This tutorial provides an elementary development of the key concepts that describe the behavior of rocket propulsion systems.

The following concepts will be discussed in this tutorial

Rockets accelerate by ejecting mass at speed from the vehicle. Being an introductory level tutorial, only two parameters suffice to describe this ejected material. These parameters are

$$\dot m_e(t)$$ -- The exhaust mass flow rate and

$$\vec v_e(t)$$ -- The exhaust velocity relative to the rocket.

The exhaust mass flow rate is the rate at which the cloud of exhaust gas left by the vehicle gains mass. Note that this quantity is always positive when the rocket engine is firing and is of course zero when the rocket is quiescent. The suffix $$e$$ in $$\dot m_e$$ and $$\vec v_e$$ denotes the exhaust. There are two other items of interest -- the fuel and the rocket itself. The parameters that describe these other two items are

$$m_f(t)$$ -- The quantity of fuel remaining in the rocket,

$$m_v\;\,$$ -- The dry mass of the vehicle (including the empty fuel tanks),

$$m_r(t)$$ -- The mass of the rocket as a whole (dry mass + fuel mass), and

$$\vec v_r(t)$$ -- The velocity of the rocket expressed in some inertial reference frame.

The rate at which the fuel and vehicle mass changes is simply the additive inverse of the exhaust mass flow rate.

Rocket designers and analysts often use

$$I_{sp} = \frac{v_e}{g_0}$$

where $$g_0$$ is standard gravity, the acceleration due to Earth's gravity at sea level, or $$ 9.80665 \mathrm{m} / \mathrm{s}^2$$. This tutorial uses the exhaust velocity rather than specific impulse to make the connection to momentum more obvious. For example, the Shuttle main engines have a specific impulse of 453 seconds when operated in vacuum. This translates to an effective exhaust velocity of 4500 meters/second.

This tutorial does not provide any of the underlying details that dictate how combustion of the fuel leads to a high velocity exhaust. A good place to start is the The Beginner's Guide to Rockets, http://exploration.grc.nasa.gov/education/rocket/index.html.

The following concepts will be discussed in this tutorial

- Characteristics of a rocket engine

This post characterizes a rocket engine.

- Equations of motion

The next post uses these charactistics along with conservation of mass and momentum to develop the equations of motion of a rocket.

- The Tsiolokovsky rocket equation

The third post in this series develops the Tsiolokovsky rocket equation. This equation explains why it took one of the most powerful machines ever built, the Saturn V rocket, to get a tiny vehicle to the Moon.

- Energy concepts

The forth post in this series examines the energy involved in making a rocket accelerate. Rockets function by converting some form of potential energy (usually chemical) into kinetic energy.

**Characteristics of a rocket engine**Rockets accelerate by ejecting mass at speed from the vehicle. Being an introductory level tutorial, only two parameters suffice to describe this ejected material. These parameters are

$$\dot m_e(t)$$ -- The exhaust mass flow rate and

$$\vec v_e(t)$$ -- The exhaust velocity relative to the rocket.

The exhaust mass flow rate is the rate at which the cloud of exhaust gas left by the vehicle gains mass. Note that this quantity is always positive when the rocket engine is firing and is of course zero when the rocket is quiescent. The suffix $$e$$ in $$\dot m_e$$ and $$\vec v_e$$ denotes the exhaust. There are two other items of interest -- the fuel and the rocket itself. The parameters that describe these other two items are

$$m_f(t)$$ -- The quantity of fuel remaining in the rocket,

$$m_v\;\,$$ -- The dry mass of the vehicle (including the empty fuel tanks),

$$m_r(t)$$ -- The mass of the rocket as a whole (dry mass + fuel mass), and

$$\vec v_r(t)$$ -- The velocity of the rocket expressed in some inertial reference frame.

The rate at which the fuel and vehicle mass changes is simply the additive inverse of the exhaust mass flow rate.

**Specific impulse**Rocket designers and analysts often use

*specific impulse*to characterize a rocket engine rather than exhaust speed. Specific impulse has units of time. There is a simple relationship between specific impulse and effective exhaust velocity:$$I_{sp} = \frac{v_e}{g_0}$$

where $$g_0$$ is standard gravity, the acceleration due to Earth's gravity at sea level, or $$ 9.80665 \mathrm{m} / \mathrm{s}^2$$. This tutorial uses the exhaust velocity rather than specific impulse to make the connection to momentum more obvious. For example, the Shuttle main engines have a specific impulse of 453 seconds when operated in vacuum. This translates to an effective exhaust velocity of 4500 meters/second.

**Further reading**This tutorial does not provide any of the underlying details that dictate how combustion of the fuel leads to a high velocity exhaust. A good place to start is the The Beginner's Guide to Rockets, http://exploration.grc.nasa.gov/education/rocket/index.html.

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