Assume we have a society that has sophisticated enough engineering to build a SSTO chassis that can survive the rigors of repeated launch (MaxQ) and re-entry (thermal stress). What thrust to weight ratio would they have to achieve from their propulsion systems in order to get the craft into orbit around an Earth-clone planet without the need for external boosters?
What thrust to weight ratio would they have to achieve from their propulsion systems in order to get the craft into orbit
This wording indicates that you think there is a threshold. All designs with a TWR lower than this will fail to reach orbit, and designs with a higher TWR will succeed. This premise is incorrect. As SF says in his comment, a winged SSTO can get away with a TWR lower than 1. So depending on body design (large wings, small wings, lifting body or cylindrical rocket) you get a large range of possible TWR figures.
Other numbers are more critical than TWR:
- You need sufficient delta-V to reach orbit.
- You need a mass fraction that's good enough to bring some payload to orbit.
Those two combined (via the Rocket Equation) give a minimum specific impulse required to get that payload to orbit. TWR is a consideration via gravity losses: the longer you take to get to orbital speed, the more gravity losses you'll have and the more delta-V you'll need to account for.
So in order to be able to calculate anything, we need 2 parameters:
- required payload
- available specific impulse
Those two are enough to calculate the starting mass of the SSTO. Economics then decides if such an SSTO is worth building.
There is a chart and the explanation at wikipedia
Being limited by the performance of the existing chemical fuels and being limited by the sane take-off mass of less than 3K metric tonns (the weight of a Saturn V, the biggest rocket ever) then dry weight (everything but the fuel itself - the body, the payload itself, engines, re-entry fuel, safety margin fuel, landing gears, wings etc - everything) must fit into less than ~10% of the total mass, close to 5%, which is very challenging task to achieve.
Usage of better fuels like hydrogen improves the thrust to weight ratio but affects the dry weight because of the decreased density and insulating material for the cryogenic fuel tanks, so overall it does not make a big difference.
In order to SSTO to be technically possible we need the next generation of fuels / engines. Something like metallic hydrogen, thermonuclear fusion engine, photon engine etc.
The question asked I am answering
What thrust to weight ratio would they have to achieve from their propulsion systems in order to get the craft into orbit around an Earth-clone planet without the need for external boosters?
I had wanted to use the Delta Clipper X but had a Eureka Moment that it was a scale testing unit and switched to this instead. To the best of my knowledge, there has not been a "Public" SSTO made or launched. Some may consider Lockheed a credible source.
https://en.wikipedia.org/wiki/VentureStar - VentureStar
While never built the work presented here seems to be consistent with a Full Scale Ship (SSTO)
Function Manned Re-usable Spaceplane Manufacturer Lockheed Martin Country of origin United States Size Height 38.7 m (127 ft) Diameter N/A Mass 1,000,000 kg (2,200,000 lb) Stages 1 Capacity Payload to LEO 20,412 kg (45,000 lb) Launch history Status Cancelled Launch sites Unknown Total launches 0 First stage - VentureStar Engines 7 RS2200 Linear Aerospikes Thrust 3,010,000 lb (13.39 MN) Fuel LOX/LH2
It gives both weight and thrust.
The following is based on the MASS because I have no clue if the Payload is included or not.
0.1643017177 lbs per Newton would be your answer in Newtons.
Or for my bud SF that likes to groan a lot :) 164.3017177 lbs per kN
Or 164,301.717699776 lbs per MN
Treat lbs of mass as lbf of weight, divide thrust in lbf by that and you have the clean dimensionless TWR
3,010,000 / 2,200,000 gives 1.36818118118182 - Just for you
For those that want a good and interesting read on Real Life SSTO's go here
The Delta Clipper, VentureStar, SpaceX, Blue Origin Are all linked together. The Delta Clipper was taken over by NASA killed in favor of their choice the VenturStar because of the landing being horizontal rather than vertical then canceled it for the Space Shuttle and guess were everyone went to work. Let us .... say the obvious, The Shuttle, Delta Clipper XA, VentureStar all ran separately and parallel to each other.