From Electricity to the First Echo
Part 1 of the series The Sciences Behind Radar. This part stays close to the physics. The wartime engineering comes in part 2, and the signal processing in part 3.
Radar was never a one-man show, and that is true of most things worth building. There is rarely a single afternoon in a single laboratory when a technology springs into being. Radio location in particular came together slowly, out of pieces that several different sciences had each worked out for their own reasons, and those pieces only became radar once someone set them side by side. A way to make waves came from one place, a way to measure time came from another, a way to pull a faint signal out of noise came from a third, and the mathematics underneath all of it was older than any of them. This series is about those pieces and where they came from, written for readers who already know a matched filter from a moving target indicator and might enjoy seeing the genealogy behind the hardware they use every day.
The Century When Electricity Grew Up
For most of history electricity meant a spark or the jolt from an electric fish, a curiosity with no steady source behind it. The nineteenth century changed that quickly, and the speed of the change is worth a moment, because it says something about how science actually moves. The first thing to arrive was a steady source. Alessandro Volta stacked his pile in 1800 and gave experimenters a continuous current for the first time, and a continuous current is what you need to run a careful experiment rather than to admire a flash. Within 20 years Hans Christian Orsted noticed in 1820 that a current deflected a nearby compass needle, which tied electricity and magnetism together after a long stretch of treating them as separate things, and Andre-Marie Ampere turned that single observation into a quantitative account of the forces between currents almost at once. Michael Faraday closed the loop in 1831 by showing that a changing magnetic field drives a current, which is the principle behind every generator, every motor, and eventually every transmitting antenna. Georg Ohm had already pinned down the relation between voltage, current, and resistance in 1827.
Why did all of this happen so fast, when the underlying mathematics had been available for centuries and the raw phenomena had been noticed in scattered ways for far longer? Part of the answer is the steady current source, which made controlled experiment possible. The rest of the answer is money. The telegraph, spreading from the late 1830s onward, created a real market for electrical knowledge and for precise instruments, and the great submarine cable projects of the 1850s and 1860s forced the science of electrical measurement into being, because a cable that failed under the Atlantic was an expensive way to learn that a theory was wrong. Out of that pressure came standardized units and the careful work on measurement that William Thomson, later Lord Kelvin, helped to lead.
Electricity grew up in a single century not because one genius appeared but because a steady source, a body of waiting mathematics, and an economy that would pay for the answer all showed up together.
That same combination appears again when radar itself gets built, which is the subject of the next part.
The Theory and the First Things It Detected
The synthesis arrived in 1865, the year I would circle if I had to pick one, when James Clerk Maxwell pulled electricity, magnetism, and light into a single field theory. If a Jayhawk had been in the room, I like to think he would have shouted Rock Chalk as the last equation closed. Maxwell was not thinking about aircraft and could not have imagined the use, yet he handed everything that followed the one fact that radar cannot live without, that an electromagnetic disturbance travels at a finite and knowable speed and carries energy away from its source. Range measurement rests entirely on that finiteness, since a wave moving at a fixed velocity turns a measured time into a measured distance, and distance is the first thing any radar wants to know. In my own head a flashlight and an antenna are doing the same job at different wavelengths, throwing energy outward and waiting to see what comes back, and Maxwell is the reason that picture is physics rather than just a nice image.
Heinrich Hertz made the idea something you could watch on a bench. Through the late 1880s he generated and detected the waves Maxwell had predicted, and along the way he showed that they reflected from metal sheets and refracted through large prisms of pitch, behaving in every way like light given a longer wavelength and made invisible. The reflection from metal is the seed of the whole field, because an object that sends energy back is an object a receiver can hear. Hertz treated his results as a confirmation of theory and died young, never suspecting that the reflection he had demonstrated would become an industry.
The next figure deserves more attention than the usual histories give him. Working in Calcutta in the late 1890s, Jagadish Chandra Bose ran experiments at millimeter wavelengths, reaching frequencies as high as 60 gigahertz, and in doing so he built much of the hardware that radar would later need and then reinvent. He used a waveguide to channel the radiation, a pyramidal horn that he called a collecting funnel and that we would now simply call a horn antenna, dielectric lenses, a set of polarizers, and a galena point contact detector that was in effect an early semiconductor diode for sensing the waves. He presented this work to the Royal Institution in London in January 1897, and a century later the radio astronomer Darrel Emerson, writing in the IEEE Transactions on Microwave Theory and Techniques, traced just how thoroughly Bose had anticipated the millimeter wave engineering that the wartime laboratories would later treat as new. Bose even speculated in 1897 that the sun might emit radiation at these wavelengths and that the atmosphere might absorb some of it, a guess that radar work would bear out decades later, when the water vapor absorption near a wavelength of 1 centimeter turned up during wartime measurements in 1944.
Two more early steps belong here. In 1897 the Russian physicist Alexander Popov, experimenting with wireless between ships, noticed that a third ship passing between his transmitter and receiver disturbed the signal, and he remarked that the effect might be used to detect a vessel, which is about as early as the idea gets stated out loud. A few years later, in 1904, the German engineer Christian Hulsmeyer went further and built a working device he called the Telemobiloskop, patenting it and demonstrating it as it detected ships across a river in fog. He sold none, partly because it could give a bearing but not a range, and partly because no one had yet decided they needed such a thing. Both men are usually filed under curiosities, yet together they show the idea of radio detection sitting fully formed and simply waiting for a reason to exist.
The Older Foundations Underneath
Everything so far sits on a layer of mathematics that is much older, and far more international, than the nineteenth century names might suggest, and it is worth ending here because it puts the rest in proportion. A radar measures phase and angle, which means it lives on trigonometry, and trigonometry has a long and shared history. The Greek astronomers Hipparchus and later Ptolemy built the first tables of chords nearly 2000 years ago to predict the motions of the sky. The functions we actually use took their modern shape in India, where Aryabhata tabulated what we now call the sine around the year 499 and used it for astronomy. The word sine itself carries that journey inside it, since the Sanskrit term jya passed into Arabic as jiba, was later read as the similar looking word jaib meaning a fold or a bay, and was finally rendered into Latin as sinus, the fold of a garment, by a 12th century translator. The function every radar engineer writes constantly is named, through a chain of translators, after a small misreading.
The mathematics kept developing in places the standard story tends to skip past. In the Islamic world al-Khwarizmi systematized algebra in the 9th century, and his name, latinized, is the root of the word algorithm, which is a fitting ancestry for a field that now lives largely in code, while al-Battani refined the trigonometry of the sky around the same period. Centuries later, in southern India, the Kerala school led by Madhava of Sangamagrama, who lived roughly from 1340 to 1425, worked out the infinite series for the sine, the cosine, and the arctangent, expressing the trigonometric functions as power series and even bounding the errors, which puts them at the threshold of the calculus. These are the same series that Newton, Gregory, and Leibniz arrived at independently in Europe 2 to 3 centuries later, and they reached Western scholarship only in 1834, through a paper by Charles Whish. Whether the knowledge traveled west earlier, along trade and missionary routes, is still an open question among historians, and an interesting one, though the priority itself is not in doubt. Even magnetism, which gives the cavity magnetron of part 2 its name and its operating principle, has a deep and partly Chinese lineage, since Chinese scholars described the lodestone compass long before Europe did and Shen Kuo wrote about magnetic declination in 1088.
None of this is meant to take anything away from Maxwell or Faraday or the wartime engineers who come next. The point is gentler than that, and I think more interesting.
The mathematics and physics that radar runs on were assembled slowly, by many people, across many centuries and many parts of the world, and the names most of us learned in school capture one recent and well documented stretch of a much longer human effort.
Knowing the earlier stretches takes nothing away from the later ones. It simply makes the whole thing feel like what it actually is, a shared effort that no single country and no single era can claim on its own. With that in view, the second part turns to the moment the pieces finally came together, under the pressure of a coming war and the spending it set loose.
References
- Whittaker, E. T. (1951). A History of the Theories of Aether and Electricity. Thomas Nelson and Sons.
- Maxwell, J. C. (1865). A Dynamical Theory of the Electromagnetic Field. Philosophical Transactions of the Royal Society of London.
- Hertz, H. (1893). Electric Waves (D. E. Jones, Trans.). Macmillan. Original experiments, 1887 to 1888.
- Emerson, D. T. (1997). The Work of Jagadis Chandra Bose, 100 Years of Millimeter-Wave Research. IEEE Transactions on Microwave Theory and Techniques, 45(12), 2267 to 2273.
- Hulsmeyer, C. (1904). German Patent DE165546, Telemobiloskop.
- Plofker, K. (2009). Mathematics in India. Princeton University Press.
- Roy, R. (1990). The Discovery of the Series Formula for Pi by Leibniz, Gregory and Nilakantha. Mathematics Magazine, 63(5), 291 to 306.
- Whish, C. M. (1834). On the Hindu Quadrature of the Circle, and the Infinite Series of the Proportion of the Circumference to the Diameter Exhibited in the Four Sastras. Transactions of the Royal Asiatic Society of Great Britain and Ireland.
Title image - Part 1 of the series The Sciences Behind Radar. Background - Nadir sounding antenna array pattern from my NASA P-3 deployment, with a fragment of the monostatic RCS derivation for a dielectric object.
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