Mars Entry

By launching from Earth with a few kilometers per second more velocity, the velocity leaving the Earth-Moon system can be greatly increased, and the transit time from Earth to Mars reduced from a 259 day Hohmann to a 90 day oblique trajectory (FAST 90). This costs extra boost, but the reduced travel time reduces consumables, shielding, and zero-gee atrophy for crewed missions.

However, the entry velocity at Mars will increase from around 7 km/s to 12 km/s, faster than Apollo 16's return from the Moon. In order to remain within the narrow band of atmosphere where the drag is "just right", the lift must be adjusted by vehicle pitch angle. For a constant lift to drag ratio (0.3 for Apollo) and a high velocity, the drag and the gee forces can be quite high. The equatorial radius of the Earth is 6371 km, while the radius of Mars is 3396 km, so the radial acceleration to stay in a circular trajectory ( v²/r ) increases inversely proportional to radius. Earth's radius at 80 km altitude is 1.88 times Mars radius at 40 km altitude.

That neglects gravity and density altitude; Apollo peak entry acceleration occured at 80 km (?) altitude (Earth's atmosphere is denser), Mars peak entry acceleration might occur at 40 km altitude (like Mars Pathfinder). A more accurate computation of radial acceleration at 12 km/s:

The maximum gee force on Apollo 16 was actually 7.19 gees, not 3.3 gees, so there is a scaling error factor of 2.2, perhaps due to buffeting, path corrections, and gremlins. If the 2.2 error factor was applied to FAST 90 day Mars entry, the gee forces would be 30 gees. The ratio of Mars FAST 90 to Apollo acceleration in the table is 4.1 times.

The maximum heating rate for Apollo 16 was 346 BTU/ft²-sec, or 3.9 MW/m² (!), with a total heat load of 27939 BTU/ft² or 317 MJ/m². While the chemistry of ionization of CO₂ will be different from N₂+O₂, let's presume the heat load is similar. However, the shorter entry time for Mars corresponds to a higher heating rate, about 16 MW/m², assuming the same vehicle mass to area ratio.

This may be optimistic; the speed of sound in Earth's nitrogen atmosphere is 282.5 m/s (12 km/s → Mach 42.5) while the speed of sound in the colder Mars CO₂ atmosphere is 240 m/s (12 km/s → Mach 50), and important phenomena are proportional to the Mach number cubed. CO₂ is more difficult to ionize, and has bending vibrations that diatomic molecules do not; that may help shock heated CO₂ plasma absorb more heat.

Skipping Entry Mars escape velocity is 5 km/s. Entering vehicles must slow to less than 5 km/s to exit Mars atmosphere into a , high periapsis Mars orbit. The energy difference between 12 km/s and 5 km/s is almost 8 times the energy difference between 5 km/s and 0 km/s; while a skip may help a vehicle arrive at the right Martian longitude, it does not solve the accuracy, gee force, or heat shedding problems.

Parachutes: Martian atmospheric pressure is 0.00628 times Earth's (less dense), Martian gravity is 0.376 gees (same effect as more dense), and Martian scale height is higher (11 km vs 7 km, less dense). The Earth's atmosphere is about 1.2 kg/m³, Mars is about 0.02 kg/m³, 60 times less dense. For the same terminal velocity, parachutes must be 0.376×60 or 22 times larger. Assume that we jettison the red-hot heat shield to reduce the weight on the parachutes and the heat load on the capsule, and that airbags can deploy on landing, to emulate the final ocean splash of the Apollo capsule.

Then there is the return journey. If that is also 90 days (for the same logistical and atrophy reduction reasons), then it will arrive at Earth with the same increase-over-escape-velocity as the launch towards Mars. If Earth reentry is at 14 km/s rather than 11 km/s, the gee forces and heating rate increase to 1.62 times Apollo 16. Not as rigorous as Mars entry was, but consider that the astronauts have endured a total of 6 months in zero gee, and the many more months on Mars at 0.371 gee, with bone loss throughout the mission.

Concerns:

• 1 The quadrupled gee loads at Mars (relative to Apollo) may injure astronauts who have suffered zero-gee bone loss for 3 months.
  • Total mission-time atrophy (almost two years to next opposition) may be fatal at Earth FAST reentry.
• 2 The higher Mars entry heating rate may push engineering limits.
• 3 The higher required structural strength and parachute mass for Mars entry will seriously reduce payload fraction.

Land animals are not fish in "air suits", spacelife will be different than landlife as well. We are adapted to our environment, not weightlessness, radiation, and long confinement. The "humans" who travel to Mars may be technologically adapted homo sapiens, perhaps with many small mechanical, electronic, and microbial implants. More likely, genetically engineered to live permanently in space, tolerant of radiation, zero gee, and hibernation. One-way machines may be the closest approximation to spacelife for foreseeable future.

Spreadsheets

With more initial launch velocity at Earth, a more oblique course with less delta V at Mars is possible; there are many possibilities. The LibreOffice spreadsheet lists a few.

• FastMars.ods spreadsheet

• FastMars90.pdf screenshot

• FastMars120.pdf screenshot

References:

• GDN personal email

• Apollo By The Numbers... also, statistical tables here

  • p305 (pdf page 315) Apollo 16 Entry, Splashdown, and Recovery: velocity 36196.1fps → 11032.57 m/s (assumed relative to rotating surface)

• Apollo Mission Reports with graphs of entry trajectories, see analysis here

• 1967 entry trajectory planning document

• NASA Mars Fact Sheet

• Wikipedia Mars article

  • note: Mars equatorial rotation velocity is 255 m/s at 40 km altitude compared to 471 m/s for Earth at 80 km altitude. Rotation velocity is assumed to be already subtracted to produce the entry velocities given.

• Wikipedia Martian atmosphere article

• Wikipedia Mars atmospheric entry

• Sitting Kills, Moving Heals by Joan Vernikos. Optimal gravity for human beings may be 1 gee or higher.

D.R Chapman

• An Analysis of the Corridor and Guidance Requirements for Supercircular Entry Into Planetary Atmospheres 1960, 47 pages

• TABLES OF Z FUNCTIONS FOR ATMOSPHERE ENTRY ANALYSES cite

• On the corridor and associated trajectory accuracy for entry of manned spacecraft into planetary atmospheres 1959

• An Approximate Analytical Method for Studying Entry into Planetary Atmospheres 1958

Related

• Flight-path characteristics for decelerating from supercircular speed 1961

• Second-order analytic solutions for aerocapture and ballistic fly-through trajectories 1984

• Entry system options for human return from the Moon and Mars

• An approximate analytical method for studying atmosphere entry of vehicles with modulated aerodynamic forces Levy 1960

Crazy Alternative - Harenodynamic Braking with "Deimos Dust"

Escape velocity from Deimos orbit to an interplanetary orbit is 1.35 km/s . Deimos is 1.47e15 kg of rock and sand, which can be mechanically converted into arbitrarily small grains of dust, sorted by size electrostatically in high vacuum.

In 1983, Krafft Ehricke published the intriguing paper MoreLater