Falcon 9 flight trajectory

[pagheca]

Hi,

I would like to understand better which trajectory the Falcon 9 follows during ascent.

During the launch it is evident that the trajectory bend quite soon and become almost tangential. This saves a lot of fuel from gravity drag. The problem is that if you want to RTLS, the additional horizontal component of the velocity must be compensated for, inverted etc. This would cost a lot, really a lot, in terms of fuel. You really need to do an almost vertical launch (at least in the first 100 km) to RTLS. Alternatively, you need much higher exhaust velocity to reach orbital speed at the orbital altitude.

So, I was wondering if someone has a reference or something for the trajectory actually used by Falcon 9 v1.1 before first stage separation in particular before first stage separation. Something relating the altitude with the angle respect to the vertical. By mean of the other published parameters (thrust, weight, etc.) it would then be possible to calculate the complete flight parameters.

Thanks

[Jcc]

Hi,

I would like to understand better which trajectory the Falcon 9 follows during ascent.

During the launch it is evident that the trajectory bend quite soon and become almost tangential. This saves a lot of fuel from gravity drag. The problem is that if you want to RTLS, the additional horizontal component of the velocity must be compensated for, inverted etc. This would cost a lot, really a lot, in terms of fuel. You really need to do an almost vertical launch (at least in the first 100 km) to RTLS. Alternatively, you need much higher exhaust velocity to reach orbital speed at the orbital altitude.

So, I was wondering if someone has a reference or something for the trajectory actually used by Falcon 9 v1.1 before first stage separation in particular before first stage separation. Something relating the altitude with the angle respect to the vertical. By mean of the other published parameters (thrust, weight, etc.) it would then be possible to calculate the complete flight parameters.

Thanks

The fuel requirement to RTLS is greatly reduced due to the fact that the stage has already burned most of its fuel, and separated from the upper stage. But you have a point, there may be a trade off that favors a somewhat more vertical trajectory as a result of needing to return the stage.

[Silmfeanor]

You really need to do an almost vertical launch (at least in the first 100 km) to RTLS.

Not nearly almost vertical - a bit more lofted perhaps, but certainly not anywhere near vertical.

[MP99]

ISTM that the more vertical the first-stage trajectory, the easier the first-stage recovery.

However, ISTM that the intention should be to give the best chance of delivering the payload to orbit, and this ends up with the opposite constraint. For a very light payload, the first stage can afford a *very* flat trajectory, and still have prop left to achieve an RTLS, despite needing a huge boost-back. In the event of a first-stage issue pre-MECO, this will maximise the chance that second stage can achieve the contracted orbit, at expense of the first stage abandoning hope of recovery.

As payload size increases, the overall vehicle has much less margin, and at the limit of reusability ISTM it must fly a more lofted trajectory which both delivers the needed dV from 1st & 2nd stages, while leaving just enough prop to RTLS the first stage.

So, ISTM the requirement to maximise chance of payload-to-orbit implies the same un-lofted trajectory as disposable for very small payloads, with lofting increasing where payloads are prepared to trade a higher mass for a greater chance of failure during second-stage burn.

cheers, Martin

[Avron]

ISTM that the more vertical the first-stage trajectory, the easier the first-stage recovery.

However, ISTM that the intention should be to give the best chance of delivering the payload to orbit, and this ends up with the opposite constraint. For a very light payload, the first stage can afford a *very* flat trajectory, and still have prop left to achieve an RTLS, despite needing a huge boost-back. In the event of a first-stage issue pre-MECO, this will maximise the chance that second stage can achieve the contracted orbit, at expense of the first stage abandoning hope of recovery.

As payload size increases, the overall vehicle has much less margin, and at the limit of reusability ISTM it must fly a more lofted trajectory which both delivers the needed dV from 1st & 2nd stages, while leaving just enough prop to RTLS the first stage.

So, ISTM the requirement to maximise chance of payload-to-orbit implies the same un-lofted trajectory as disposable for very small payloads, with lofting increasing where payloads are prepared to trade a higher mass for a greater chance of failure during second-stage burn.

cheers, Martin

I think you can work out just how vertical. musk mentioned staging at Mach 6 .. I am not sure what the stage velocity was in this last flight for comparison

[pagheca]

Thanks for the answers, but just to clarify:

As many people know Elon recently said that: "If we do an ocean landing (for testing purposes), the performance hit is actually quite small, maybe in the order of 15 percent. If we do a return to launch site landing, it’s probably double that, it’s more like a 30 percent hit (i.e., 30 percent of payload lost).”

Now, I tried (I'm not the first one, I know, I know...) to check both these numbers. The first, 15%, is realistic. I do not say that I got exactly that number because there are too many uncertainties (atmospheric and gravity drag, exhaust speed at various altitude, etc. etc.), but I think you can do that including the control and landing (even if the last part of the flight is not very efficient as the thrust must be reduced), if you can delay the Merlin burn to use as much of atmospheric drag you can without destroying the engines, on powered descent.

However, when you add a not negligible horizontal component of the velocity, whatever you do you have to zero it after staging, and then go back to return to site. This is a 2 x DV_hor, where DV_hor is the horizontal component of the velocity at staging.

If you try for a Falcon 9 v1.1, it just doesn't work. The only possibility is to stage with a very little horizontal velocity component.

But if you reduce the horizontal component until staging, you just don't have enough time to get to orbit with the right DV with the available thrust, because you spend a lot more fuel on both the stages to compensate for the additional gravity drag. Therefore, you cannot reach orbit with the 2nd stage only if you separate at Mach 6.

As any Mr. Nobody on Earth , I trust on Elon Musk, but I got stuck here and can't find a reasonable solution. That's why I would like to find out which trajectory is planning to use. You need a much more powerful 1st stage. But then the number Elon said (30%) doesn't make sense as he referred to the Falcon 9, not to a generic rocket.
a
Cheers,
p

[Roy_H]

Your initial premise is way off the mark. What is important to achieve is orbital velocity, the height requirement is almost incidental. Going to a steeper launch profile is simply a waste of fuel. Yes it would result in less fuel to return to launch site, but at the expense of not achieving orbital velocity and having your satellite crash back to earth. Think about Virgin Galactic's Spaceship 2, it will take 8 people to space (100 km up) with a short 1 minute burn and a rocket so small it only takes up half of the spaceship, but attains zero orbital velocity.

[aero]

You can use the rocket equation and get pretty accurate answers for stage 2 between staging and orbit because there is little to no aerodynamic drag at that altitude and gravity drag is only about 500 m/s between staging and orbit. SpaceX has a better measure of gravity drag from their F-9 flight data, but I don't know how we could get it.

By using the rocket equation for stage 2 you can determine just how high and fast you need to be at S1 MECO.

[Pete]

Spacex already adjusts the trajectory to match needs.
Compare:
Ses-8 launch.. Heavy payload, high mission demands. No flyback planned.Minimize gravity losses.
The vehicle passes through 48km altitude and 64km downrange.
At that point the vehicle was moving at only very slight angle to the horizon.
At that altitude, air pressure is less than one thousandth sea level, so air drag losses are not too extreme. Gravity losses are reduced a lot by building horizontal velocity as soon a possible.

Cassiope launch: Planned recovery/return of first stage, low mass payload so plenty of fuel margin:
This launch passed through 61km altitude for only 45km downrange, and was at that time pointing roughly 45 degrees from the horizontal.
This would increase gravity losses a lot, while reducing air-drag losses only a little bit. But, it would reduce downrange distance the first stage would need to recuperate a *lot*, and likely more importantly would reduce horizontal component of velocity at meco greatly, thus making the flyback easier.
Smaller horizontal to cancel, smaller distance to fly back, greater vertical altitude and velocity allowing *much* longer time for the returning first stage to do its thing.

[pagheca]

Thanks again for the answers, everyone.

Pete:

"The vehicle passes through 48km altitude and 64km downrange."
"This launch passed through 61km altitude for only 45km downrange, and was at that time pointing roughly 45 degrees from the horizontal."

that's exactly the kind of information I would like to find to have a better estimate through the Tsiokolsky equation. Can you please tell me where to find them?

 I found some estimate for the graviti and atmospheric drag during ascent. Much more difficult is to get something during descent because everything depends on how and when you use the residual propellant.

However, maybe I've not been very clear, but I think that, while evaluating how good are the chances to do a powered descent, I think people underestimate the propellant needed for a RTLS. The real challenge is the RTLS, not the powered descent, because the V_hor component. And without RTLS forget about recycling the rocket in a matter of hours or days.

Cheers,

[Silmfeanor]

that's exactly the kind of information I would like to find to have a better estimate through the Tsiokolsky equation. Can you please tell me where to find them?

From voice-over or information viewed during launches - there is not a total graph available.

I think people underestimate the propellant needed for a RTLS. The real challenge is the RTLS, not the powered descent, because the V_hor component.

RTLS is also lofted. Also, the stage is almost empty. Turning on 3 Merlin 1D's for even a short while really makes a big difference. SpaceX has done the math, presumably- and it's not gonna  be anything close to vertical. More lofted, for sure.
Attached is a russian proposal for a boostback trajectory - but keep in mind that this is a very different mass fraction of stages compared to the SpaceX model. The 2nd stage is way bigger. SpaceX trajectory will require more velocity from the first stage, and thus will be flatter.

[guckyfan]

However, when you add a not negligible horizontal component of the velocity, whatever you do you have to zero it after staging, and then go back to return to site. This is a 2 x DV_hor, where DV_hor is the horizontal component of the velocity at staging.

You have an error in that statement. There is no need to build up the same speed for the return leg. The flight time back is a lot longer because the stage is still climbing, before it comes down. So the speed on the return leg can be a lot less.

[pagheca]

thanks Slimfeanor. That's quite clear.
guckyfan:

"There is no need to build up the same speed for the return leg. [...] the speed on the return leg can be a lot less."

Frankly speaking I do not see that. Whatever you do you have to revert the horizontal speed compoent because the speed at lift-off is 0, and the speed at landing must be again 0 (in the rest reference frame). It's a matter of kinetic energy conservation.

Can you explain better your point please?

thanks for your time, guys.

[guckyfan]

Frankly speaking I do not see that. Whatever you do you have to revert the horizontal speed compoent because the speed at lift-off is 0, and the speed at landing must be again 0 (in the rest reference frame). It's a matter of kinetic energy conservation.

Can you explain better your point please?

thanks for your time, guys.

No problem, I hope I can make myself clear.

Your statement was you need to bring the forward speed to zero - correct.
Next you say that you need to build up the same speed in reverse direction for the return leg. Not correct, the flight time is longer so you need less speed for the return flight.

Edit: Most of that return speed will be braked by air drag so no need to again brake to zero from that speed.

[pagheca]

You are right guckyfan: I wrote "DV_hor", as delta-v horizontal component, but actually  wrote several times "horizontal component of the velocity". What I meant was delta. Thanks for noticing.

[Jcc]

You are right guckyfan: I wrote "DV_hor", as delta-v horizontal component, but actually  wrote several times "horizontal component of the velocity". What I meant was delta. Thanks for noticing.

I think the error he was pointing out was that you implied that you need to build up the same horizontal velocity for the RTLS as you have going down range. That is not so, is the F9 stages at Mach 6, you may only need to go Mach 1 or 2 on the return and take longer to do it.

[guckyfan]

I think the error he was pointing out was that you implied that you need to build up the same horizontal velocity for the RTLS as you have going down range. That is not so, is the F9 stages at Mach 6, you may only need to go Mach 1 or 2 on the return and take longer to do it.

That's correct. It is what I tried to say.

[pagheca]

What really matters is the delta-v in rocket propulsion. Specially when the gravitational drag must not be taken in account (and we are talking about the horizontal velocity). So, in terms of propellant to be used for such a maneuver, it doesn't matter if you build up speed slowly or not or if you have more or less time.

[guckyfan]

What really matters is the delta-v in rocket propulsion. Specially when the gravitational drag must not be taken in account (and we are talking about the horizontal velocity). So, in terms of propellant to be used for such a maneuver, it doesn't matter if you build up speed slowly or not or if you have more or less time.

We still did not come through to you, it seems. We are not talking about fast or slow acceleration. We are talking of total need of speed. The stage flies much slower back than it did on launch so less delta-v and a lot less fuel needed.

[pagheca]

Sorry - you are fully right. I got your point now.

The DV to be used is V_hor, not 2 x V_hor plus  "something" that may be quite little and depends on the time available before landing. I got stuck into a wrong line of thinking. Apologies for insisting!

[imspacy]

And without RTLS forget about recycling the rocket in a matter of hours or days.

I beg to disagree...
Suppose SpaceX has a floating barge somewhere downrange, supporting booster landing and some refuel capability....
The booster can then use atmospheric aero drag to reduce both vertical and horizontal speed, no need to eliminate horizontal speed much less get a return component.... so only minimal delta-v is needed to minimally reduce/control speed to avoid reentry damage, and for a high-gee landing..
Then fuel it up enough to RTLS, send it back... if the booster is designed for re-use, this shouldn't be a problem.
Of course, a slow boat back is not a problem either... so what if it takes a few days for the boat trip back.. a trivial expense ($10k?) compared to throwing away a $50 million vehicle.

We all have to readjust our mindset for reusability... for example, so what if the booster airframe needs to be twice as big for the same payload, when you save 96% of the cost (airframe) and only spend on fuel (4%)..

[pagheca]

I fully agree with you on the need to develop reusability.

What doesn't seem right is:

1) if you do not RTLS you cannot, as Elon Musk claimed several time, relaunch in a matter of hours. Musk never mentioned a barge. He mentioned a real RTSL.
2) a 30% fee on the payload seems to me extremely optimistic for RTLS. I'm not talking qualitatively. I just did my homework and the numbers show we are completely out of the game with a Falcon 9 v1.1, even in the most optimistic scenario.

Again: I'm not saying Elon Musk is wrong. He is clearly on top of that. What I mean is which flight profile may allow an RTLS.

Again 2: powered descent is clearly feasible. RTSL seem a completely different business and would require much more powerful rocket and engines.

cheers

[Jcc]

While landing on a barge may be possible, and would allow more payload, it is apparently a lot more complicated than landing on land and more prone to failure, so that is not the first choice. A landing platform that is big enough and stable enough to be reliable would also be quite expensive to buy and maintain.

[pagheca]

just to point out how good the aerodynamic drag on the first stage can be, I just noticed that the dry to wet ratio of the 1st stage of a Falcon is not that different from the one of a 330 ml beer can (ok, the height to diameter ratio is not).

Falcon 9 v1.1 1st stage: 18000/390000 = 4.6% (other sources give a dry mass slightly higher)
330 ml beer can: 14/(330+14) = 4.1%

This gives an idea of how much sophisticated must be the design and material used here, considering a beer can doens't features 9 engines so far as I know , and must not survive to a Max Q and the stresses of a launch. Amazing...

[gospacex]

Going to a steeper launch profile is simply a waste of fuel. Yes it would result in less fuel to return to launch site, but at the expense of not achieving orbital velocity and having your satellite crash back to earth.

Wrong.
It's far from being pointless for first stage to throw second stage way above atmosphere with significant vertical velocity component.
It allows second stage to fire more horizontally, having less gravity losses.

[ArbitraryConstant]

What really matters is the delta-v in rocket propulsion. Specially when the gravitational drag must not be taken in account (and we are talking about the horizontal velocity). So, in terms of propellant to be used for such a maneuver, it doesn't matter if you build up speed slowly or not or if you have more or less time.

As the first stage is moving downrange prior to relight, acceleration does matter since total displacement downrange will be increasing with time.

[Avron]

Whatever calcs are made, leave some margin on landing, as you want to shut the center engine down in a controlled manner and not have a RUD on landing, that will defeat the purpose

[meekGee]

And without RTLS forget about recycling the rocket in a matter of hours or days.

I beg to disagree...
Suppose SpaceX has a floating barge somewhere downrange, supporting booster landing and some refuel capability....
The booster can then use atmospheric aero drag to reduce both vertical and horizontal speed, no need to eliminate horizontal speed much less get a return component.... so only minimal delta-v is needed to minimally reduce/control speed to avoid reentry damage, and for a high-gee landing..
Then fuel it up enough to RTLS, send it back... if the booster is designed for re-use, this shouldn't be a problem.
Of course, a slow boat back is not a problem either... so what if it takes a few days for the boat trip back.. a trivial expense ($10k?) compared to throwing away a $50 million vehicle.

We all have to readjust our mindset for reusability... for example, so what if the booster airframe needs to be twice as big for the same payload, when you save 96% of the cost (airframe) and only spend on fuel (4%)..

"real" RTLS is of course preferable, but it's not an absolute.

The land-and-fly-back concept might win for the center core.  It is still RTLS in that there is no transport of the rocket by other means, and the time span can be measure in < 1 hour.  Once it lands, it join the regular flow as if there was no refueling.

For Mars launches from TX, the location of the refueling pad is pretty much fixed, which further simplifies things.

[TrevorMonty]

They have priced F9 launches based on fact it is expendable, recovery is optional.  There is a lot of unknowns in recovery but you can be assured they will apply all knowledge gained to any LV the Raptor is used in.

[pagheca]

They have priced F9 launches based on fact it is expendable, recovery is optional.  There is a lot of unknowns in recovery but you can be assured they will apply all knowledge gained to any LV the Raptor is used in.

Actually Musk is committed to make F9 a resuable vehicle. He mentioned several time this is the real aim of SpaceX. All the rest is a mean to reach this goal (and actually allow a human mission to Mars). He stated he would consider a failure in doing so a personal failure.

F9 is designed to become reusable. What I question is if a RTSL is practical or not. Anyway, Blue Origin is doing the same, with an even more larger in diameter first stage (that would allow much larger aerodynamic drag to help).

[CuddlyRocket]

They have priced F9 launches based on fact it is expendable, recovery is optional.  There is a lot of unknowns in recovery but you can be assured they will apply all knowledge gained to any LV the Raptor is used in.

Actually Musk is committed to make F9 a resuable vehicle. He mentioned several time this is the real aim of SpaceX. All the rest is a mean to reach this goal (and actually allow a human mission to Mars). He stated he would consider a failure in doing so a personal failure.

Musk being committed to F9 reusability does not mean that the F9 isn't priced based on costs incurred if it were to always be an expendable rocket. Reusability is not guaranteed (although I personally think they will make it work) and it therefore makes sense for prices at present to be based on expendability. Once reusability is demonstrated prices can be adjusted (hopefully down! ).

Also, F9 is IMO a self-financing development vehicle - they are using it to develop the knowledge and techniques required for reusability whilst pulling in the funds. But I'd be surprised if they weren't already planning its successor; with methalox engines etc (though it might turn out that it's cost effective to keep the F9 for smaller payload missions).

[pagheca]

Whatever calcs are made, leave some margin on landing, as you want to shut the center engine down in a controlled manner and not have a RUD on landing, that will defeat the purpose

What RUD means? I couldn't find that acronym over the internet.
Thanks

[Lee Jay]

Whatever calcs are made, leave some margin on landing, as you want to shut the center engine down in a controlled manner and not have a RUD on landing, that will defeat the purpose

What RUD means? I couldn't find that acronym over the internet.
Thanks

Rapid Unplanned Disassembly.

[guckyfan]

What RUD means? I couldn't find that acronym over the internet.
Thanks

Rapid Unscheduled Disassembly.

Some rude people call it an explosion.

[pagheca]

Ok, thanks.

One more question: is someone aware of how far downrange was exactly the landing site for the latest Falcon 9 v1.1 flight?

[pagheca]

really no one is able to answer the question I asked in my previous message?

Sorry to insist, but I need it for my simulations.

Thanks

[neoforce]

really no one is able to answer the question I asked in my previous message?

Sorry to insist, but I need it for my simulations.

Thanks

I'm pretty sure that answer isn't publicly available.  As stated in the post SES-8 article at http://www.nasaspaceflight.com/2013/12/ses-8-success-trajectory-future-spacex-possibilities/:

sources note there was also a boost back test during the SES-8 mission, or at least the restart of the first stage post staging.

So, we don't even know when the restart of the first stage happened.  SpaceX keeps some things close to their vest and releases things when it suits them. 

If you are insisting on information from SpaceX, you should always remember what the Man in Black said:  "Get used to disappointment."

[pagheca]

"Nobody knows" is actually an answer to my question... Thanks! I will try put this as an unknown in my simulation.

p.s. My plan is to wrote an extended simulator in MathCAD rather than excel or google drive spreadsheet. It doesn't allow me to solve the general equations of motion to minimize propellant usage, but I may iterate onto a few free parameters to see which obtains the best result. I'm now including an atmospheric model into it and would like to do the same using a reasonable model of the Merlin 1D throttle. Once I have a working testbed I will convert everything to python.

[starsilk]

really no one is able to answer the question I asked in my previous message?

Sorry to insist, but I need it for my simulations.

Thanks

try looking for the location of the 'american islander'.

[Lobo]

Going to a steeper launch profile is simply a waste of fuel. Yes it would result in less fuel to return to launch site, but at the expense of not achieving orbital velocity and having your satellite crash back to earth.

Wrong.
It's far from being pointless for first stage to throw second stage way above atmosphere with significant vertical velocity component.
It allows second stage to fire more horizontally, having less gravity losses.

Yea...

Is there a reason that F9 couldn't ascend mostly vertical and then the 2nd stage pitches and adds the additional required dV to get to orbital velocity?  That would prevent the F9 booster for getting very far down range and would essentially fall right back to the launch pad, needing only course corrections, and maybe a retro burn prior to getting too far in the atmosphere to slow down so it doesn't hit the atmosphere too fast.  Basically what the Shuttle SRB's did, and would have done if SRB Sep had been before the Shuttle started it's pitch.  Of course, you don't want burnt out SRB's crashing back down onto a populated area.  ;-)
So they really probably did want them to be jettisoned after the Shuttle pitched away from the Florida coast.  With a "smart" booster like F9, couldn't you keep mostly vertical until staging?
Maybe you'd still want to be 10-20 miles off the coast in case of a problem, the stage would fall into the ocean off the Florida coast, rather than risk falling into the populated coast.  F9's RCS system and engines could then guide it back to a landing site at the Cape if everything is operating properly.

[pagheca]

" couldn't you keep mostly vertical until staging?"

I guess the main problem here is the additional gravity loss related to a vertical trajectory.

I haven't understood yet how to evaluate the propellant tag due to this (as many people, I use numbers from similar vectors), but I guess the optimal configuration is someway in the middle. The physical and technical factors I found impacting on this are:

1) the altitude of staging
2) the speed of staging (very important)
3) the downrange distance
4) the thrust: low trust means that building up altitude too fast may cost more propellant, even if you reduce the aerodynamic drag in this way. For example, a simple computation shows that if you launch an F9 vertically you can't get to 300 km altitude with orbital velocity. You need some additional time to build up speed.
5) the timing of the burning(s). This is by far the most difficult to find out as you have infinite ^ infinite ways to burn.

they combine altogheter with the atmospheric drag to give you the most performant trajectories.

On top of this, I think there is the problem of a too short curvature radius that at those high speed would add stresses to the 2nd stage structure and gimbal, but this are just guesses.

I'm not a rocket scientist (although I'm a professional scientist with over 25 years of experience in instrumentation) so I'm not 100% sure yet about this. I'm still learning. Someone else may add wiser comments.

p.s. you are a senior member, so probably you know all of this, but I wrote it down for all the users of this forum.

[billh]

really no one is able to answer the question I asked in my previous message?

Sorry to insist, but I need it for my simulations.

Thanks

try looking for the location of the 'american islander'.

I seem to remember someone posting about seeing the FlightAware data for Elon's plane.

[pagheca]

[try looking for the location of the 'american islander'.

Smart. Maybe I found mentions of the NOTAM, thanks.

http://www.zarya.info/blog/?p=1557

[pagheca]

By using the map posted at http://forum.nasaspaceflight.com/index.php?topic=32859.90 and measuring the distance from Vandenberg launch pad to the approx center of the controlled return area, the downrange distance of the Cassiope launch results to be ~550 km (340 mi.).

thanks in particular to Starsilk

[Proponent]

That's quite a contrast to at least one of the Falcon 9 v1.0 flights, where the first stage apparently impacted much further away.

[cambrianera]

That's quite a contrast to at least one of the Falcon 9 v1.0 flights, where the first stage apparently impacted much further away.

Staging velocity for F9 v1.0 was over 3000 m/s, for v1.1 around 2000 m/s; you can expect also more horizontal trajectory to impart more horizontal velocity to second stage and payload.

[guckyfan]

That's quite a contrast to at least one of the Falcon 9 v1.0 flights, where the first stage apparently impacted much further away.

Staging velocity for F9 v1.0 was over 3000 m/s, for v1.1 around 2000 m/s; you can expect also more horizontal trajectory to impart more horizontal velocity to second stage and payload.

They also braked for reentry. That would further shorten the flight distance.

[pagheca]

They also braked for reentry. That would further shorten the flight distance.

BTW, the only two marks publicly available during powered descent show the same velocity, like if the ACS was aiming to a constant descent speed (Thrust = Mg). It could be an interesting "optimal theorem".  Do you know if anyone speculated about this in the forum?

[cambrianera]

BTW, the only two marks publicly available during powered descent show the same velocity, like if the ACS was aiming to a constant descent speed (Thrust = Mg). It could be an interesting "optimal theorem".  Do you know if anyone speculated about this in the forum?

Here,
http://forum.nasaspaceflight.com/index.php?topic=32859.msg1109900#msg1109900
follow the discussion and you will find some contribution.

[hrissan]

I may be wrong, but here is one reason the "straight up" trajectory may be suboptimal.

If the stage falls vertically, atmospheric pressure and the braking force may increase too quickly.

By falling more horizontally, you can shed more speed per meter of descent, which would require less aggressive braking burn.

[Kabloona]

BTW, the only two marks publicly available during powered descent show the same velocity, like if the ACS was aiming to a constant descent speed (Thrust = Mg). It could be an interesting "optimal theorem".  Do you know if anyone speculated about this in the forum?

Here,
http://forum.nasaspaceflight.com/index.php?topic=32859.msg1109900#msg1109900
follow the discussion and you will find some contribution.

There was an extensive discussion, and general consensus was a simple error in video editing.

[rst]

I may be wrong, but here is one reason the "straight up" trajectory may be suboptimal.

If the stage falls vertically, atmospheric pressure and the braking force may increase too quickly.

By falling more horizontally, you can shed more speed per meter of descent, which would require less aggressive braking burn.

Just bear in mind that due to the peculiar landing conditions, the F9R booster may have to be falling at a certain minimum speed in order to be able to land.

The peculiarity is that it's landing on an engine whose thrust exceeds the weight of the stage, so that while the engine is firing, it's always accelerating up.  Under these circumstances, the only way to land is to time the burn so that upward velocity goes to zero exactly when the stage hits the ground --- or, at any rate, close enough that the legs can do the rest of the braking (or handle the fall after engine cutoff).

So, let's say that from velocity v, a burn starting at height h gets you to a safe landing at the lowest throttle setting.  If you come in faster, and start the burn at the same height, you can just throttle up to burn off the excess velocity.  But if you come in slower, the only thing you can do is start the burn from a lower height, and burn for less time.  And short enough burns may get really tricky to time due to engine startup transients.

[Kabloona]

I may be wrong, but here is one reason the "straight up" trajectory may be suboptimal.

If the stage falls vertically, atmospheric pressure and the braking force may increase too quickly.

By falling more horizontally, you can shed more speed per meter of descent, which would require less aggressive braking burn.

Just bear in mind that due to the peculiar landing conditions, the F9R booster may have to be falling at a certain minimum speed in order to be able to land.

The peculiarity is that it's landing on an engine whose thrust exceeds the weight of the stage, so that while the engine is firing, it's always accelerating up.  Under these circumstances, the only way to land is to time the burn so that upward velocity goes to zero exactly when the stage hits the ground --- or, at any rate, close enough that the legs can do the rest of the braking (or handle the fall after engine cutoff).

So, let's say that from velocity v, a burn starting at height h gets you to a safe landing at the lowest throttle setting.  If you come in faster, and start the burn at the same height, you can just throttle up to burn off the excess velocity.  But if you come in slower, the only thing you can do is start the burn from a lower height, and burn for less time.  And short enough burns may get really tricky to time due to engine startup transients.

What you are discussing is the "terminal" phase of descent, ie maybe last 10,000 feet and below, when the stage has already hit terminal velocity, which will be a function of ballistic coefficient, and is just about to perform the landing burn. At this point the stage will likely be falling more or less straight down, though probably will include a divert maneuver during the landing burn.

What hrissan was discussing is the much higher/faster portion of the trajectory when the stage is well above terminal velocity and has yet to shed much of its velocity due to aero drag, and may still have significant horizontal velocity. That is the phase where this discussion of trajectory shape is applicable. And the question there is, how best to shape the trajectory to shed the several hundred m/sec the stage will be carrying at high altitudes *before* it slows to terminal velocity in lower atmosphere.

But the trajectory shaping at high altitudes will not affect terminal velocity, which is ultimately a function of the stage's ballistic coefficient and thus independent of whatever path the stage takes.

[jg]

*before* it slows to terminal velocity in lower atmosphere.

Ok but do there is any obvious way to show that such an object would reach terminal velocity faster than the pressure build up during descent? To me it is not so obvious.

thanks

yes - maybe there is - sorry

Heavy and much denser meteors actually reach terminal velocity.

pagheca

What really matters is not the density, but the mass versus the drag of the stage while oriented engine first.  That will determine how quickly it slows.

And yes, many dense stone or nickle/iron meteorites reach terminal velocity (and have done numbers on people's houses and even a car (see http://en.wikipedia.org/wiki/Peekskill_meteorite). You don't want to be hit by a one foot size rock at terminal velocity: it will ruin your whole day.

[Kabloona]

What you are discussing here is basically the ballistic coefficient of the stage, which will be much lower than than that of, say, a meteor, because a large volume of the stage will be empty tanks, and because legs will be extended at some point.

http://en.wikipedia.org/wiki/Ballistic_coefficient

The stage will of course reach terminal velocity, but we don't quite know what that number is, though there has been some speculation here:

http://forum.nasaspaceflight.com/index.php?topic=31513.msg1105554#msg1105554

In this Russian example posted previously by Lars J, terminal velocity appears to be 130 m/sec.

http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=32718.0;attach=544671

[jg]

What you are discussing here is basically the ballistic coefficient of the stage, which will be much lower than than that of, say, a meteor, because a large volume of the stage will be empty tanks, and because legs will be extended at some point.

http://en.wikipedia.org/wiki/Ballistic_coefficient

The stage will of course reach terminal velocity, but we don't quite know what that number is, though there has been some speculation here:

http://forum.nasaspaceflight.com/index.php?topic=31513.msg1105554#msg1105554

In this Russian example posted previously by Lars J, terminal velocity appears to be 130 m/sec.

http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=32718.0;attach=544671

Yes, though the details matter here: what the mass fraction is of the first stage, whether the legs are strong enough to be opened/deployed far enough before landing to help reduce the terminal velocity further once the terminal velocity of the stage with legs closed has been reached, and the like...

If the legs can be opened earlier, then you get more velocity reduction for "free" in the terminal phase of landing by increasing the drag a lot by opening the legs....

The other interesting question is what the maximum velocity the stage can tolerate at the beginning of atmospheric reentry to avoid too much heating; or whether pretty much all the fuel use will be for "fly back" rather than killing velocity.

I guess we'll probably have to "wait and see" what the trade-offs are, unless there is someone in the forum who wants to take a serious look at analyzing the weight/strength/drag characteristics of the legs....  Fun problem, but I did physics/astronomy as an undergraduate rather than aero engineering.

Quite the complex situation....

[pagheca]

Thanks for the links.

As usual, people can speculate forever if there is a lack of evidence and real computations.

[Pete]

What you are discussing here is basically the ballistic coefficient of the stage, which will be much lower than than that of, say, a meteor, because a large volume of the stage will be empty tanks, ...

Just a reminder, the empty Falcon9 first stage is *light* for its size.
The density is only about that of polystyrene foam.

[pagheca]

the 1st stage, INCLUDING the engines, has about the same wet/dry weight ratio of a standard beer can.

Also if it has a different length/diameter ratio, try to throw an empty can from a skyscraper and you get an idea of the dynamic involved in the reentry...

[rst]

What hrissan was discussing is the much higher/faster portion of the trajectory when the stage is well above terminal velocity and has yet to shed much of its velocity due to aero drag, and may still have significant horizontal velocity. That is the phase where this discussion of trajectory shape is applicable. And the question there is, how best to shape the trajectory to shed the several hundred m/sec the stage will be carrying at high altitudes *before* it slows to terminal velocity in lower atmosphere.

So the braking burn he was discussing was not the final one, but the earlier ones at high altitude.  Thanks.

[cambrianera]

the 1st stage, INCLUDING the engines, has about the same wet/dry weight ratio of a standard beer can.

Also if it has a different length/diameter ratio, try to throw an empty can from a skyscraper and you get an idea of the dynamic involved in the reentry...

Not exactly, mass= proportional to dimension^3, air resistance=proportional to dimension^2,  therefore  scaling up gives larger terminal velocity.
By the way, this kind of discussion went out when I noted that second stage is approximately 50:1 scale of 500cc beer can (lenght, diameter and thickness)
http://forum.nasaspaceflight.com/index.php?topic=32180.msg1121913#msg1121913.

[pagheca]

Not exactly, mass= proportional to dimension^3, air resistance=proportional to dimension^2,  therefore  scaling up gives larger terminal velocity.
By the way, this kind of discussion went out when I noted that second stage is approximately 50:1 scale of 500cc beer can (lenght, diameter and thickness)
http://forum.nasaspaceflight.com/index.php?topic=32180.msg1121913#msg1121913.

My point is totally different.

I'm talking about the wet/dry mass ratio, not the shape. This ratio can't be scaled up and has no direct relation to the terminal velocity. I used this analogy "to get an idea" of how light is the first stage of a descending Falcon 9, despite the mass of the 9 engines and the much more stringent design constraints. To me it looks really amazing that you can design a "beer can" to leave the atmosphere, reach Mach 6 and re-enter it without crashing everything.

[cambrianera]

Not exactly, mass= proportional to dimension^3, air resistance=proportional to dimension^2,  therefore  scaling up gives larger terminal velocity.
By the way, this kind of discussion went out when I noted that second stage is approximately 50:1 scale of 500cc beer can (lenght, diameter and thickness)
http://forum.nasaspaceflight.com/index.php?topic=32180.msg1121913#msg1121913.

My point is totally different.

I'm talking about the wet/dry mass ratio, not the shape. This ratio can't be scaled up and has no direct relation to the terminal velocity. I used this analogy "to get an idea" of how light is the first stage of a descending Falcon 9, despite the mass of the 9 engines and the much more stringent design constraints. To me it looks really amazing that you can design a "beer can" to leave the atmosphere, reach Mach 6 and re-enter it without crashing everything.

Realy hate to be pedantic, but part of what you wrote is "try to throw an empty can from a skyscraper and you get an idea of the dynamic involved in the reentry".
That's not correct, hence my post.

 

[rockettrey]

Because we are discussing launch loft/trajectory here and there in this thread, I am emboldened to ask a question that I have wondered about for years.  Because SpaceX is involved with and doing something similar to my thoughts on this matter (with this launch), I now absolutely have to ask the question.  I just wished I took orbital mechanics in college...

Shuttle (and others) execute a roll program a few seconds after launch where they would negate some of their vertical acceleration for horizontal acceleration presumably to help reach orbital velocity and altitude together- possibly a compromise for something like fuel (weight) or time.  Why wouldn't a launch vehicle go vertical at first to get out of the atmosphere (and drag) as fast as possible, and THEN work on the horizontal component (escape velocity) where drag losses are much lower? 

My question for you smart rocket scientists out there- is SpaceX possibly thinking along these lines?  This would also have the side benefit of reducing the boost back distance.  I am ABSOLUTELY not qualified to speculate on that- I can only ask the question....but eagerly await informed answers!

[NovaSilisko]

Because we are discussing launch loft/trajectory here and there in this thread, I am emboldened to ask a question that I have wondered about for years.  Because SpaceX is involved with and doing something similar to my thoughts on this matter (with this launch), I now absolutely have to ask the question.  I just wished I took orbital mechanics in college...

Shuttle (and others) execute a roll program a few seconds after launch where they would negate some of their vertical acceleration for horizontal acceleration presumably to help reach orbital velocity and altitude together- possibly a compromise for something like fuel (weight) or time.  Why wouldn't a launch vehicle go vertical at first to get out of the atmosphere (and drag) as fast as possible, and THEN work on the horizontal component (escape velocity) where drag losses are much lower? 

My question for you smart rocket scientists out there- is SpaceX possibly thinking along these lines?  This would also have the side benefit of reducing the boost back distance.  I am ABSOLUTELY not qualified to speculate on that- I can only ask the question....but eagerly await informed answers!

Gravity.

Every second you go straight vertical is 9.81 m/s/s delta-v lost*. Atmospheric drag tapers off relatively quickly, but you still have nearly 1g of downward force in LEO.


_{*somebody please inform me how wrong I am here, I feel like I might be ;_;}

[Enceladus]

Because we are discussing launch loft/trajectory here and there in this thread, I am emboldened to ask a question that I have wondered about for years.  Because SpaceX is involved with and doing something similar to my thoughts on this matter (with this launch), I now absolutely have to ask the question.  I just wished I took orbital mechanics in college...

Shuttle (and others) execute a roll program a few seconds after launch where they would negate some of their vertical acceleration for horizontal acceleration presumably to help reach orbital velocity and altitude together- possibly a compromise for something like fuel (weight) or time.  Why wouldn't a launch vehicle go vertical at first to get out of the atmosphere (and drag) as fast as possible, and THEN work on the horizontal component (escape velocity) where drag losses are much lower? 

My question for you smart rocket scientists out there- is SpaceX possibly thinking along these lines?  This would also have the side benefit of reducing the boost back distance.  I am ABSOLUTELY not qualified to speculate on that- I can only ask the question....but eagerly await informed answers!

Gravity.

Every second you go straight vertical is 9.81 m/s/s delta-v lost*. Atmospheric drag tapers off relatively quickly, but you still have nearly 1g of downward force in LEO.


_{*somebody please inform me how wrong I am here, I feel like I might be ;_;}

You're on the right track. It's called gravity drag and the concept is a little hard to grasp. But basically, yes. You want to spend as little time as possible boosting straight up, but for aerodynamic purposes, you want to maximize this time. So the real flight plan is a complex compromise.

[baldusi]

I believe that the gravity loss is the integral of sin(alpha(t)) x g(altitude) where alpha is the angle wrt to horizontal.

[e of pi]

Because we are discussing launch loft/trajectory here and there in this thread, I am emboldened to ask a question that I have wondered about for years.  Because SpaceX is involved with and doing something similar to my thoughts on this matter (with this launch), I now absolutely have to ask the question.  I just wished I took orbital mechanics in college...

Shuttle (and others) execute a roll program a few seconds after launch where they would negate some of their vertical acceleration for horizontal acceleration presumably to help reach orbital velocity and altitude together- possibly a compromise for something like fuel (weight) or time.  Why wouldn't a launch vehicle go vertical at first to get out of the atmosphere (and drag) as fast as possible, and THEN work on the horizontal component (escape velocity) where drag losses are much lower? 

My question for you smart rocket scientists out there- is SpaceX possibly thinking along these lines?  This would also have the side benefit of reducing the boost back distance.  I am ABSOLUTELY not qualified to speculate on that- I can only ask the question....but eagerly await informed answers!

Perhaps better belongs in one of the public-side Q&A threads, but basically it boils down to the fact that there's more than one type of loss. Aerodynamic drag, of course, is one of them. However, long and skinny rockets are pretty low-drag (not, of course, by coincidence, but it's a good shape). Another, though, is what's often called "gravity drag" or "gravity losses." This is basically the effect of gravity pulling the rocket "down" for the duration of the engine burn. It's a lot more complicated than this, but think about it this way: take a rocket that can do a delta-v of 9800 m/s. It can, basically, make orbit. Now, have it sit on the pad, and throttle the engines so that it burns through all the fuel while hovering right over the pad, over a period of about 17 minutes. The rocket hasn't made orbit, it's still hovering right over the pad when the tanks run dry. So...where'd all the performance go? Fighting these "gravity losses" or "gravity drag."

A post here lists some sample values for these two terms for some real launch vehicles:
http://forum.nasaspaceflight.com/index.php?topic=9959.msg189860#msg189860
As you can see, gravity losses are much larger than the aerodynamic drag. While there may be some benefit to a more "lofted" trajectory (that is, steeper initial trajectory) to reduce boostback requirements, the effect isn't really coming from lower drag--you're increasing the gravity losses, but if the decreases in the first stage's required fuel for boostback is enough, it might pay. That'd be some interesting optimization, but it's not really as much related to aerodynamics.

[edkyle99]

There is an optimal ascent trajectory (pitch-over plus pitch-rate) for every direct insertion orbit altitude for a specific rocket/payload combination.  It balances the need to climb out of the atmosphere quickly to minimize drag and to maximize vacuum specific impulse with the need to pitch over and accelerate while minimizing gravity losses.  The better question for F9-10 might be this.  Was a steeper than optimal ascent trajectory purposefully flown to move the first stage landing zone closer to Florida?

 - Ed Kyle

[deruch]

Because we are discussing launch loft/trajectory here and there in this thread, I am emboldened to ask a question that I have wondered about for years.  Because SpaceX is involved with and doing something similar to my thoughts on this matter (with this launch), I now absolutely have to ask the question.  I just wished I took orbital mechanics in college...

Shuttle (and others) execute a roll program a few seconds after launch where they would negate some of their vertical acceleration for horizontal acceleration presumably to help reach orbital velocity and altitude together- possibly a compromise for something like fuel (weight) or time.  Why wouldn't a launch vehicle go vertical at first to get out of the atmosphere (and drag) as fast as possible, and THEN work on the horizontal component (escape velocity) where drag losses are much lower? 

My question for you smart rocket scientists out there- is SpaceX possibly thinking along these lines?  This would also have the side benefit of reducing the boost back distance.  I am ABSOLUTELY not qualified to speculate on that- I can only ask the question....but eagerly await informed answers!

Since you specifically ask in relation to the Shuttle, an additional concern that the trajectories of manned craft may also need to deal with is ballistic reentries in the event of a failure.  A flatter than optimal (based solely on the physics) trajectory may be required when needing to ensure the survivability of a crew in the event of a launch failure.

[aero]

Did anyone get an accurate time for MECO?

We know that a full burn is 183 seconds and Stage 1 consumes 850 klb, or 386,364 kg of prop. That is 2111.27 kg/s. I'd like to guess how much prop was reserved for boost back and landing.

[Proponent]

For anyone who has a little math under his belt, the short piece attached may shed a little light on velocity losses suffered by a rocket ascending to orbit.  Criticism welcome.

[fatjohn1408]

Did anyone get an accurate time for MECO?

We know that a full burn is 183 seconds and Stage 1 consumes 850 klb, or 386,364 kg of prop. That is 2111.27 kg/s. I'd like to guess how much prop was reserved for boost back and landing.

It was over 9000.

[Paul_G]

....... Why wouldn't a launch vehicle go vertical at first to get out of the atmosphere (and drag) as fast as possible, and THEN work on the horizontal component (escape velocity) where drag losses are much lower? 

I always had difficulty in trying to understand why rockets didn't go straight up. Then I came across things like Kerbal Space Programme, or SimpleRocket on iPhone/Andriod, and these tools let you visualise what happens if you try ti go straight up, and once you see the resulting trajectories from a 'straight up' launch, you get to understand the concept (if not the maths) of gravity loss, and how increasing the horizontal aspect of your trajectory gets you into orbit quicker, and with less fuel.

Paul

[Jim]

There is an optimal ascent trajectory (pitch-over plus pitch-rate) for every direct insertion orbit altitude for a specific rocket/payload combination.  It balances the need to climb out of the atmosphere quickly to minimize drag and to maximize vacuum specific impulse with the need to pitch over and accelerate while minimizing gravity losses.  The better question for F9-10 might be this.  Was a steeper than optimal ascent trajectory purposefully flown to move the first stage landing zone closer to Florida?

 - Ed Kyle

There is also the vehicles' ability to handle aeroloads. More "fragile" vehicles would have lofted trajectories vs a robust vehicles like ICBM's with SRM's which quickly go almost horizontal.

[Icepilot]

From watching the video & assuming the speed/height/downrange commentary marked the minutes, we have:
            km altitude   km/sec    km downrange
T+1m     13                0.45         2.5
T+2m     54                1.4         21
T+3m   112                1.7         51

MECO was at T+2m41sec. So the first stage was 100 km high, 1.6 km/sec total speed, about 45 km downrange with a horizontal component of about 0.5 km/sec.
So SpaceX needs a single engine to provide an empty first stage a delta-v of maybe 0.6 km/sec?
How well do long cylinders perform as lifting bodies?

[Space Ghost 1962]

There is an optimal ascent trajectory (pitch-over plus pitch-rate) for every direct insertion orbit altitude for a specific rocket/payload combination.  It balances the need to climb out of the atmosphere quickly to minimize drag and to maximize vacuum specific impulse with the need to pitch over and accelerate while minimizing gravity losses.  The better question for F9-10 might be this.  Was a steeper than optimal ascent trajectory purposefully flown to move the first stage landing zone closer to Florida?

 - Ed Kyle

There is also the vehicles' ability to handle aeroloads. More "fragile" vehicles would have lofted trajectories vs a robust vehicles like ICBM's with SRM's which quickly go almost horizontal.

Been thinking that one way to "optimize" reuse cost affecting GLOW would be to intentionally reduce structural mass and retropropulsive propellant losses. You'd fly more lofted and might get a lower bound on what you might get away with RLV vs ELV performance hit.

That would drive both costing/margins as well as give the designers a new threshold with, say, composite inserts, to trade improvements against.

[modemeagle]

Here are some graphs from my simulation of this flight.

[LouScheffer]

There is an optimal ascent trajectory (pitch-over plus pitch-rate) for every direct insertion orbit altitude for a specific rocket/payload combination.  It balances the need to climb out of the atmosphere quickly to minimize drag and to maximize vacuum specific impulse with the need to pitch over and accelerate while minimizing gravity losses.  The better question for F9-10 might be this.  Was a steeper than optimal ascent trajectory purposefully flown to move the first stage landing zone closer to Florida?

 - Ed Kyle

There is also the vehicles' ability to handle aeroloads. More "fragile" vehicles would have lofted trajectories vs a robust vehicles like ICBM's with SRM's which quickly go almost horizontal.

The Apollo astronauts commented on how the launch from the moon pitched over right away, accelerating almost horizontally, in contrast to the launch from Earth

[woods170]

There is an optimal ascent trajectory (pitch-over plus pitch-rate) for every direct insertion orbit altitude for a specific rocket/payload combination.  It balances the need to climb out of the atmosphere quickly to minimize drag and to maximize vacuum specific impulse with the need to pitch over and accelerate while minimizing gravity losses.  The better question for F9-10 might be this.  Was a steeper than optimal ascent trajectory purposefully flown to move the first stage landing zone closer to Florida?

 - Ed Kyle

There is also the vehicles' ability to handle aeroloads. More "fragile" vehicles would have lofted trajectories vs a robust vehicles like ICBM's with SRM's which quickly go almost horizontal.

The Apollo astronauts commented on how the launch from the moon pitched over right away, accelerating almost horizontally, in contrast to the launch from Earth

No atmosphere, and thus no aeroloads, to worry about. Only considerations for early pitch over is lunar mountains nearby, like at Apollo 15 and 17 landing sites.