# How much is the ideal rocket equation affected by air drag?

• vjk2
In summary, the Tsiolkovsky rocket equation is an ideal equation that does not take into account atmospheric drag or gravity. These factors must be considered in a numerical simulation in order to accurately calculate the rocket's velocity and altitude. However, simplifications can be made for easier calculations.
that's why it's called the ideal rocket equation...Drag is a tremendous factor in real applications.

Depends on:
size and shape of the rocket (obviously, bigger and flatter have more drag)
where in the atmosphere (higher up, thinner air, less drag)
how fast the rocket is moving (non-trivial function due to compressibility of the air)

see http://en.wikipedia.org/wiki/Drag_(physics )

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Well, how to calculate?

With a numerical simulation.
In addition to air drag, you have to consider gravity as well.

mfb said:
With a numerical simulation.
In addition to air drag, you have to consider gravity as well.

er, actually the ideal rocket equation is entirely about gravity...

There is no gravity in the ideal rocket equation.
There is a way to re-write the equation to get the gravitational acceleration on Earth into it, but that is just a unit conversion. In a similar way, the distance to moon does not depend on the length of my monitor, but I can express it as multiple of that length if I like.

$\textbf F = \textbf F_{gravity} + \textbf F_{thrust} + \textbf F_{drag}$

Depends how complicated you want to get. For a full simulation, you have to start with the rotation of the Earth at the launch site, and use this as the rocket's initial motion. Gravity drops off slowly (${1\over r^{2}}$), thrust increases slightly as the atmospheric pressure is no longer "bottling it up", and drag peaks and falls off as the rocket reaches the speed of sound, which varies with air temperature.

You can simplify a lot of that - flat, non-rotating Earth, constant thrust, drag as some simple, approximate function - but there is still no simple equation to say, "after 30 seconds, the rocket has velocity v at altitude h." Rocket science...

## 1. How does air drag affect the ideal rocket equation?

The air drag force acts in the opposite direction of the rocket's motion, slowing it down and reducing its acceleration. This decreases the overall efficiency of the rocket and affects the ideal rocket equation by decreasing the amount of thrust that can be produced.

## 2. Is air drag a major factor in rocket design?

Yes, air drag is a significant factor in rocket design. It must be carefully considered and minimized in order to achieve optimal performance and efficiency in flight. This is especially important for rockets that are designed to travel at high speeds and altitudes.

## 3. How do scientists account for air drag in the ideal rocket equation?

In the ideal rocket equation, air drag is accounted for by including a drag coefficient in the equation. This coefficient takes into account the shape and size of the rocket, as well as the properties of the surrounding air, and is used to calculate the amount of drag force acting on the rocket.

## 4. Can air drag be completely eliminated in rocket flight?

No, air drag cannot be completely eliminated in rocket flight. However, it can be minimized through careful design and engineering. This is often achieved by streamlining the shape of the rocket and using materials that reduce drag, such as lightweight and aerodynamic materials.

## 5. How does air density affect air drag in rocket flight?

Air density plays a significant role in air drag during rocket flight. The denser the air, the greater the drag force acting on the rocket. As a rocket gains altitude and enters thinner air, the amount of drag decreases, allowing it to achieve higher speeds and more efficient flight.

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