Abstract: A framework to create new specific analytical solutions of the equations of motion for hyperbolic boundary value problems is presented. The method relies on a closed-form integral equation for mass density, involving a term that combines sources, geometry, ambient values, and radiation. Products of the density integral result in new more complicated solutions. The …
Category Archives: Aeronautics
The Three Pillars of Rocketry Culminating in Human Spaceflight
Below is an article that is upcoming in the NASA Alumni newsletter without images. “The Earth is the cradle of humanity, but one cannot live in the cradle forever.” – Konstantin Tsiolkovsky Modern rocketry began with foundational work by pioneers such as Tsiolkovsky, Oberth, Goddard, and the American Rocket Society. Their theoretical and experimental advances …
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Research Notes on The American Rocket Society
“The dream of yesterday is the hope of today and the reality of tomorrow.” – Robert H. Goddard While Dr. Robert H. Goddard was advancing rocketry through private experiments, another group of American enthusiasts independently pursued space exploration. Formed in the early 1930s, the American Rocket Society (ARS) emerged as an organization that not only …
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Research Notes on Hermann Oberth
“To boldly go where no man has gone before.” – Hermann Oberth Hermann Oberth’s theoretical breakthroughs transformed rocketry from speculative fiction into science, thus influencing the development of modern space exploration. His mentorship of Wernher von Braun and contributions to the V-2 rocket program set foundational principles that shape the field. Germany’s major figure in …
Early Rockets and Review Notes
One of the earliest documented uses of rockets was in China. Father Antoine Gaubil, a French Jesuit missionary and historian, described an event in his 1739 writings, “When it was lit, it made a noise that resembled thunder and extended 24 km. The place where it fell was burned, and the fire extended more than …
Hypersonics History of Reentry
Lately, I have been examining the entire history of hypersonics research and technology, with a particular focus on the re-entry problem and ablation for small vehicles, such as those from ballistic missiles. While reviewing the writings of Wernher von Braun, I was amused to find that he joked about using frozen balsa wood as a …
Kelly Johnson on X-Plane Programs
Our present research airplanes have developed startling performance only by the use of rocket engines and flying essentially in a vacuum. Testing airplanes designed for transonic flight speeds at Mach numbers between 2 and 3 has proven, mainly, the bravery of the test pilots and the fact that where there is no drag, the rocket …
Rodi and Algebraic Stress Models
Rodi examined nonlinear algebraic stress models by approximating the convective transport terms of the Reynolds stress tensor and normalizing Reynolds stress with turbulent kinetic energy, coupled with a transport equation for turbulent kinetic energy. This approach simplifies the Reynolds stress transport terms, resulting in an algebraic equation essential for determining the Reynolds stress tensor. This …
Saffman \(k-\omega^2\)
Saffman’s \(k-\omega^2\) turbulence model, initiated by Saffman’s research, plays a role in the two-equation models dedicated to turbulence research since the time of Kolmogorov in the 1940’s. The basics of Saffman’s model is shown in the portrayal of a statistically steady or ‘slowly varying’ inhomogeneous turbulence field alongside the mean velocity distribution. This model states …
Baldwin Barth One-Equation Model Reviewed
During the present semester, I reexamined the Baldwin-Barth one-equation turbulence model. This model constitutes a reformulation of the $k$ and $\epsilon$ equations, culminating in a single partial differential equation for the turbulent eddy viscosity, denoted as $\nu_t$, multiplied by the turbulent Reynolds number, $Re_t$. The model’s closure for the Reynolds-averaged Navier-Stokes (RANS) equations was a …
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