Heat Shield Nose Cones during Launch and Atmospheric Exit
Reducing Total Launch Costs
A launch loop may launch a million 5 tonne cargo vehicles a year, with nonreturnable nose cones. The (larger) !SpaceX nose fairings cost $20M each; scaling by area ( say, 0.1 ). and assuming an 80% aerospace learning curve (twice as many is a 20% cost reduction) from 20 per year to 1 million (50,000 times as many is a 97% cost reduction) then each nose cone might cost "only" $60,000 .
However, 60 billion dollars for expendable nose cones per year is still way too much. At 10 cents per kilowatt hour, the energy cost of launching 5 billion kilograms is "only" 12 billion dollars. The nose cones would cost five times as much as the launch. Can we make them with less expensive materials and shapes than !SpaceX fairings?
Reducing System Vulnerability at Lower Altitudes
Launch Loops (and someday there will be many) may put billions of tonnes of material into Earth orbit, some of it devoted to tracking errant material and capturing it, reducing the collision hazards that this vast collection of orbiting object represent. There will be mistakes, some material will be hard to detect or collect or recycle, and some of those billions of tonnes will rain back down into the atmosphere as space debris.
The launch loop main track could be as high as 120 km, where the air density ρ is 2e-8 kg/m³. A blunt nosed vehicle exiting the loop at v = 11 km/s would encounter a Newtonian drag pressure ρv² = 2.5 Pa (25 micro-atmospheres) and kinetic energy loss of of 27 kW/m²; very very small compared to the tens of kilowatts per square meter encountered during reentry.
However, space debris in Earth orbit below GEO eventually decays into LEO circular orbits; perigee drag lowers apogee until the orbit circularizes. The decay rate of these orbits is proportional to air density as well, which means the debris lingers near that altitude longer, and the debris flux is higher. We can approximate debris flux as inversely proportional to density, and the time between collisions as proportional to density. A launch loop will have tracking and avoidance systems; debris on a collision course can be deflected below the array. However, this will divert the loop from paying launch, and some debris may slip through unnoticed, with potentially catastrophic consequences.
Deploying the loop at 80 km altitude, where the density is 2e-5 kg/m³, increases drag and heating 1000x, but will decrease orbiting debris flux by the same amount, reducing collision flux proportionally.
Denser Atmosphere, More Heat and Drag
With a 15 degree conical nose, the coefficient of drag for Newtonian flow is 0.14, so the drag loss is 4 MW/m². If the nose cross section is 3 m² and vehicle mass is 5000 kg, the 12 MW drag loss is subtracted from 300 GJ; 30 seconds of 12 MW drag on the hyperbolic trajectory out of the atmosphere is 360MJ, or a 0.12% loss, trivial. A fraction of an extra second of acceleration will add enough delta V to compensate.
While most of the lost energy will heat and chemically shock the air displaced by the vehicle's passage, some will heat the nose cone, and will heat it the most at the stagnation point at the blunt center of the nose. The Chapman formula shows that the stagnation point heat flux is proportional to the inverse square root of the nose radius; a 1 cm radius nose will have twice the stagnation heating of a 4 cm radius nose. If the nose cools only by black body radiation, it will be 20% hotter at the stagnation point, and that could destroy the material. On the other hand, the 1 cm nose has 1/16th of the area, and 1/8th of the total heat flux. So, if a small nose can be actively cooled and the energy absorbed or ablated (perhaps by extruding an evaporating aerospike), it can survive the heat flux.
Most of the nose will be a cone or an ogive shape. The heat flux on the cone will be much lower than that at the nose, so materials with lower heat resistance may save some expense.
China's FSW Wooden ( ! ) Heat Shields
The Chinese Fanhui Shei Weixing Earth observation satellites returned film cannisters in reentry vehicles with oak ( ! ) heat shields.
- 15 cm thick heat shield made of white oak
- 23 flights between 1975 and 2005
Wood is cheaper (and heavier) than Phenolic Impregnated Carbon Ablator (PICA) heat shields; if we can reduce heat shield cost to $6000 while adding the additional cost of 200 kg of mass ( $500 ) for our nose cone, we are ahead.
Low Density Nanowood
But there is (possibly) a third option. Let's pessimistically assume that our nose cone must be 15 cm thick in the airstream direction, with an area of 3.14 square meters, a total volume of about 0.5 m³. Researchers at the University of Maryland report a new nanowood material in Science Advances magazine, with a thermal conductivity of 0.03 W/m-K (approaching aerogel) and a density of 0.13. This nose cone would mass 65 kg with a material cost less than $1000, see table S1 on page 18 of the paper's supplemental materials. With high volume automated production, the nose cones may cost and weigh much less than our (arbitrary) $6000 / 200 kg goal.
Personally, I hope this leads to hundreds of well paying high tech jobs in Oregon's depressed lumber energy. The article presumes basswood (linden), but Oregon Douglas fir might work as well.