Space X to build reusable launch vehicle

charliem · Post by **charliem** » Thu Oct 27, 2011 3:14 pm

charliem wrote:I suspect that is not going to be the hardest challenge, but controlling the reentry so the stage doesn't snap, and to keep it stable and vertical for landing.

Falcon 9 reaches a much higher speed and altitude than most of the boosters used in other launchers (for example the Space Shuttle), and that means stronger forces at reentry.

If we take the 3.2 km/s that the 2nd launch video says was the inertial speed at separation, and the 1,200 km that the 1st stage of the 1st Falcon 9 flight traveled before crashing (and suppose it was the same for the second), then we can deduce the angle of ascension at staging, about 38 degrees.

That means that the vertical speed was ~1.9 km/s, and the horizontal speed ~2.5 km/s (inertial).

With that v-speed the first stage should be able to get to an altitude of ~300 km (separation happened at ~120 km high).

Going down it'd reentered the atmosphere at the same 120 km, and a velocity of mach ~5.5, when it started to decelerate.

If it couldn't reorient itself to an engines first fall, I'm not surprised that it didn't survive in one piece.

Skipjack · Post by **Skipjack** » Thu Oct 27, 2011 4:52 pm

Charliem, this is a very good analysis. One thing, I think that the crash site would be quite a bit downrange from the staging event. The stage would still coast for quite a distance before it crashes into the ocean.
That is at least what I would expect to happen.
No idea how much of a difference that would make.

charliem · Post by **charliem** » Thu Oct 27, 2011 6:00 pm

Skipjack wrote:Charliem, this is a very good analysis. One thing, I think that the crash site would be quite a bit downrange from the staging event. The stage would still coast for quite a distance before it crashes into the ocean.

Thanks Skipjack, and you are right.

The trajectory is only parabolic outside the atmosphere, inside it is more vertical, before staging and after reentry.

Staging happens just 100-150 km downrange, then 1,000 km more coasting (for 390 s), then reentry, coming to ~1,200 km.

According my calcs total flight time for the 1st stage should be about 12-13 minutes but I have not been able to find any source to confirm that.

Skipjack · Post by **Skipjack** » Thu Oct 27, 2011 9:33 pm

Staging happens just 100-150 km downrange

Wow, that close to the launch site? I did not know that! It thought it was maybe 800km or so.
So that would mean that most of the deltaV would be spent slowing down and only very little would be needed for actually returning the stage to the launchsite!
Not sure how much that really changes about the calculations, but it sure is an interesting bit of information!
I was looking for that piece of information but could not find it anywhere. Where did you run into it?

charliem · Post by **charliem** » Thu Oct 27, 2011 11:18 pm

I didn't find that piece of data.

Instead I reviwed the videos about the first two Falcon 9 launches, reread its user manual, and extracted all the data they mentioned about time, speed, altitude, and distance.

Then did a numerical integration to obtain the flight profile using those few data to adjust the unknown parameters.

The results are not 100% accurate, but I think don't differ much from the real path.

KitemanSA · Post by **KitemanSA** » Fri Oct 28, 2011 12:48 am

So how much skipping would be needed to bring the first stage around and down to the same location?

charliem · Post by **charliem** » Fri Oct 28, 2011 1:26 am

Skipjack wrote:
Staging happens just 100-150 km downrange
So that would mean that most of the deltaV would be spent slowing down and only very little would be needed for actually returning the stage to the launchsite!

About 2.5 km/s to counter all the horizontal speed for the 1st stage, plus aprox. 0.4 km/s more to make it go back those 100-150 km in the 390 s it remains outside the atmosphere, and another, maybe, 0.5 km/s to land.

Total: ~3.4 km/s.

More that what my calcs say is available, but I don't have all the numbers, and the difference is not that much.

Skipjack · Post by **Skipjack** » Fri Oct 28, 2011 1:37 am

more to make it go back those 100-150 km

Assuming it takes the same time to decelerate that it took to accelerate, I would guess that it would be more like 200 to 300 km by then, because it would still continue to coast away from the launch site while it decelerates...
But then, it would not have to fight gravity too while it is decelerating and it has much less mass to deal with... Hmm...
That said, once it has accelerated in the opposite direction, it would probably not have to go very fast. Just enough to coast/glide the distance back to the launch site. That is going to be interesting. I wonder whether they will have something to help it glide, orient itself. Maybe something like the unfolding parasol thingy that TGV wants to use for their RLV.

Skipjack · Post by **Skipjack** » Fri Oct 28, 2011 1:47 am

Also worth factoring in is that the thing would probably still keep coasting vertically, even while it was already decelerating horizontally.
That could be very beneficial because you would not have to accelerate that much horizontally to make it back to the launch site before reaching an altitude of 0. You only need half (?)the speed to make it back.
Of course this also makes the calculations a lot more complicated...

charliem · Post by **charliem** » Fri Oct 28, 2011 2:25 am

Skipjack wrote:
more to make it go back those 100-150 km
Assuming it takes the same time to decelerate that it took to accelerate, I would guess that it would be more like 200 to 300 km by then, because it would still continue to coast away from the launch site while it decelerates...
But then, it would not have to fight gravity too while it is decelerating and it has much less mass to deal with... Hmm...

You just made me realize the why behind something that bothered me before. For braking the 1st stage after separation the video shows that it'd use 3 of its 9 engines. Why not just one?

Because its mass is much lower than at lift-off that number gives the maximum possible deceleration without surpassing the limitations of the hardware (6 g?). That implies that the 2.5 km/s can be shed in less than 1 minute, and the stage travels about 100 km more downrange in that time.

Yep, you are right, those 0.4 km/s won't be enough to come back, more like twice that.

Skipjack · Post by **Skipjack** » Fri Oct 28, 2011 2:32 am

Yep, you are right, those 0.4 km/s won't be enough to come back, more like twice that.

But would you really need that given the fact that you would probably still be gaining altitude by then?

krenshala · Post by **krenshala** » Fri Oct 28, 2011 5:18 am

If they do land the first stage back at (or next to) the initial launch site, that is definitely going to make for an interesting flight profile/path.

It sounds like the main issues are delta-v available to the first stage after MECO and separation, mass of the stage at that time, and whether it can be upgraded to take the stresses that were tearing up the stage for previous F9 launches.

Skipjack · Post by **Skipjack** » Fri Oct 28, 2011 10:54 am

It sounds like the main issues are delta-v available to the first stage after MECO and separation, mass of the stage at that time, and whether it can be upgraded to take the stresses that were tearing up the stage for previous F9 launches.

I think that those stresses were there, because the stage was decelerated by the atmosphere on reentry. Decelerating it outside the atmosphere with the engines, could potentially fix the problem. Then all you have is a comparably mild stress at terminal velocity, not mach 5...

charliem · Post by **charliem** » Fri Oct 28, 2011 12:59 pm

Skipjack wrote:
Yep, you are right, those 0.4 km/s won't be enough to come back, more like twice that.
But would you really need that given the fact that you would probably still be gaining altitude by then?

Yeah. No matter how much altitude it gains or how long remains outside the atmosphere, the coming back is gonna take some delta-v.

For my calcs I supposed that the 1st stage is above 120 km for ~390s after separation, less time'd imply having to come back faster, so more delta-v. It's just how much speed it'll need to do back those 200-300 km in the allowed time.

Skipjack · Post by **Skipjack** » Fri Oct 28, 2011 10:10 pm

It's just how much speed it'll need to do back those 200-300 km in the allowed time.

I wonder how much cross range their stage would have. I guess somewhere between 0:1 and 1:1?
So at an altitude of 200km, it could have a 200km crossrange, best case scenario. I doubt that it would even make that much though, but then it would probably be VERY bouyant...
So many questions and unknowns. Precise predictions will be very difficult.
I would guess that they will be able to shave at least a little bit of the distance to the landing site off with just "gliding".