### Author Topic: Size and mass estimates for booster vs balloon launch.  (Read 1236 times)

#### matterbeam

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##### Size and mass estimates for booster vs balloon launch.
« on: 09/24/2017 01:17 AM »
This thread was inspired by the discussion here: https://forum.nasaspaceflight.com/index.php?topic=42656.0

Let us suppose that the dry mass of the payload launched from the suborbital craft's cargo bay is 1000kg.
Let us suppose it uses a small hypergolic engine like the AJ10-190 with 3071m/s exhaust velocity and 33.4kN of thrust.
A TWR of 0.8 allows for a payload initial gross mass of up to 4255kg, so a mass ratio of 4.255

The payload would have a deltaV of 4447m/s.

The suborbital plane must launch the payload at a velocity of 3352m/s to allow it to reach LEO. If we use the Space Shuttle as a reference, the spaceplane dry mass is roughly three times the payload mass, giving the suborbital spaceplane a dry mass estimate of 12765kg, or 17020kg with payload.

Raising the apoapsis of a 20km altitude orbit to 200km increases the deltaV required by about 55m/s. With a 200m/s margin for safety, the deltaV requirement rises to 3607m/s.

The suborbital shuttle will use a cryogenic rocket and needs to provide a TWR of 1. The Vinci engine with 180kN of thrust and 465s of vacuum Isp fits the bill. The spaceplane would need a mass ratio of 2.2 to provide the necessary deltaV.

This would put the spaceplane's fully loaded mass at 37528kg. Two Vinci engines will provide a TWR of just above 1.

Now we have a reasonable estimate of the mass and performance of a suborbital spaceplane that can put a 1000kg dry mass satellite into low orbit. It would be about 37.5 tons and require two Vinci engines.

The stratospheric balloon launch option:

This option involves lifting up the spaceplane to a 20km altitude using a massive hydrogen balloon.

The booster launch option:

This option involved boosting the spaceplane up to 20km altitude using a recoverable booster. For the sake of a fair comparison, this option releases the spaceplane at negligible horizontal and vertical velocity.

What would the stratospheric launch require?

It would need a balloon large enough to lift a 37.5 ton payload up to 20km. Hydrogen has a lifting capacity of 1.202kg per cubic meter. Therefore, 31221m^3 of hydrogen is needed. This is a sphere about 39 meters wide on the ground and will expand 18.5 times at 20km altitude to 577588m^3. It is nearly the size of the Red Bull Stratos balloon at maximum expansion.

What would the booster launch require?

A booster that reaches 20km altitude needs to deliver just 625m/s. To compensate for gravity losses and drag, we might need to deliver 850m/s of deltaV. An RP-1/LOX rocket engine like SpaceX's Merlin-1C is suitable. It has 420kN of thrust and Isp of 275s on the ground and 304s in vacuum. It should average 288s for this launch profile. This would require a mass ratio of 1.35. We will increase this to 1.4 to accommodate a very rough booster dry mass of 1875kg for a gross mass of 16875kg (booster dry mass is 11% of gross mass). Total gross mass on the launchpad is 54.3 tons.

With these figures, we can describe the booster as a rather small 16.8 ton stage using two Merlin-1C engines for a takeoff TWR of 1.8.  Adding a 350m/s powered landing and recovery ability at 275s Isp will require an additional 260kg of propellant, for a total booster mass of 17135kg and a total gross launchpad mass of 54663kg.

The question becomes whether a 17135kg recoverable booster, which is 4% of the mass of a Falcon 9 first stage, is more cost efficient than a stratospheric hydrogen balloon which can lift 37.5 tons to 20km.
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#### envy887

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##### Re: Size and mass estimates for booster vs balloon launch.
« Reply #1 on: 09/24/2017 02:35 AM »
Nice analysis!

One thing that missing is gravity loss for the spaceplane, since it stages with little vertical velocity. This will require about 350 m/s additional dV to orbit (total should be around 9,250 m/s, while you have 8,900 m/s), but doesn't change the comparison of booster v. balloon launch at all.

Also, consider this comparison: the above 3 stage systems (either booster or balloon as first stage) vs 2-stage system. Simply replace the hydrolox with kerolox, and the twin 180 kN Vinci engines with a pair of 845 kN Merlin D engines.

The same volume prop tank holds 83,900 kg of kerolox for a gross takeoff mas of 100,900 kg, average I_sp of 305 s, and booster dV of 5,300 m/s, enough to push directly to a Mach 12 staging velocity. The 1690 kN of thrust rockets it off the pad with a TWR over 1.7:1.

Subcooled kerolox bulk density and Merlin's high TWR, along with the relatively low staging velocity, allow a gorund-launched kerolox booster to beat the air-launched hydrolox booster...

#### matterbeam

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##### Re: Size and mass estimates for booster vs balloon launch.
« Reply #2 on: 09/24/2017 03:39 PM »
Thanks envy887!

I hadn't considered the gravity losses, true. 350m/s extra deltaV from the suborbital stage increases its mass ratio from 2.205 to 2.38, so an additional gross stage mass of 2992kg and an additional gross launchpad mass of 7361kg. That's a 13% overall increase.

Personally, I believe a winged kerolox rocketplane with an expendable payload stage is the best option for cheaper access to space, with SpaceX's VTVL recoverable booster being the next best thing.

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#### JakeSparkleChicken

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##### Re: Size and mass estimates for booster vs balloon launch.
« Reply #3 on: 09/26/2017 11:31 PM »
You should check out Zero2Infinity's BlooStar.  They do a stratospheric balloon launch with the oddest little rocket that takes full advantage of the fact that it doesn't need to be too terribly aerodynamic.  Onion staging and the whole nine yards.  They've got a scale test under their belts, with further testing coming up in the next few months.

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