Sometimes Even a Low Ballistic Coefficient Needs a Little Help


This week has many of us thinking about Kicksat and its imminent reentry into Earth’s atmosphere. Here’s an idea for reentering a small spacecraft more gently, maybe Kicksat’s size or maybe the size of one of its 104 Sprites: fill a heat shield with water, and as the heat of reentry converts it to steam, expel it out of tiny rocket nozzles to slow the descent and simultaneously remove that heat.

The key to successful entry into a planetary atmosphere is somehow intentionally dissipating all the kinetic energy of the vehicle. That dissipation will happen one way or another, whether you want it or not. If you don’t plan ahead, the vehicle enters the atmosphere and aerothermal heating raises its temperature until, most likely, it burns up. There are several ways to avoid this fiery end, as we currently understand thermal protection systems. You can cover your spacecraft with ceramic tiles or ablative material. The former heats up but insulates the spacecraft. The latter burns away, taking energy with it. Another approach is to enter slowly, using rocket engines, Buck Rogers style. The lower the speed, the less the vehicle heats up. The technology involved in this slow reentry, known as supersonic retropropulsion, may be a great solution, but it’s not very mature. Maybe helicopter-style autorotation would work. That hasn’t panned out yet, either.

But there’s another option: go small. Very tiny meteoroids, as well as larger manmade hollow objects (such as satellite propellant tanks) survive reentry because of their low ballistic coefficient. That’s a number that tells us the importance of aerodynamic drag in comparison to the reentering body’s own momentum.  A low number means that the body is light for its area, like a leaf on the wind.  A heavy number means it’s denser, like a bullet. Higher drag slows down the reentering body before its speed reaches the point where aerothermal heating destroys it.

Size matters here. Small objects of a given density offer greater surface area for the mass. That’s why the tiny water droplets in mist stay airborne, while raindrops head straight for the ground. Aerodynamics governs the flight of those droplets, but gravity governs raindrops, all because of the ratio of surface area to mass. If you prefer, here’s a mathematical expression of this principle. A sphere’s volume V (therefore its mass, M, for some constant density) increases with the radius R to the third power. Its surface area A increases with R2. The ratio of mass to area therefore increases with R3/R2, which simplifies to R. This ratio determines the ballistic coefficient. So, the smaller R is, the lower the ballistic coefficient, all other things being equal. This principle motivates NASA’s current work on inflatable heat shields.

left_hand_of_lightness Justin Atchison is now a Senior Aerospace Engineer at the Johns Hopkins Applied Physics Lab. Back in 2006, when he was a grad student at Cornell he took a look at this question of how flight dynamics scale, laying the groundwork for what would become the Sprite project. Here’s the output of one of his simulations, which shows how the peak temperature that a simple vehicle encounters during reentry depends on its shape–the thickness and area of a plate, in the case of a Sprite. Any errors in the output are my fault, having revived his simulation years after he last had it working.

slide length vs thickness vs temperature

The three-dimensional graph above shows that a sheet-like object, whose surface area is high for its mass, reenters at low temperatures. Consider a spacecraft comprised of electronics printed on a thin film. Such a sail-like object would reenter without even breaking a sweat, so to speak. Even commercial-grade electronics could continue to operate.

But sometimes even a spacecraft with a low ballistic coefficient needs a little help. So how about this. Go ahead and let the thermal-protection system heat up, reaching 200 °C, the temperature of commercially available high-temperature electronics. That would happen for a body of any reasonable dimensions. Water initially stored in the heat shield at about 1 atmosphere of pressure boils, and reaches higher pressure. Heating up from 273 kelvins (that’s 0 °C) to 473 kelvins (that’s 200 °C) increases the pressure about 68%, according to the Gay-Lussac law. The steam bursts a diaphragm at this pressure, and it vents through rocket nozzles distributed around the perimeter of the heat shield, near the top. This thrust and the deceleration that the vehicle has already been experiencing keeps the water low, near the hottest surface, separating it from the steam that flows out through these rocket nozzles.

Let’s look at the specifics for a CubeSat-size system. We’ll devote 500 grams to water and about 500 grams to the spacecraft and its structure, including this heat-shield-as-pressure-vessel. Let’s say that each nozzle has a 1 mm throat diameter and a 1 cm exit diameter. From basic rocket equations, the steam’s exit velocity is 178 m/s, with a specific impulse of about 18 seconds. That’s not fantastic, but it’s comparable to low-end cold-gas propulsion systems. The total impulse out of this system is 94 kg-m/s. But at least as important is the 438,000 J of energy removed with the steam, as well as the 1,183,000 J of energy required, separately, to vaporize that much water, and which therefore never reaches the spacecraft itself.

So, this system offers four ways to keep the spacecraft cool as it reenters: (1) water as an insulator; (2) water-to-steam as a way to absorb energy via vaporization; (3) steam as a storage medium for energy; and (4) a little supersonic retropropulsion to slow down the reentry during what would be the worst time for aerothermal heating.

There remain some trade-offs. Better propulsion is possible if we let the heat shield become even hotter before the diaphragm bursts and the steam is expelled. But we don’t want a hot vehicle. A more exotic propellant might do better, but we might prefer the safety and simplicity of water for reasons that outweigh propulsion efficiency per se.

The lesson learned here is that some innovation may be possible by rethinking what we reenter and how. Maybe commercial uses of space, such as sending manufactured goods back to Earth as downmass from the International Space Station, would be more cost-effective if very small capsules were returned, rather than large ones: protein crystals grown as advanced pharmaceuticals and dropped back to Earth with a tiny transponder so they can be gathered up and sold. There would be no need for a team of technicians to recover and unpack a large capsule full of supplies and equipment from ISS, with the cost and schedule impact of that activity on commerce.

Maybe this is a way to return scientific samples from asteroids or other planetary bodies. Do-it-yourself atmospheric entry may be the way that citizen scientists learn about the origins of life on earth and the prospects of life elsewhere.


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