SpelSim Description
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Contents
SpelSim is a Space Elevator calculator (eventually a simulator).
You can select values for all of the key parameters of the system,
and the program will calculate and display the key values of the
space elevator cable under those conditions.
All numbers are expressed in the MKS system,
using meters (m), kilograms (kg), and seconds (s).
Units for a field are shown to the right of the value.
Fields which display no units to the right of the value are unitless.
The notation (m^2) means meters squared;
m/(s^2) means meters per second squared.
The interface panel is divided into three columns, one each for
- Planet (around which the cable orbits)
- Material (of which the cable is composed)
- Cable (for the configuration of the cable)
Each column is indicated by the corresponding keyword in bold.
To the right of the bold label in each column
is a preselected set of known items from which you can choose.
If you wish to set your own values for that column, select the "custom" entry.
Editable fields in that column will turn white.
Output-only fields will stay gray, and have italic labels.
These fields contain values which are calculated based on your inputs.
To change a value, select the "custom" entry for that column,
edit the value in the desired field, or delete it and type in a new value,
and press Enter.
When you press Enter, all of the output-only values will be
recalculated and displayed.
If the values you select do not give a sensible answer,
you may see question marks in some fields.
For example, if you select a weak material on a planet with strong gravity
and slow rotation, the required values may exceed what can be represented
in a double variable (about 10^300), so you will get question marks for the
cable values.
You can select values for the following planet parameters:
- Mass - mass of the planet in kilograms.
- Radius - radius of the planet in meters.
This will affect the calculation of surface gravity and all of the
altitude numbers.
Note that in reality, planets are not perfectly spherical, so do not
have just one simple radius.
Real rotating planets bulge slightly at the equator due to the rotation,
and have other nonuniformities (such as a mountains or continental plates)
that lead to deviations from a perfect sphere.
This simulation ignores these details, but note that this can have an
effect on some of the numbers, especially the calculated altitudes,
which might thus be off a small amount from the values you expect.
- Period - period of rotation in seconds.
If you want to know the rate of rotation expression in radians per second,
divide 2*pi by the rotation period.
This is the sidereal rotation; note that the period of Earth is slightly
less than one full day because the Earth is moving around the Sun at the
same time as it rotates around its own axis.
The following values for the planet are calculated and displayed:
- Surface gravity - in meters per second squared (acceleration).
Calculated as G*M/(r^2), where
G is the universal gravitational constant (6.6e-11 kg*(m^3)/(s^2)),
M is the mass of the planet,
and r is the radius of the planet.
This value does not take into account the apparent centrifugal force
caused by the rotation of the planet.
- Density - in kilograms per cubic meter.
Calculated as M/V where M is the mass of the planet and V is its volume,
where V is (4/3)*PI*(r^3) where r is the radius of the planet.
This is an average density for the whole planet.
In reality, most planets are denser at their core and less dense at
their surface.
- Synchronous altitude - the height in meters above the surface of the planet
at which a satellite orbiting in the planet's equatorial plane
will appear from the planet to remain in a stationary point in the sky.
Calculated as G*M*(p^2)/4*(PI^2)-r where
G is the universal gravitational constant,
M is the mass of the planet,
r is the radius of the planet.
and p is the period of rotation of the planet.
Note that the calculated synchronous altitude for Earth is 35,793 km
rather than the standard 35,786 km.
This is due to inaccuracies in the model caused by assumptions such as
that the planet is a perfect sphere.
For comments about the values used for the known planets,
download the kit, unpack the source, and look in the file
src/net/jimmc/spelsim/Planet.java.
You can select values for the following material parameters:
- Strength - the tensile strength of the material in Pascals.
1 Pascal = 1 Newton per meter squared.
1 Newton = 1 kg*m/(s^2), so 1 Pascal = 1 kg/(m*s^2).
For real world materials, the strength can vary quite a bit depending
on which formulation of that material is used.
For example, there are different kinds of Nylon that range in strength
from 20 to 200 MPa (mega-Pascals).
- Density - in kilograms per meter cubed.
There are no additional values calculated and displayed for a material.
You can select values for the following cable parameters:
- Capacity - the amount of mass the cable is capable of lifting from
the surface of the planet, in kilograms.
Changing this number by a constant factor C will change the base area
and cable mass by that same factor C, but nothing else will change.
- Length - the total length of the cable in meters.
As the cable is made longer, the required counterweight at the other
end becomes smaller.
In real life, there comes a point where the cable tapers off to such
a small size that it can't practically be made any longer.
This simulation, however, merely continues to make the cable thickness
smaller and smaller as the cable goes out.
Note that with a large cable length, the counterweight mass (see CW/Mass)
can be extremely small.
For slowly rotating planets such as Luna or Mercury, you will need a
much longer cable.
- Safety Factor - the derating factor to use on the strength of the
material selected for the cable.
If you select a material with a strength of 100, you don't want to design
the cable to assume a strength of 100, since any small errors can put you
past the strength of the material and it will break.
The Safety Factor field allows you to select how much of a safety buffer
you want to have.
The maximum design stress used in the cable is the material strength
divided by the safety factor.
Most of the below values for the cable
are calculated numerically rather than functionally.
The cable length is divided into a large number of separate elements
which are treated as point masses connected by a massless cable.
Today's computers are fast enough to do this calculation quickly
even when using many thousands of elements to model the cable.
The following values for the cable are calculated and displayed:
- Mass - total mass of the cable.
- CW/Mass - the ratio of the counterweight mass at the end of the cable
to the cable mass.
As the cable gets longer, this number gets smaller.
If the cable is exactly the same length as synchronous altitude,
then counterweight mass and thus the CW/Mass ratio is infinite.
If the cable is shorter than synchronous altitude, then the
counterweight mass would have to be negative in order to keep the
cable up. You will see this as a negative CW/Mass value; this tells
you that the cable will not stay in synchronous orbit because
it is too short.
- Base Area - the area of the cross section of the base of the cable in
square meters.
This is calculated as (C*g)/(S/F) where
C is the cable capacity,
g is the gravity at the base of the cable (the planet's surface gravity),
S is the material strength,
and F is the safety factor.
- Taper - the ratio of the area of the cross section at
the thickest part of the cable (at synchronous altitude)
to the base area.
Stronger and lighter materials give a smaller taper, which is crucial
to the feasibility of building a working cable, since a large taper
means a large mass.
Note also that a smaller safety factor gives a smaller taper.
- C of Gravity - the altitude in meters above the surface of the planet
of the center of gravity of the cable and counterweight.
Note that this value is below the center of mass.
- C of Mass - the altitude in meters above the surface of the planet
of the center of mass of the cable and counterweight.
- C of Centrifugal - the altitude in meters above the surface of the planet
of the "center of centrifugal force" of the cable and counterweight.
Note that this is above the synchronous altitude
and above the center of mass.
The fact that the center of centrifugal force is above the center of
gravitational force means there will be a torque on the cable any time
it strays from vertical, and that torque will tend to keep the cable
vertical.
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March 17, 2003