably more sophisticated.

If you want, I can go one stage further and reverse-engineer the actual scales on the circular calculator and work through a hypothetical calculation step-by-step exactly as a GE engineer would have used it in 1959.
Micael
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Re: Jamming and countermeasures calculators

Post by Micael »

Oooh, now that is interesting indeed. Thanks Craig!
Craiglxviii
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Joined: Thu Nov 17, 2022 7:25 am

Re: Jamming and countermeasures calculators

Post by Craiglxviii »

Yes. I’ve now looked at it as an actual analogue computer rather than just a curiosity, and the layout makes much more sense once you treat the colours as three separate calculation paths.

The circular device appears to be GE’s Model 188 Electronic Countermeasures Calculator, made as a Perrygraf slide chart. The surviving reverse-side photograph is marked Copyright 1959, General Electric Co., Utica, New York and “Slide-Chart by PERRYGRAF, Maywood, Ill.” Collections of specialist slide rules also catalogue a GE “188 Electronic Countermeasures Calculator.”

What the three colours do

The equations printed in the middle are effectively the instruction key.

The red path calculates the ordinary radar echo:

S=\frac{P_rG_r^2\lambda^2\sigma}
{(4\pi)^3R^4}

The blue path calculates the received jammer power:

J=\frac{P_jG_jG_r\lambda^2B_r}
{(4\pi)^2R^2B_j}

And the black path combines the two and solves directly for range:

R=
\sqrt{
\frac{1}{4\pi}
\frac{P_r}{P_j}
\frac{G_r}{G_j}
\frac{B_j}{B_r}
\frac{J}{S}
\sigma
}

That colour coding is why you can see black, blue and red reference marks around the circumference and in the “ALIGNMENT GUIDE”.

So it is really three calculators laid on top of one another.

The quantities are:

Marking

Meaning

P_r

radar transmitted power

P_j

jammer transmitted power

G_r

radar antenna gain

G_j

jammer antenna gain towards the radar

B_r

radar receiver bandwidth

B_j

jammer bandwidth

\lambda

wavelength

\sigma

target radar cross-section

R

range

S

received radar echo

J

received jamming signal

The later US Navy EW engineering handbook derives the same basic relationship: jammer power is a one-way 1/R^2 problem, whereas the target echo is a two-way radar path and therefore behaves as 1/R^4. It calls the resulting threshold the crossover/burn-through calculation.

How you would actually use the wheel

This is the clever part.

It is not like a modern calculator where you enter seven numbers and press equals. You progressively accumulate multiplication and division by rotating logarithmic scales.

Because

\log(ab)=\log a+\log b

a rotation corresponding to one parameter simply adds its logarithm to the running calculation. Division is a rotation in the opposite sense. Powers such as R^2, R^4 and the final square root are already built into the spacing of the engraved scale.

That is also why the scales look so oddly stretched in places.

The operator would choose one of the three coloured paths and follow the corresponding coloured index marks. The order of the multiplicative terms is not fundamentally important, so GE could arrange them around the disc wherever they fitted most conveniently.

A realistic worked example

Suppose a 1959 engineer wants to answer:

“How close can an aircraft carrying this jammer get before a radar has enough target return to overcome 10 dB of jamming superiority?”

Use:

Radar transmitter power:

P_r=1,000,000\ {\rm W}

Jammer power:

P_j=1,000\ {\rm W}

Radar gain:

G_r=35{\rm \ dB}

That is a linear gain of:

10^{35/10}=3162

Jammer antenna gain towards the radar:

G_j=10{\rm \ dB}=10

Jammer bandwidth:

B_j=100{\rm \ MHz}

Radar receiver bandwidth:

B_r=1{\rm \ MHz}

Target radar cross-section:

\sigma=10{\rm \ m^2}

Required effective jamming ratio:

J/S=10{\rm \ dB}=10

Now use the black range path.

Conceptually the wheel performs:

R=
\sqrt{
\frac{1}{4\pi}
\times
\frac{1,000,000}{1,000}
\times
\frac{3162}{10}
\times
\frac{100}{1}
\times
10
\times
10
}

Inside the square root:

\frac{1}{12.566}
\times1000
\times316.2
\times100
\times10
\times10

which is approximately:

2.516\times10^8

Square root:

R\approx15,863{\rm \ m}

or:

R\approx8.57\ {\rm nautical\ miles}

So with those assumptions the calculator would tell the engineer that the 10 dB effective-jamming boundary is about 8.6 NM.

Outside that range, jamming has more than the required 10 dB advantage.

Inside it, the radar echo begins increasing faster than the jammer signal and the stipulated 10 dB jamming margin is lost.

That is essentially a burn-through calculation. The Navy handbook defines burn-through similarly: the range at which J/S falls to the minimum value required for the jammer to remain effective.

Now use the red and blue calculators separately

This demonstrates why GE included all three equations.

Take the same system at exactly 10 NM and give it a wavelength of:

\lambda=10{\rm\ cm}=0.1{\rm\ m}

First calculate the genuine radar return using the red scales.

S=
\frac{
10^6
\times3162^2
\times0.1^2
\times10
}
{
(4\pi)^3
\times18520^4
}

Result:

S\approx4.28\times10^{-9}{\rm W}

or about:

-53.7{\rm\ dBm}

Now use the blue path for the jammer:

J=
\frac{
1000
\times10
\times3162
\times0.1^2
\times10^6
}
{
(4\pi)^2
\times18520^2
\times100\times10^6
}

which gives:

J\approx5.84\times10^{-8}{\rm W}

or:

-42.3{\rm\ dBm}

Therefore:

J/S=13.63

and:

10\log_{10}(13.63)=11.34{\rm\ dB}

So at 10 NM the jammer has an 11.3 dB advantage.

That makes sense because our required 10 dB boundary was at 8.57 NM.

At exactly 8.57 NM, the same calculation gives roughly:

S=7.96\times10^{-9}{\rm W}

and:

J=7.96\times10^{-8}{\rm W}

which is exactly a factor of ten:

J/S=10=10{\rm\ dB}

That is a nice check that we have interpreted the printed equations correctly.

Why wavelength disappears from the black calculation

This is one of the nicest features of the calculator.

Both the radar return and jammer equations contain \lambda^2:

S\propto\lambda^2

and

J\propto\lambda^2

So when GE divides J by S to obtain the range equation, wavelength cancels completely.

That means you need the wavelength scale when calculating J or S individually, but not when directly calculating the self-screening burn-through range.

That is why the black equation printed on the face contains no \lambda.

Why bandwidth matters

The term

\frac{B_r}{B_j}

in the blue equation is also important.

If a jammer spreads 1 kW over 100 MHz but the radar receiver only accepts 1 MHz at a time, only about one hundredth of the jammer’s spectral power lies inside the radar’s receiver bandwidth.

Hence the calculator explicitly includes both jammer bandwidth and receiver bandwidth.

A narrow-band jammer would therefore appear much “stronger” to a radar receiver for the same total transmitter power than a very broad noise jammer.

Conversely, on the black range equation this appears inverted as:

\frac{B_j}{B_r}

because GE has algebraically rearranged the expression to solve for R.

Why the reverse side exists

The reverse is not unrelated decoration.

It contains a calculator for antenna gain and beamwidth of parabolic reflectors, with frequency, wavelength and dish diameter scales. It even states:

“Antenna Gains along the Jammer-Radar Line of Sight Must be used.”

That is exactly the G_r and G_j information required by the front-side ECM calculation.

So an engineer could take, say, a 6-foot dish operating at a given wavelength, use the back to estimate its gain, then flip the calculator over and feed that value into the jamming calculation.

The other reverse-side sections cover radar target return, receiver noise and approximate radar signal-to-noise performance. The contemporary GE pocket guide pictured with these calculators also has sections headed Radar Range Equation, Receiver Noise, Countermeasures Nomograms, and Gain and Beamwidth of Circular Parabolic Reflectors.

So it really is a little analogue radar/EW engineering suite.

One caveat: I can reconstruct the mathematics and the function of the coloured scales with high confidence, but without the original 1959 instruction leaflet I would not claim that I know the exact prescribed sequence of “turn disc A, align this hairline, then turn disc B” down to every hand movement. The maths shows unequivocally what each scale group is doing, though, and we can reverse-engineer that physical sequence from a sufficiently sharp straight-on photograph.

If you want, I can do that next: take this actual photograph, identify every individual scale and index around the circumference, and write a literal “GE Countermeasures Calculator operating manual” — e.g. “set 1 kW here, rotate this index to 35 dB here, read 8.6 NM here.”
Craiglxviii
Posts: 3792
Joined: Thu Nov 17, 2022 7:25 am

Re: Jamming and countermeasures calculators

Post by Craiglxviii »

Yes. Looking at the photograph more closely, I think we can get considerably nearer to an actual operating procedure.

There is one important qualification: I have not found GE’s original instruction sheet for this exact face, so I don’t want to invent a factory-prescribed sequence such as “move tab 2 before tab 3” and present that as fact. What I can reconstruct is the actual scale logic and a mechanically valid way of operating it. The surviving examples are catalogued as GE electronic-countermeasures calculators, including a GE 188, and a surviving 1958–61 GE set includes the circular slide rule with its contemporary pocket guide.

First: what you’re actually holding

This is more sophisticated than an ordinary circular slide rule. It is a multi-disc logarithmic nomogram. Several concentric discs can move independently around the centre rivet.

The photograph gives us three calculation systems:

Black — combined countermeasures/range calculation

R=\sqrt{\frac{1}{4\pi}
\frac{P_r}{P_j}
\frac{G_r}{G_j}
\frac{B_j}{B_r}
\frac{J}{S}\sigma}

Blue — jamming signal arriving at the radar

J=
\frac{P_jG_jG_r\lambda ^2B_r}
{(4\pi)^2R_j^2B_j}

Red — genuine target echo arriving at the radar

S=
\frac{P_rG_r^2\lambda ^2\sigma}
{(4\pi)^3R_t^4}

That distinction is also physically encoded into the coloured indices.

The subscripts are therefore:

Marking

Meaning

r

radar

j

jammer

t

target

P_r

radar transmitter power

P_j

jammer transmitter power

G_r

radar antenna gain

G_j

jammer antenna gain toward radar

B_r

radar receiver bandwidth

B_j

jammer bandwidth

R_j

jammer-to-radar range

R_t

target-to-radar range

\lambda

wavelength

\sigma

target radar cross-section

J

received jamming power

S

received target echo

And MC on the calculator is the period terminology for megacycles per second — what we’d now call MHz.

⸻

Reading the actual face

There are several features which now make sense.

At about 9 o’clock is the:

ALIGNMENT GUIDE

with black, blue and red lines.

That is effectively the calculator’s reference/home position for the various moving discs.

At approximately 6 o’clock you have the large:

INDEX

with the black/blue/red pointer. Around it is the power scale — 0.01 W, 0.1 W, 1 W, 10 W, 100 W, 1 kW, 10 kW and so forth — together with a range scale.

At about 8–10 o’clock, the blue section contains:

* G_j in dB
* B_r in MC
* a special bandwidth scale carrying wording to the effect of “for P_j in watt/MC”

That last one is quite clever. If jammer output is specified as spectral power density — watts per megacycle — rather than total transmitter watts, the calculator can work from that directly instead of requiring you to calculate P_j/B_j separately.

At about 12–2 o’clock, the red section carries:

* R_t, NM
* wavelength \lambda
* G_r, dB.

At about 2–4 o’clock are the pink/red scales. From their units and their role in the equations these are the scales for the remaining target/bandwidth quantities, including \sigma and B_j.

And right around the outside is the crucial:

J/S (dB)

scale.

That’s what turns this from merely a radar-equation calculator into an ECM calculator.

⸻

So how would a GE engineer actually use it?

Let’s do the most interesting calculation: find the range for a specified J/S ratio.

This is the black equation.

We’ll use our earlier hypothetical system:

Radar power:

P_r = 1\,MW

Jammer power:

P_j = 1\,kW

Radar antenna gain:

G_r = 35\,dB

Jammer antenna gain:

G_j = 10\,dB

Radar receiver bandwidth:

B_r = 1\,MC

Jammer bandwidth:

B_j = 100\,MC

Target radar cross-section:

\sigma=10\,m^2

Required jammer-to-signal ratio:

J/S = +10 dB

Here’s the reconstructed physical operation.

1. Start by putting the calculator into alignment. Bring the coloured reference marks on the moving discs into correspondence with the black, blue and red lines of the ALIGNMENT GUIDE at roughly 9 o’clock. Think of this as zeroing the separate logarithmic accumulators rather than zeroing a measuring instrument.
2. Enter the power ratio P_r/P_j. Use the power scale around the lower circumference and the INDEX. Register 1 kW for P_j, then transfer/register 1 MW for P_r using the corresponding black reference. What the machine has actually stored is not either absolute number but their logarithmic displacement:
P_r/P_j=1000
In slide-rule language, you’ve just entered three decades.
3. Enter the gain ratio G_r/G_j. The jammer gain is on the blue G_j(dB) scale and radar gain on the red G_r(dB) scale. Register G_j=10 dB and G_r=35 dB against their corresponding transfer/index marks.
Because gain is already expressed logarithmically, the calculator merely needs their difference:
35-10=25\,dB
which corresponds to:
G_r/G_j \approx316
No conversion to 316 would have been necessary for the operator. That’s one reason GE supplied a dB scale.
4. Enter the bandwidth ratio B_j/B_r. Use the receiver-bandwidth scale on the blue side and the jammer-bandwidth scale on the right-hand/pink section. Register:
B_r=1\,MC
and
B_j=100\,MC
The logarithmic displacement accumulated by the discs is consequently:
B_j/B_r=100
5. Enter radar cross-section. On the \sigma scale on the right, register:
\sigma=10\,m^2
The scale graduation already embodies the way \sigma appears underneath the final square root. The operator does not manually take its square root.
6. Enter the desired J/S. Move/register the black calculation against:
J/S = +10 dB
on the outermost J/S scale.
Again, there is no need to turn that into the linear value 10; GE has done the logarithmic conversion in the engraved spacing.
7. Read R on the range scale marked NM. With all of those logarithmic displacements accumulated, the black range index should land at roughly:
R ≈ 8.6 nautical miles.

That’s the whole calculation.

The mathematical check is:

R=
\sqrt{
\frac1{4\pi}
(1000)(316.2)(100)(10)(10)
}

R=15,863m

R=8.57NM

So if we had the physical calculator in front of us and my reconstruction of the index transfer sequence is correct, about 8½ NM is what the wheel should show.

⸻

What’s particularly ingenious about the operation

The user isn’t really “entering” 1 MW, then 1 kW, then 35 dB etc. in the way we think of a calculator.

Each movement simply stores an angular displacement proportional to the logarithm of a ratio.

After the power operation the discs contain:

\log(P_r/P_j)

The gain operation adds:

\log(G_r/G_j)

The bandwidth operation adds:

\log(B_j/B_r)

then J/S and \sigma are added.

The range graduation is compressed by a factor of two because the answer is a square root.

So by the time you reach the range scale, the mechanical position represents:

\frac12
[
-\log(4\pi)
+\log(P_r/P_j)
+\log(G_r/G_j)
+\log(B_j/B_r)
+\log(J/S)
+\log\sigma
]

which is exactly:

\log R

That’s why this thing can apparently “solve” quite a frightening-looking equation just by turning plastic discs.

⸻

Running it backwards

And this is arguably even more useful.

Suppose the range is already known:

R = 20 NM

and you want:

“What J/S can this jammer produce at 20 NM?”

You don’t need another calculator.

You set the power, gain, bandwidth and RCS exactly as before, but this time register 20 NM on the R scale and read the answer from the J/S dB scale.

Likewise, one can rearrange it to answer questions such as:

What jammer power is required?

What antenna gain is necessary?

What J/S exists against a given target RCS?

That’s the beauty of a slide rule: there isn’t really an “input” and an “output”. The scale relationship itself is the equation.

⸻

The blue calculation: received jammer power

The blue route answers a different question:

“How much jammer power actually reaches the radar receiver?”

It uses:

J=
\frac{P_jG_jG_r\lambda^2B_r}
{(4\pi)^2R_j^2B_j}

So physically you would use the blue/associated scales to register:

P_j → jammer output

G_j → jammer antenna gain

G_r → receiving radar antenna gain

\lambda → wavelength

B_r → radar receiver bandwidth

B_j → jammer bandwidth

R_j → jammer/radar separation

and the resulting scale position gives J, received jammer power.

There’s an important clue printed directly on the rule: the alternative “B_r for P_j in watt/MC” scale.

That means GE allowed two ways of specifying a noise jammer.

If you know total jammer power and total jammer bandwidth, use:

P_j\times B_r/B_j

But if you’re given spectral power directly — for example so many watts per MC — you can skip the B_j division and multiply the spectral density directly by receiver bandwidth.

That’s a very period-appropriate bit of practical ECM engineering.

⸻

The red calculation: target return

The red route answers:

“How strong is the real radar echo?”

S=
\frac{P_rG_r^2\lambda^2\sigma}
{(4\pi)^3R_t^4}

So the red scales take:

radar power P_r

radar gain G_r

wavelength \lambda

target RCS \sigma

target range R_t

and return S.

Notice the R_t^4 scale. That’s why the red target-range graduations have a very different spacing from an ordinary logarithmic range scale.

The rule itself is doing the fourth power.

⸻

And now the reason for the black calculation becomes obvious

For a self-screening jammer — jammer carried by the target aircraft — we can take:

R_j=R_t=R

Divide J by S.

The \lambda^2 terms cancel.

One radar antenna gain cancels.

The R^4/R^2 leaves R^2.

Rearrange for R, and you obtain precisely the black equation printed on the calculator:

R=
\sqrt{
\frac1{4\pi}
\frac{P_r}{P_j}
\frac{G_r}{G_j}
\frac{B_j}{B_r}
\frac JS
\sigma
}

That is why the black calculation doesn’t ask you for wavelength.

And if the J/S value you’ve entered is the minimum J/S required for the jammer to remain effective, that range is the burn-through range. Modern EW engineering references define burn-through in exactly that fashion: the target range at which J/S reaches the minimum value needed for effective jamming.

One distinction I would make from my previous answer

I wouldn’t now say simply “red scales = S, blue scales = J, black scales = R” as though each were an entirely independent slide rule.

It’s subtler than that.

The colours show the calculation paths and index relationships, but some physical quantities are necessarily shared between them. G_r, for example, participates in both the jammer-received-power and target-return equations. The several concentric discs let GE reuse those logarithmic relationships rather than duplicating every scale.

That also explains all the apparently cryptic coloured arrows scattered around the circumference.

How confident am I in the reconstruction?

I’m highly confident about what the scales calculate, because the equations are literally printed on the device and the visible scale labels correspond to their variables.

I’m also confident about the use of the coloured indices as logarithmic transfer/reference marks and the Alignment Guide as the common registration reference.

Where I would stop short of certainty is saying that GE’s original instruction book necessarily told the operator:

“Move the blue tab first, followed by the inner red tab, followed by the black tab…”

rather than another mathematically equivalent order. The underlying multiplication is commutative, but the physical disc arrangement may have made GE prescribe one particular sequence for convenience.

There is actually a surviving GE Pocket Guide associated with these calculators, and its contents include Radar Range Equation, Receiver Noise, Countermeasures Nomograms, and Gain and Beamwidth of Circular Parabolic Reflectors; the wider surviving GE set is dated to the 1958–61 period.

So we are tantalisingly close to being able to settle even that.

The next thing I’d do is reconstruct the individual moving discs themselves from the photograph — work out which printed scale physically belongs to which layer and which coloured arrow moves with it. That would let us say, without hand-waving, “grab this tab, rotate it until 10 dB is opposite this line; then grab this tab…” and effectively recreate the missing GE operating instructions.
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