1. Buoyancy and Lift
a) lift
Any vehicle operating in a medium may obtain lifting forces from three
primary sources:
static lift, dynamic lift, and powered static lift.
The most economical of these forces from the production of lift point of
view is undoubtedly the static lift wherein buoyant force is generated
by the displacement of a portion of the supporting medium by the body.
For a waterborne vehicle, this lift is embodied in the displacement ship,
and for airborne vehicles, this is the balloon.
The inefficiency of the static lift vehicle comes when it is required to
move through the surrounding medium. Due to the nature of displacement
buoyancy, these vehicles tend to be very large and, as a result, they develop
a great deal of dynamic drag when in motion. The dynamic effects of the
motion can be used to an advantage, however, if the motion can be used
to generate lift. by shaping the body, or a portion thereof, as a lift
producing foil, a lifting force may be developed to support the weight
of the body, provided sufficient forward speed is attained. In air this
is the airplane, while in water this the hydrofoil craft.
A principle disadvantage of the dynamic lift vehicle is that it requires
forward motion of some finite velocity to generate the lift. As a result,
this vehicle can neither fly very slowly nor can it remain airborne at
zero forward velocity (hover). If these attributes are required, one must
provide some sort of internal powering for the static lift, such as a vertical
jet exhaust, or a propeller with a vertical downflow. In air this is the
helicopter or special aircraft, and on water (or in close proximity to
the earth) this is the air cushion vehicle or hover craft.
Having defined these primary sources of lifting force, one might observe
that it is possible to use two of these sources, or even all three, in
combination. By doing so, one moves from the pure lifting force source,
for example static lift, to a hybrid source, such as a partial static lift
and a partial dynamic lift. This is exactly the technique used with Simon.
Its envelope produces static lift, while the two motors provide powered
static lift and dynamic lift.
b) Static Lift of an Airship
Obviously, when looking at an airship, the amount of static lift is
the most important. Because it plays the decisive role on whether an airship
will float or not, it will be looked at closer in the following.
The principal tenet of static lift is that a body displaces a volume of
the surrounding medium whose weight is equal to or greater than the total
weight of the immersed body. If the weight is equal, the body is said to
have neutral buoyancy, while if the weight of the body is less than that
of the displaced air, the body has a positive buoyancy. The lift of he
in air is obtained as following
(1)
The greatest static lift is to be obtained from hydrogen with
helium a close second. It has to be noted that although the weight of a given
volume of helium is approximately twice that of an equal volume of hydrogen, inasmuch
as the lift is the difference between the weight of the gas and the weight
of air, the lifting capacity of hydrogen is but about eight percent greater than
that of helium.
When considering the high degree of flammability of hydrogen, one might ponder
why that gas is even considered as a static lift source. The answer lies
in the economics of its procurement. Wherein helium must be mined or extracted
from minute quantities in the atmosphere, hydrogen can be obtained inexpensively
from the electrolysis of water.
Due to the natural impurities that are present in helium as it is recovered
from the earth, and due to the cost of extensive refining, commercial helium
is seldom available at greater than 98 percent purity. This means that
the lifting force of helium depends on its purity and is never 100 percent.
c) Temperature and Pressure
Very important for the correct use of aerostatic systems is the knowledge
of the weather and its tendencies. The most important influences emerge
through air pressure and temperature changes.
As the airship ascends, the lifting gas expands due to the reduction of
the ambient air pressure. This pressure can be expressed as an index, the
standard atmosphere (ISA), which indicates the air density for different
altitudes above sea level . To prevent overpressure inside the airship
hull as the airship rises, ballonets and valves are used to level out the
differences in pressure. With valves, the pressure may be regulated by
radio signals. Ballonets are small balloons inside the hull of an airship,
filled with air and, as pressure rises, losing air automatically. There
is some altitude at which, with the ballonets completely empty, it is just
possible to return to the ground with the ballonets filled to capacity.
This altitude is called pressure height. Flight above pressure height will
result in the ballonets becoming completely filled prior to the airship
reaching the ground on its descent and then some other measures must be
taken to maintain the shape and pressure of the envelope. The most common
measure is the addition of air to the lifting gas using the previously
mentioned safety valve.
Unless the pressure airship is considerably above the pressure height,
a decrease in altitude or an increase in barometric pressure will have
little or no effect on the static lift inasmuch as the lifting gas will
contract and the airship will no longer be at pressure height.
Because of local heating, usually from the sun on the envelope, it is possible
for the lifting gas to be at a different temperature than the surrounding
air. If the sun heats the lifting gas so that it is at a higher temperature
than the surrounding air, a condition called superheat, the same weight
of lifting gas displaces a larger volume of air, and therefore a larger
weight of air. This produces an increase in static lift.
Inasmuch as the specific density of the gas is inversely proportional to
the ratio of absolute temperatures, the percentage increase in static lift
due to a temperature increase may be found from the relationship
(2)
Because of these large influences of the sun, winds and
air pressure on aerostatic systems, it is recommended to let an airship
fly at sunrise or sunset, in order to avoid strong currents.
2. The Envelope
a) Dimensions - the Look of a Zeppelin
The envelope or hull is the main part of an airship because, as the
wings of a plane, the envelope decides if an airship is going to fly. Most
radio-controlled airships are nonrigid and their envelope is usually in
the shape of a cigar that is kept in form by internal overpressure. Rigid
models often encounter serious overweight problems because of an adverse
weight to volume ratio. The most difficult task is to choose a material
which makes the envelope light, tough, and most important of all, helium-tight.
The envelope is often the factor that keeps people from building model
airships because it is something that cannot be found in other aircraft
model building.
It is very important to give an airship its special design. Some people
might find it nostalgic or even a waste of time to design an airship in
its unique form. This is simply not true. The previously mentioned cigar-shaped
hull gives an airship stability, low air resistance and a maximum amount
of lift. Tried and tested, very reliable and effective designs are the
Goodyear blimp design, Prill's semirigid design, or, of course, Zeppelin's
own, more than 100 slightly variable designs . For Simon, another aspect
was the feasibility of the hull construction with limited means and minimum
expenses. Along with this considerations came the demands Simon had to fulfill.
It had to be the smallest blimp possible for outside operation. Thus, the
design of an ellipsoid of rotation (EoR) combined with a middle cylinder
(MC) was chosen, as described in the construction of Simon, after the simple
formula for the volume of an EoR (3) and a cylinder (4)
(3)
(4)
b) Volume, Lifting Force, and
Weight
In chapter 1. b) Static Lift of an Airship, it becomes clear that the
lifting force of an airship is directly related to the volume of its hull
by equation (1). The weight, however, determines both of these values.
The airship needs a lifting force at least as big as the overall weight
of its components to be able to float in the air. Since temperature changes
and pressure variations influence the ideal lifting force, it becomes necessary
to calculate an ideal lifting force and volume big enough to overcome these
influences. More is better than less. Also, it is often very difficult
to calculate the overall weight of an airship in advance.
It is recommended to actually construct as many of an airship's parts as
possible, i. e. the gondola, the propulsion, the fins, before deciding
on the exact volume of its hull.
For Simon, an ideal lifting force about 10% bigger than its weight was
calculated. This left enough elbowroom for weather moods and eventual changes
or improvements and additions to the blimp.
3. The Gondola
a) Funtions
In general, the gondola of a radio-controlled airship contains the
receiver and batteries and has the motors attached to its outside or back.
The easiest solution is probably to have one motor aft, but it is definitely
more effective in terms of steering to have two motors, one on each side
like on most of today's blimps. The alternative to gondola mounted motors
is to have them in separate gondolas on the sides of the ship or underneath
it, as it has been done with the historic zeppelins. Having them at a distance
from the other equipment helps to distribute the weight load and avoids
interference of their magnetic fields with the receiver. Also, the danger
of damaging the hull is smaller. To completely avoid this danger, impeller
motors may be used . Furthermore, if the motors can be operated independently,
a wide separation increases the maneuverability of the airship.
b) Form and Dimensions
A gondola needs to combine two things. First, the weight of it has
to be as small as possible and the stability very high, to bring up the
question of the material to be used. Secondly, it has to be large enough
to enclose the batteries and electronics. As a third aspect, an aerodynamic
form might be considered. Because the exact center of gravity of an entire
blimp can hardly be calculated, it is a good idea to leave space inside
to move the batteries around and balance the blimp as a whole.
Glassfibers and epoxy, GFC, is the preferred material in such situations
because of their toughness and lightness. Processing may prove to be hard,
since GFC is normally formed through overpressure or an applied vacuum,
but if not done so, the outcome simply lacks smoothness.
4. Flight Dynamics
a) Steering
There are many possibilities to control and steer a floating airship
in the air. For Simon, a most sensitive and weather conditions independent
solution was developed. Simon has two motors, on each side, connected through
a movable axle, that can tilt up and down. This feature is called vectored
thrust (VT).
VT allows for very exact vertical steering of an airship. It may replace
the less effective rudders, which tend to react slow because of the only
low speeds of an airship.
VT produces powered static lift and may play an important role in fine-calibrating
the float of an airship. It makes it possible for an airship to descend
without the use of a valve or other means of letting off helium.
Since the two motors of Simon can be operated independently forth and back
and are separated by over 1 m from each other, they provide a great horizontal
maneuverability. One motor may thrust forwards, the other backwards. Backward
thrust is a little smaller than forward thrust because of the special shape
of the propellers.
As mentioned, a special feature important for any airship is the possibility to operate
the motors forth and back, to produce thrust in both directions. in combination
with VT, this enables the airship to ascend, descend, and make sharp turns
in both directions.
b) Friction and Drag
In order to choose the right motorization for an airship, friction
and air resistance may not be neglected. Friction depends on the material
used. For Simon a Mylar foil is used for the hull, which is fragile but
tough and insulating. With mylar, friction is very small, not relevant.
It's different with air resistance. An aircraft always produces resistance,
drag in the air, depending on its size and velocity after the equation
(5)
The index of air resistance cr may be found through wind
channel tests for different bodies. The index of an EoR lays in between
0.05 and 0.5, depending on the length to width ratio of the body.
In Simon's case, the calculation of air resistance is important because
it determines the power of the motors to choose. All calculations conducted
ignored possible winds and other atmospheric influences on air resistance
since the calculation was only theoretically possible with a cr estimated
to be 0.35.
c) Stabilization
Tail surfaces are needed to stabilize an airship. At the University
of Toronto, extensive studies showed the influences of stabilizers for
an airship, and the conclusion drawn recommended to always use fins with
an airship.
Tail surfaces and rudders need to be designed so that they allow effective
control of the directions of the airship. Because of Simon's VT and independently
controlled motors, rudders are not necessary to further control him. Also,
they are only of limited practical use because of small speeds as mentioned
earlier in this report. Stabilizers are used and designed in a way to stabilize,
but not to overstabilize. Overstabilization means a limitation of the airship's
agility through too large fins. Again, with too small fins, the ship often
progresses in a wave-like motion.
Tail surfaces for airships are built in the same way as those for radio-controlled
planes, just lighter and especially with more surface. Light balsa wood
or styrofoam structures covered with Monokote are recommended. That is
exactly how Simon's stabilizers are built. Its four fins have an adequate
height of 0.55 m each, and a length of 0.40 m.
5. Electronics and Motorization
a) Electronics
Inside the gondola, all the electronics needed to properly control
an airship are arranged. They may include a servo to tilt the motors, accumulators,
speed controllers, a receiver for the radio-control system and batteries
supplying it with power.
Usually, accumulators are bought connected to one another in series . It
is possible to use other accumulators than those for model planes and cars;
Li-accumulators (used in notebook computers) are no more expensive and
considerably lighter. Whatever is chosen, it has to be light!
b) Motorization
There is always the option of using either combustion engines or electric
motors for model aircraft. The advantage of electric power is that it allows
for very precise throttling combined with electronic speed controllers.
Even though an electric system is generally heavier than a combustion engine,
the added benefit of reversibility will drastically improve low speed maneuverability.
In addition, an electric system keeps the same weight and does not affect
buoyancy, unlike an engine that burns gas and makes an airship lighter
during flight. Usually, large propellers with few rounds per mminute (possibly through
a reduction gear) are more efficient than small, fast turning propellers.
Possibly, impeller propellers may be used. Because of their turbine-like
making, they provide excellent protection of the hull from eventual propeller
hits. Also, they are easy to glue to a tilting axle for VT. normal electric
motors need to be welded to the axle. Their disadvantage is fewer thrust
compared to normal propellers.
Simon uses normal 0.115 m, 6-9 propellers for thrust, combined with two
110 W motors. They proved to be dependable and efficient.
6. Etceteras
a) Flight Certification
Fundamentally, radio-controlled balloons and airships are subject to
the same restrictions as other radio-controlled flying models.
There is the question of the use of hydrogen as the lifting gas for balloons and
airships instead of the much more expensive helium. Common belief is that it
is forbidden. The rumor is wrong; a restriction only exists for commercial
employment of manned airships with hydrogen. Still, hydrogen is usually much harder to
obtain because of its dangers.
There are no exact building regulations and determinations of "small
and light" aerostats. When planning a craft of more than 20 kg total
mass, sketches and calculations should be shown, however, to the authorities
for permission.
b) Meteorology and Atmospheric Effects
As mentioned in chapter 1. c) Temperature and Pressure, the lift of
the different gases changes through many different meteorological influences,
and a small airship is hard to control in even weak currents. Additionally,
the danger of losing the airship due to an upward current is always high
for an inexperienced airship pilot. If possible, the tryout and inaugural
flight of a small airship should be made indoors, or if not possible during
the morning of a calm summer day.The authors are talking from experience...
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