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Sommerfeld on Electromagnetic Stealth During WW-II

In his authoritative two volume radar cross section handbook, George Ruck has pointed out the desirable features of radar absorbers.

“The search for suitable radar absorbing materials (RAM) was initiated in the early 1940’s both in the United states and Germany.

Ideally, the optimum RAM would be a paint-like material effective at all polarizations over a broad range of frequencies and angles of incidence.


*Edison Medalist in 1928. (Eleven years after Tesla.)

Unfortunately, such a material does not exist and the probability of its being developed is rather remote.”(38)

Arnold Sommerfeld (1868-1951) presents a surprising discussion of German war research on stealth and radar absorbing materials in the optics volume of his famous Lectures on Theoretical Physics.(39) He relates that the case where the magnetic permeabilities between two media (air and target) are unequal (µ1 ≠ µ2) is “of some historical interest”.

“During the war the problem arose to find, as a counter measure against allied radar, a largely nonreflecting (“black”) surface layer of small thickness. This layer was to be particularly non-reflecting for perpendicular or almost perpendicular incidence of the radar wave. In this case the angle of incidence and the angle of transmission are both almost equal to zero. The problem is solved by making the ratio of the two wave impedances equal to unity: m 12 = (E1/H1)/(E2/H2) =  1   (1)

The criterion is, thus, not the index of refraction but the ratio of wave impedances.”

Sommerfeld’s suggestion is similar to the idea of making the radar target surface a “conjugate match” to eliminate radar reflections. If one could make the impedance of the second medium be the same as free-space, the target would become radar invisible. He continues:

“In order to ‘camouflage’ on object against radar waves, one must cover it with a layer for which this ratio of wave resistances has the value 1 in the region of centimeter waves. According to [the law of reflaction and the boundary conditions] this means that if we call the constant of the desired material ε and µ and those air ε0 and µ0, then                                                                 =              (2)

Hence,  the problem concerns not only the dielectric constant but also the relationship between the dielectric constant and the permeability. A substance must be formed whose relative permeability µr = µ/µ0 is of the same magnitude as its relative dielectric constant Є/Є0.

This case is discussed by Ridenour in Volume 1 of the famous MIT Rad Lab series,(40)  and in a well known analytical reference by Weston.(41) Sommerfeld continues,

But the problem is not yet solved. For at its back surface the layer borders on the object (metal) which is to be camouflaged, and this second surface still reflects strongly. Hence, the further condition must be imposed that the layer should absorb sufficiently strongly. This requires a complex rather than a real dielectric constant and because of the requirement (Eq. 2) a corresponding complex permeability. The material must, therefore, be ferromagnetic and must possess a strong hysteresis or a structural relaxation that acts correspondingly. Thus, a difficult technological problem was posed which, though not unsolvable, required extensive preparatory work. Because of the urgent war situation, the solution which had to be used resulted from the following considerations …”

Sommerfeld then changes the course of his ideas. He proceeds to describe the reduction in radar reflection by a rather conventional means that does not build upon the requirement of Equation (2). Instead, what he discusses next is covering the surface with layers of lossy dielectric material, each strata being less than ¼ wavelength thick, neglecting entirely any effects attributable to µ. (“In this manner the reflected intensity could be reduced to 1% of the value given by Fresnel’s formula …”(42)) After the war, a number of papers were published by Sommerfeld’s colleagues at Gottingen and Munich, in Zeitschrift fur Angewandte Physik, on the topic of radar absorption. (Just scan the magazine’s annual index for 1956-1959.) Presumably, after the war the German workers were less constrained in publishing their research on the topic of RAM than Allied scientist.* Even at this late date most significant western RAM publications are classified, particularly those related to the stealth bomber technology.

In his 1947 MIT Rad Lab Volume, Ridenour comments that,

“Absorbent materials have been produced in Germany for the radar camouflage of U-boats. The type of absorber that was actually put into service was of the interface kind. The dielectric constant and permeability were produced by a high concentration of spheroidal metal particles (carbonyl iron). The concentration of metal was 80% by weight, and values of dielectric constant and permeability were ε = 7, and µ = 3.5. An absorber of the second kind was also developed in Germany. It consisted of a series of layers whose conductivity regularly increased with depth. The layers were separated by foam-type plastic whose dielectric constant was close to 1. The absorption was excellent from 4 to 13 cm [2.3-7.5 GHz]. However, the complete absorber was a rigid structure 2.5 inches thick, and it was never actually used.”(43)

Is there any connection between the remarks of Sommerfeld and the supposed German version of the “Philadelphia Experiment”, which has been rumored to have occurred at the Kiel Shipyards in Germany during World war II? Surprisingly, after hinting at ferromagnetic materials, Sommerfeld did not tell us how to produce magnetic radar camouflage. We will try our hand at supplying the missing details below. But first, we review conventional linear RAM.


1994 Tesla Symposium at Colorado Springs


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Polyphase Currents and Rotating Fields

Tesla’s Reflections on Radar and Ships Wrapped in Coils of Wire



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