Kerbin Scale Height

[Aliplayer1]

Hello everyone, I was looking for data on the atmospheric pressure of Kerbin in different altitudes when I saw the formula for atmospheric pressure on Wikipedia.

The constant H is called the Scale Height and its value for Kerbin according to this  Web Page is 5600m. Now the problem here is that after using stock barometer, logging the data using kOS and calculating the scale height I found out that the scale at 0m is around 3900 and as the altitude rises the values converge towards 5600m but never reach the number.

This is really confusing and I would really appreciate it if someone could help me, Thanks. 

 

[Snark]

Hello!  Moving your post to Gameplay Questions, since it's about KSP rather than IRL science and spaceflight.

1 hour ago, Aliplayer1 said:

Hello everyone, I was looking for data on the atmospheric pressure of Kerbin in different altitudes when I saw the formula for atmospheric pressure on Wikipedia.

That is, indeed, the simple formula for pressure as a function of altitude-- but it makes the simplifying assumption that temperature and composition don't vary with altitude.

1 hour ago, Aliplayer1 said:

Now the problem here is that after using stock barometer, logging the data using kOS and calculating the scale height I found out that the scale at 0m is around 3900 and as the altitude rises the values converge towards 5600m but never reach the number.

This is really confusing and I would really appreciate it if someone could help me, Thanks. 

It used to be that KSP had a pretty simple atmospheric model that directly followed that formula.  However, quite a few versions ago, they shifted to a more complex, realistic model in which the profile of Kerbin's atmosphere with altitude more closely models the actual atmosphere of Earth.

Therefore, although this formula still works okay as a rough approximation... it won't give exact figures for Kerbin anymore.  I suspect that this may be what you're running into.

You can find more details here:

https://wiki.kerbalspaceprogram.com/wiki/Kerbin#Atmosphere

In particular, note this:

Quote

Like all other atmospheres in the game, Kerbin's atmosphere fades exponentially as altitude increases. The scale height varies with altitude, which is a change from pre-1.0 versions of the game.

 

[OHara]

4 hours ago, Aliplayer1 said:

logging the data using kOS and calculating the scale height I found out that the scale at 0m is around 3900 and as the altitude rises the values converge towards 5600m but never reach the number.

Could you give us an example of your numbers?  What Snark says about scale height varying is true, but I did not think it would vary that much.  

For example, suppose
 p_70 = 100 kPa on the runway at 70 m above sea level
 p_770 = 90 kPa flying at 770 m above sea level

I don't know exactly the value of p₀ in the formula, but I can divide it out
     90 kPa  = p₀ exp[−770/H]
   100kPa = p₀ exp[−70/H]   

0.9 = exp[−700/H]
H = −700m ÷ log(0.9)  = 6600 m

[Guest]

Firstly the wiki pages are a mixed bag reliability wise. Some are fine but some are outdated I find.

Now, as I read it, the scale height (H)  ~ 5600m is a marker with value of 2.718. So if you have a pressure at sea level (let's say 100pa), if you go up to 5600m, then the pressure should be (100 / 2.718 =) 37pa. Go up another 5600m (to 11200m) and it should be (37 / 2.718 =) 13.5pa and so on. 

Now the issue with this is, although we're told the pressure decreases 2.718 times every 5600, we’re not told how that 2.718 is distributed over the 5600. It may be proportional (~ 0.005 per meter) (straight line on a graph) or may not (curved line ie ratio changes). However, given they state a fixed amount it decreases at a fixed altitude, there's a good chance it is proportional as you wouldn't have variable pressure changes over such a small period or the player would notice. Finally with that said, the pressure fall off may be non-linear near the surface (by design for balance or to reflect air density etc) hence your calculations showing 3900 instead of 5600 initially even though the wiki doesn't mention that.

tl:dr = basically what Snark said as ive just realised but in an unnecessarily longer fashion