Parachutes - how do they work?

[Free Trader Beowulf]

Hi,

So, I'm trying to create a spreadsheet to calculate terminal velocity for pods and stuff coming in to land using just parachutes.

My calculations aren't working and I need some help from anyone who knows this stuff.

I'm starting with the drag equation:

F{D}=0.5 ÃÂ v^2 C A

Assuming drag equals the force from gravity and rearranging appropriately, I get:

V{term} = sqrt( 2 M g / ÃÂ C A)

where

V{term} is terminal velocity

M is vehicle mass in kg

g is local gravity

ÃÂ is local air density

C is surface area

A is drag coefficient

The drag of a given craft is potentially quite complex, given tip, surface and tail drag and small motions of the craft changing their relationship.

However, I'm only really interested in touchdown speed, with parachutes fully deployed. So I assume the only relevant drag is from the chutes and I further assume that it's all tip drag, in KSP terms.

So, to get that I've looked at the drag cubes for the parachutes and taken the fourth triplet, which is the drag data for the Y- axis.

My assumptions should mean any errors are in the direction that would make my calculations of terminal velocity too high, as I'm ignoring some sources of drag.

But I can live with that, I want to know if a given payload can be safely parachuted to the ground with a given set of parachutes.

So, I take a simple case, a Mk 1-2 pod is 4.12 tons, and a mk-16xl parachute is .3 tons. From the drag cube I get a fully deployed area of 114.9 m^2 and a drag coefficient of 11.6.

g is 9.81 m/s^2 and air density is 1.22 kg/m^3 I calculate:

V{term} = sqrt( 2 * 4.42 * 1000 * 9.81 / 1.22 * 114.9 * 11.6 )

V{term} = sqrt ( 86720.4 / 1626.0648 )

V{term} = sqrt ( 53.331453 )

V{term} = 7.303 m/s to three decimal places

However, when I actually launch a capsule like that on an SRB and let it parachute back down to Kerbin, the terminal velocity never drops below 8 m/s.

It never stabilises entirely, but it's in the region of 8.5 m/s. It's definitely higher than my prediction.

I've tried a couple of different tests and my calculations are never accurate. Oddly the mk1 pod I tested under a small parachute fell more slowly than I predicted, I guess its drag isn't negligible when compared to a small parachute.

but the Mk1-2 tests always touch down at a higher velocity than I predict.

Not a big deal on Kerbin, where I can test things, but a big problem for my Duna and Laythe missions, potentially. If I get an error of 1 or 2 m/s for Kerbin, I might get a much higher error for descents in Duna's thinner atmosphere.

So, er, anyone know what I've missed?

Thanks

Edited August 13, 2015 by Free Trader Beowulf

[rofltehcat]

How do you get the data using the "drag cube"? Maybe take a look in the .cfg files of the parts. They have many different drag modifiers but I don't really know how to use them in calculations.

mk16 XL:

stowedDrag = 0.22

semiDeployedDrag = 1

fullyDeployedDrag = 500

...

name = ModuleDragModifier

dragCubeName = DEPLOYED

dragModifier = 25

[Free Trader Beowulf]

How do you get the data using the "drag cube"? Maybe take a look in the .cfg files of the parts. They have many different drag modifiers but I don't really know how to use them in calculations.

mk16 XL:

stowedDrag = 0.22

semiDeployedDrag = 1

fullyDeployedDrag = 500

...

name = ModuleDragModifier

dragCubeName = DEPLOYED

dragModifier = 25

The drag cube data is in physics.cfg - they look like this:

PART

{

url = Squad/Parts/Utility/parachuteMk16-XL/parachuteMk16-XL/parachuteLarge

DRAG_CUBE

{

cube = PACKED,

0.6278962,0.6383756,0.7139156,

0.6278962,0.6383814,0.7139156,

1.108058,0.7323978,0.6995487,

1.108058,0.9454046,0.1663975,

0.6278962,0.639505,0.7139157,

0.6278962,0.6373008,0.7139157,

0,0.2645478,0,

1.233453,0.6659461,1.233453

cube = SEMIDEPLOYED,

16.39305,0.5255063,1.822568,

16.39305,0.5255054,1.822568,

9.336478,0.1339835,18.06131,

9.336478,0.1646374,18.50363,

16.39305,0.5256646,1.822569,

16.39305,0.5253168,1.822569,

0,9.230829,-1.072884E-06,

3.459486,18.59851,3.459489

cube = DEPLOYED,

53.47527,18.69657,6.152891,

53.47527,18.69662,6.152891,

114.9405,12.06728,18.4375,

114.9405,11.60791,18.7325,

53.47527,18.71372,6.152892,

53.47527,18.67829,6.152892,

0,9.2347,-9.536743E-07,

12.15423,18.60625,12.15423

}

}

Buried in all that is the data I quoted. Piecing it together from previous discussions of aerodynamics, it seems the drag cube consists of six sets of three values, plus some other stuff. One set is for each face, with the three values being area, drag coefficient and "depth".

I just can't quite close the loop to turn that into an accurate prediction of terminal velocity.

It also seems that the drag cubes are generated automatically by KSP.

I think the values you've listed are left over from previous versions of KSP, certainly I used to use them and they used to work well, but I don't think they are current anymore.

[FancyMouse]

My guess is, the pod below the chute may occlude some area of the chute, causing your drag to be overestimated (hence a higher terminal velocity than expected). Can you try to make the chute farther from the pod bottom (like pod-girder-chute) and does that make the number closer to your computation?

[Free Trader Beowulf]

My guess is, the pod below the chute may occlude some area of the chute, causing your drag to be overestimated (hence a higher terminal velocity than expected). Can you try to make the chute farther from the pod bottom (like pod-girder-chute) and does that make the number closer to your computation?

I did some more science and it looks like your guess is right.

I launched a 3 man pod with two radial parachutes and two girders sticking out on either side.

If the parachutes were on the ends of the girders, it fell at the predicted 7.7 m/s. In that position they were clear of each other and only partially overlapped the pod.

If they were on the pod terminal velocity was 9 m/s.

So the pod is occluding the parachutes, and they might be occluding each other.

So my calculation isn't too far wrong - I could even calculate the correct value for a simple pod under a single parachute, maybe, as I know the drag cubes for the pods.

But even without doing that, I know that I need to spread parachutes out, try to mount them where they won't be occluded by their payload and my predictions shouldn't be too far off.

Nice one, FancyMouse.