Speed and altitude at first stage separation of Falcon 9 and Heavy

[Heresy42]

Hello everyone,

Does anyone know the speed and altitude at which the first stage of Falcon 9 separates? What would they be for the two outer cores of Falcon Heavy?

All I've found online is:
1/ Mach 10 for the first stage of Falcon 9 (cf. http://forums.randi.org/archive/index.php/t-261780.html)
2/ 50 miles for the first stage of Falcon 9 (cf. http://www.nytimes.com/2013/08/15/science/space/latest-spacex-rocket-test-successfully-goes-sideways.html?_r=0)

I was looking for "better" references. SpaceX itself doesn't seem to mention it.

Thank you in advance.

[aero]

Sometimes the SpaceX live video shows the speed and altitude on the screen during launch and hence on the recorded video. I picked 100.2 km and 7400 km/hr (2055.6 m/s) off the screen at staging for the Cassiope launch. But I think the launches  may all be a little different. Keep your cursor on the pause button as you view the video so you will have time to write the numbers down.

Have to wait for a launch to use that method for the heavy.

[Lar]

Some believe those numbers are not accurate, that they lag... and not necessarily in predictable ways. So this method is believed to be able to give rough numbers but not really precise/accurate ones..

[aero]

Some believe those numbers are not accurate, that they lag... and not necessarily in predictable ways. So this method is believed to be able to give rough numbers but not really precise/accurate ones..

Not precisely accurate but the attached graph shows what it looks like. At that scale it could be off by quite a bit but I speculate there is one or two digits of precision.

[Lar]

Unless SpaceX is deliberately cooking the numbers to hide capabilities (or, as Lurker Steve might suggest, because they're faking it and aren't any good) one digit seems achievable but 2 is iffy. But for what OP wants, 1 digit should be fine.

[Llian Rhydderch]

Hello everyone,

Does anyone know the speed and altitude at which the first stage of Falcon 9 separates? What would they be for the two outer cores of Falcon Heavy?

All I've found online is:
1/ Mach 10 for the first stage of Falcon 9 (cf. http://forums.randi.org/archive/index.php/t-261780.html)
2/ 50 miles for the first stage of Falcon 9 (cf. http://www.nytimes.com/2013/08/15/science/space/latest-spacex-rocket-test-successfully-goes-sideways.html?_r=0)

I was looking for "better" references. SpaceX itself doesn't seem to mention it.

Thank you in advance.

There was an early discussion of the velocities (but not the altitudes, I believe) in a Popular Mechanics article by Rand Simberg (and he is technically trained in Aerospace Engineering).  The recent media package for the CRS-3 mission had specific velocity and altitude for this upcoming Falcon 9 v1.1 flight.  Both sources can be found in the Wikipedia article on the SpaceX reusable technology program.

I know that is not everything you wanted to know, but it is some of it.

[Heresy42]

Thank you aero, Lar and Llian Rhydderch for your quick and pertinent replies.

Taking the values of the speed and altitude from the recorded video of a launch is smart and one digit of precision is fine for my application.

According to the Popular Mechanics article by Rand Simberg (http://www.popularmechanics.com/science/space/rockets/elon-musk-on-spacexs-reusable-rocket-plans-6653023):

The key, at least for the first stage, is the difference in speed. "It really comes down to what the staging Mach number would be," Musk says, referencing the speed the rocket would be traveling at separation. "For an expendable Falcon 9 rocket, that is around Mach 10. For a reusable Falcon 9, it is around Mach 6, depending on the mission.

According to the media package for the CRS-3 mission:

Approximately 161 seconds into flight, the first-stage engines are shut down, an event known as main-engine cutoff, or MECO. At this point, Falcon 9 is 80 kilometers (50 miles) high, traveling at 10 times the speed of sound. Three seconds after MECO, the first and second stages will separate.

Values are fairly consistent.

[Jcc]

I was under the impression that stage separation for the F9R will be at Mach 6 to reduce the boost back requirement. The CRS-3 press kit says staging will be at Mach 10, although in is case there will not be boost back, just a braking burn.

Evidently, they develop the flight plan to suit the mission, and there is flexibility as to the staging velocity. Part of the trade off may involve a more lofted trajectory, which adds gravity loss, but by staging at a lower down range velocity it reduces fuel needed for boost back.

[Heresy42]

Thanks for your reply, Jcc. That makes sense.

[Roy_H]

This was discussed at great length some time ago in the "First stage recovery at down-range locations"

According to MODEMEAGLE with his charts: http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=29214.0;attach=489078
If I read the charts correctly, the last chart in the second last group shows the core FH stage crossfeed to landing at something just over 1600km, which puts it in the Florida Keys from Brownsville, TX.

[MP99]

I was under the impression that stage separation for the F9R will be at Mach 6 to reduce the boost back requirement. The CRS-3 press kit says staging will be at Mach 10, although in is case there will not be boost back, just a braking burn.

Evidently, they develop the flight plan to suit the mission, and there is flexibility as to the staging velocity. Part of the trade off may involve a more lofted trajectory, which adds gravity loss, but by staging at a lower down range velocity it reduces fuel needed for boost back.

I don't think any lofting of the trajectory is relevant. An expendable launch could still do ~M10, if it happened to fly the same lofted trajectory.

More likely, since prop is not reserved for boost-back, more is available pre-MECO.

BTW, I believe that a GTO launch may stage a little faster than a LEO one, since mass will be a little lower at MECO.

Cheers, Martin

[Heresy42]

Thanks Roy_H and MP99 for your replies. This is good to know.

[Jcc]

I was under the impression that stage separation for the F9R will be at Mach 6 to reduce the boost back requirement. The CRS-3 press kit says staging will be at Mach 10, although in is case there will not be boost back, just a braking burn.

Evidently, they develop the flight plan to suit the mission, and there is flexibility as to the staging velocity. Part of the trade off may involve a more lofted trajectory, which adds gravity loss, but by staging at a lower down range velocity it reduces fuel needed for boost back.

I don't think any lofting of the trajectory is relevant. An expendable launch could still do ~M10, if it happened to fly the same lofted trajectory.

More likely, since prop is not reserved for boost-back, more is available pre-MECO.

BTW, I believe that a GTO launch may stage a little faster than a LEO one, since mass will be a little lower at MECO.

Cheers, Martin

This doesn't make any sense to me, perhaps you can explain further. 

Yes an expendable launch could do M10, that's the point. Reusable launches will perhaps have lower down range velocities at staging, first because they have reserved more fuel, and second because they put more energy in the vertical direction, gaining more potential energy and less kinetic energy. So less energy needed to reverse horizontal velocity to boost back.

[MP99]

I was under the impression that stage separation for the F9R will be at Mach 6 to reduce the boost back requirement. The CRS-3 press kit says staging will be at Mach 10, although in is case there will not be boost back, just a braking burn.

Evidently, they develop the flight plan to suit the mission, and there is flexibility as to the staging velocity. Part of the trade off may involve a more lofted trajectory, which adds gravity loss, but by staging at a lower down range velocity it reduces fuel needed for boost back.

I don't think any lofting of the trajectory is relevant. An expendable launch could still do ~M10, if it happened to fly the same lofted trajectory.

More likely, since prop is not reserved for boost-back, more is available pre-MECO.

BTW, I believe that a GTO launch may stage a little faster than a LEO one, since mass will be a little lower at MECO.

Cheers, Martin

This doesn't make any sense to me, perhaps you can explain further. 

Yes an expendable launch could do M10, that's the point. Reusable launches will perhaps have lower down range velocities at staging, first because they have reserved more fuel, and second because they put more energy in the vertical direction, gaining more potential energy and less kinetic energy. So less energy needed to reverse horizontal velocity to boost back.

I think the confusion is in the phrase "down range velocities".

I believe M10 is it's inertial speed. Some component of this will be vertical, and some will be "down range", IE horizontal.

My point is regardless of whether the speed is M10 in a depressed or lofted trajectory, horizontal component of velocity will be lower for a lofted trajectory.

Cheers, Martin

[groundbound]

My point is regardless of whether the speed is M10 in a depressed or lofted trajectory, horizontal component of velocity will be lower for a lofted trajectory.

Cheers, Martin

In addition, a larger vertical component allows for a longer and higher boostback arc and so reduces the need for return velocity.

[Hop_David]

I was under the impression that stage separation for the F9R will be at Mach 6 to reduce the boost back requirement. The CRS-3 press kit says staging will be at Mach 10, although in is case there will not be boost back, just a braking burn.

Evidently, they develop the flight plan to suit the mission, and there is flexibility as to the staging velocity. Part of the trade off may involve a more lofted trajectory, which adds gravity loss, but by staging at a lower down range velocity it reduces fuel needed for boost back.

I don't think any lofting of the trajectory is relevant. An expendable launch could still do ~M10, if it happened to fly the same lofted trajectory.

I don't think this is true.

A vertical path is more expensive for two reasons.

As you acquire horizontal velocity, gaining altitude takes less delta V due to an Oberth benefit. If we were traveling in a 7.9 km/s circular orbit just above earth's surface, it would only take .03 km/s to raise apogee 100 km. If we were standing still, it'd take about 1.4 km/s to reach a 100 km altitude. This is assuming an instantaneous burn. A real world vertical burn would suffer an additional gravity loss of 9.8 m/s^2 for each second of burn.

There is also a savings from doing a single diagonal burn rather than separate vertical and horizontal burns. Here's a picture:

In the above example, there's a 1.3 km/s penalty for doing two separate burns.

So due to the Oberth benefit and triangle inequality, there is strong motivation to start leaning eastward as soon as possible to give the burn a horizontal component.

[CuddlyRocket]

So due to the Oberth benefit and triangle inequality, there is strong motivation to start leaning eastward as soon as possible to give the burn a horizontal component.

If you're RTLS doesn't the Oberth benefit start cancelling out after you reverse direction?

[MP99]

I was under the impression that stage separation for the F9R will be at Mach 6 to reduce the boost back requirement. The CRS-3 press kit says staging will be at Mach 10, although in is case there will not be boost back, just a braking burn.

Evidently, they develop the flight plan to suit the mission, and there is flexibility as to the staging velocity. Part of the trade off may involve a more lofted trajectory, which adds gravity loss, but by staging at a lower down range velocity it reduces fuel needed for boost back.

I don't think any lofting of the trajectory is relevant. An expendable launch could still do ~M10, if it happened to fly the same lofted trajectory.

I don't think this is true.

A vertical path is more expensive for two reasons.

<snipped>

I understand why it's not optimal, but nevertheless if the *first stage* uses all its dV in expendable mode, it will be doing something close to Mach 10 at MECO, regardless of which direction its velocity vector is pointing. (Gravity losses will cut it back somewhat if it does your direct vertical ascent, but that's not really relevant.)

I wasn't suggesting this is a trajectory you would fly on an expendable launch, merely pointing out the M10 number is irrelevant to discussions of lofted trajectories for RTLS flights.

cheers, Martin

[cambrianera]

Falcon9 v1.0 and v1.1 have different balance between first stage DV and second stage DV.
V1.1 first stage grew about 50-60% in mass, while second stage doubled.
This result in reduced staging velocity.
Hop_David, lofting of trajectory must take into account atmosphere; when you are in lower layers (less than 40 km) you can't raise your speed without drag losses, hence a lofted trajectory until this height can be balanced against gravity losses: after that, your observations are 100% on spot.

[Hop_David]

So due to the Oberth benefit and triangle inequality, there is strong motivation to start leaning eastward as soon as possible to give the burn a horizontal component.

If you're RTLS doesn't the Oberth benefit start cancelling out after you reverse direction?

RTLS = Return To Launch Site? Reversing direction?

I wasn't comparing vertical RTLS to horizontal boost back RTLS.

I was looking at vertical lofting RTLS vs the more typical path taken by expendables.

In another forum I was told vertical reuse would result in a 15% hit on payload. And that horizontal boost back reuse would result in a 30% hit on payload. It was that engineer's opinion that 8 reuses would be needed to cut launch costs in half.

Is this correct? I don't know. It wasn't worth that fellow's time to provide cites or the details of his math.

5 quantities I'm hoping to learn are:
Booster mass at lift off.
Booster mass at MECO
Booster velocity at MECO (including direction, horizontal and vertical components)
Booster altitude at MECO.
Booster distance from launch pad at MECO.

I imagine all 5 of these quantities would vary from scenario to scenario.

----

In addition to vertical lofting RTLS and horizontal boostback RTLS there is also the possibility of landing on a platform downrange. This was discussed in the comments of a Parabolic Arc thread. In my opinion the most persuasive commenter was Hug Doug.

A Sea Launch type platform downrange would add to the expense.