Approaching the Nose Cone

An important attribute of a nose cone was its shape, and engineers were reduc­ing drag to a minimum by crafting high-speed airplanes that displayed the ultimate in needle-nose streamlining. The X-3 research aircraft, designed for Mach 2, had a long and slender nose that resembled a church steeple. Atlas went even further, with an early concept having a front that resembled a flagpole. This faired into a long and slender cone that could accommodate the warhead.21

This intuitive approach fell by the wayside in 1953, as the NACA-Ames aero – dynamicists H. Julian Allen and Alfred Eggers carried through an elegant analysis of the motion and heating of a re-entering nose cone. This work showed that they were masters of the simplifying assumption. To make such assumptions successfully represents a high art, for the resulting solutions must capture the most essential aspects of the pertinent physics while preserving mathematical tractability. Their paper stands to this day as a landmark. Quite probably, it is the single most impor­tant paper ever written in the field of hypersonics.

They calculated total heat input to a re-entry vehicle, seeking shapes that would minimize this. That part of the analysis enabled them to critique the assertion that a slender and sharply-pointed shape was best. For a lightweight nose cone, which would slow significantly in the atmosphere due to drag, they found a surprising result: the best shape, minimizing the total heat input, was blunt rather than sharp.

The next issue involved the maximum rate of heat transfer when averaged over an entire vehicle. To reduce this peak heating rate to a minimum, a nose cone of realistic weight might be either very sharp or very blunt. Missiles of intermediate slenderness gave considerably higher peak heating rates and “were definitely to be avoided.”

This result applied to the entire vehicle, but heat-transfer rates were highest at the nose-cone tip. It was particularly important to minimize the heating at the tip, and again their analysis showed that a blunt nose cone would be best. As Allen and Eggers put it, “not only should pointed bodies be avoided, but the rounded nose should have as large a radius as possible.”22

How could this be? The blunt body set up a very strong shock wave, which pro­duced intense heating of the airflow. However, most of this heat was carried away in the flow. The boundary layer served to insulate the vehicle, and relatively little of this heat reached its surface. By contrast, a sharp and slender nose cone produced a shock that stood very close to this surface. At the tip, the boundary layer was too thin to offer protection. In addition, skin friction produced still more heating, for the boundary layer now received energy from shock-heated air flowing close to the vehicle surface.23

This paper was published initially as a classified document, but it took time to achieve its full effect. The Air Force did not adopt its principle for nose-cone design until 1956.24 Still, this analysis outlined the shape of things to come. Blunt heat shields became standard on the Mercury, Gemini, and Apollo capsules. The space shuttle used its entire undersurface as a heat shield that was particularly blunt, rais­ing its nose during re-entry to present this undersurface to the flow.

Yet while analysis could indicate the general shape for a nose cone, only experi­ment could demonstrate the validity of a design. At a stroke, Beckers Mach 7 facil­ity, which had been far in the forefront only recently, suddenly became inadequate. An ICBM nose cone was to re-enter the atmosphere at speeds above Mach 20. Its kinetic energy would vaporize five times its weight of iron. Temperatures behind the bow shock would reach 9000 K, hotter than the surface of the Sun. Research scien­tist Peter Rose wrote that this velocity would be “large enough to dissociate all the oxygen molecules into atoms, dissociate about half of the nitrogen, and thermally ionize a considerable fraction of the air.”25

Though hot, the 9000 К air actually would be cool, considering its situation, because its energy would go into dissociating molecules of gas. However, the ions and dissociated atoms were only too likely to recombine at the surface of the nose cone, thereby delivering additional heat. Such chemical effects also might trip the boundary layer from laminar to turbulent flow, with the rate of heat transfer increas­ing substantially as a result. In the words of Rose:

“The presence of free-atoms, electrons, and molecules in excited states can be expected to complicate heat transfer through the boundary layer by additional modes of energy transport, such as atom diffusion, carrying the energy of dissociation. Radiation by transition from excited energy states may contribute materially to radiative heat transfer. There is also a possibility of heat transfer by electrons and ions. The existence of large amounts of energy in any of these forms will undoubtedly influence the familiar flow phenomena.”26

Within the Air Force, the Aircraft Panel of the Scientific Advisory Board (SAB) issued a report in October 1954 that looked ahead to the coming decade:

“In the aerodynamics field, it seems to us pretty clear that over the next 10 years the most important and vital subject for research and development is the field of hypersonic flows; and in particular, hypersonic flows with [temperatures at a nose-cone tip] which may run up to the order of thousands of degrees. This is one of the fields in which an ingenious and clever application of the existing laws of mechanics is probably not adequate. It is one in which much of the necessary physical knowledge still remains unknown at present and must be developed before we arrive at a true understanding and competence. The reason for this is that the temperatures which are associated with these velocities are higher than temperatures which have been produced on the globe, except in connection with the nuclear developments of the past 10 or 15 years and that there are problems of dissociation, relaxation times, etc., about which the basic physics is still unknown.”27

The Atlas program needed a new experimental technique, one that could over­come the fact that conventional wind tunnels produced low temperatures due to their use of expanding gases, and hence the pertinent physics and chemistry asso­ciated with the heat of re-entry were not replicated. Its officials found what they wanted at a cocktail party.

This social gathering took place at Cornell University around Thanksgiving of 1954. The guests included university trustees along with a number of deans and senior professors. One trustee, Victor Emanuel, was chairman of Avco Corpora­tion, which already was closely involved in work on the ICBM. He had been in Washington and had met with Air Force Secretary Harold Talbott, who told him of his concern about problems of re-entry. Emanuel raised this topic at the party while talking with the dean of engineering, who said, “I believe we have someone right here who can help you.”28

That man was Arthur Kantrowitz, a former researcher at NACA-Langley who had taken a faculty position at Cornell following the war. While at Langley during the late 1930s, he had used a $5,000 budget to try to invent controlled thermo­nuclear fusion. He did not get very far. Indeed, he failed to gain results that were sufficient even to enable him to write a paper, leaving subsequent pioneers in con­

trolled fusion to start again from scratch. Still, as he recalls, “I continued my inter­est in high temperatures with the hope that someday I could find something that I could use to do fusion.”29

In 1947 this led him to the shock tube. This instrument produced very strong shocks in a laboratory, overcoming the limits of wind tunnels. It used a driving gas at high pressure in a separate chamber. This gas burst through a thin diaphragm to generate the shock, which traveled down a long tube that was filled with a test gas. High-speed instruments could observe this shock. They also could study a small model immersed within the hot flow at high Mach that streamed immediately behind the shock.30

When Kantrowitz came to the shock tube, it already was half a century old. The French chemist Paul Vieille built the first such devices prior to 1900, using them to demonstrate that a shock wave travels faster than the speed of sound. He proposed that his apparatus could prove useful in studying mine explosions, which took place in shafts that resembled his long tubes.31

The next important shock-tube researcher, Britain’s William Payman, worked prior to World War II. He used diaphragm-bursting pressures as high as 1100 pounds per square inch and introduced high-speed photography to observe the shocked flows. He and his colleagues used the shock tube for experimental verifica­tion of equations in gasdynamics that govern the motion of shock waves.32

At Princeton University during that war, the physicist Walter Bleakney went fur­ther. He used shock tubes as precision instruments, writing, “It has been found that successive shots’ in the tube taken with the same initial conditions reproduce one another to a surprising degree. The velocity of the incident shock can be reproduced to 0.1 percent.” He praised the versatility of the device, noting its usefulness “for studying a great variety of problems in fluid dynamics.” In addition to observations of shocks themselves, the instrument could address “problems of detonation and allied phenomena. The tube may be used as a wind tunnel with a Mach number variable over an enormous range.” This was the role it took during the ICBM pro­gram.33

At Cornell, Kantrowitz initiated a reach for high temperatures. This demanded particularly high pressure in the upstream chamber. Payman had simply used com­pressed air from a thick-walled tank, but Kantrowitz filled his upstream chamber with a highly combustible mix of hydrogen and oxygen. Seeking the highest tem­peratures, he avoided choosing air as a test gas, for its diatomic molecules absorbed energy when they dissociated or broke apart, which limited the temperature rise. He turned instead to argon, a monatomic gas that could not dissociate, and reached 18,000 K.

He was a professor at Cornell, with graduate students. One of them, Edwin Resler, wrote a dissertation in 1951, “High Temperature Gases Produced by Strong

Shock Waves.” In Kantrowitz’s hands, the versatility of this instrument appeared anew. With argon as the test gas, it served for studies of thermal ionization, a physi­cal effect separate from dissociation in which hot atoms lost electrons and became electrically charged. Using nitrogen or air, the shock tube examined dissociation as well, which increased with the higher temperatures of stronger shocks. Higher Mach values also lay within reach. As early as 1952, Kantrowitz wrote that “it is possible to obtain shock Mach numbers in the neighborhood of 25 with reasonable pressures and shock tube sizes.”34

Other investigators also worked with these devices. Raymond Seeger, chief of aerodynamics at the Naval Ordnance Laboratory, built one. R. N. Hollyer con­ducted experiments at the University of Michigan. At NACA-Langley, the first shock tube entered service in 1951. The Air Force also was interested. The 1954 report of the SAB pointed to “shock tubes and other devices for producing extremely strong shocks” as an “experimental technique” that could give new insights into fundamen­tal problems of hypersonics.35

Thus, when Emanuel met Kantrowitz at that cocktail party, this academic physi­cist indeed was in a position to help the Atlas effort. He had already gained hands – on experience by conducting shock-tube experiments at temperatures and shock velocities that were pertinent to re-entry of an ICBM. Emanuel then staked him to a new shock-tube center, Avco Research Laboratory, which opened for business early in 1955-

Kantrowitz wanted the highest shock velocities, which he obtained by using lightweight helium as the driver gas. He heated the helium strongly by adding a mixture of gaseous hydrogen and oxygen. Too little helium led to violent burning with unpredictable detonations, but use of 70 percent helium by weight gave a con­trolled burn that was free of detonations. The sudden heating of this driver gas also ruptured the diaphragm.

Standard optical instruments, commonly used in wind-tunnel work, were avail­able for use with shock tubes as well. These included the shadowgraph, schlieren apparatus, and Mach-Zehnder interferometer. To measure the speed of the shock, it proved useful to install ionization-sensitive pickups that responded to changes in electrical resistance as shock waves passed. Several such pickups, spaced along the length of the tube, gave good results at speeds up to Mach 16.

Within the tube, the shock raced ahead of the turbulent mix of driver gases. Between the shock and the driver gases lay a “homogeneous gas sample” (HGS), a cylindrical slug of test gas moving nearly with the speed of the shock. The measured speed of the shock, together with standard laws of gasdynamics, permitted a com­plete calculation of the pressure, temperature, and internal energy of the HGS. Even when the HGS experienced energy absorption due to dissociation of its constituent molecules, it was possible to account for this through a separate calculation.36

The HGS swept over a small model of a nose cone placed within the stress. The time for passage was of the order of 100 microseconds, with the shock tube thus operating as a “wind tunnel” having this duration for a test. This nevertheless was long enough for photography. In addition, specialized instruments permitted study of heat transfer. These included thin-gauge resistance thermometers for temperature measurements and thicker-gauge calorimeters to determine heat transfer rates.

Metals increase their electrical resistance in response to a temperature rise. Both the thermometers and the calorimeters relied on this effect. To follow the sudden temperature increase behind the shock, the thermometer needed a metal film that was thin indeed, and Avco researchers achieved a thickness of 0.3 microns. They did this by using a commercial product, Liquid Bright Platinum No. 05, from Hanovia Chemical and Manufacturing Company. This was a mix of organic compounds of platinum and gold, dissolved in oils. Used as a paint, it was applied with a brush and dried in an oven.

The calorimeters used bulk platinum foil that was a hundred times thicker, at 0.03 millimeters. This thickness diminished their temperature rise and allowed the observed temperature increase to be interpreted as a rate of heat transfer. Both the thermometers and calorimeters were mounted to the surface of nose-cone models, which typically had the shape of a hemisphere that faired smoothly into a cylinder at the rear. The models were made of Pyrex, a commercial glass that did not readily crack. In addition, it was a good insulator.37

The investigator Shao-Chi Lin also used a shock tube to study thermal ioniza­tion, which made the HGS electrically conductive. To measure this conductivity, Shao used a nonconducting shock tube made of glass and produced a magnetic field within its interior. The flow of the conducting HGS displaced the magnetic lines of force, which he observed. He calibrated the system by shooting a slug of metal having known conductivity through the field at a known speed. Measured HGS conductivities showed good agreement with values calculated from theory, over a range from Mach 10 to Mach 17-5. At this highest flow speed, the conductivity of air was an order of magnitude greater than that of seawater.38

With shock tubes generating new data, there was a clear need to complement the data with new solutions in aerodynamics and heat transfer. The original Allen – Eggers paper had given a fine set of estimates, but they left out such realistic effects as dissociation, recombination, ionization, and changes in the ratio of specific heats. Again, it was necessary to make simplifying assumptions. Still, the first computers were at hand, which meant that solutions did not have to be in closed form. They might be equations that were solvable electronically.

Recombination of ions and of dissociated diatomic molecules—oxygen and nitrogen—was particularly important at high Mach, for this chemical process could deliver additional heat within the boundary layer. Two simplified cases stood out. In “equilibrium flow,” the recombination took place instantly, responding immediately to the changing temperature and pressure within the boundary layer. The extent of ionization and dissociation then were simple point functions of the temperature and pressure at any location, and they could be calculated directly.

The other limiting case was “frozen flow.” One hesitates to describe a 9000 К airstream as “frozen,” but here it meant that the chemical state of the boundary layer retained its condition within the free stream behind the bow shock. Essentially this means that recombination proceeded so slowly that the changing conditions within the boundary layer had no effect on the degrees of dissociation and ionization. These again could be calculated directly, although this time as a consequence of conditions behind the shock rather than in the boundary layer. Frozen flow occurred when the air was rarefied.

These approximations avoided the need to deal with the chemistry of finite reac­tion rates, wherein recombination would not instantly respond to the rapidly vary­ing flow conditions across the thickness of a boundary layer but would lag behind the changes. In 1956 the aerodynamicist Lester Lees proposed a heat-transfer theory that specifically covered those two limiting cases.39 Then in 1957, Kantrowitz’s col­leagues at Avco Research Laboratory went considerably further.

The Avco lab had access to the talent of nearby MIT. James Fay, a professor of mechanical engineering, joined with Avco’s Frederick Riddell to treat anew the problem of heat transfer in dissociated air. Finite reaction-rate chemistry was at the heart of their agenda, and again they needed a simplifying assumption: that the airflow velocity was zero. Fiowever, this condition was nearly true at the forward tip of a nose cone, where the heating was most severe.

Starting with a set of partial differential equations, they showed that these equa­tions reduced to a set of nonlinear ordinary differential equations. Using an IBM 650 computer, they found that a numerical solution of these nonlinear equations was reasonably straightforward. In dealing with finite-rate chemistry, they introduced a “reaction rate parameter” that attempted to capture the resulting effects. They showed that a re-entering nose cone could fall through 100,000 feet while transi­tioning from the frozen to the equilibrium regime. Within this transition region, the boundary layer could be expected to be partly frozen, near the free stream, and partly in equilibrium, near the wall.

The Fay-Riddell theory appeared in the February 1958 Journal of the Aeronauti­cal Sciences. That same issue presented experimental results, also from Avco, that tested the merits of this treatment. The researchers obtained shock-tube data with shock Mach numbers as high as 17-5. At this Mach, the corresponding speed of 17,500 feet per second approached the velocity of a satellite in orbit. Pressures within the shock-tube test gas simulated altitudes of 20,000, 70,000, and 120,000 feet, with equilibrium flow occurring in the models’ boundary layers even at the highest equivalent height above the ground.

Most data were taken with calorimeters, although data points from thin-gauge thermometers gave good agreement. The measurements showed scatter but fit neatly on curves calculated from the Fay-Riddell theory. The Lees theory underpredicted heat-transfer rates at the nose-cone tip, calling for rates up to 30 percent lower than those observed. Here, within a single issue of that journal, two papers from Avco gave good reason to believe that theoretical and experimental tools were at hand to learn the conditions that a re-entering ICBM nose cone would face during its moments of crisis.40

Still, this was not the same as actually building a nose cone that could survive this crisis. This problem called for a separate set of insights. These came from the U. S. Army and were also developed independently by an individual: George Sutton of General Electric.