Chapter 8
Near Earth Space Flight with Orbiter - Energy and Thermal Considerations - Newton's
Thought Experiment - Bull's Dream
A Database for Shuttle Flight from the time of Main Engine Cutoff,
MECO, to
the ISS
No Orbiter trajectory
timeline was found on any NASA website visited by the writers. A website pseudo timeline
was found with an attribution to NASA. A screen image, shortened, of the
site is shown next:
The site might create the impression that
the data was real, but emails to William Harwood elicited the information that it
was from a computer model of an Orbiter ascent produced at NASA and that the information
was not available to the general public.
Given the absence of factual trajectory
data, the writers decided to study this computer-model output in detail, and then
from the study decided that it could be employed to obtain realistic conditions
for Orbiter at the time of Main Engine Cutoff, MECO, a point in time just prior
to the jettison of the Main Fuel Tank.
The computer simulation of Orbiter's trajectory
concluded at MECO. Deriving the conditions at that point would the allow the
authors to obtain both the trajectory of the fuel tank to its ocean splash-down
and the trajectory of Orbiter from MECO to its rendezvous with the International
Space Station.
Processing Ascent Data
The first step was to get the data into
machine-readable form. A practical way of doing that is to use an OCR (Optical
Character Reader) Scanner. OCR software is often included with popular scanners.
The image was saved in a file and standard
image software was used to display and print a copy.
The printout required suitably large
font so that the numerical figures were easily recognized by the OCR (Optical Character
Reader) device. Once the image was scanned, its data was saved into a spreadsheet
where the desired processing was done. See columns of that spreadsheet next:
Processing the data consisted of removing
redundant row entries corresponding to SRB separation and MECO events. Next, the
data was converted from standard units of measure (feet, etc) to metric units.
Examining the table of data closely reveals
the time column as suspect since some duplicate values exist. We assume this is
due to the fact that the simulation used a fractional time between calculations,
which was rounded or truncated to the nearest integer. Doing a straight linear interpolation
of the time from t = 0 to t = 510s, for each row, provides a new uniformly spaced
time column, E.
For each row we calculate the radial distance
as the radius of the Earth plus the altitude, Column N. The radial component of
velocity, Vr, is obtained from the rate of change of radial distance with
respect to time.
Since we are given the total velocity,
Vi, we can get the tangent velocity, Vt, from (Vi2
– Vr2)0.5.
This is in column
P. Having Vt and Vr, we can get the elevation for the velocity vector as atan(Vr
/ Vt). This is Elev in column Q.
The Azimuth of the Velocity of an Orbiter at MECO
To obtain the azimuth of the velocity
at MECO, we employ the following strategy.
Assume the STS has in fact reached an
orbit where the inclination is close to that of ISS, 51.6 degrees.
We can obtain computer-modeled
values attributed to NASA for the Latitude and Longitude of MECO from the
web site
where Latitude and Longitude are given within a few seconds
of MECO.
Using the parameters that have been determined
thus far, we can employ the expanded spreadsheet to get the actual azimuth of the
velocity. Using the parameters along with an initial guess of the azimuth of 51.6
degrees and trying a few variations on this value will easily produce an azimuth
such that the inclination is ~51.6. We expect an azimuth close to 51.6 since MECO
is not far from the launch point.
The Time of MECO and the Time to ISS Rendezvous
The time taken from launch to MECO can
be seen to be about 510.17 seconds. According to one
NASA reference it will require
about a further 43 hours to rendezvous with the ISS.
The External Tank (ET) Trajectory
Approximately 30 seconds after MECO, the ET is
freed from Orbiter and continues in a separate sub-orbital
trajectory that
leads to a splashdown in a remote region of either the Indian or Pacific Ocean.
We use our 3-dimensional modeling spreadsheet to calculate
its trajectory.
For initial parameters we take values for the ET at MECO
that are the same as for the Orbiter and assume they track with each other for a short
time until separation. The primary difference between Orbiter and the ET simulations
is due to different physical characteristics e.g. mass and shape. Also,
the ET does not have any significant ability to propel itself with rocket motors.
For the simulation we will assume that the parameters defining the physical aspects of the ET remain constant
from MECO onward.
The ET mass is about 27,000 kg without propellant, (mass varies with ET model and
there
are several models). The mass of the propellant is about 730,000 kg. We will assume that
the MECO event occurs as a controlled event before the ET has exhausted
all
propellant. This means a few percent of the propellant remains in the ET at MECO.
For the simulation we will take the amount to be about 1.7% of the initial amount.
This yields a total mass for the ET at MECO of about 40,000 kg.
The tank is shaped like a cylinder with a length of 46.88 m and diameter 8.40 m.
Equating the ET cross sectional area with an equivalent sphere results in a sphere
of radius 11.196 m. A detailed description of the tank reentry explains that the tank
is deliberately tumbled for reentry to ensure its destruction into small, harmless
pieces, as it passes through the lower atmosphere. To simplify the simulation we
ignore destruction and account for the tumbling action by taking the Cd as 2.0,
twice the value employed for Orbiter.
The following figure shows the trajectory for the chosen parameters. The simulation
shows that the splashdown for the ET is in the Indian Ocean near the equator. For the
set of parameters we have used, the splashdown occurs about 2400 seconds after MECO at Latitude
1.828 deg North and Longitude 64.934 East.
Energy and Thermal Considerations
As noted earlier, the ET is destroyed before impacting Earth. We can convince ourselves that
this is the case by looking at the energy involved in the simulation. At MECO, the
ET total energy is about 390,767 kWh whereas at splashdown it is 1,366 kWh. The change
in energy is due to air resistance losses that translate mostly into temperature
increases to the air and to the
ET material.
The ET consists of an enclosing shell as well as internal
tanks, pumps, piping, electrical components and so forth. For this study we assume
that the ET mass is entirely composed of its shell material. Although the
shell is an aluminium-lithium alloy, from the
previous link we note that lithium amounts to only a few percent of the alloy metals
and therefore, for our study, we treat the ET as composed entirely of
aluminium.
We assume, as a guess,
that the ET absorbs half the energy loss, the other half going to
the atmosphere. Since we assume that the ET is made totally of aluminium, we can estimate its temperature rise as a function of the
energy loss. The formula for temperature change with energy is:
Change in energy = change in T * mass * specific heat of aluminium (= 0.9 kJ/kg)
Aluminium melts at 660 deg Celsius. At MECO its temperature has been reduced to a
low value due to being in the upper atmosphere as well as carrying liquid hydrogen
and oxygen for the rocket. We can assume its temperature is below 0 and the change
in temperature is 700-Celsius degrees from that point to its melting point.
Change in energy = 700 * 27000 * 0.9 kJ = 1.7e10 J = 4,700
kWh
After absorbing 4,700 kWh of energy, the aluminium will start to
melt with further energy input.
With about half of 390,000 kWh available, this very approximate analysis shows there
is ample energy to melt the ET even if only a fraction of the energy is transferred
into the ET structure as heat.
The following charts show the altitude and energy profile
for the ET trajectory, assuming the characteristics of the ET are constant (no disintegration).
Note that from MECO to about 1,500 seconds the trajectory follows a sub-orbital
path where the energy remains relatively constant. At that point however, the ET
encounters the denser, lower atmosphere of Earth and energy is rapidly dissipated
due to the resistance of the air. The ET speed slows considerably and near the end
the trajectory tends to be in free fall towards the centre of the Earth at the terminal
velocity of the ET. This is seen in the altitude graph as the linear portion after
2,000 s.
Comments on Other Proposed Orbits
Gerald Bull used a super cannon to propel a dart shaped Martlet 2 to the standing
record altitude of ~ 180 km. He later proposed
to use a cannon to fire an object into orbit
from Iraq. See
The HARP Project and the Martlet.
If the proposed projectile were the record achieving Martlet 2, is there a mountain in Iraq that is sufficiently high that a super cannon placed on the mountaintop could propel it into an Earth orbit?
Newton's Thought Experiment, (ignoring atmospheric resistance), that he used to explain orbits, envisaged a cannon ball shot from a very high mountain that could attain an Earth orbit.
A simulation with the 3-D spreadsheet may shed some light
on the practicality of both Gerald Bull's Dream and Newton's Thought Experiment
when there is Earth's atmosphere to contend with.
Some Assumptions and Parameters
Presume a mountain with Mount Everest's altitude, taken
to be 8,848 metres, a much greater altitude than any Iraq mountain.
Choose as the object the Martlet 2 that still holds the 180 km altitude record.
In the absence of atmosphere it would require a muzzle velocity of ~7,904 m/s to
achieve a circular orbit at the altitude of 8,848 m. That velocity is much in excess
of the 2,100 m/s that we presumed as the value achieved in creating the 180 km altitude record.
It may be that in the future, considerably greater muzzle velocities will be
achieved, perhaps employing an Electromagnetic Pulse to propel the object.
See the
Kirkcudbright gun
that anticipates a muzzle velocity of ~4,500 m/s. This velocity would only succeed in driving a Martlet 2 about 2 degrees of a full 360 degree
orbit before its orbit
intersected Earth's surface.
Use the 3-D Spreadsheet to Model the Achievement
of an Earth Orbit from Everest's Altitude.
Choose an equatorial orbit so that the Z coordinate of
the orbit will be zero.
Stop the Earth and its atmosphere from rotating so that
the rotation does not add to or subtract from muzzle velocity.
Choose the Martlet 2 parameters as 84 kg of mass,
a radius of 0.065 m and a Cd of 0.0127, as were employed when modeling its altitude
record achievement.
A tangential muzzle velocity of 12,000 metres/second was
required to achieve very slightly over one orbit before impacting Earth's surface. See the X, Y and Phi, (angle around the equator), plots
for this case next:
The Earth's surface is included in the X, Y plot for reference.
Note that the orbit of the projectile is eccentric and that the time intervals of
the Phi plot are
an hour apart.
See the effect of increasing muzzle velocity to 12,950 m/s next:
Very few degrees of orbit have gained but the orbit eccentricity
has increased greatly. Note that the time markers are now 10 hours apart.
Further experiments show that the effect of increased muzzle velocity is to ever increase the eccentricity with little increase in Phi.
Conclusions re Escape from Earth
As it is believed that nowhere in space does the density of the atmosphere become identically zero, even an extremely high velocity
object will always travel in a near elliptical and slowly decaying orbit although
the object may be attracted
by or captured by the attraction of other space objects encountered during its
travel.
This look at the effect of atmosphere does not detract from the value of
Newton's airless Thought Experiment.
Nor does it detract from Bull's Dream. Although there is not much detail about the
matter in the records of Bull's work, it is known that he envisaged that an object
such as the Martlet 2 would release a smaller object at a given altitude that would
behave as rocket powered and achieve a somewhat circular but decaying Earth orbit. We have not seen sufficient detail to model Bull's
Dream.
Orbiter's Path from MECO to the International Space Station
The computer output attributed to NASA and published
on the web by W. Harwood provides a believable level of detail about Orbiter's path
from launch at the Kennedy Space Centre to the time of MECO. For Orbiter's path after MECO there
appears to be comparatively little detail available on the Web.
NASA has been providing press kits for the shuttle missions
such as, the aforementioned http://www.shuttlepresskit.com/STS-116/Presskit_STS116.pdf,
from which the following pair of images has been excerpted.
The authors have located little detail on Orbiter's path from MECO
to the ISS prior to the manual proximity operations phase.
As a consequence, the authors made the decision to create a more detailed and, hopefully more intellectually satisfying, navigation scenario
for that part of the mission.
Next
Chapter 9 treats aspects of Orbiter's trip to the International Space Station.
The Chapter suggests a navigation system employing Adaptive Conditional Feedback
Control that makes use of computers for modeling Orbiter's engines and the atmosphere,
for the control of the engines and for providing the time varying coordinates of
Orbiter and the ISS by means of a GPS-like system.
Some elementary orbital navigation techniques are presented.
Models are created both for a first-pass and for a delayed rendezvous of Orbiter and
the ISS.
The Chapter concludes with a summary of the subject matter that Hands-On Math has
addressed and raises a question for consideration.