SpaceX Falcon 9/Dragon COTS Demo (C2+) GENERAL DISCUSSION

[jabe]

What's the best approach to calculating the delta-v per second consumed by Dragon as it holds position a fixed distance below the station on the r-bar?

Clohessy-Wiltshire equations. If using the NASA LVLH frame (Rbar = z axis), take the z equation, set x-dot to zero, and solve for z-double-dot as a function of z:

z-double-dot = 3*n^2*z

where n is the mean motion (orbital rate), about 0.0011 rad/sec for ISS orbit.

Note that for most spacecraft, including Dragon, the same delta-v in different axes may result in different propellant consumption due to the different canting of RCS thrusters.

I was thinking of the same question. anda FABULOUS answer... A quick question, I'm assuming x the distance to the station?
jb

[Jorge]

What's the best approach to calculating the delta-v per second consumed by Dragon as it holds position a fixed distance below the station on the r-bar?

Clohessy-Wiltshire equations. If using the NASA LVLH frame (Rbar = z axis), take the z equation, set x-dot to zero, and solve for z-double-dot as a function of z:

z-double-dot = 3*n^2*z

where n is the mean motion (orbital rate), about 0.0011 rad/sec for ISS orbit.

Note that for most spacecraft, including Dragon, the same delta-v in different axes may result in different propellant consumption due to the different canting of RCS thrusters.

I was thinking of the same question. anda FABULOUS answer... A quick question, I'm assuming x the distance to the station?
jb

Not in the frame I'm using (NASA LVLH frame). This frame is described as follows:

Origin - center of mass of target (ISS)
+z - points toward center of Earth (+Rbar)
+y - points out-of-plane "starboard", opposite the angular momentum vector (-Hbar)
+x - completes a right-handed system, points in the direction of the velocity vector (+Vbar)

And of course, dot means velocity and double-dot means acceleration.

[jabe]

Not in the frame I'm using (NASA LVLH frame). This frame is described as follows:

Origin - center of mass of target (ISS)
+z - points toward center of Earth (+Rbar)
+y - points out-of-plane "starboard", opposite the angular momentum vector (-Hbar)
+x - completes a right-handed system, points in the direction of the velocity vector (+Vbar)

And of course, dot means velocity and double-dot means acceleration.

Thx for clarification..have to do some reading now..the dot part was the only part I was sure about
jb

[sdsds]

OK. So if I get this right, when Dragon is momentarily motionless in this ISS-centered frame, and is in a co-planar orbit directly below ISS, z is positive and thus z-double-dot is positive and thus if the Dragon were in free drift it would accelerate down towards the Earth? That makes sense since its angular velocity is matching that of ISS in its higher (slower) orbit. So Dragon at that moment is at the apogee of an elliptical orbit.

To hold in the ISS frame Dragon will thus thrust directly upwards towards ISS. And if Dragon thrusters could provide exactly the right amount of thrust the vehicle could hold its position without thrusting at all along the x (Vbar) axis? So that's the ideal (minimum) amount of thrust required. And it grows only linearly with z?

But looking at the CW equation for x (which I think is x-double-dot = -2*n*z-dot), if any net acceleration along the Rbar is experienced, then z-dot becomes non-zero and there is acceleration along the Vbar. And things get really whacky, and Dragon better have a darn good control system deciding which way to thrust to get back to the hold point, or it could consume plenty of propellant in the process!

[oiorionsbelt]

Darn it Jorge, first nice day in Seattle in goodness knows how long and you've got sdsds and me doing math

[Jkew]

Darn it Jorge, first nice day in Seattle in goodness knows how long and you've got sdsds and me doing math

Make that three people in Seattle doing math on the first nice day

Thanks Jorge, this has introduced me to something new.

[Norm38]

What's the reason that the station rotates anyway?  Why not stay fixed to the sun so the arrays don't have to track.  Docking is harder.  And doesn't the acceleration mess with experiments? 
What's the benefit?

[Halidon]

Oh come on, "first" nice day is a little exaggeration. 

[Robotbeat]

Oh come on, "first" nice day is a little exaggeration. 

"Whereabouts unknown"?

Remember, there are also Earth-facing instruments on board. Plus ground-facing antenna, etc. However, neglecting coriolis forces, there still ought to be a zero-gravity point somewhere on the station (where the "artificial gravity" of spinning slowly cancels out the fact that not all points on the station are at the center-of-gravity (or equivalent).

[docmordrid]

Long Florida Today story -

http://www.floridatoday.com/article/20120422/SPACE/304220028/SpaceX-grows-up-ISS-test-key-next-step

[Jim]

What's the reason that the station rotates anyway?  Why not stay fixed to the sun so the arrays don't have to track.  Docking is harder.  And doesn't the acceleration mess with experiments? 
What's the benefit?

attitude control is easier. 

[sdsds]

One wonders exactly what ULA public relations means by the rhetorical question in a recent tweet:

Who's ready for a launch? Looking forward to an early May launch of the AEHF-2 mission.

http://bit.ly/JOgkJf

Who's ready for a launch? We are! ;-)

[oiorionsbelt]

yes I noticed that too 

[oiorionsbelt]

BTW that tweet from ULA and Chris's L2, COTS 2+ launch slip came within minutes of each other.
Same/similar source/friends?

[mr. mark]

Maybe ULA's comment should read, who's going to the ISS in the next few weeks...not us.

The knives are out for SpaceX...Cesar had it better.

[Chris Bergin]

BTW that tweet from ULA and Chris's L2, COTS 2+ launch slip came within minutes of each other.
Same/similar source/friends?

No, we were working it in L2 well before. Once it got past a single source (rules of journalism, never run with a single source unless it's someone like Elon talking about his own launch) I went on the public side and Twitter with caution. Then it was started to look nailed on, with multiple sources, noted it and then Elon tweeted, followed by SpaceX.

[Galactic Penguin SST]

To lighten up our moods, here's me hoping that the launch will eventually come between May 15 and May 17 - that would make Chris et al. mad with at least 6 launches inside 72 hours!
(there's already Soyuz TMA-04M + Ariane 5 VA206 + H-IIA F21 + Proton-M/Nimiq 6 + 1 military Soyuz launch during these 3 days, not to mention 2 Chinese launches are expected in the May timeframe)

[Jim]

Maybe ULA's comment should read, who's going to the ISS in the next few weeks...not us.

The knives are out for SpaceX...Cesar had it better.

The ULA comment are justified. 

ISS is not the destination of choice for most spacecraft.  Conversely, Spacex is not going to GTO anytime soon either.  Or Mars, or Jupiter, or HEO, or Moon, etc

As far as Spacex is concerned, people in glass houses shouldn't throw stones.

[Chris Bergin]

To lighten up our moods, here's me hoping that the launch will eventually come between May 15 and May 17 - that would make Chris et al. mad with at least 6 launches inside 72 hours!
(there's already Soyuz TMA-04M + Ariane 5 VA206 + H-IIA F21 + Proton-M/Nimiq 6 + 1 military Soyuz launch during these 3 days, not to mention 2 Chinese launches are expected in the May timeframe)

Holy moly! They better send up some traffic cops ahead of that.

[beancounter]

Maybe ULA's comment should read, who's going to the ISS in the next few weeks...not us.

The knives are out for SpaceX...Cesar had it better.

The ULA comment are justified. 

ISS is not the destination of choice for most spacecraft.  Conversely, Spacex is not going to GTO anytime soon either.  Or Mars, or Jupiter, or HEO, or Moon, etc

As far as Spacex is concerned, people in glass houses shouldn't throw stones.

No it's not.  But it's not unexpected.  This is a test flight, not the CRS therefore delays are to be expected.  SpaceX has demonstrated that they're in the game and they will fly and succeed before too long.  ULA comment is simply driven by fear of an up and coming competitor and looking to make cheap shots.  Anyone who thinks otherwise is fooling themselves. 
SpaceX may have a way to go but they're clearly serious about the business.  They may also be prepared to spruke a bit but so what, IMO they're entitled. 
It never fails to amaze me how ready some in the U.S. Congress and certain posters on this blog are so quick to discount, deride and generally dump on a U.S. company who is trying to make a difference and attempting to grow it's business, bringing revenue and jobs to the U.S.  But that's not confined to the U.S. in any way so maybe not such a surprise.  JM2CW.