Konstantin Eduardovich Tsiolkovsky (; Russian: Константи́н Эдуа́рдович Циолко́вский, IPA: [kənstɐnʲˈtʲin ɪdʊˈardəvʲɪtɕ tsɨɐlˈkofskʲɪj] ; 17 September [O.S. 5 September] 1857 – 19 September 1935) was a Russian rocket scientist who pioneered astronautics. Along with Hermann Oberth and Robert H. Goddard, he is one of the pioneers of space flight and the founding father of modern rocketry and astrona change in the rocket's speed ( Δ v {\displaystyle \Delta v} ) exhaust velocity of the engine ( v e {\displaystyle v_{e}} ) initial ( m 0 {\displaystyle m_{0}} ) and final ( m f {\displaystyle m_{f}} ) mass of the rocket After writing out this equation, Tsiolkovsky recorded the date: 10 May 1897. In the same year, the formula for the motion of a body of variable mass was published in the thesis of the Russian mathematician I. V. Meshchersky ("Dynamics of a Point of Variable Mass," I. V. Meshchersky, St. Petersburg, 1897). His most important work, published in May 1903, was Exploration of Outer Space by Means of Rocket Devices (Russian: Исследование мировых пространств реактивными приборами). Tsiolkovsky calculated, using the Tsiolkovsky equation, that the horizontal speed required for a minimal orbit around the Earth is 8,000 m/s (5 miles per second) and that this could be achieved by means of a multistage rocket fueled by liquid oxygen and liquid hydrogen. In the article "Exploration of Outer Space by Means of Rocket Devices", it was suggested for the first time that a rocket could perform space flight. In this article and its sequels (1911 and 1914), he developed some ideas of missiles and considered the use of liquid rocket engines. The outward appearance of Tsiolkovsky's spacecraft design, published in 1903, was a basis for modern spaceship design. The design had a hull divided into three main sections. The pilot and copilot would occupy the first section, while the second and third sections held the liquid oxygen and liquid hydrogen needed to fuel the spacecraft.

Our study identifies a subtle deviation from Newton's third law in the derivation of the ideal rocket equation, also known as the Tsiolkovsky Rocket Equation (TRE). TRE can be derived using a 1D elastic collision model of the momentum exchange between the differential propellant mass element (dm) and the rocket final mass (m1), in which dm initially travels forward to collide with m1 and rebounds to exit through the exhaust nozzle with a velocity that is known as the effective exhaust velocity ve. We observe that such a model does not explain how dm was able to acquire its initial forward velocity without the support of a reactive mass traveling in the opposite direction. We show instead that the initial kinetic energy of dm is generated from dm itself by a process of self-combustion and expansion. In our ideal rocket with a single particle dm confined inside a hollow tube with one closed end, we show that the process of self-combustion and expansion of dm will result in a pair of differential particles each with a mass dm/2, and each traveling away from one another along the tube axis, from the center of combustion. These two identical particles represent the active and reactive sub-components of dm, co-generated in compliance with Newton's third law of equal action and reaction. Building on this model, we derive a linear momentum ODE of the system, the solution of which yields what we call the Revised Tsiolkovsky Rocket Equation (RTRE). We show that RTRE has a mathematical form that is similar to TRE, with the exception of the effective exhaust velocity (ve) term. The ve term in TRE is replaced in RTRE by the average of two distinct exhaust velocities that we refer to as fast-jet, vx1, and slow-jet, vx2. These two velocities correspond, respectively, to the velocities of the detonation pressure wave that is vectored directly towards the exhaust nozzle, and the retonation wave that is initially vectored in the direction of rocket propagation, but subsequently becomes reflected from the thrust surface of the combustion chamber to exit through the exhaust nozzle with a time lag behind the detonation wave. The detonation-retonation phenomenon is supported by experimental evidence in the published literature. Finally, we use a convolution model to simulate the composite exhaust pressure wave, highlighting the frequency spectrum of the pressure perturbations that are generated by the mutual interference between the fast-jet and slow-jet components. Our analysis offers insights into the origin of combustion oscillations in rocket engines, with possible extensions beyond rocket engineering into other fields of combustion engineering.

In this paper, an integrated optimization is carried out to find the optimal hybrid rocket engine design for a modular multistage launch vehicle targeting a 500 km polar circular orbit. A single hybrid rocket engine unit is reused across the whole launch vehicle, with each stage constituted by a cluster of a specified number of units. Only the nozzle exit diameter of the units is allowed to change across each stage. This clustering approach is aimed at reducing the costs of the launch vehicle and at simplifying the optimization procedure. After a brief mission analysis based on Tsiolkovsky’s equation, a three-stage configuration is chosen for the launch vehicle, employing 16, 4, and 1 engine units for, respectively, the first, second, and third stage. A neural network-based surrogate model is employed to approximate the complex hybrid rocket internal ballistics, with the aim to reduce the computational cost of the optimization process. The surrogate model is trained to map a reduced number of design parameters to the performance and mass budget of a single engine unit using data from a 0-D hybrid rocket engine model. The accuracy of the trained network in predicting crucial features is then assessed. Finally, the trained network is integrated into a multidisciplinary optimization process. The aim is to identify the optimal rocket engine design and launch vehicle ascent trajectory that maximize the payload capacity to the target orbit.

To support the material delivery demand of large-scale lunar colonies, this paper establishes a unified physical dynamic model for space elevators and traditional chemical rockets. Different from existing separated single-carrier theoretical derivations, this study simultaneously incorporates radial force balance and transverse Coriolis oscillation loss into elevator energy calculation, quantitatively correcting the energy consumption increment caused by cable lateral swing, which fills the gap of simplified energy models ignoring lateral disturbance loss. For multi-stage rockets, the Tsiolkovsky rocket equation is improved by introducing system loss coefficient to quantify the extra energy consumed by nozzle loss and gravity loss. Comparative quantitative calculations show that the payload ratio of space elevators reaches 46.85%, which is 23.78 times higher than rockets, and the unit mass energy consumption is only 10.7% of chemical launch vehicles, though rockets possess slight advantages in single trip time. Numerical results further reveal that Coriolis disturbance accounts for 8%–12% of the elevator’s total energy cost, a critical factor neglected by most previous static models. The established dynamic model provides standardized energy and time evaluation indexes for multi-modal Earth-Moon logistics schemes, and lays a physical foundation for subsequent transportation capacity allocation optimization and life-cycle environmental impact assessment.

The aim of this research is to analyze a potential Mars Sample Return (MSR) mission through the study of an optimized design of the Mars Ascent Vehicle (MAV) propulsion system. The main goal of the MSR mission is to return to Earth samples of rocks and dust collected by a rover operating on the surface of Mars, and conveyed to the MAV into an Orbit Sample (OS) canister. The MAV must accomplish an initial ascent phase from the Mars surface to a circular Low Mars Orbit (LMO) with a radius of 500 Km and 30° inclination, and then with its second stage it must circularize into the target LMO where it releases the OS payload. A combination of the MAV and a second vehicle, the Mars Earth Return Vehicle (MERV) orbiter, is required to fulfill the final return phase from Mars to the Earth. After completing three different phases of rendezvous operations, with a final Hohmann Transfer the MERV is able to bring the OS to Earth with its payload. A spreadsheet model enables the evaluation of two different MAV architecture: a two-stage solid rocket, and a two-stage hybrid rocket. The study is based on the main rocket science equations, including the Tsiolkovsky Rocket Equation that calculates the change in velocity $\Delta V$ for the two stages of the MAV and the amount of propellant needed for both stages. From the analysis it can be noted that the two-stage hybrid design has significant advantages, firstly in terms of Gross Lift Off Mass GLOM (270 Kg) when compared to the solid solution (

THIS article presents some results of theoretical research carried out by the author, based on work begun in 1946 when he was, for a time, concerned with rocket ballistics. It serves to amplify part of the theory given by R. C. Knight (Math. Gazette, Vol. 32, No. 300, July 1948, pp. 187–194). The two sections which follow are entirely separate; the first concerns the stability of spinning rockets and the second the potentialities of multi‐stage rockets. Acknowledgment is due to the Chief Scientist, Ministry of Supply, for permission to communicate this paper.