GARGOYLES AND FLIGHT
Written
by Marco Previtera, AKA Shadowrider.
Shadowrider77@hotmail.com
Introduction: How can a
gargoyle fly?
‘He leaps from the top of a building with his
wings extended’…ok, thank you, but what is the mechanism that allows such a
creature to fly? Being an aerospace engineer, I’ve always been interested in
anything involving flight. So, ever since I saw ‘Gargoyles’ the first time, I
have always wondered about how the aerodynamic principles that for million
years have allowed many kinds of creatures to run the sky, both by natural and
artificial means, could apply to a gargoyle. Now, thanks to the owner of this
site, Fleur Rine, who agreed to publish this article, I have the chance to
provide a public answer.
Ok, just a warning: this is not intended as
an in-depth aerodynamic essay. Both for reasons of space and time, and with the
intent of allowing some comprehension even to those who have not a particular
knowledge in dynamics of fluids or in vectorial calculus operators, I will keep
the theorical part to a minimum, focussing instead on the practical aspects of
the question…let’s say that I will tell you the results without explaining how
I obtained them. Plus, I will avoid
considering some aspects of the question.
For example, in the whole article I will happily ignore all the boundary
layer effects, and I will consider all factors as time-invariant and also, I
will not consider in the slightest way the fact that a flying object needs not
only an external balance of forces, but eventually an internal one. Also, since
we will be considering speeds that are very inferior to that of sound, I will
conventionally consider air as an incompressible fluid
If anyone will want to know more about
aerodynamics and about flight mechanics, I will put a small bibliography in the
end of this article. I will eventually give Fleur an email address to contact
me, so if any of you will have any question about what I’m gonna write, feel
free to contact me, and I’ll answer as soon as possible.
Ok, there’s nothing more I must foresay, at
least so it seems to me, so, let’s start…
[NOTE: through all of this article, I will
use only the measure units of the International System: meters, kilograms and
so on…]
Chapter 1: Fundamentals of
flight
Consider an airplane in flight. Now, what we
want is for it to fly at a constant altitude, with a uniform speed, and on a
straight trajectory. This condition is called usually level flight. When an airplane is in condition of level flight, no
acceleration of any kind (linear or angular) is present, and, since
acceleration on a solid object is equal to mass multipled by the vectorial summatory of the forces acting
on the object itself, if we want to obtain level flight we must obtain that all
forces are balanced with each other. We must obtain equilibrium.
But, what are the forces that act on a flying
object like an airplane? Let’s look at the picture below:
It is a EF 2000 ‘Typhoon’ in level flight, if
you’re wondering. Now, let’s see the forces in detail:
W is the weight. There is no great need of
explanation, just remember that here weight is not the same of mass. Weight
here is a force - equal to mass by
gravitational acceleration. For example, if we imagine the plane to be close
enough to the surface of Earth (within a 200-300 kms from surface, more or
less…actually, we could go even to 2000 kms from surface without significant
variations of gravitational constant, but it is not our case), 1 kgweight = 9.8 Newton = 9.8 m/s2 *
1kgmass. For our purposes,
weight can be considered with good approximation directed orthogonally to the
surface of Earth.
T is the engine thrust. Jets, rockets or
propellers make little difference here. Thrust should require some more
explanation (it is an aerodynamic force itself, after all), but, as will become
clear quite soon, we will pass over it for the time being.
D is aerodynamic drag. It is a force
generated by the relative movement of air around a moving object. Anything
moving in an atmosphere is subject to an aerodynamic drag, whose actual
strenght is determinated by the speed at which it’s moving, the shape of the
object and so on. For airplanes and flying obects (except montgolfiers and
similar things) in particular there is one more component of the drag…a very
important component, too. I will return to it soon.
Now, we want to obtain balance, as I
said…meaning that all forces must
balance each other. Now, thrust can balance drag, but how we balance weight? We
could use thrust to balance weight as well, but we would need a propulsion
system of great power. Plus, it is such
an inelegant solution. What we do, instead, is introduce a new force…
L is the aerodynamic lift. As the name
suggests, it is like the drag, a force generated by relative movement of air,
and it tends to lift the object, giving it an acceleration upwards. Now, what
we want to know is how lift is generated. The answer is in the wings.
Imagine if you could take an airplane wing,
cut it longitudinally, and then observe the section obtained. What you’d see is
something like this:
This shape is called wing profile, and it is its shape that creates the lift (This
profile in particular is that of a low-performance small aircraft.
High-performance aircrafts have dramatically different profiles, due to
different needs at speeds close or superior to speed of sound. Military
supersonic jets have profiles that look like simple foils – those are called
superlaminar profiles). When the
profile is hit by a flow of air (from an aerodynamical point of view, there is
little difference between a still object in moving air, and a moving object in
still air), its shape causes air on the upper face to accelerate, and air on
the lower face to decelerate. But (given the correct conditions, and here we
assume we have said conditions) pressure * velocity = constant, so an
increase of velocity causes a decrease of pressure. Consequently, pressure
below the wing profile increases, and decreases above. This pressure gradient
creates a thrust upwards that is what we call lift. Now, we can apply the same
concept to a complete, finite wing, and calculate the lift it will produce.
(The finite wing shall not produce the same lift of a wing profile, but
something less, due to a series of aerodynamic and structural factors.)
After some calculations, we obtain something
like…
L =
1/2*ρ*v2*S*Cl (it is
the simplest case…we will see why in a moment)
L is the lift, of course. Ρ (rho) is the
density of the atmosphere in which we are moving (close to surface of Earth it
is 1.225 Kg/m3). V is the
relative airspeed, measured far enough from our wing. S is the surface of the wing (seen from above).
Cl is the lift
coefficient, and it is a very complex factor. It depends on the wing
profile, of course (different profiles have different performances), but also
on the shape of the wing (seen from above), on the wing extension (wing span divided by wing chord – see drawing above for wing chord), and on the angle of attack (the angle formed by the
wing chord and the relative direction of air. Since we are discussing about
gargoyles, and gargoyles are gliders, and gliders cannot fly with high angles
of attack, we will assume that angle of attack has always very small values,
close to zero). Discussing here how the Cl is precisely obtained would be too long, and of little
interest. I will just underline how an increase of Cl will of course
cause a direct increase of the effective lift.
Now,
to be precise: the expression of the lift I wrote above applies only in one
particular case, that of a wing whose Cl is constant on the whole wingspan. If –like is usual in
actual aircrafts and even more in flying creatures – the Cl varies
greatly as we move from the root of the wing to its tip, we are supposed to
integer the whole wingspan to obtain the lift.
But, usually the Cl variation is not easily representable by
a mathematical function, if not for very short traits of the wing itself, so
the actual calculation, especially for living creatures, results very complex
and requires a lot of time (a Cray-class computer could need at least six
months of continuous work to calculate the Cl of a finite wing,
although usually are employed numerical methods to decrease this time with a
good approximation of the result). For our current purposes, though, the
expression written above is sufficient, since we will consider Cl as
an average value.
Now
that we have discussed lift, we will return quickly to the drag. As I said, drag applies to all objects
moving in an atmosphere – the force we all experience everytime we are in a car
or on a train is caused by the attrition of air around the moving object, and
is called shape-induced drag. In the
case of an airplane (but it also applies to some categories of racing cars,
like Formula 1 for example) there is a second component of the drag that does
not apply to other moving objects. It would be too long to explain here, but
the same pressure gradient that creates the lift, also creates an aerodynamic
force that opposes that movement. An aerodynamic force that opposes movement is
a drag, so we can identify a lift-induced
drag. Now, if we calculate the drag force acting on the whole aircraft, we get:
D=1/2*ρ*v2*S*Cd
Cd
is the drag coefficient (other
factors are same as previous) and for the complete aircraft (wings, fuselace
and everything else) can be expressed as
Cd=Cd0+Cl2/(π*λ*e)
Where
Cd0 is the shape-induced drag of the fuselace and of the wing,
λ is the wing extension (see above), and e is a parameter that depends on
the shape of the wing, and that we determine experimentally (usually spans from
0.7 to 0.9). Now, please notice that in the expression of the complexive drag
of an airplane, the lift coefficient appears. And, it is squared. Hence, increasing the Cl of
an airplane does increase the lift, but it also increases the drag – and drag
will increase very faster than lift.
Now,
a final consideration. We can imagine how, according to the different phases of
flight, we could wish to have different values of Cl – a higher
value for low-speed flight, and a lower one to decrease drag at higher speed.
Flying creatures, like birds and bats, have understood this very well. In fact, they can actually modify their wing
shape and profile while flying, eventually differentiating it in very small
sectors of their wings. We humans, since we started building machines that
imitate what Nature has achieved in millions years of evolution, tried to do
the same. And, even if we are still far from reaching the level of the
creatures we try to inspire to, we obtained some results. It is possible that
even more noticeable results in this field will be obtained in future.
CHAPTER 2: GLIDERS
Now
that we have some understanding of the forces that act on an aircraft, we will
focus on the particular case of a glider. A glider is, by definition, a flying
vehicle (or creature) that has no propulsion system. If we consider the force
balance diagram we have seen above, in the case of a glider we must eliminate
the thrust. This gives us a problem: how can we obtain a balance of forces
without the thrust? How can we balance the drag? The answer is that we cannot.
There is no way in which we can obtain a perfect balance of forces (this,
naturally, is if we consider a glider moving in steady air). Consequently, a
glider shall not be capable of level flight. But what we can do, though, is
trying to come close to an
equilibrium. To obtain this, we must do two things: first, we must make it so
that the complexive drag (and weight) is as small as we can obtain, and second,
we must make it so that lift balances at least part of the drag:
Lh and Lv are
respectively the horizontal and vertical components of the lift force. As we
can see, a glider must use the lift to balance both the weight and the drag. It
implies that a glider will be forced to meet the airflow with at least a small
angle of descent, and consequently a glider in calm air will constantly
decrease its altitude. Both natural and artificial gliders, though, have learnt
to use the ascending thermal airflows
that tend to appear in some conditions, and that allow a glider to keep its
altitude, and eventually to increase it. We must notice, though, that for such
a mechanism to work, both weight and complexive drag must be very low. In particular, the shape of
the whole object must be as aerodynamic as possible, with very smooth surfaces
and a very simple structure, so to decrease shape-induced drag; plus, the wings
tend to have a great extension and an
extended surface, and consequently a very small chord: such a wing, in fact,
can generate a lift sufficient to sustain the glider even at low speeds and
with a very small lift coefficient, hence decreasing the lift-induced drag. The
albatros bird (an extremely efficient glider, able to cross oceans with just a
few flaps of his long wings), or even the common seagull (who is also a good
glider, although it is far from the albatros’ performances), are a good example
of this.
CHAPTER 3: GARGOYLES
Let’s see, now, how what we learnt above can
be applied to a creature like a gargoyle. To do this, we’ll analyze a random
gargoyle…
Yes,
of course I picked up a random image. Why are you asking?
Anyway,
let’s make some dimensional analisys…
Estimated
weight: 80-100 kg (the wings must have a skeletal and muscular structure, and
this adds weight)
Estimated
wing surface: 4 – 5 m2 (and I’m being generous…)
Now,
we want the gargoyle to be able to glide at moderately low cruise speed, more
or less 60/80 km/h…so, what we want to determinate is the Cl that is
needed to obtain this. (I will use average values for speed and weight)
90 kg = 1/2*ρ*(70 km/h)2*5 m2*Cl
we get a Cl of…
3.11!!!
This is high for a glider. It is very, very high…in aeronautics, it is
rare to have values above 2 for gliders. With such a lift coefficient, the
lift-induced drag alone would be of about 80 kgs (remember that here lift must
compensate weight and drag…and we
imposed for the lift an absolute value of 90 kgs) and I am not even considering
the shape-induced drag (Gargoyles do not have a very aerodynamic shape - too
many appendaces and rough surfaces). With such a lift coefficient, a gargoyle
could hardly glide for very short distances – they certainly could not fly
around for hours like we see them doing in the series. Actually, if the value
of shape-induced drag is high enough, they could not be able to glide at all!
The actual problem is that the gargoyles as we have seen them on TV have too
small wings - in order to effectively glide, they should have at least four
times the wing surface they have, and their wings should be much longer and
thinner than they are. But this would cause problems when the gargoyles, once
landed, are supposed to move around with their wings folded on their backs…
Ok, so we have demonstrated that the
gargoyles as we are used to see them would not be that great flyers in the real
world…but, since we are talking about fiction, I will ignore this result for
the remaining part of this article.
CHAPTER FOUR: MANEUVERS
In this chapter I will show how a gargoyle
can make basic flight maneuvers.
Rolling and turning
We have seen above how a gargoyle, just like
a bird, can modify his own wing profile to increase or decrease the lift
coefficient according to flight conditions. This same mechanism allows the
gargoyle also to roll on his side, by variating the profile of just one wing.
On the left, we have our gargoyle (ok, it
doesn’t look like a gargoyle that much - unluckily, I have to write this article in my spare time, and
I have no time now to put together something better) on level flight situation.
Each of the wings is producing the same lift force. On the right, our gargoyle
has modified the profile of his right wing, causing it to produce more lift
force than the left wing. The asimmetry of forces that is so produced will
cause the gargoyle to roll on his left side. Now, look at the diagram below:
It is a
simplified balance of forces for a flying object or creature in an inclined
trim. As we can see, the weight force is still perfectly vertical, but the lift
is now inclined. The vertical part of the lift we consider balanced by the
weight, but the horizontal part is not balanced by anything, and consequently
it will induce an acceleration towards the side. It is this force that allows
turning.
An elementary consideration now, is that if
we want our gargoyle to keep his altitude in the rolling and in the turning, we
must increase the total lift. This is because during the turn only the vertical
component of the lift itself will have to balance the whole weight.
Consequently, our gargoyle will have to increase the Cl of both his
wings for the duration of the maneuver, with a subsequent increase of induced
drag, and loss of speed. Plus, for a series of dynamic reasons, the upper (or
external, as you wish) wing will produce more drag than the lower one. This
will create an angular momentum that will tend to make the gargoyle bend
towards the external of the turn. On the airplanes this problem is usually
solved with a proper use of the vertical rudder – for the gargoyle, we can
suppose that he will extend the arm that is on the internal side of the turn to
compensate the effect by increasing drag force on his internal side, thus
creating an angular momentum opposite to the one created by the wings.
(Actually, it is possible that gargoyles who have a very long facial beak, like
Brooklyn, are somehow advantaged in such a situation, being able to compensate
the momentum by simply turning their head and using the beak as a rudder)
Diving and climbing
“…I am
hunting high and low
Diving
from the sky above
Looking for more and more
Once
again…”
(Ok, just a little quoting…a little vice of
mine I cannot give up. The song is “Hunting high and low”, the band is the
Stratovarius…)
Not so much to say about diving and climbing,
actually…
A dive is used to quickly gain speed,
basically by converting potential gravitational energy into kinetic energy. To
maximize energy gain, it is intelligent to decrease drag as much as possible. A
gargoyle in diving will probably behave like, for example, a hawk, reclining
his wings backwards and partially retracting them, so as to leave exposed to
airflow just as much wing surface as it is needed to allow a minimum of flight control. Plus, for a series of
reasons that would be too long to explain here, a reclined (arrow-like) wing is
much more effective than a straight one in high-speed flying. It must be
underlined that exiting a dive is a very stressful maneuver for an aeronautic
structure, so we must suppose that gargoyles’ wing skeleton and muscular frame
are much stronger than they appear.
For
the climb, well, a Gargoyle has no propulsion, so he cannot simply pull
the nose up and increase throttle like an airplane would. A gargoyle is a
glider, and even worse, a gargoyle is not a very efficient glider, due to his
relatively high shape-induced drag. A gargoyle shall be able to gain altitude
only in presence of an ascending airflow, and in this case will have to try and
change himself in something similar to a pure glider. Consequently, our
gargoyle will have to stretch out his wings as possible, so to increase his
wing surface, and to decrease his Cl. It may appear a paradox that a
gargoyle must decrease his lift coefficient to climb, but we must consider that
here our objective is to minimize drag while keeping the lift force just a
little greater than weight. Now, one could object, wing surface does appear in
the drag expression as the lift coefficient. True, but lift coefficient appears
there with a 2 index, while surface appears with a 1 index, so decreasing lift
coefficient is the most logical choice. Naturally, by doing so our climb rate
will be very small in the best case, but this is unavoidable for gliders in
general.
Some better climbing performance can be
obtained by gaining speed with a dive and then using it to a short climb, but
in this case the gargoyle shall not be able to regain all the altitude lost
(would be a violation of the Second Principle of Thermodynamics!). Such a maneuver can anyway be of some use in
combat situations, to get rid of an insistent pursuer.
* * * * *
Appendix: considerations about
airborne combat
First consideration: gargoyles are not real
flyers, but gliders, and, as we discussed above, not very efficient gliders.
Second consideration: a gargoyle, due to his
flight assect, has a limited range of view.
Third consideration: gargoyles refuse (with
the exception of Demona) to use any kind of ranged weapon.
Now, in the Middle Age, even with the
considerations expressed above, gargoyles could be uncontested dominators of
the battleskies, but nowadays, they result to be little more than cannon fodder
in airborne fighting.
Just consider their basic airborne opponent,
the Steel Clan Robot. Like a gargoyle, it has arms and legs, allowing it to
catch an opponent, or to hit him at very close range. It has the same wing
structure of a gargoyle, allowing it a similar dynamic behaviour, but it has a
jet engine system, and this allows it not only to outspeed, but eventually to
outmaneuver its gargoyle opponents. Just the fact that a SCR can make a quick
climb with just a burst of engine thrust allows it a whole series of combat
maneuvers that are forbidden to a gargoyle. The same presence of engine thrust,
as well as the fact that a SCR, being a robot, is little or no sensitive to
violent accelerations, allows it a very better maneuvering performance even on
those maneuvers that even a gargoyle can make (narrower turns, just to mention
one). Finally, a SCR has ranged weapons, and since its weapons are embodied in
its arms, the SCR cannot eventually lose them. Now, all this elements together
mean, for a SCR, an immense advantage on the tactical side…such an immense
advantage, actually, that I really cannot explain to myself how could the
gargoyles win so many battles against steel clan robots. Ok, probably the
robots’ artificial intelligence was not that great (the steel clan robots are
made by the same manufacturer of the Coyote series, isn’t it? Just curiosity…),
but I really cannot imagine how a steel clan robot could lose against a
gargoyle, except if it is so dumb that it simply hovers in a place, and forgets
even to shoot a blast to its target every now and then. And, for example, even
Xanatos (whose intelligence is supposed to be undoubted) alone in his exo-armor
could easily, single-handedly defeat all the gargoyles in an airborne combat.
Anyway, here are a couple of classical combat
maneuvers that I think can be applied to gargoyles as well.
This first one, for example, is a variation
of an historical maneuver used by Spitfire pilots in the Battle of Britain (I
already told you I am poor in hand-drawing).
Gargoyles A
(left) and B (right) are flying in close formation. Attacker C approaches from
behind at high speed.
A and B split
formation, forcing C to follow one of them (B in this example)
B turns to
right and slows slightly down, while A gains altitude and slows down as well. C
pushes on B.
B suddenly
slows down and furtherly turns right. C slows down to avoid surpassing B. A
dives and attacks C from behind.
This second maneuver derives from a classical
acrobatic figure called Himmelman. The point here is of shaking an insistent
pursuer from one’s tail and possibly force him to a head to head.
1) A gargoyle (on the
left) is pursued by an opponent. The gargoyle begins a turn to the right. The
opponent turns as well, pointing its nose towards the gargoyle to cut the turn
and reduce distance.
2) The gargoyle
continues turning and starts a sharp climb, quickly decreasing speed. The
opponent is forced to imitate the maneuver so to keep contact with target.
3-4) The gargoyle, now at low speed, quickly increases
his Cl and makes a very narrow turn (practically spinning on a
wingtip) pointing his nose below and starting a dive.
5-6) The gargoyle and his opponent are now
head to head, but the gargoyle has the advantage of being diving from above, what allows him to go in for a strike or
to get a quick escape.
[As it is easy to guess, this last maneuver
is appliable by a gargoyle only if the opponent is another gargoyle, or anyway
a gliding creature. An engined opponent (SCR or a cyber-member of the Pack) in
fact is not forced to slow down in the climb, so it could easily intercept the
gargoyle from behind while it’s still gaining altitude)
* * * * * * *
Bibliography
For a very well-explained description of the
basics of aerodynamic flight, I recommend “Fundamentals of Flight”, by Richard
Shevell. A bit more rigorous but also less ‘newbie-friendly’ is “Introduction
to Flight” by L. Anderson.
For a more precise physical comprehension of
the nature and causes of aerodynamics forces I recommend “Fundamental mechanics
of Fluids” by I.G. Currie. Personally, anyway, I think that the most complete
and accurate explanation of aerodynamic forces is in the notes for the
Aerodynamics course by professor Luigi P. Quartapelle of Politecnico di Milano,
notes that can be found in the website of the university at www.polimi.it, in the page of the Dept. of
Aerospace Engineering. The notes are in English so there’s no problem of translation,
but I must warn that they are written to be used only by those who have already
a discrete knowledge of dynamics of fluids and a perfect padronance of integral
and derivative operators.
Another note: The ‘random’ gargoyle was drawn
by Christi Smith Hayden. Visit her
website at www.therockaway.com