PAPER AIRPLANE AERODYNAMICS
This is intended to explain the aerodynamics specific
to paper airplanes. For a general description of why airplanes
fly and why they crash, I recommend reading the aerodynamics sections
of either of my books The World Record Paper Airplane Book
or The Kids Paper Airplane Book. I wanted to include a
section like this in my books, but due to space constraints, could
not. This also allows me to get more technical in some areas.
Hopefully its not too technical, some of the details get complex,
but most of the principles are straight forward. My goal is that
most of this information should be understandable by high school
students, and for it all to be accurate. I also plan to some day
(soon?) put together a complete guide to aerodynamics on my web
Its important to realize the basics of why paper
airplanes fly, and why full size airplanes fly, are identical.
They create lift and drag, and are stable or unstable for the
same reasons. However paper airplanes look different than most
airplanes. The reason they generally look different is for very
practical reasons, but not necessarily due to aerodynamics. There
are also some definite aerodynamic differences between paper airplanes
and full size planes. These difference are not so apparent, but
do affect how paper airplanes fly.
2.0 Why Paper Airplanes Look Different Than Real Planes
Most full size planes have wings, a tail, and a fuselage
(body) that holds the pilot and passengers. Most paper airplanes
have just a wing and fold of paper on the bottom that you hold
when you throw the plane. There are several reasons for the differences.
2.1 Folding time
The main reason why paper airplanes look different
than real planes is to allow the paper airplane constructor to
make a plane as easily and quickly as possible. Adding a tail
and any other pieces to a paper airplane would require more folds,
and probably scissors, tape and glue. The simplest airplane is
the flying wing, and that's what most paper airplanes are.
2.2 The Tail Is Not Needed
The horizontal tails on full size planes have an
elevator (control surface across the back edge of the horizontal
tail) which the pilot rotates (back edge) up to make the plane
nose up and fly slower, or down to nose the plane down and speed
up. Paper airplanes accomplish the same thing by bending the back
edge of the wing up to fly slower, of down to fly faster.
Several full size airplanes have been flown successfully
without tails. The Northrop XB-35 and B-2, and the sailplanes
of the Horton brothers were all stable, good flying airplanes.
Many people assume a tail is needed for stability - but the above
mentioned planes, and millions of paper airplanes prove different!
B-2 Flying wing bomber
The horizontal tail of a plane allows the weight
to move forward and aft more while remaining stable and controllable.
Where a plane balances if it were supported at only one point
is called the Center of Gravity (CG). The CG can move further
forward or aft due to different passenger and cargo loadings,
and due to fuel burn (most jets carry about half their empty weight
in fuel). All airplanes become unstable if the CG moves aft of
a point called the Neutral Point. As the CG moves forward of the
neutral point, the plane gets progressively more stable, and progressively
needs more up elevator. Elevators on tails can be more effective
than elevators on the back of wings, so planes with tails can
have a greater CG range than planes without tails. With paper
airplanes their CG does not move, so they are fine without a tail.
A tail is also needed to balance the pitching moment (tendency to make the plane rotate nose up or down) caused by flaps. Flaps are the control surfaces on the back edge of the wing which are deflected down to allow the plane to takeoff and land slower. Paper airplanes do not need to fly any slower, so they do not need flaps, or the tail needed to balance the flaps.
The tail of a real plane usually also has a vertical
tail. The vertical tail acts like the fins of an arrow to keep
the nose of the plane pointed in the direction its headed, this
is called positive directional stability. The Fuselage (center
body of a plane, on paper airplanes its the part you hold for
throwing) acts like the vertical stabilizer of real airplanes.
Sometimes bending the wingtips up on paper airplanes also helps
to add directional stability. The combination of the fuselage
and wingtips on paper airplanes allows them to have positive directional
stability without a vertical tail.
2.3 Wing Shape
Paper airplanes usually have short "stubby" wings, called "low aspect ratio" wings. The distance from wing tip to wing tip is called wing span, and the distance from the front to the back of the wing is called the chord. The ratio of wing span to average chord is called "aspect ratio", and is an important characteristic of wings. For subsonic (less than the speed of sound) airplanes wing drag is reduced by increasing wing span and decreasing wing chord, both increase the aspect ratio. For that reason aspect ratio is a good indicator of overall wing drag. Notice that sailplane(glider) designers are extremely concerned with wing drag, and use high aspect ratio (big wing span, narrow chord) wings. Getting back to paper airplanes, or more correctly paper gliders, notice their wing shape is much different from real gliders because they have low aspect ratio wings. There are several good reasons for this difference.
2.4 Exotic Shapes
Real airplanes have to be optimized to perform some
mission. Since its tough to beat the basic wing/fuselage/tail
configuration for aerodynamic efficiency, most planes look that
way. The mission of a paper airplane is to provide a good time
for the pilot. Sometimes that means the amazement of seeing something
radical fly through the air. The combinations of wings, tails,
fuselages, and other parts that can be made to fly is endless.
Beyond the traditional paper airplane designs there are many exotic
shapes that don't look like they should fly. One of these is the
"hoop shape", known as the Vortex in my original book.
Another exotic shape is in my 1997 calendar called the X-Plane.
It is basically two wings attached in the middle and at different
angles to form an "X" shape. Other more familiar shapes,
but not thought of as airplanes, can also be made to fly. One
of these is the Starship from my 1997 calendar, which looks like
a futuristic space craft, but it actually flies. With paper airplanes
its easy to make airplanes that don't look like real airplanes.
3.0 Low Reynolds Number Flight
Paper airplanes are smaller and fly slower than most
other aircraft. So how does that affect their aerodynamics? Back
in 1883 Osborne Reynolds, professor of engineering at the University
of Manchester (England) carried out experiments to determine why
fluid forces through pipes changed for different conditions. Basically
what he discovered is how viscosity affects the way fluids behave.
All fluids (a fluid is anything that flows - air, water, maple
) have some viscosity, or stickiness, to them. As
a fluid flows over a surface, the fluid molecules closest to the
surface cling to the microscopic roughness of the surface. As
you move away from the surface there is a small transition distance
where the fluid's viscosity limits the change in speed of the
adjacent molecules, until at a certain distance the fluid is at
full speed. The narrow region near the surface where the fluid
is less than full speed is called the boundary layer. All boundary
layers start as "laminar" where the molecules travel
in a straight line, with a smooth transition in fluid velocity
from the surface to the outer edge of the boundary layer. Further
downstream disturbances and waves form in the boundary layer and
transition the smooth orderly laminar boundary layer into a "turbulent"
boundary layer. Turbulent boundary layers have a laminar sub-layer
next to the surface, but are mainly characterized by swirling
random eddies throughout the boundary layer.
A number was devised which gives the relative importance of viscosity in fluid flow. It is called the Reynolds Number, and it is the ratio of momentum forces to viscous forces in a fluid. The bigger the number, the less influential the viscosity. The viscosity is essentially a constant for a fluid (it changes a bit with temperature), but momentum is proportional to the speed of a fluid over a surface times the distance it has traveled over the surface. For air it is roughly:
Re=Reynolds number (non-dimensional)
V=Velocity relative to surface (miles per hour)
L=Length over surface fluid has traveled (feet)
So for a paper airplane (remember, this is about paper airplanes) Re=9340*10*.4=37,000
By comparison the wings of a four passenger airplane
have a Reynolds Numbers of up to about 6,000,000. Also, remember
the transition from laminar to turbulent? That happens at a Reynolds
number of no less than about 10,000, so the first ½ to ¼
of the flow over a paper airplane's wing is laminar. Since the
Reynolds Number is much less than for full sized airplanes, this
means viscosity is much more dominant, resulting in more drag,
and more difficulty in creating lift.
The low Reynolds Number of paper airplanes also means
thin wings are best. As wings get thicker, the air has to work
harder to make it around the airfoil. At high Reynolds numbers
with turbulent boundary layers this is easy. At low Reynolds Numbers
and laminar boundary layers, this is very difficult. If a thick
(say 10% of chord or more) airfoil is used on a paper airplane,
the air cannot make it around the airfoil and separates about
midway across the wing resulting in huge amounts of drag, and
little lift - the paper airplane won't fly. I try to keep my wings
no thicker than about 3% to 5% of the chord length, so its important
to fold your wings nice and flat. Mother nature knows this. Birds
fly faster than paper airplanes, and they have thick curved airfoils.
Insects are closer in Reynolds number to paper airplanes, and
they have thin flat wings - look at a butterfly's wings some time.
4.0 Making Them Fly
The "secrets" to making paper airplanes
fly well are largely the same adjustments which make hand launched
gliders fly well. Most people have the unfortunate idea that a
good paper airplane needs no adjustments after the basic folds
are finished. All real airplanes have trim tabs to make small
adjustments to the plane, and all paper airplanes need small adjustments
to fly their best. There are a few basic adjustments and principles
which will transform the paper airplane novice into a paper airplane
expert. The following flying tips are generally covered in my
books, but I go into a little more detail here.
One of the most common paper airplane mistakes is
to leave the wings folded down at an angle. That is called "anhedral",
and it reduces the lateral stability of your paper airplane. What
you want is called "dihedral" which is when the wing
tips are the highest part of the wing. The resulting lateral stability
will help keep your paper airplane flying straight, or perhaps
in a gradual turn. With lateral instability your paper airplane
will either roll over on its back and crash, or enter into an
ever tightening spiral which becomes a spiraling dive. Just remember
- keep your wing tips up.
Technically dihedral provides a stabilizing rolling
moment due to sideslip. For example if the plane yaws to the left
(positive sideslip), the right wing has a slightly increased angle
of attack (AOA) because of the dihedral, while left wing's AOA
is decreased (this is most easily imagined if you think about
90 degrees of sideslip). The resulting rolling moment is to the
left, which is stabilizing. During a level turn, the yaw rate
combined with the stabilizing yawing moment due to yaw rate results
in a little bit of sideslip, positive for right turns, negative
for left. That small amount of sideslip together with a stabilizing
rolling moment due to sideslip (dihedral effect) results in the
plane wanting to roll out of the turn. With anhedral, the plane
wants to roll into the turn, resulting in a "graveyard spiral".
The tendency to roll into or out of a turn is called the spiral
mode, which is controlled mainly using dihedral. Most real airplanes
have to limit the amount of dihedral they use to keep the Dutch
roll mode, a rapid left and right oscillation, under control.
While dihedral makes the spiral mode more stable, it reduces the
damping of the Dutch roll. I have rarely witnessed any Dutch roll
problems with paper airplanes, likely due to increased yaw rate
and roll rate damping associated with low airspeeds. As a result
all paper airplanes should be flown with plenty of dihedral.
4.2 Weight Forward is Good
As mentioned in section 2.2, where a paper airplane
balances is called the Center of Gravity (CG), and there is a
specific CG position known as the Neutral Point which provides
neutral pitch stability. If the airplane has a CG ahead of this
point, the plane is stable, if its behind this point its unstable.
Naturally all airplanes without computer assisted flight controls
need a CG ahead of their neutral point. For rectangular wings
the neutral point is ¼ of the distance from the nose to the
tail. For delta wings (such as the common dart paper airplane)
the neutral point is ½ of the distance from the nose to the
Stability means the plane, if disturbed, will return
to its original state. For pitch stability it means the plane
will seek a single airspeed. A plane which is unstable in pitch
will either pitch up into a stall, or nose dive, but won't settle
out anywhere in between. A stable airplane will tend to oscillate
up and down a few times, but converge on a steady flight speed.
Many typical paper airplane designs are stable, but just barely.
As a plane becomes more and more stable, it wants to fly faster
and faster. To counter this tendency, up elevator must be used
to produce a good trim airspeed. This is why many of the classic
paper airplane designs are nearly neutrally stable. Few people
realize good pitch stability requires a heavy nose and some up
elevator. The classic designs rely on the small inherent "up
elevator" effect (positive zero lift pitching moment) resulting
from the swept wing, and possibly the airfoil shape. Thus many
classic paper airplanes can be flown with no elevator adjustment.
Sometimes they fly well, many times they don't, and they always
have poor stability.
I like to add a tiny amount of up elevator to the
classic pointed nose paper airplanes, to make sure they don't
dive. If I have the time and materials, I like to add a few layers
of tape or a paper clip to the nose of the plane to improve its
stability. Most "square" paper airplanes have plenty
of weight in the nose, and require some up elevator to fly well.
Actually the amount of up elevator needed on a paper airplane
is a good indicator of its pitch stability. Build a paper airplane
(any kind) and place a paper clip on the nose. Make a few flights
to determine the best amount of up elevator needed. Now move the
paper clip back an inch or two, and repeat. The amount of up elevator
needed is reduced, and the plane becomes more sensitive to elevator
adjustments. When the paper clip has been moved back to a point
where you are using nearly no elevator deflection, and you can't
get the plane to fly well, you have the CG at the neutral point
(try to balance the plane on a finger, the point where it balances
is the neutral point).
4.3 What about the airfoil shape?
Most people who are reading this know that airplane
wings are "Cambered" which means they have generally
a curved shape, with the top of the airfoil rounded and the bottom
fairly flat. As explained in section 3.0, paper airplane wings
must be thin to work well. In addition, they need very little
camber, and generally any curvature is limited to the front portion
of the wing. I have had people ask me why I don't advocate cambered
airfoils for paper airplanes in my books. Since most paper airplanes
are flying wings, only small amounts of camber are practical,
as large amounts of camber create nose down pitching moments which
need tails to balance. Generally I do use a little curvature at
the leading edge of the wing. I have noticed that paper airplane
performance is not noticeably degraded with flat, uncambered airfoils.
The reason for this is likely due to low Reynolds numbers. Remember
that a large portion of the boundary layer across the front of
the wing is laminar flow, but for high lift we need a turbulent
boundary layer. The use of a flat uncambered wing produces a large
pressure gradient at the leading edge, which likely aids the transition
to a turbulent boundary layer, which could likely be the reason
for little camber in insect wings. Also, swept wings with uncambered
leading edges promote vortex flow just behind the leading edge
on the upper surface. Although lift coefficients at these Reynolds
numbers aren't large enough to promote a large amount of vortex
lift(vortex lift increases exponentially with lift coefficient),
any vortex flow likely helps the transition to a turbulent boundary
5.0 World Record Paper Airplane - Time Aloft
I developed the world record paper airplane when
I was about 13 years old, and I'm still trying to figure out exactly
how it works. I was trying to "invent" new types of
paper airplanes, combining folds from different types of paper
planes. This particular plane started with a couple of folds from
a pointed paper plane, then square paper plane folds, and finally
adding wing tip fins (I had read about winglets, and wanted to
add them to the plane). When I flew it outside, it flew higher
and longer than my previous planes. I liked to fly paper airplanes
outside, and I began using the new plane as I could launch it
very high to catch rising air currents. It wasn't until I looked
through a Guinness Book of Records a year or two later that I
realized its potential ability to break the record. At that point
I began improving the plane, and my throw, in order to challenge
the record. I feel lucky that my efforts have paid off, but I
am still learning why it works the way it does, and improving
the plane and the throw.
Over the 20+ year span life of this paper airplane,
the folds have changed only a little, but the fine tuning bends
and tweaks keep changing as I learn more about aerodynamics, and
as the plane teaches me more about aerodynamics. Its important
to realize this paper airplane's mission is to stay in the air
for as long as possible. It accomplishes this in two distinct
phases which have many conflicting aerodynamic characteristics.
The first phase is the launch phase, where I throw it vertically
at 60 miles per hour, and it ascends vertically to about 60 feet.
It slows to nearly a stop (sometimes it really does stop and then
tail slides), then begins the second phase of slow steady gliding
flight. The first phase lasts about 3 seconds, the second about
17 (on a world record throw). Here are some of the conflicting
|Launch phase||Gliding flight|
|Short wings better||Long wings better|
|Trim at zero lift||Trim at high lift|
|Heavy better (thick paper)||Light better (thin paper)|
Time aloft for a paper airplane can be optimized by either throwing a paper airplane with a short wing span real high, and having it glide downward fairly quickly (what I do), or making a fragile long wing span plane and launching it gently from as high as you can reach, or something in between. The primary tradeoff is wingspan - short wings can withstand a fast throw, but don't glide so well. Long wings glide great, but can't be thrown hard. I have seen paper airplanes made from one sheet of paper which had wing spans of 3 feet, and descended at only 6 inches a second (1/6 the vertical speed of mine). A basketball player with a vertical reach to 10 feet could seriously challenge my record. I think better flight times, and for me more fun is had, with the smaller swifter planes.
5.1 Launch phase
The trick is to get the paper airplane gliding from
as high as possible. To achieve this I launch the plane as fast
as possible, straight up. As it ascends the force of gravity and
the force of drag slow it down until it stops. From there the
plane's natural stability ensures it begins slow gliding flight.
Throwing anything straight up is not entirely natural.
For maximum height and for a good transition to gliding flight,
the throw must be within 10 degrees of vertical. Also for maximum
height, the throw must be as fast as possible. I used some of
the principles of biomechanics (science of the mechanics of the
body ) together with baseball throwing techniques and shot put
throwing techniques to develop the throw I use. I would like to
thank my high school coach Mike Lauten for enrolling me in his
biomechanics class. I estimate the plane leaves my hand at 60
miles per hour. This is based on two independent methods. First,
I have had my baseball pitches clocked with a speed gun at about
65 miles per hour, and I think my paper airplane throws are about
the same speed. The second method was mathematical. Knowing the
plane reaches a height of from 50 to 60 feet, and the drag coefficient
of the plane, I determined the launch energy required (kinetic,
.5*mass*v*v) to equal the potential energy (weight*height) plus
drag energy (integrated drag*velocity over the launch time), the
resulting launch speed was about 60 miles per hour.
A major reason why the world record plane is successful
is the ascent. During the ascent the plane's angle of attack is
near zero, resulting in near zero lift and allowing the plane
to go virtually straight up. This is crucial for two reasons.
In slow flight the plane is adjusted to produce a lift coefficient
of about 0.7. If the plane were rigid, it would trim to the same
lift coefficient at all speeds, with a sharp pull up into a loop
at speeds higher than 10 mph. At the speed I launch it, it should
enter into a 40 g loop, but it doesn't. The second reason zero
lift is important is because of drag. If the plane stayed at its
0.7 lift coefficient, it would more than double the drag during
the ascent and not allow the plane to climb high enough for a
record flight (roughly 50% of the kinetic energy from the throw
is used to overcome drag, the other 50% is converted into potential
energy in the form of altitude). The plane does not go to exactly
zero lift, and spirals a bit during the ascent to maintain a near
vertical trajectory. Sometimes I have to add some rudder deflection
to aid the spiraling to improve the ascent. I have also experimented
with introducing intentional asymmetries into the plane to aid
So why and how does the plane go to near zero lift?
I'm not really certain, but I think I have the answer. As I said,
it would trim to a 0.7 lift coefficient and enter a 40 g loop
if it were rigid, but it isn't rigid. I suspect the reflexed section
(the up elevator) to pushes the rear portion of the wing down,
producing a more curved airfoil which wants to pitch the nose
down and trim at a lower lift coefficient. Also the weight of
the fuselage at the middle of the plane results in a large root
bending moment as the plane pulls g's, so that the wings flex
upward (added dihedral) which effectively lowers the angle of
attack and lift coefficient the plane ascends at, with the wings
returning to their original dihedral as the plane slows. I need
to take some high speed video to analyze what happens during the
The airfoil of the plane also affects the launch.
I have tried using highly cambered airfoils optimized for slow
gliding, but they tend to degrade the ascent. I wrote a computer
program to reproduce the flight of the world record paper airplane
to learn what parameters were most important for a long flight.
One of the most important things I learned was that Cdo, zero
lift wing drag, is more important in the ascent than it is in
the descent. The airfoil optimized for slow gliding is not optimized
for zero lift, and produces extra drag during the ascent. What
is needed is an airfoil which produces low drag during slow, high
lift flight, but more importantly has low drag during the ascent.
I believe a nearly flat, uncambered airfoil does this. Certainly
a flat airfoil is ideal for low drag at zero lift, but it can
work at higher lift coefficients also. The flat wing at high lift
results in a steep pressure gradient near the front of the wing
on the upper surface, which likely aids transition to a turbulent
boundary layer which is needed for low drag at high lift. I plan
to do more airfoil tests during the spring of '97 to help find
the best airfoil for long flight.
I have found pitch stability to be important also.
The plane not only needs to be stable, but it needs to have just
the right amount of stability. Pitch stability is controlled by
how nose heavy the plane is, and that is controlled by the size
and number of folds down the sheet of paper. The flexibility effects
apparently only produce a small change in pitching moment, so
the stability must be fairly weak to allow a significant change
in trim angle of attack. Too little stability results in erratic
gliding flight, with frequent stalls as the plane drifts slower
than the desired angle of attack. One way to improve gliding stability
is to tighten the turn radius. As a plane circles in flight it
introduces a pitch rate. Natural pitch damping tends to try to
nose the airplane down with positive pitch rate. As pitch rate
increases with angle of attack, so does the nose down pitching
moment due to pitch rate, thus providing added pitch stability
to the plane. The tighter the circling, the better the stability.
A drawback to this scheme is the increased load factor, and degraded
gliding performance as the plane circles more tightly. Many times
I set the circle size, by adjusting the rudder deflection, just
small enough to keep the plane from porpoising (pitching up and
down) into a stall. Generally circles less than 20 or 30 feet
in diameter noticeably increase sink rate.
5.2 Gliding Flight
The goal for gliding flight is to descend vertically as slowly as possible. This represents the lowest rate of change of potential energy(power) which is the minimum product of drag times velocity. Generally the minimum sink rate for gliders is just above stall, and that's true for paper airplanes as well. For those interested in the details and math, finding the minimum power required involves taking the equation for powered required, differentiating with respect to velocity, and setting this equal to zero (standard calculus procedure for finding the minimum or maximum of a function. Starting with the basic parabolic drag curve;
D=.5 * rho * v*v * S * ( Cdo + Cl*Cl/(pi*e*AR))
D=drag in pounds
rho=air density (slugs per cubic foot, .002377 at sea level)
v=paper airplane velocity (ft/sec)
S=wing area (square ft, .234 for world record plane)
Cdo=Drag coefficient at zero lift (about .07)
Cl=lift coefficient (about .7 for minimum sink)
e=span efficiency factor, estimate .7
Converting Cl in terms of v (cl=2*wt/(rho*v*v*S)) wt=weight (lb, .01 for a sheet of paper)
and multiplying times v yields
Power=P=.5*rho*v*v*v*S*Cdo + 2*wt*wt/(pi*e*b*b*rho*v) (ft-lb/s)
Differentiate, set equal to zero, yields Cl=sqrt(3*Cdo*pi*e*AR)
and therefor v=sqrt(2*wt/(rho*S*sqrt(3*Cdo*pi*e*AR)))
This gives a lift coefficient and airspeed for minimum
sink rate of about .7, and 8.4 ft/s (6 mph)
Substituting the minimum sink results into the power
equation, and knowing that vertical velocity is power/weight,
gives the following:
Min Vert Velocity=Vvmin=1.05*(rho**-.5)(f**.25)(wt**.5)(e**-.75)(b**-1.5)
This equation gives the minimum vertical velocity of paper airplanes, sailplanes, 747s, ...
For the world record paper airplane this gives a
minimum sink speed of about 2.5 ft/sec
Note that the main drivers for sink speed are weight
and wing span, and to a lesser amount on f. The weight is determined
by the thinnest paper which can withstand the launch throw, which
is about 24 pound paper, which is about .01 pounds per sheet.
The wing span of the world record plane is about 7.5 inches, and
is limited by the launch speed (longer spans become too "floppy",
and cannot hold a reasonable dihedral angle after the launch phase).
"f" is determined by Cdo, and I have worked quite a
bit on this parameter. I have to be careful when adjusting the
elevator deflection for my plane, to trim it near, but not past
the stall angle of attack (determined by throwing, readjusting,
throwing... until it looks right). During the fall of '96 I decided
to try to design a better airfoil section for my plane to decrease
the Cdo. I used the PROFOIL program(see my aeronautical engineering
links) to design several candidate airfoils. The new airfoil shape
seemed to work. Previously only a small fraction of the planes
I build really seam to "float", many sink at over 3
or even 4 feet per second (for a world record attempt I make about
100 planes over several weeks, and use the few best ones which
launch and glide the best). I reasoned that if I could find a
better airfoil shape I would not only have a better plane, but
one I could make more consistently. Unfortunately the new airfoil
shape degrades launch performance (see sect. 5.1.2), so the new
airfoil has been abandoned.
I have also tried a version of the world record plane
which does not have a fuselage, it is a flying wing with no dihedral,
but uses the wingtips canted up and out at an angle for the dihedral
effect. The idea is to eliminate the "V" shape of the
fuselage and use that part of the paper to maximize the wing span
to reduce the sink rate. Unfortunately I have not been able to
achieve good ascents, with low launch heights as a result. This
modification noticeably affects the flexibility which allows good
Another area for study is washout, the relative angle
of attack of the tip of the wing compared to the root of the wing.
This could improve the span-wise lift distribution which could
improve the "e" in the sink rate equation. As the plane
is folded, there is a tendency for positive washout, with the
wing tips at a higher angle of attack than the root. I have tried
to construct test planes with the wings set with negative washout,
with the tips at a lower angle of attack than the root. This is
more typical for real airplanes as it promotes a better stall
pattern, with the root stalling first. It should also provide
a better span lift distribution for reduced induced (drag due
to lift) drag. Initial tests showed degraded launch characteristics,
and no noticeable glide improvement. I think I will try for zero
washout, as this should provide the lowest drag during the ascent.
I have also recently found a report which relates that low aspect
ratio wings (less than 2) have a tendency to have increased suction
peaks at the wing root, which might provide a lift distribution
similar to negative washout.
5.3 Other miscellaneous ramblings
As I mentioned above, not all my world record planes
can set a record. Most have flight times from 10-14 seconds. Maybe
10% can get to 15-17 seconds, and about 1% can get to 20 seconds.
One of the goals of my research and testing is to be able to make
the "good" planes on a repeatable basis. The best way
I know to do this is to understand the physics involved, and then
work on solutions. I have found that the physics involved can
get quite complex, and it is difficult to get definite answers
from my tests. I do think I am making progress, and hope to continue
to improve my understanding and ability to consistently make good
5.3.2 Completely different planes
I sometimes feel I am in a rut, as I have basically
been trying to improve the same design for 20 years. I do actually
try to invent new design to tackle the world record. So far none
has worked as well as the original, but I keep trying. I suspect
there are much better designs waiting to be discovered, and no
doubt in the future one of these better designs will hold the
5.3.3 Weather, England, and new records
Yes the weather can affect an indoor flight. In March of 1996 I participated in a BBC paper airplane contest in London, England. The building was huge, but was unheated, with cool rainy conditions outside. Paper airplanes hate humidity. I'm not sure if its due to the relative humidity, or absolute humidity, but generally if its rainy outside, the paper is going to have even worse than normal structural properties. Normally I rely on the resilience of the paper to hold the wings at the proper dihedral angle during gliding flight. Even on dry days, the paper eventually "fatigues" and is unable to support the root bending moment of the wing, resulting in "floppy" wings with increasing dihedral angles. On humid days I may get only two or three good world record throws from a plane. The problem is that it takes at least 2 or 3 flights to make the proper adjustments to the rudder and elevator for optimum flight times. Back to the contest, I was having a horrible time trying to get my planes adjusted before the wings fatigued. Going into the last round of the competition I was in third place (15 seconds, the best flight of the day being about 16 seconds). I was extremely lucky to get a 17.3 second flight on my last throw to win the contest. My plane design uses the maximum wing span for dry conditions, with many of the competing designs having shorter spans which were less affected by the conditions, allowing them valuable adjustment throws. The skill of the other contestants was outstanding. Some of the other participants have even subsequently submitted record flight claims to Guinness - so far they have not had their record flights authenticated, but it may only be a matter of time. But I'm not going down without a fight! I'm still working on my planes.
6.0 References for Paper Airplane aerodynamics
There are few technical references for paper airplanes.
Naturally paper airplane books talk about paper airplane aerodynamics,
but usually in a simplistic manner. There are many reference to
low speed flight which are applicable to paper airplanes. Here
are a few.
Savage, Stuart B., "The indoor hand launched glider", Flying Models Magazine, Jan/Feb 1960
[This is a very good reference, as hand launched
gliders and paper airplanes have the same aerodynamics]
M.M. O'Meara and T.J.Mueller, "Experimental Determination of the Laminar Separation Bubble Characteristics of an Airfoil at Low Reynolds Numbers", AIAA-86-1065, May 1986
[Not directly applicable to paper airplanes, but covers some of the wing flow physics, and contains many
"Proceedings of the Conference on Low Reynolds Number Airfoils" - These conferences have been held
several times - I see the Proceedings referenced
a lot in low Reynolds number papers.
Blackburn, KD and Lammers, JL, "The World Record Paper Airplane Book", Workman, 1994
[Why paper airplanes fly, and why they crash]
Blackburn, KD and Lammers, JL, "Kids Paper Airplane Book", Workman, 1996
[Similar content to 1st book, concerning
why paper airplanes fly, more hands-on experiments to demonstrate
principles. Also a teachers guide for this book is available from
the publisher with more paper airplane information]
Hoerner, S.F., "Fluid Dynamic Drag", Hoerner, 1965
[The "Bible" of drag. Includes references
to low Reynolds number drag throughout]
Hoerner, S.F., "Fluid Dynamic Lift", Hoerner, 1985
[Some relevant info, but limited]
Abbott, I.H. and von Doenhoff, A.E., "Theory of Wing Sections", Dover Publications, Inc.
New York, 1959
[A good reference]
Selig, M.S. and Donovan, J.F. and Fraser, D.B., "Airfoils at Low Speeds", H.A.Stokely, publisher, 1989
[Dr Selig at the U. of Illinois is one of the leading
people in low Reynolds number research. There have been several
releases of his "Airfoils at Low Speeds", also known
as "Soartech", with some info available on the internet]