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:

Planet

Surface R

Surface G

ΔV

Altitude

R@ alt.

Centrif.

G @ alt.

Diff.

÷0.3 L/D

V & H

Earth

6378 km

9.81 m/s²

11 km/s

80 km

6458 km

18.8 m/s²

9.6 m/s²

9.2 m/s²

31 m/s²

3.3 g

Apollo 16

Mars

3396 km

3.71 m/s²

12 km/s

40 km

3436 km

41.9 m/s²

3.6 m/s²

38.3 m/s²

127 m/s²

13.6 g

FAST 90

Mars

3396 km

3.71 m/s²

8 km/s

40 km

3436 km

18.6 m/s²

3.6 m/s²

15.0 m/s²

50 m/s²

5.3 g

FAST 120

Mars

3396 km

3.71 m/s²

7.3 km/s

40 km

3436 km

15.5 m/s²

3.6 m/s²

11.9 m/s²

37 m/s²

4.2 g

Pathfinder

Mars

3396 km

3.71 m/s²

5.6 km/s

40 km

3436 km

9.1 m/s²

3.6 m/s²

5.5 m/s²

18 m/s²

2.0 g

Curiousity

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 the shock heated plasma absorb more heat.

Skipping Entry ... No: Mars escape velocity is 5 km/s, and circular orbit velocity is 3.6 km/s. Entering vehicles must slow to perhaps 4 km/s to remain in a short period orbit. The energy difference between 12 km/s and 4 km/s is 8 times the energy difference between 4 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 (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:

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.

References:

MarsEntry (last edited 2016-12-27 18:03:29 by KeithLofstrom)