Author Topic: Falcon 9 flight trajectory  (Read 54824 times)

Offline pagheca

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Re: Falcon 9 flight trajectory
« Reply #40 on: 12/10/2013 05:23 pm »
" 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.
« Last Edit: 12/10/2013 05:51 pm by pagheca »

Offline billh

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Re: Falcon 9 flight trajectory
« Reply #41 on: 12/10/2013 05:27 pm »
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.

Offline pagheca

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Re: Falcon 9 flight trajectory
« Reply #42 on: 12/10/2013 05:33 pm »
[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



Offline pagheca

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Re: Falcon 9 flight trajectory
« Reply #43 on: 12/10/2013 06:46 pm »
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


Offline Proponent

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Re: Falcon 9 flight trajectory
« Reply #44 on: 12/11/2013 01:02 pm »
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.
« Last Edit: 12/11/2013 01:02 pm by Proponent »

Offline cambrianera

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Re: Falcon 9 flight trajectory
« Reply #45 on: 12/11/2013 01:18 pm »
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.
Oh to be young again. . .

Online guckyfan

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Re: Falcon 9 flight trajectory
« Reply #46 on: 12/11/2013 01:20 pm »
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.

Offline pagheca

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Re: Falcon 9 flight trajectory
« Reply #47 on: 12/11/2013 05:27 pm »
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?

Offline cambrianera

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Re: Falcon 9 flight trajectory
« Reply #48 on: 12/11/2013 06:59 pm »
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.
Oh to be young again. . .

Offline hrissan

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Re: Falcon 9 flight trajectory
« Reply #49 on: 12/12/2013 03:21 pm »
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.

Offline Kabloona

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Re: Falcon 9 flight trajectory
« Reply #50 on: 12/12/2013 05:23 pm »
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.

Offline rst

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Re: Falcon 9 flight trajectory
« Reply #51 on: 12/12/2013 05:37 pm »
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.

Offline Kabloona

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Re: Falcon 9 flight trajectory
« Reply #52 on: 12/12/2013 05:59 pm »
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.
« Last Edit: 12/12/2013 07:03 pm by Kabloona »

Offline jg

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Re: Falcon 9 flight trajectory
« Reply #53 on: 12/12/2013 07:01 pm »
Quote
*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.

Offline Kabloona

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Re: Falcon 9 flight trajectory
« Reply #54 on: 12/12/2013 07:12 pm »
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
« Last Edit: 12/12/2013 07:22 pm by Kabloona »

Offline jg

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Re: Falcon 9 flight trajectory
« Reply #55 on: 12/12/2013 07:44 pm »
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....

Offline pagheca

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Re: Falcon 9 flight trajectory
« Reply #56 on: 12/12/2013 08:06 pm »
Thanks for the links.

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

Offline Pete

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Re: Falcon 9 flight trajectory
« Reply #57 on: 12/12/2013 08:18 pm »
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.

Offline pagheca

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Re: Falcon 9 flight trajectory
« Reply #58 on: 12/12/2013 08:42 pm »
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...
« Last Edit: 12/12/2013 08:46 pm by pagheca »

Offline rst

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Re: Falcon 9 flight trajectory
« Reply #59 on: 12/12/2013 08:51 pm »
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.

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