Parachute guidelines

[ThePsuedoMonkey]

Edit: check the second post for current info. Initial post left as is for posterity. Also, finally fixed the typo in the title!

Based on some experimentation, I've created some ball-park estimates of touchdown speed vs the mass fraction of parachutes equipped on a given lander. (using version 0.20)

-redacted-

I say "ball-park" since these experiments were all at Kerbin sea level, and extrapolated via the barometric pressure of the other planets given in the wiki, and does not factor in the differences in gravity. All test flights were taken to a 100km apoapsis (+/- 1km) and uncontrolled until touchdown. Not shown is the difference between standard and drogue 'chutes (though it is comparable to the difference between the Kerbin and Duna curves). Please point out any errors that you find. (kerbin data sample)

Edited August 13, 2013 by ThePsuedoMonkey

[ThePsuedoMonkey]

I had a bit more time today, so I've double-checked the data and corrected for the differences in gravity. Remember that drogue 'chutes are about 1/3 as effective as the other parachutes per unit mass. Note that the x-axis is logarithmic and spans from 1% to 100%.

-snip-

Sea-level and projections for other elevations (gravity and pressure), so those assume enough time in atmosphere to slow your lander down. I had to split it into two graphs in order to keep the finer detail though:

Edited August 5, 2013 by ThePsuedoMonkey
Condensed into one graph, higher peak elevation

[Specialist290]

Quite nice This looks like another one for the Drawing Board.

[Tokay Gris]

Hm... "Mass fraction" of parachutes would be the mass of the parachutes divided by the mass of the vessel?

So, If my vessel weights 90 tons, I'd need 18 tons of parachutes to land on Duna? That would be like 180 MK-16...or 60 MK-16-XL.

Or the same for Kerbin, I'd need 3,6 tons of parachute, equalling 36 MK-16 or 12 MK-16-XL...

I have 7 MK-16-XL and 16 MK-25 parachutes on my Lander. Not quite sure about its mass at the moment (am on nightshift, can't look, but it was around 90 on the launchpad).

Not enough for Kerbin, I did need engines to assist.

Oh, well. There goes the idea of an all-parachute landing on Duna....

[Tokay Gris]

Oh, and I forgot!

Thanks a lot for your work! I've been looking for that kind of data for AGES now.

[ThePsuedoMonkey]

No problem I've seen the equation float around sometimes, but I think it's easier to look at a graph.

And yes, the mass fraction is referring to (mass of parachutes)/(payload mass plus parachutes). If you don't have any parachutes on a lander, you'd divide its mass by [one minus the mass fraction on the chart] to find the mass of parachutes to add. (e.g. a 90T lander would need an additional ~13T of parachutes to land at 6 m/s near Kerbin sea level) I'll try and include elevation at some point as well, but I think that might get messy.

[jgkamat]

Oh, well. There goes the idea of an all-parachute landing on Duna....

I think thats the point of duna. Thats why curiosity/spirit/opportunity/ect couldn't use only parachutes.

[firerider521]

I've seriously needed data like this ever since I considered landing on Duna in the first place. I wanted to number crunch but I didn't know how.

Thank you so much.

[Tokay Gris]

I think thats the point of duna. Thats why curiosity/spirit/opportunity/ect couldn't use only parachutes.

I am not quite sure gravity doesn't play a role in this.

Landing velocity with a given mass and given number or parachutes (or fraction of parachute mass) must surely differ depending on gravity.

I will try that once my lander gets to Duna and see what happens if I reduce the number of parachutes....

Or maybe I have a misunderstanding here....

[Daze]

Amazing work!

[ThePsuedoMonkey]

It's been a while and 0.21 updated the terrain, so I've made another plot that condenses the info from the other two (only shows sea-level and one very high altitude for each body) with a higher peak elevation. Double-posting the plot here in case this post gets put on page 2.

[Crown]

Would you share your equations for these graphs?

One thing, I think, that is amazing about KSP is that most of the things can be reproduced by using maths.

But the parachute thing is bugging me a bit.

From Wikipedia we get the equation for Terminal velocity:

.

Then we combine air density and atmospheric pressure:

; ; R_specific is the specific gas constant and T absolute temperature

But how does the "drag" value from the part file (for deployed parachutes 500) come into this equation? Is it just the C_D value?

And I am missing a value for the area. What values did you use for these two?

[Cartz]

Would you share your equations for these graphs?

One thing, I think, that is amazing about KSP is that most of the things can be reproduced by using maths.

But the parachute thing is bugging me a bit.

From Wikipedia we get the equation for Terminal velocity:

.

Then we combine air density and atmospheric pressure:

; ; R_specific is the specific gas constant and T absolute temperature

But how does the "drag" value from the part file (for deployed parachutes 500) come into this equation? Is it just the C_D value?

And I am missing a value for the area. What values did you use for these two?

I refer you here sir to the KSP wiki. Specifically:

In the game, the force of atmospheric drag (F_D) is modeled as follows:^[1]

Where ÃÂ is the atmospheric density (kg/m³), v is the ship's velocity (m/s), m is the ship's mass (kg), d is the coefficient of drag (dimensionless), and A is the cross-sectional area (m²).

Note that the cross-sectional area is not actually calculated in the game. It is instead assumed that it is directly proportional to the mass (1m³/kg). Use the ship's mass (kg) in the formula.

...

As an example, the coefficient of drag for a craft consisting simply of a Mk1-2 Command Pod (mass 4, drag 0.2) and a deployed Mk16-XL Parachute (mass 0.3, drag 500) is:

So in the case of 10^-1 (i.e. 10% of craft by mass is parachutes) of a 10 (or 20, or 200, or 2 million) ton vessel:

(0.9x * 0.2) + (0.1x * 500) / x = Cd

(0.9(10) * 0.2) + (0.1(10) * 500) / x(10) = Cd

50.18 = Cd

[ThePsuedoMonkey]

No problem! The info I used is from the wiki page on atmosphere, but I'll summarize it here:

Unfortunately, we can't really use that equation for terminal velocity, since it ignores the reduction in gravity with increasing distance from the planet, and the cross-sectional area of rockets aren't calculated in stock KSP yet. So KSP needs a slightly different model; the drag equation is as normal but since the cross-section isn't calculated, rather it is assumed to be directly proportional to mass. Next, the drag coefficient becomes the weighted mean of everything on the ship (i.e the sum of {each parts mass times its own drag}, divided by total mass). The air density is still proportional to pressure via your equation, which simplifies to in the Kerbal universe. The pressure still scales as the exponent you gave (for p_k), but note that the scale height is only 5km for the planet Kerbin.

Now we can proceed as normal and set that equal to the gravitation force in order to find the general expression for terminal velocity: . There is supposed to be an "m" in the numerator so that it cancels with the "area", but I am just linking to the equations from the wiki (the author ignored it since it cancels out in the end).

Edit: Cartz beat me to it. (does it count as a ninja if I take forever to write things? )

Edited August 13, 2013 by ThePsuedoMonkey

[Savvy]

Thank you for these charts! Just wondering, what soft did you use to make the graphs ?

[Laie]

That looks like gnuplot -- a piece of software with a long history and a command-line interface. It is very powerful and versatile, but you'll probably spend quite some time browsing the docs before you get anything done. Whether that's worth it is up to you (though IMO, if you want to graph functions or data more often than twice I year, I think you should give it a try).

[Savvy]

That looks like gnuplot -- a piece of software with a long history and a command-line interface. It is very powerful and versatile, but you'll probably spend quite some time browsing the docs before you get anything done. Whether that's worth it is up to you (though IMO, if you want to graph functions or data more often than twice I year, I think you should give it a try).

Actually I'm pretty sure it's Matlab, but thanks for your help I'll sure give it a try!