Looking at Starship Gamble. #SpaceX

Don’t trade on this blog since 4 billion years of evolution are against my judgment and maybe even God himself. 

 

So we play with numbers here first then we make some conclusion.

 

Empty Starship we are told weighs about 120,000 kg.  At 200 miles orbit, this translates into 30,175,000 Joule/kg (kinetic energy per kilogram).  You have to dissipate this energy on re-entry into the atmosphere and things get hot and violent.  For 30 minute descent, this translates into heating and compression air 557,112 horsepower machine (for full 30 minutes).

So there is the ballistic factor:

• Ballistic Factor=W/(Cd*A)
• You cannot change the W=weight
• But you can change the A=area resisting the flow, and together with
• The Coefficient of Drag=Cd, by maneuvering the Starship during reentry.

There is another measure involved which is Cl=Coeefficient of Lift, as a body goes through the atmosphere it produces lift together with drag (or if it is a ball Cl=0). Starship is designed to produce lift so Cl is not zero. L/D ratio relates Lift to Drag. If Lift is larger than zero the reentry can be spread in time.

The Ballistic Factor ratio of the kinetic energy to the innate ability to convert it into heating of air by compression and friction.

The Ballistic Factor for Starship can go from 205kg/m2 just hitting air sideways to 8000 kg/m2 going the cone first. The coefficient of Drag respectively from Cd=1.5 to .3.  The coefficient of Lift  Cl=0 to .8.  (all numbers estimates, and approximations to show the possible ranges, not precise values)

So what is the gamble quoted in the title?  Let’s see a graph;

As Starship enters the atmosphere at 120km above Earth the air is so thin that it flows over the ship like water from your faucet producing a clear orderly column of water, before you open it up so that it becomes turbulent (mixing) – it is called laminar flow. The surface of the ship heats up from the friction of the air, in the greatest proportion to overall dissipated energy.  As the density of air rises and velocity drops a lesser fraction of the energy goes into spacecraft, but the overall amount of energy is dissipated grows so that the rate at which the heat flows into the spacecraft skin does not drop precipitously.  At 30km the frictional heating and compression of air become so intense that besides convection the surface heats up due to radiative heat, as the air surrounding the ship heats up to thousands of degrees.  The energy radiated toward the ship is proportional to the fourth power of the absolute temperature of the air. As air dencity increases and velocity drops further, there is appearing turbulent convection (transfer of heat when there is a contact of the fluid with solid) besides radiative heating.

Elon’s gamble is to maneuver (change A, Cd, and Cl) the Starship so that heating rate (a critical parameter) can be controlled and spread over time as well as the dominant type of heat transfer, with radiative heat transfer being most advantages because Starship cladding is made from stainless steel polished to reflect at least 90% of the radiative heat.

The above graph shows the results of optimization to strike a balance between structural capabilities and limits on heat transfer.  Elon’s gamble is to move beyond that and aggressively manage the velocity of reentry and by extension the heat transfer rate to the ship, by leveraging the reflective surface of stainless steel Starship.  This might be much more complicated and daring than it seems. The descent engines and the movable surfaces are available to achieve this.  This has never been tested.

Structurally, Starship aimed at integrating the fuel tanks into the shell. There was also a change in material from ANSI 316L to 304L which is unclear why since both are low carbon (since L(ow)) versions of 316 and 304 respectively. The cryogenic test failed as stainless steel might experience corrosion in welds and that depends mostly on carbon content.  Liquid oxygen is not a forgiving fuel to store as over certain pressure the stainless tank might ignite.  (over 1000lbf/in2). The structural issue lingers since many aerospace material are lighter and more suitable with greater strength to weight ratios than stainless. Eleven % of the Space Shuttle weight was dedicated to ceramic tiles.  That was 8,600 kg out of 78,000 kg.  The stainless steel cladding, if 3mm single layer thick, weighs about 34,000kg out of 120,000kg estimated Starship weight (28%).  There seems to be a stainless steel weight penalty.  Will its benefits outweigh the cumbersome process to which was subject the Space Shuttle? Add on top of this the fuel penalty since you take this mass up and then land the Starship just like the other SpaceX rockets.

I am not able to run a detailed analysis, but all I see are weight penalties traded for an idea of getting rid of ceramic tile insulation, at least at this stage of design. The idea can fail altogether or can pass (not likely) the test of reentry but the weight penalties can be such that it might be equally, or even more, unprofitable as the idea of landing the booster stages of rockets on ships. 

 

Let’s put it into narrative.

The Space Shuttle had aerospace alloy + composites (if am correct) construction and used ceramic tiles to protect the craft from reentry heating.

The tiles were causing maintenance and reliability problems, but allowed to lower structural weight of the craft. The problems with the tiles basically defeated the concept of reusable craft. One mission was lost due to their failure.

Elon is constantly looking to beat the paradigm of space travel and picks following strategy.

• Get rid of tiles, and use mirror (as close as possible) stainless steel to reflect off radiative heat of reentry.
• Provide the Starship with lift capability to extend the reentry time and control the amount of heat absorbed.
• Allow the Starship to increase its ability to change ballistic factor by change in Area and Cd, all by maneuvering but this is limited by the maximum deceleration forces.
• Maneuvering allows control of velocity at given density of air so that desired heat transfer regime can be extended. Mirror finish might reflect 90% radiative heat.
• Passive controls by low heat conductivity of stainless steel, and possibly second stainless skin.
• Under this scenario reentry becomes complex and dynamic maneuvering procedure with larger g forces on the frame and crew (possibly at times). Also heating becomes complex and dynamic due to maneuvering, not to mention heating stresses due to temperature differences.

Now, let’s turn our attention to structural weight problems and their tried solutions.

• Use of the cavity enclosed by the skin as structurally integrated fuel tank. Cryogenic test failed probably due to field welds quality. Other issue is the weld chemical corrosion besides just quality issues.
• If indeed fuel tanks would be integral and exposed to directly absorb heat energy upon reentry the pressure in them can rise toward catastrophic failure. (Playing devils advocate)
• If the idea of integral tanks to survive we can not dismiss the possibility of second skin (3mm thick?) to isolate them from reentry heat.
• Non stainless steel internal tanks might the best solution here. Increased weight though.
• The weight of single 3mm thick skin layer is about 34 tons. This is 28% of the 120 ton empty weight. For the Space Shuttle the weight for all the tiles was just 11% of empty weight of ~75 tons. Add second skin?

Assessment of stainless steel as structural material is rather to disadvantage of stainless steel. Light aerospace type aluminum alloys beat stainless with 4 time that strength per unit of weight. Stainless is either chosen for corrosion resistance, for forming, esthetics, and low thermal conductivity (but not refractory or high temperature applications).

1. To eliminate tiles and its shortcomings stainless steel and the above reentry method is chosen.
2. The solution using stainless steel has weight penalty and increases complexity and risk
3. The struggle to lower weight of the Starship and manufacturing shortcomings of #SpaceX lead to structural test failures.
4. The goal of making rapid turnover between launches spaceship seems to be defeated by excessive structural weight as it imposes economy penalty vs. other methods, even if complex maneuvering during reentry will be successful.
5. Every pound of structure requires some amount of extra fuel to be lifted into the orbit. This phenomenon has doomed the efficiency of reusable lift rocket.

The Starship can fail in few ways.

1. Failure of the concept of maneuverable reentry, by way of structurally failure due large aerodynamic forces, by excessive heating of spaceship. These can quite complex.
2. The structural weight penalty making the Starship not economical
3. The attempts to lower structural weight of the Starship can expose it to structural failure.
4. Manufacturing methods are already exposing the craft design to failure.

One very ugly remark on the Starship; I does not look elegant as a solution to engineering problem, it look downright UGLY. You know engineers have intuition too!