Ideal rocket equation (Tsiolkovsky rocket equation)

Description

The Tsiolkovsky rocket equation, or ideal rocket equation describes the motion of vehicles that follow the basic principle of a rocket: a device that can apply acceleration to itself (a thrust) by expelling part of its mass with high speed and move due to the conservation of momentum.
The Tsiolkovsky rocket equation relates the delta-v (the maximum change of speed of the rocket if no other external forces act) with the effective exhaust velocity and the initial and final mass of a rocket (or other reaction engine).

Konstantin Eduardovich Tsiolkovsky, 17 September 1857 – 19 September 1935) was a Russian and Soviet rocket scientist and pioneer of the astronautic theory. Along with the French Robert Esnault-Pelterie, the German-Romanian Hermann Oberth and the American Robert H. Goddard, he is considered to be one of the founding fathers of modern rocketry and astronautics. His works later inspired leading Soviet rocket engineers such as Sergei Korolev and Valentin Glushko and contributed to the success of the Soviet space program. Tsiolkovsky spent most of his life in a log house on the outskirts of Kaluga, about 200 km(120 mi) southwest of Moscow. At the age of 10, he caught scarlet fever and became hard of hearing. When he was 13, his mother died. He was not admitted to elementary schools because of his hearing problem, so he was self-taught. As a reclusive home-schooled child, he passed much of his time by reading books and became interested in mathematics and physics. As a teenager, he began to contemplate the possibility of space travel. A recluse by nature, his unusual habits made him seem bizarre to his fellow townsfolk.

Scientific achievements

Tsiolkovsky stated that he developed the theory of rocketry only as a supplement to philosophical research on the subject. He wrote more than 400 works including approximately 90 published pieces on space travel and related subjects. Among his works are designs for rockets with steering thrusters, multistage boosters, space stations, airlocks for exiting a spaceship into the vacuum of space, and closed-cycle biological systems to provide food and oxygen for space colonies. Thoughts on the use of the rocket principle in the cosmos were expressed by him as early as 1883, and a rigorous theory of rocket propulsion was developed in 1896. Tsiolkovsky derived the formula shown here, which he called the “formula of aviation”.

Using the equation he calculated 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 proved for the first time that a rocket could perform space flight. 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 were in the first section, the second and third sections held the liquid oxygen and liquid hydrogen needed to fuel the spacecraft.

In 1926–1929, Tsiolkovsky solved the practical problem regarding the role played by rocket fuel in getting to escape velocity and leaving the Earth. He showed that the final speed of the rocket depends on the rate of gas flowing from it and on how the weight of the fuel relates to the weight of the empty rocket.

Tsiolkovsky conceived a number of ideas that have been later used in rockets. They include: gas rudders (graphite) for controlling a rocket’s flight and changing the trajectory of its center of mass, the use of components of the fuel to cool the outer shell of the spacecraft (during re-entry to Earth) and the walls of the combustion chamber and nozzle, a pump system for feeding the fuel components, the optimal descent trajectory of the spacecraft while returning from space, etc.Tsiolkovsky did much fruitful work on the creation of the theory of jet aircraft, and invented his chart Gas Turbine Engine. In 1929, Tsiolkovsky proposed the construction of multistage rockets in his book Space Rocket Trains. Tsiolkovsky never built a rocket; he apparently did not expect many of his theories to ever be implemented.

Legacy

Although many called his ideas impractical, Tsiolkovsky influenced later rocket scientists throughout Europe, like Wernher von Braun. Russian search teams at Peenemünde found a German translation of a book by Tsiolkovsky of which “almost every page…was embellished by von Braun’s comments and notes”. Leading Soviet rocket-engine designer Valentin Glushko and rocket designer Sergey Korolev studied Tsiolkovsky’s works as youths, and both sought to turn Tsiolkovsky’s theories into reality. In particular, Korolev saw traveling to Mars as the more important priority, until in 1964 he decided to compete with the American Project Apollo for the moon.

Related formulas

Variables

ΔvMaximum change of velocity (m/sec)
veEffective exhaust velocity (m/sec)
m0Initial total mass (including propellant) - "wet mass" (kg)
m1Final total mass - "dry mass" (kg)