Space X to build reusable launch vehicle

charliem · Post by **charliem** » Sun Oct 16, 2011 9:16 pm

Seems to me a bit surprising that no one has tried to do some calcs to the question of feasibility for turning the Falcon 9 on a VTVL vehicle, being this site full of engineers.

I'm no engineer but I'm gonna try my best. The results are highly speculative, I know, but when has that stopped anyone here from dreaming ...

Here SpaceX says that the Falcon 9 1st stage total thrust is 4.94 MN (vacuum), and each Merlin 1C engine has an Isp of 304 s (2.98 km/s, vacuum also). That means that that stage burns about 1658 kg of propellants per second. If the ignition time is 172s (from the 2nd launch video) that totals 281 t of fuel (all tonnes metric).

From the same page: Falcon 9 total weight at lift-off is 333.4 t, so the 1st stage dry weight, plus 2nd stage total weight, plus cargo, must be around 52 t.

The 1st stage fuel tank weights 9.000 lb (4.08 t, from this video).

Total thrust at lift-off is 5 MN and T/W ratio for the 9 Merlin 1C is 96, so engines mass has to be 5.3 t. That means 9.4 tonnes for the whole 1st stage (dry).

How much fuel has to remain in it to let it take down after separation?

At that moment the Falcon 9 is doing 3.2 km/s (also from the video), and if they want the stage to come back all the way to the launching pad they are going to need to counter the horizontal portion of that (I think about 2 km/s or so) and then give it a bit more.

SpaceX is planning to load its Grasshopper RLV with 26.8 t of fuel. From that much the present Falcon 9 1st stage, with Merlin 1C engines, can give a delta-v of 4 km/s at vacuum, or 3.6 km/s at sea level.

That's enough to decelerate the 1st stage. For the going down I'd use parachutes (they are already in their design) and leave just a bit of fuel for doing a powered descent for the very last part of the fall.

So, the question that remains is: will the new Falcon block 2 be able of reaching 3.2 km/s fully loaded, and still retain 27 t of fuel?

In their last August presentation SpaceX said that the Falcon 9 block 2 is going to be lighter (dry), using Merlin 1D engines with a T/W ratio of 160 (instead of 96 for Merlin 1C) and an Isp of 310 s at vacuum (vs 304 s for its older brother), and it will also carry more fuel.

I'll give it a little more thinking.

Skipjack · Post by **Skipjack** » Sun Oct 16, 2011 9:24 pm

According to this:

http://www.spacelaunchreport.com/falcon9.html

there will also be a Block3 of the Flacon9, which is supposed to be using the Merlin 1d (Block2 is only supposed to use the Merlin 1C+, not sure whether they changed plans though).
Anyway, the Block 3 is supposed to have a payload of 16 metric tonnes to LEO (5t GTO). That is ~50% more payload than the Block1 and quite an improvement.
I think that this would probably change your calculations quite a bit as well. IMHO it puts their claims of reusability into a different perspective, if you assume that they were to sacrifice the extra payload of the F9 Block3 for resusability (if the mission does not require the extra payload and it means that the rocket can be reused probably several times, then that decision should be a nobrainer) .
According to Astronautix Dragon has a gross mass of 8 metric tonnes including payload. That leaves quite a margin for extra fuel. Not sure, would have to calculate how much exactly.
I am also assuming that they will save weight by reducing the heatshield on the dragon capsule by 50% (making it still last for about 50 launches) and using 10% for the heatshield on the first stage (which wont need that much) and 40% for the second stage (less savety margins required and more frequent loss of vehicle assumed).

charliem · Post by **charliem** » Sun Oct 16, 2011 9:28 pm

Thanks a lot Skipjack. I had not seen that one.

IntLibber · Post by **IntLibber** » Mon Oct 17, 2011 1:07 am

Skipjack wrote:According to this:

http://www.spacelaunchreport.com/falcon9.html

there will also be a Block3 of the Flacon9, which is supposed to be using the Merlin 1d (Block2 is only supposed to use the Merlin 1C+, not sure whether they changed plans though).
Anyway, the Block 3 is supposed to have a payload of 16 metric tonnes to LEO (5t GTO). That is ~50% more payload than the Block1 and quite an improvement.
I think that this would probably change your calculations quite a bit as well. IMHO it puts their claims of reusability into a different perspective, if you assume that they were to sacrifice the extra payload of the F9 Block3 for resusability (if the mission does not require the extra payload and it means that the rocket can be reused probably several times, then that decision should be a nobrainer) .
According to Astronautix Dragon has a gross mass of 8 metric tonnes including payload. That leaves quite a margin for extra fuel. Not sure, would have to calculate how much exactly.
I am also assuming that they will save weight by reducing the heatshield on the dragon capsule by 50% (making it still last for about 50 launches) and using 10% for the heatshield on the first stage (which wont need that much) and 40% for the second stage (less savety margins required and more frequent loss of vehicle assumed).

The Block 3 has enough payload to launch a mercury class capsule with a lunar transfer/lander module made up of seven Falcon 1 second stage tanks and one kestrel engine, landing the full package on the moon, then leaving the moon and returning to earth with the center tank module, kestrel engine, and the mercury class capsule.

charliem · Post by **charliem** » Mon Oct 17, 2011 1:41 am

If their plan is to use the engines to stop the stage 1 in mid-air, at least horizontally, it's possible it could make it down with no heat shield altogether.

In free fall from 120 km to, say, 50 km high, deltav=sqr(2.h.g)=1.2 km/s, or ~mach 3.5, and even less if we count on air drag.

Skipjack · Post by **Skipjack** » Mon Oct 17, 2011 2:11 am

If their plan is to use the engines to stop the stage 1 in mid-air, at least horizontally, it's possible it could make it down with no heat shield altogether.

Yeah, but they showed a heat shield in the video. I guess it will be minimal. My 10% was very conservative. They might also do aerobreaking of some sort and use the shield for that.
I am still wondering whether for the long term it could be a good idea for them to combine the second stage and the Dragon capsule. That could reduce the weight quite a bit. I see very little reason for keeping them separated other than for savety and abort. Though I do wonder whether this could not be done just as well with the combined second stage and Dragon.

ladajo · Post by **ladajo** » Mon Oct 17, 2011 7:02 am

Mach 3.5 still gets purdy darn hot, even worse with a non-aero shaped structure.

Skipjack · Post by **Skipjack** » Mon Oct 17, 2011 11:34 am

Mach 3.5 still gets purdy darn hot, even worse with a non-aero shaped structure.

Not at 120 km...

charliem · Post by **charliem** » Mon Oct 17, 2011 6:26 pm

The gravitational potential energy of a stationary object of ~20 t of mass at an altitude of 120 km (supposed g constant) is U=m.g.h=23544 MJ

If they were completely converted to heat and absorbed by the object, and this had the specific heat of aluminum (0.9 J.g-1.K-1), that'd increase its temperature by 1,308 K. That's hot yes, but this implies zero radiation, zero transfer of heat to the surrounding air, and also zero powered braking. Don't forget that the way down is going to take more time than the way up (~3 min). Any object a 1.600 C and no input of new heat radiates a fair amount in only a few seconds.

Mach 3.5 in a non-powered flight, and a non-aero shaped structure (high drag) implies quick deceleration. And there is also, as soon as the dynamic pressure gets high enough, the possibility of deploying a supersonic parachute.

In the end it's just a question of which system is lighter/more efficient: powered descent, heat shield, parachutes, or a mix.

I'd say mix. Have you noticed how the SpaceX's VTVL video jumps from the braking burn after the 1st stage separation, to its final approximation to the landing pad? And in between?

By the way, I've reviewed it again, and I can't see any heat shield for the 1st stage.

IntLibber · Post by **IntLibber** » Mon Oct 17, 2011 6:29 pm

Skipjack wrote:
If their plan is to use the engines to stop the stage 1 in mid-air, at least horizontally, it's possible it could make it down with no heat shield altogether.
Yeah, but they showed a heat shield in the video. I guess it will be minimal. My 10% was very conservative. They might also do aerobreaking of some sort and use the shield for that.
I am still wondering whether for the long term it could be a good idea for them to combine the second stage and the Dragon capsule. That could reduce the weight quite a bit. I see very little reason for keeping them separated other than for savety and abort. Though I do wonder whether this could not be done just as well with the combined second stage and Dragon.

Wrong, the heat shield is only on stage 2. Stage 1 reenters engines first, with three of them running, and with thrusters maintaining an engines first orientation.

IntLibber · Post by **IntLibber** » Mon Oct 17, 2011 6:30 pm

ladajo wrote:Mach 3.5 still gets purdy darn hot, even worse with a non-aero shaped structure.

Falcon 9 first stage separation is at mach 8

Skipjack · Post by **Skipjack** » Mon Oct 17, 2011 7:51 pm

Wrong, the heat shield is only on stage 2. Stage 1 reenters engines first, with three of them running, and with thrusters maintaining an engines first orientation.

http://www.youtube.com/watch?v=p176UpWQOs4
At 33 seconds this looked like a heatshield to me.
But you are right, in later shots it does not show a heatshield, only something that looks like a bulkhead or the top of a tank (which would be odd considering that they show the blast of the second stage engine hitting it.
I think that they are not showing everything and keep things deliberately missleading. Elon Musk himself said that the video was not fully accurate.
So you may be (and probably even are) right with what you are saying here.

charliem · Post by **charliem** » Tue Oct 18, 2011 12:55 am

IntLibber wrote:The Block 3 has enough payload to launch a mercury class capsule with a lunar transfer/lander module made up of seven Falcon 1 second stage tanks and one kestrel engine, landing the full package on the moon, then leaving the moon and returning to earth with the center tank module, kestrel engine, and the mercury class capsule.

How many launches is that?

As much as I'd love to see the private sector beat NASA up in going back to the Moon, I don't think it'd be very wise in this manner if what we are looking for is to have a stable private industry off-world.

Much better to wait for a bigger and cheaper launcher, and also a business plan to make some money from going to the Moon.

I suggested starting a small multi-purpose base and putting the Rooms For Rent sign in front. Also start prospecting for resources, like water ice and maybe some other. And if water can be found in sufficient quantities, establishing fuel depots in LEO and LLO, and refill them from the Moon.

By the way. NASA is saying that they NEED a much bigger launcher if we want them to go back to the Moon, or visit Mars or the asteroids. I think they are wrong. Maybe in the future, but right now we are in a situation that I compare to when Henry Ford aimed to put a car in every salaryman hands.

What would have happened if automobiles where still done in batches of 10 or 20 a year, and switching designs every few hundreds?

About space we are still in the stage of "one size fits them all". Make it strong, make it flexible, make it safe, but equally important, make it CHEAP, and if we have to create a school-bus service with Ford-Ts, we will manage, because the school cannot afford to pay for a ten million dollar specially built bus.

What's better for a manned mission to Mars? Four launches of 50 t each at $125 M per launch, or just one launch of 130 t for $1,000 M? I think is a no-brainer.

It's a pity that no other private company that I know of is trying to make launchers besides SpaceX (ULA does not count as they are so heavily subsidized that they are almost as government owned and ruled as NASA, ESA or the chinese). Some more competition could speed things up a bit, and also take down the prices even more.

Maybe if SpaceX is successful, something I really hope, others will appear.

Skipjack · Post by **Skipjack** » Tue Oct 18, 2011 1:36 am

NASA is saying that they NEED a much bigger launcher if we want them to go back to the Moon, or visit Mars or the asteroids.

They did not say that right after the new administration took over. Think of the Augustine panel. There is also a very interesting internal NASA study that has just recently been made public, after some political pressure by Dana Rohrbacher (go Dana!).
They only started saying that when congress was about to cut the funds for some NASA centers that would still be going with a big rocket. All of a sudden they needed a big rocket again.

http://images.spaceref.com/news/2011/HA ... .Study.pdf
Very interesting read!

hanelyp · Post by **hanelyp** » Tue Oct 18, 2011 1:39 am

IntLibber wrote:Stage 1 reenters engines first, with three of them running, and with thrusters maintaining an engines first orientation.

Tail first reentry is likely dictated by a tail heavy near empty stage. Running 1 or more engines on minimal throttle may be to push the reentry shock away, helping keep the engine assembly cool. It would also be useful for attitude control. I recall a design for aero capture using a ballute and a rocket engine like that.