Air density on Kerbin?

[VincentMcConnell]

So I want to calculate when my Kerpollo Saturn V (or any other craft for that matter) goes into Maximum-Q.

The equation I saw was this:

Q=1/2pv^2.

p= Air density

V= velocity.

Here\'s the problem, though. I don\'t know what the air density is on Kerbin, and it decreases as we raise in altitude... How in the world do you calculate something like this?

[Menelmacar]

I\'ve wondered about this - I read a thread a while ago discussing it and they\'d decided it\'d be very dense, by working out drag losses. Although maybe that was when the atmosphere just stopped at 35k. However if we do get info on the air density this will mean 1)Kerbals will have low voices (if get voices/have similar vocal systems to human ones) 2) The speed of sound will be higher (I\'d love this defined, maybe we\'d get some sonic booms) - I struggle to go much faster than Mach 2 with a jet at the moment so it could provide more of a challenge.

[PakledHostage]

Here\'s the problem, though. I don\'t know what the air density is on Kerbin, and it decreases as we raise in altitude... How in the world do you calculate something like this?

Here\'s a plot that might help:

It was created by launching a rocket sonde to 80km, recording temperature, pressure and density along the way using a sensor plugin. Specifically:

dAtmosphericPressure = FlightGlobals.getStaticPressure();

dAtmophericDensity = FlightGlobals.getAtmDensity(dAtmosphericPressure);

dExternalTemperature = vessel.flightIntegrator.getExternalTemperature();

Density is 1.2 x e ^(alt/-5000)

Pressure is 1.0 x e ^(alt/-5000)

The complicating factor is that the aerodynamic drag model in the game doesn\'t use \'q\' in the normal way. The game\'s drag equation has an extraneous mass term and there also seems to be an extra density scaling factor of 0.0008 that gets applied to the density equation I\'ve quoted above. Check out the Mini Challenge: Max Altitude with this supplied spacecraft challenge and the Kerbal Science: The atmosphere of Kerbin thread for details.

People like Closette, Kosmo-not and The_Duck seem to be the authorities on this.

[closette]

The drag force on each part of your craft is given by F_Drag = ¹/₂maximum_drag x mass x density x speed²

where the density as a function of height in this equation is given by 1.223125 x 0.008 x Exp[-height/5000 meters], as described by PakledHostage above.

and the total drag is just the sum of the drag forces on all parts.

For the Goddard challenge rocket flown at close to optimal ascent speed, by modeling the forces I found that 'max Q' occurred during the initial ascent phase at only ~ 250 m altitude, and decreased slowly from there. That would be approximately true for any rocket ascending vertically at a fuel optimal speed.

Model flight profile and .craft file attached if you are interested, and I have reposted a graph of drag and velocity vs. altitude for the close-to-optimal ascent profile and unpowered fall back to Kerbin.

Please take a look at the ascent profile, which would be similar in shape for most spacecraft up to 18km. After the initial boost at 100% throttle, the combined effects of (1) decreasing mass and (2) especially the rapidly decreasing density with altitude, more than compensate for the increasing velocity-squared term in the drag equation, so that the total drag force decreases smoothly all the way to MECO.

On the fall back down to Kerbin\'s surface (here from 34500 m, but similar for re-entry from orbit) most of us have seen the rapid deceleration that occurs around 8-10 km altitude due to the exponentially thickening atmosphere.