Space X to build reusable launch vehicle

[charliem]

at 90 km that'd be > mach 15.

you are off by an order of magnitude here.

Well, sure I can be wrong with my calculations, but I've rechecked them and can't see the mistake.

I took the equation for drag from here (the forum soft doesn't like this URL so copy and paste): http://en.wikipedia.org/wiki/Drag_(phys ... h_velocity]

This is the table of air densities that I used (the one in SI units).

Could not find any source for a human body drag coefficient but from here I take that a number between 0.5 and 2.0 is reasonable.

By definition the terminal velocity is that at which the force exerted by gravity equals the drag force, so the calc is simple.

Fg=Fd --> m.g=1/2.D.Cd.A.v^2 --> v=sqr(2.m.g/D/Cd/A)

where m is the mass, D is air density, Cd the drag coefficient, and A the reference area

Do your own numbers, and if you find where I'm mistaken please do tell me.

[GIThruster]

So I guess the question is whether the improved performance of the 1D can allow the remaining fuel to provide enough delta-v to counter that acceleration between 100 and 40 km. If it works, I would think it should be able to divert the stage back towards the launch pad at the same time.

So, it comes down to available and required delta-v again.

Well, not at the same time. Remember, all the horizontal V is away from the launch. To return to the launch area, you not only need to remove all that V, but have a remaining negative V. If you don't remove enough of the V before 60km, the stage will break up, which is just what has been happening.

[Skipjack]

charliem, there have been many suborbital launches to 100+ km of many differently shaped vehicles and I cant remember any of them requiring major heat shielding. At Mach 15 you would definitely need that.
The SS1 and SS2 barely reach Mach 3.5 and that is on the way up, not the way down. Certainly, they are shaped like gliders and not human bodies, but still...
I just dont see why there would be such a huge difference.

[Skipjack]

Well, not at the same time. Remember, all the horizontal V is away from the launch. To return to the launch area, you not only need to remove all that V, but have a remaining negative V. If you don't remove enough of the V before 60km, the stage will break up, which is just what has been happening.

Yepp and I am pretty sure that this will take the bulk of the fuel.
It is not that far of a distance to go back though, as we have learned (only 300km).
It takes a lot less energy to slow down an almost empty stage with the help of gravity (the trajectory should still be mostly upwards at that point?) than accelerating a full first and full second stage plus payload against gravity...

[charliem]

charliem, there have been many suborbital launches to 100+ km of many differently shaped vehicles and I cant remember any of them requiring major heat shielding. At Mach 15 you would definitely need that.
The SS1 and SS2 barely reach Mach 3.5 and that is on the way up, not the way down. Certainly, they are shaped like gliders and not human bodies, but still...
I just dont see why there would be such a huge difference.

I think I've found the origin of the discrepancy.

The terminal velocity of a ship with a drag coefficient of 1, characteristic area 10 m2, weighting 1.2 t, at 80 km high (not at sea level) is 11 km/s (~mach 32, more than the orbital speed at than altitude).

But, if you leave a body in free fall at 100 km, when it crosses the 80 km line it's only doing 619 m/s, much much less than the terminal speed.

Although, if you leave that same body fall from not 100 but 200 km, the speed at 80 km will be 1500 m/s, much faster but still well under the terminal velocity (so it would keep accelerating). And if falling from 280 km at that level its speed is now 1927 m/s.

I've done a first aproximation numerical integration counting for gravity and drag, and it says that if our theoretical ship reaches 100 km its max speed on the way down is 975 m/s (mach 2.9) at an altitude of 45 km, and max decceleration 2.8 g at 27.5 km (if falling like a stone, with zero gliding).

If it falls from 200 km max speed is 1600 m/s at 50 km and max decceleration 5.5 g at 35 km.

If it falls from 280 km max speed is 2010 m/s at 55 km and max decceleration 8.1 g at 35 km.

So the most relevant question is: what's the maximum altitude the ship reaches before coming back down?

[Skipjack]

If it falls from 280 km max speed is 2010 m/s at 55 km and max decceleration 8.1 g at 35 km.

The Apollo capsule came in much hotter, but I doubt they had such strong deceleration forces (not that pleasent either, but 8.1 Gs seems extremely rough). Normal capsules returning from the ISS certainly dont reach forces like that. Long term astronauts would suffer severely otherwise.
Now, if you consider that a capsule comes in with Mach 25 already, the G- forces would have to be even larger than you described for a part that simply is accelerated by gravity from a complete standstill, no?

Edit: of course the trajectory will play a role as well. If you reenter at a more shallow angle and therefore spend more time in the thinner atmosphere, you will decelerate more gradually...
Of course all that adds to the list of assumptions that we will have to make complicating predictions about what SpaceX is doing and how well that is going to work.

So the most relevant question is: what's the maximum altitude the ship reaches before coming back down?

Yes, that is a good question. I dont think it would reach the full 300km that it would reach if there was no active breaking. I guess that they will break part of the upwards motion as well as the horizontal motion as well.

[charliem]

Change the conditions and you'll change the numbers. The ones I wrote are for a ship following a pure vertical trajectory, with no lift capability at all, falling like a stone, etc.

To lessen speed and acceleration you can:

• 1) Augment the area,
  2) Choose a shape with higher drag coefficient.
  3) Decrease mass.
  4) Give the ship some gliding capability, with a reasonable L/D ratio you can obtain an upward force to brake before getting to the denser portions of the atmosphere.
  5) Change the trajectory to get more braking in the upper atmosphere.
  6) Make it reenter from a lesser altitude.
  etc

Using the known numbers for the Falcon 9 first stage my integration says that, depending on the trajectory and final mass, the g forces it suffers while going down could exceed 10 g and mach 5.5. Of course there are a lot of suppositions in those calculations so the real numbers are probably different, but this shows that very strong forces and high speeds cannot be dismissed that easily.

[charliem]

I,ve been thinking about the possibility of some kind of air brakes for Falcon9-1st.

For example using an inflatable structure around the top of the stage, a ballute, kind of.

It'd increase its specific area, modify its drag coefficient, probably enhance its stability, and maybe even give it a bit more lift, Moreover it'd avoid the problem of inflating a drogue parachute in very thin air.

[Skipjack]

For example using an inflatable structure around the top of the stage, a ballute, kind of.

Yeah, that is something I suggested earlier. They already had inflatable floatation devices for sea recovery. So that is not a big stretch.

[93143]

Normal capsules returning from the ISS certainly dont reach forces like that.

They do if something goes wrong and they have to make a ballistic reentry. Soyuz capsules have a reasonable L/D if they have attitude control, but that one time the service module failed to separate and the reentry went pear-shaped, the crew was subjected to about 9 gees.

[Skipjack]

They do if something goes wrong and they have to make a ballistic reentry. Soyuz capsules have a reasonable L/D if they have attitude control, but that one time the service module failed to separate and the reentry went pear-shaped, the crew was subjected to about 9 gees.

Yeah, but that is returning from orbital speeds, not from a standstill...

[charliem]

Too many unknowns to determine what happened to the first stages from the F9 flights one and two.

I wonder if SpaceX got enough telemetry from them during reentry, if at all. From their declarations looks like they didn't.

I suppose they'll rig the next few launches with more sensors and recording gear to try collect more info, essential for building a VTVL vehicle.

Two data we lack that are important to calculate the flight profile during reentry are dry mass and drag coefficient (anyone with access to a wind tunnel? ... ). Using 15 mt and 0,82 a simple spreadsheet says that when crossing the 30 km line deceleration is only 1.5 g, but if keeps increasing until a maximum of ~ 10 g between 15,000 and 10,000 meters of altitude.

If these numbers are not way off they suggest the possibility of deploying a drogue parachute much earlier. It should be doable at 30,000 meters (speed mach 5.6, air pressure 1/67 than at sea level), maybe even a bit higher. That'd flatten a bit the deceleration profile, increasing it a higher altitudes, but decreasing the 10 g peek later in the fall.

[charliem]

I've also been giving some thought to the launch escape / powered landing system for the Dragon capsule, and it doesn't look easy.

It implies a quite high weight penalty.

At lift-off a Dragon weights 10.2 mt (4.2 dry weight plus 6.0 of payload) and at landing 7.2 mt (4.2 dry plus 3.0 payload).

In case of malfunction at lift-off, to be able of getting far enough form the rocket, and fast enough, the LES has to be able to accelerate quite hard. The Soyuz LES can do more than 12 g using solids.

Obtaining such high accelerations with liquid fuel rockets (mandatory if your intend to use them for power landing, or at least hybrids) would mean sacrificing a good chunk from the cargo mass:

• 11.2 t * 12 g / 80 T/W = 1.7 mt

And we still have to add the fuel.

I'll estimate it only for the powered landing (the escape system could use the parachutes and splash down on the sea).

Terminal velocity for the Dragon capsule is 150-200 m/s, and it weights 7.2 mt. The total amount of propellants needed will depend on how gentle and slow the final approach.

Braking hard it would take burning only 550-600 kg of fuel in 2-3 secs, but also subjecting the crew to more than 8 g. So we have to add the fuel needed to do a more gentle touch down.

With a "mini-Merlin 1C" you could hover 7200 kg using ~24 kg/s of fuel, while a "super-Draco" thruster would need ~30 kg/s. Lets say 15 secs of "hovering" and the total propellants weight rises to around 1 mt.

And there's another setback. According to the videos shown by SpaceX the Dragon landing rockets fire at an angle of about 45 degrees, and that implies a loose in thrust of ~30%, so the real weight for the engines and fuel should be proportionally higher, 2.4 mt and 1,4 mt.

¡¡¡ So they'd have to use the whole cargo capacity, and even a bit more !!!

I see some possible ways to alleviate the problem:

• 1) Decrease the maximum acceleration for the LES, 6 instead of 12 g should be enough. That'd decrease the engines mass by half.
  2) Develop engines with a T/W ratio much higher than 80.
  3) Decrease the capsule terminal velocity (parachutes? air brakes?).
  4) Reduce the time of the powered landing phase as much as possible (more gs, minimum hover).
  5) Make the Draco block 2 heavier (although that'd also mean having to redesign the launcher, block 3?).

[Skipjack]

Charliem, I think (not sure), that the LES thrusters will replace some of the OMS thrusters on the dragon capsule and they will end up having a dual function.
I still think you are way overestimating things here. Just think about it. There have been very serious VTOL SSTO designs that use powered landing. We are just talking about a first stage here and the capsule. This should be much, much easier to achive than a full SSTO.

[charliem]

Charliem, I think (not sure), that the LES thrusters will replace some of the OMS thrusters on the dragon capsule and they will end up having a dual function.
I still think you are way overestimating things here. Just think about it. There have been very serious VTOL SSTO designs that use powered landing. We are just talking about a first stage here and the capsule. This should be much, much easier to achive than a full SSTO.

You might be right Skijack. We have so little hard data that all we can do is speculate, and to date there's no way of knowing how near or far from reality are our speculations.

In the end it's just a question of entertaining ourselves ... and I like physics and engineering more than crosswords

I was hopping that someone over here, or in the other forums I follow, had some hard data, or maybe a few more knowledgeable suppositions, but i seems that this thing is almost as closed as "our" Polywell ...

About the LES doubling as part of the OMS thrusters. It sounds plausible, although in the video from SpaceX looks like they don't. Anyhow a Draco thruster gives only 400 N, while the LES ones have to be much more powerful, no less than 36,000 N each if they are going to be able to accelerate the capsule at 2+ g.

I hope they don't delay much more the 3rd Falcon 9 launch. With a bit of luck SpaceX will give us some more data bones to munch then.