Huygens probe design and subystems
==================================
 
The probe subsystems are carefully described in INSTRUMENT_HOST.CAT and
are not repeated here. Useful information on the probe design can be
found in JONES1997, KLAUSEN2002.
 
Calibration
===========
 
There are four types of calibration of the engineering parameters:
1: polynomial. Example: the accelerometers (parameters D7004, D7005,
   D7006).
2: value interpretation. Example: the parameter E2004R value can be 0 or 1.
   0=NOT DEPLOYED,1=DEPLOYED
3: interpolation. Example: the temperature sensors.
4: No calibration. Example: the radar altitude is measured in meters.
 
The calibration documents can be found in the CALIB directory.
 
Radar calibration
=================
 
The digital data have been affected by a hardware bug, which caused the
upper bits of the digital 15-bit altitude word to change their logical
state in a seemingly random fashion. In addition, due to the 15-bit
limitation of the digital altitude word, any radar data above 32767 m are
affected by a register overflow. In addition to these digital data errors,
the radar has been found to be sensitive to temperature changes and is
affected by systematic errors that depend on the probe altitude. The raw
digital altitude data have been processed in order to eliminate these known
errors and to calibrate the measured altitude. This is documented in the
file entitled HUYGENS_RADAR_ALTITUDE_CALIBRATION, located in the CALIB
directory.
 
Aerodynamical database
======================
 
In the DOCUMENT directory, and below /AEDB, a document entitled EADS-
ST_HUYGENS_AEDB.PDF presents an update of the Huygens Entry Module (EM)
AErodynamic DataBase (AEDB). This update results from the Delta-Flight
Acceptance Review recommendations held on February 3rd and 4th, 2004. Due
to the very limited set of computations, the updated AEDB (unlike the
previous one) is preferably used for design issues, since real gas and
rarefaction effects have been only poorly described.
 
Two ASCII documents provide the relevant coefficient values:
HUY_AERDB1_ALCATEL.TXT and HUY_AERDB2_ALCATEL.TXT .
 
Huygens Mass ablation model
===========================
 
From  GABORIT2003 [15 December 2003, PhD thesis
title: Modeles et methods experimentales qui supportent
une mission spatiale: reconstruction de la trajectoire
d'une sonde dans une atmosphere planetaire.
Universite de Paris VII Jussieu, page 39, section 2.4.2.]
 
Variables:
ms: mass
ms,o: initial mass (319 kg)
t: time
eta_eff: factor that characterises the efficiency
of the energy transfer between the incidence flux and
the Huygens probe.
ro: Density of the atmosphere
So: Surface of the Probe.
L_abl: ablation enthalpy
v, V: Velocity
Vo: Maximum Probe velocity
Cx: Aerodynamical coefficient
 
dms/dt = -eta_eff * ro * V^3 So /  ( 2 * L_abl)
 
dv/dt = - ro V^2 So Cx / (2 * ms)
 
ms(t) = ms,o * exp (2 * sigma * (V^2(t) - Vo^2(t) )
 
ms,o = 319kg
sigma = eta_eff / ( Cx * L_abl)
 
Sigma has been calculated by matching the expected delta-mass
(from Alcatel) to the previous formulas.
The calculated value is ~4.18 * 10^-10 m^-2.s^2
 
The mass ablation is estimated to be: 9.7 kg.
 
Spin reconstruction
===================
 
ENGINEERING PARAMETERS USED
 
The engineering parameters used as data inputs for the spin
reconstruction are:
 
1) RASU - Radial Accelerometer Sensor Unit is a set of two highly
sensitive accelerometers that provides the radial acceleration.
The raw values are used by the on-board processor to compute a
near real time spin rate estimation for distribution to the
instruments in the DDB (Data Descent Broadcast). RASU is
telemetered at 4 Hz with a 0.47 mg accuracy. Due to the loss of
chain A (LEBRETONETAL2005), only one of the raw RASU
datasets is available on-ground. Nevertheless, analysis of the
processed DDB for both chains (available from the instruments
internal telemetry), indicates that both sensors were measuring
similar values and functioning nominally.
 
Usage: RASU raw telemetry is archived as HK_CDMS_RASU_D8005A.TAB.
 
2) AGC (raw telemetry archived as HK_CDMS_RASU_D8005A.TAB) - Automatic
Gain Control: this telemetry parameter is the control word of the
second coherent AGC loop in the digital part of the receiver. Reported
at 8Hz, it is proportional to the signal power received on board
Cassini. The AGC has been flight-calibrated, being the conversion to
signal-to-noise ratio Es/N0 based on the Probe Relay Test analysis.
 
Usage: AGC raw telemetry is obtained from the archived parameters
 
AGC_raw (digital number) = 256 * HK_PDRS_PSAB_R60047.TAB +
HK_PDRS_PSAB_R60037.TAB.
 
These raw data are calibrated based on the following interpolation
(from PRT#4, day4 flight test data):
 
AGC raw: 612.9438 607.1000 599.8319 590.6696 580.7143 568.5962 554.3304
536.7500 517.0385 475.5833 448.0714 418.8846 388.2768 357.2596 325.9554
295.4000 266.7857 240.8214 215.3393 193.3482 173.7589 155.5893 140.6538
AGC calibrated: -4.6862 -3.6862 -2.6862 -1.6862 -0.6862 0.3138 1.3138
2.3138 3.3138 5 6 7 8 9 10 11 12 13 14 15 16 17 18
 
THE SPIN RATE RECONSTRUCTION
 
*The spin sign: the reversal anomaly
 
As explained in detail in (Perez-Ayucar et al, 2005) the analysis of the
radio link patterns confirmed an unexpected spin reversal in the mission:
the AGC patterns before and after the inversion correlate well only if one
is time-reversed. As a result, the Huygens in-flight spin direction has
been estimated as counter-clockwise (CCW) (seen in the velocity direction;
spin value >0) for the early part of the descent (consistent with the spin
imparted at separation from Cassini), and clockwise (CW) for the whole
stabilizer chute phase (spin value <0). This is non-compliant with the
Probe specification.
 
*The absolute azimuth reconstruction
 
The AGC analysis remarkably provides absolute azimuth as a function of
time, with respect to a known point in the sky, Cassini.
 
The estimation of the azimuth can be performed by integrating the spin
rate, in turn obtained from the radial acceleration (RASU). However,
this method is not accurate enough as it relies on an integration and
therefore it is subject to biases and to the assumption of an initial
absolute reference. Another finer method, the AGC manual counting,
remarkably provides absolute azimuth as a function of time, with
respect to a known point in the sky, Cassini.
 
The Probe Transmitting Antennas (PTA) are not ideal but present an
azimuthal asymmetry (Clausen et al., 2002). As Huygens spun down to the
surface, the received power at Cassini showed periodic variations every
rotation. The PTA gain pattern was measured before launch in a
representative mock-up, so by comparison one can estimate the absolute
Orbiter azimuth in a Probe body-fixed frame. It is assumed that the
Probe is vertical and spins ideally, so that the elevation is
considered fixed (at least for several spin periods) and equal to the
PAA. The elevation slowly evolves with time, and is also taken into
account.
 
After obtaining an absolute azimuth profile in the Probe fixed
reference frame, a geometric conversion is applied to express it on
Titan's local frame.
 
Regarding the inherent error in the identification of the peaks, the
main contributors are: 1) the tested Antenna Gain Pattern data is
limited to a 2 deg step (for both azimuth & elevation). This influences
both the selection of the PAA and the matching of the peak in azimuth;
2) the AGC sampling rate (8Hz) implies that as the period of the signal
decreases, fewer points are available and therefore the angular
resolution decreases; 3) the pixel size when visually identifying the
peaks on a screen. All those contributions are independent; hence a
root-of-squares estimator has been computed. Although dependent on
time, its value never exceeds +/- 5 deg.
 
Regarding the error in the frame conversion, an attitude disturbance in
tip - tilt induces an azimuth error when converting from the PTA
(Huygens body fixed) reference frame to the Titan's local surface
frame. A complex estimation was carried out in (Sarlette, 2005b).
 
 The error estimation is:
 
-Max values up to ~30deg @ start of mission
-Less than 3deg @ touchdown
 
* The spin actual rate reconstruction
 
The most accurate way of obtaining the spin rate is by the derivative
of the absolute azimuth obtained as described from AGC. Nevertheless,
the azimuth values from the manual counting method are not optimum at:
 
- the spin peak, where the rotation (~10 rpm) is fast wrt the
sampling rate of 8Hz. Fewer samples per period are hence available. In
addition the rather strong attitude disturbances in this interval
(rough early descent with the stabilizer parachute) are also reflected
in the AGC.
 
- the spin reversal: as the Probe stopped spinning, the repetition
pattern was not present, and the peak identification uncertain.
Spectrogram (AGC-FFT method) is a coarser but useful method to fill in
these gaps. The dynamic FFT does not provide absolute azimuth, only a
heavily-filtered spin rate, which in turn can be time-integrated to
find azimuth values. Unfortunately, the frequency resolution achieved
by an FFT analysis for an 8Hz signal is directly proportional to the
duration of its periodic cycles. During a large part of the descent and
close to the surface the rotation was slow (less than 3 rpm) and
therefore the spin resolution is coarse. The method is only used around
the spin peak.
 
In the spin inversion, a more appropriate method relies on the
occurrence of RASU values. RASU cannot be used directly to derive the
spin rate since only positive values are transmitted in the telemetry
(design feature). The high sensitivity of the sensor is such that
attitude disturbances other than the centrifugal spin are clearly
recorded, as wobbling, pendulum motion, etc... Assuming that the
disturbance implies an offset in the measured acceleration, equally
distributed around its mean value, the smoothed median is a good
indicator of the instantaneous radial acceleration. Again, the method
does not provide absolute azimuth, only a filtered spin rate, which in
turn can be time-integrated to obtain azimuth values. The error in this
method is large for low spin rates. The spin rate is computed as a
square root of the raw acceleration, so the fixed quantization step
(~0.47mg) in the RASU telemetries implies a variable step when
expressed in rpm, increasing as the spin rate decreases. Many of the
near surface measurements are therefore in the level of the
quantization step, and the retrieval of the spin rate is not as
reliable as in the AGC method. Note that RASU data are cut at 0g.
 
Therefore, the consolidated spin rate of the Probe has been
reconstructed using these combined methods:
 
Time period on 14Jan2005           Values used (method)
-------------------------         -----------------------
09:11:14.67 - 09:15:53.45         AGC manual counting
09:15:52.43 - 09:26:41.67         RASU median smoothed
09:27:15.41 - 09:35:06.20         AGC FFT
09:35:10.47 - 11:37:09.76         AGC manual counting
11:38:11.00 - 12:47:29.755        RASU
 
The reconstructed value of the spin rate can be found in:
/DATA/SPIN_RATE
 
Measurements uncertainties
==========================
 
Information on measurement uncertainties is given for
the three sensors:
 
- Radar altimeter: ~ 3.6 meters.
- RASU: error (%) = 0.4817202 x ACC (m/s2)^(-0.9652554)
- CASU: error (%) = 3.660834 + ACC (m/s2)^(-0.98493632) (without stiction)
 
Discussion on the engineering parameters
========================================
 
Some of the Huygens Probe engineering parameters are discussed in the
following documentation (in the /DOCUMENT folder):
- INDUSTRY_DOCUMENTS/PERFORMANCES_ANALYSIS_2005.PDF
- INDUSTRY_DOCUMENTS/POST_FLIGHT_ANALYSIS_2006.PDF
- PUBLICATIONS/PEREZ_ATTITUDE_2005.PDF
- PUBLICATIONS/PEREZ_LINK_2005.PDF
- PUBLICATIONS/SARLETTE_ATTITUDE_2005.PDF
- PUBLICATIONS/HUYGENS_OVERVIEW_NATURE2005.PDF
 
Temperature sensors
===================
 
Temperature sensors location can be found in the document
/DOCUMENT/TEMPERATURE_SENSORS/TEMPERATURE_SENSORS.PDF .