Author Topic: Falcon 9 flight trajectory  (Read 54825 times)

Offline pagheca

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Falcon 9 flight trajectory
« on: 12/07/2013 05:23 pm »
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

Offline Jcc

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Re: Falcon 9 flight trajectory
« Reply #1 on: 12/07/2013 05:45 pm »
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.

Offline Silmfeanor

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Re: Falcon 9 flight trajectory
« Reply #2 on: 12/07/2013 07:13 pm »
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.

Offline MP99

Re: Falcon 9 flight trajectory
« Reply #3 on: 12/07/2013 09:02 pm »
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
« Last Edit: 12/07/2013 09:03 pm by MP99 »

Offline Avron

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Re: Falcon 9 flight trajectory
« Reply #4 on: 12/07/2013 09:28 pm »
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

Offline pagheca

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Re: Falcon 9 flight trajectory
« Reply #5 on: 12/08/2013 12:28 am »
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

« Last Edit: 12/08/2013 12:32 am by pagheca »

Offline Roy_H

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Re: Falcon 9 flight trajectory
« Reply #6 on: 12/08/2013 02:23 am »
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.
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Offline aero

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Re: Falcon 9 flight trajectory
« Reply #7 on: 12/08/2013 03:39 am »
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.
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Offline Pete

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Re: Falcon 9 flight trajectory
« Reply #8 on: 12/08/2013 05:11 am »
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.

Offline pagheca

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Re: Falcon 9 flight trajectory
« Reply #9 on: 12/08/2013 10:30 am »
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,

Offline Silmfeanor

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Re: Falcon 9 flight trajectory
« Reply #10 on: 12/08/2013 10:47 am »
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.

Quote
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.

Offline guckyfan

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Re: Falcon 9 flight trajectory
« Reply #11 on: 12/08/2013 11:10 am »
Quote
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.


Offline pagheca

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Re: Falcon 9 flight trajectory
« Reply #12 on: 12/08/2013 11:18 am »
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.

Offline guckyfan

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Re: Falcon 9 flight trajectory
« Reply #13 on: 12/08/2013 11:22 am »

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.

« Last Edit: 12/08/2013 11:24 am by guckyfan »

Offline pagheca

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Re: Falcon 9 flight trajectory
« Reply #14 on: 12/08/2013 11:32 am »
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.

Offline Jcc

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Re: Falcon 9 flight trajectory
« Reply #15 on: 12/08/2013 12:02 pm »
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.

Offline guckyfan

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Re: Falcon 9 flight trajectory
« Reply #16 on: 12/08/2013 12:11 pm »

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.


Offline pagheca

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Re: Falcon 9 flight trajectory
« Reply #17 on: 12/08/2013 12:37 pm »
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.


« Last Edit: 12/08/2013 12:40 pm by pagheca »

Offline guckyfan

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Re: Falcon 9 flight trajectory
« Reply #18 on: 12/08/2013 12:42 pm »
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.

Offline pagheca

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Re: Falcon 9 flight trajectory
« Reply #19 on: 12/08/2013 12:48 pm »
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! :)




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