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

#### vjk2

Related Aerospace and Astronautics Engineering News on Phys.org

#### Travis_King

that's why it's called the ideal rocket equation...Drag is a tremendous factor in real applications.

#### tfr000

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 [Broken])

Last edited by a moderator:

#### vjk2

Well, how to calculate?

#### mfb

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

#### vjk2

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....

#### mfb

Mentor
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.

#### tfr000

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

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...