A couple days ago I made a facetious remark that Beagle-2 probably
augered into the Martian surface at Mach 5. Unfortunately people began
quoting that number as if it were a true estimate. Just for laughs
I made some estimates about Beagle-2's trajectory. First of all, there
is remarkably little hard information in the Beagle-2 website for backing
out a trajectory. However I did find some diagrams that provided
enough information to enable a crude trajectory to be reversed engineered.
Initially I could not construct a valid trajectory because I used a
base diameter provided in a BBC article. The BBC incorrectly stated that
the aeroshell diameter was 640 mm. This is actually the diameter of the lander.
The aeroshell diameter is 924 mm. The Beagle-2 aeroshell is a scaled down
Huygen aeroshell. I know Huygen's geometry so from Beagle-2's base diameter
I could calculate all other dimensions. The diagram from the Beagle-2 website
states that the entry velocity is 20,000 kph at an altitude of 120 km and that
peak decelleration was 13.3 g at 24.7 km. Also both the BBC and Beagle-2
websites stated the entry mass was 68.84 kg. From this information I
could estimate an inertial entry vector at 120 km which is:

velocity = 5.79 km/sec
entry angle = -15.6 deg

The azimuth angle is unknown along with many other parameters. Assuming
a "cold" adiabatic wall in radiative equilibrium, my first cut trajectory
gave me a peak stagnation point wall temperature of 1628 deg.C. The Beagle
2 website showed a peak wall temperature of 1700 deg.C. The Beagle-2 website
also showed the peak decelleration occurring at 70 seconds after entry. I
calculated peak decelleration to occur at 72 seconds after entry. Given that
I guessed most of the entry vector, this accurracy is about as good as can
be expected.

The peak dynamic pressure was 8.86e+03 Pascals at 72.2 sec. after entry. The
peak stagnation pressure was 1.73e+04 Pascals at 72.2 sec. after entry. The
peak heat flux was 56.96 W/cm^2 at the stagnation point. Modern thermal
protective materials don't start ablating until 80 W/cm^2. The Beagle-2
designers could have used balsa wood or some other low tech thermal protection
material along with simple thermal response modeling. Such a low heat flux
is more the exception than the rule. The peak heat flux for Mars Pathfinder
was 106 W/cm^2 which required a sophisticated thermal protection design.

Assuming the heat shield did not jettison because the electronics was frozen
or there was a pyrotechnic failure, Beagle-2 would have started tumbling after
136 seconds from entry. At that point, the best aerodynamic model is a
sphere rather than a 60 deg. sphere-cone. With that assumption, Beagle-2
would have impacted the Martian surface 172.31 sec. after entry at a velocity
of 291 meters/second (Mach = 1.1) or 651 miles/hour. Note that the time of
tumbling (parachute deployment) to impact time is 36.31 seconds (things happen
fast during Mars EDL). I calculate the parachute deployment altitude for a
60 deg. sphere-cone Beagle-2 to be 7.076 km. The Beagle-2 website shows the
pilot chute deployment altitude to be 7.1 km. Had Beagle-2 used a 70 deg.
sphere-cone, its deployment altitude would have been 7.9 km. Given there's
36 seconds from parachute deployment time to impact, the added 900 meters can
be the difference between success and failure.

Gary