This thread was inspired by the discussion here:

https://forum.nasaspaceflight.com/index.php?topic=42656.0Let 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.