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1999
Performance study of the 1911 Wright Brothers
model B aircraft and propeller
Robert Egenolf
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PERFORMANCE STUDY OF THE 1911 WRIGHT BROTHERS
MODEL B AIRCRAFT AND PROPELLER
Robert Egenolf
Mechanical Engineering Department
Rochester Institute of Technology
Rochester, New York
A Thesis Submitted in
Partial Fulfillment of the
Requirements for the
Degree of
MASTER OF SCIENCE
In
Mechanical Engineering
Approved by: Professor
_
Kevin Kochesberger, Thesis Advisor
Professor
_
Dr Alan Nye, Professor
Professor
_
Dr. Ali Ogut, Professor
Professor
_
Dr. Charles Haines, Department Head
PERMISSION TO REPRODUCE
Thesis Title.
PERFORMANCE STUDY OF THE 1911 WRIGHT BROTHERS
MODEL B AIRCRAFT AND PROPELLER
I, Robert Egenolf, hereby
Rochester Institute
of
reproduction can not
1999
grant permission to the
Wallace Memorial
Library
of
Technology to reproduce my thesis in whole or part. Any
be
used
for
commercial use or profit.
the
FORWARD
I
would
like to take this opportunity to thank the
throughout my college career
and
in reaching my
To my advisor, Kevin Kochesberger, I
and effort
he
would also
put
forward
people who
have helped
me
goal of graduation.
would
like to
extend
my thanks in the time
helping me conceive this project and bring it to fruition.
like to thank him for the
plane rides
down to the
wind tunnel at
I
Langley,
Virginia.
To Ken Blackburn, I
help with
sorting
out
would
like to
extend
the inputs for the software
this thesis. Without his tremendous effort, I
my
gratitude and
program and all of
would still
thanks for all of his
his
be in the dark
advice
on
regarding
many
of
these
issues.
To my family, Joyce, Bruce,
and
Eric, I would like
their constant support throughout my education,
not
have
skills.
accomplished
my
here
at
to extend my gratitude for
RIT
and even
beforehand. I
goals without their encouragement and confidence
could
in my
ABSTRACT
A
propeller
is to be
presented.
be
were operating.
examined
generated
in
data
be
compared
Theoretical data
will
dedicated to the efficiency
Model B
the
aircraft
procedure
efficiency
study
of
in
be
better
further
shown
software.
which will
efficiency
at
regarding
evaluation.
(2)
a
Model B's flight.
a software program
drag
study
conducted on
be discussed
the
as well as
include graphs, specifically
will
Following this chapter will be
incorporate the
A final
propellers will
Finally, theoretically
the time of the
software program will
Outputs
Wright
a
drag
software graphs and produce the
chapter will
discuss these
results and
avenues of study.
results of
relatively
the
performance evaluation of
close correlation
by the Wright Brothers themselves.
software program and
chapter.
theories
propellers, and
itself. The inputs for the
for operating the
an
and the
the situation in which the
from two sources; (1)
gathered
prediction of
the Model B aircraft,
Final
numbers
recreate
and available power at certain speeds.
recommend
the
to
to the known values
aircraft's cruise speed and climb rate.
have
order
Following this brief history,
order to understand
will
aircraft and
Background, contemporary aviation history,
analysis will precede the evaluation
Brothers
1911 Wright Brothers Model B
performance evaluation of the
found in the
the
to the original numbers measured and calculated
Cruise
speed and overall
drag study respectively,
notebooks of
the 1911 Wright Model B aircraft
the Wrights.
match
These
efficiency
closely
numbers can
as predicted
with
by
the target
be found in the final
TABLE OF CONTENTS
Pages
I.
Greek Letters
7
II.
Dimensionless Parameters
7
III.
Variables
7-8
IV.
List
of
Tables
9
V.
List
of
Graphs
9
VI.
List
of
Figures
9-10
Chapter 1
-
Introduction
1.1
11-12
Contemporary History
12-13
1.2 Background
1.3 Wright Brothers Experiments
and
Analysis
of
the Propeller 14-18
21-22
1.4 Objective
Chapter 2
-
Propeller
Theory
2.1 Simplified Momentum
2.2 Blade Element
Chapter 3
Chapter 4
Chapter 5
Chapter 6
-
-
-
-
23-28
Theory
28-34
Theory
Propeller Software Program Inputs
and
Results
3.1 Propeller Software Background
35-39
3.2 Selected Inputs for the Propeller Program
41-43
3.3 Output Results from the Software Program
44-49
Performance Evaluation
of
the Wright Model B Aircraft
4.1
Drag Analysis Procedure of the Wright Model B
4.2
Drag Study
Discussion
of
Numerical Analysis
and
Results
50-55
56-65
Results
6.1 Climb Speed
and
6.2 Performance
at
Climb Rate
CL Max
66
66
6.3 Cruise Speed
66
6.4 Propeller Performance
66-67
Conclusions
and
Recommendations
6.1 Conclusions
68-70
6.2 Recommendations
70-72
VII.
References
73-74
VIII.
Notes
75-76
I. Greek Letters:
Q
: angular
velocity
p
:
density
r\
:
efficiency
-
: pi
u. : axial
velocity
a : angle of
O
blade
:
blade
cj) :
incidence
angle
angle
-
angle of
: effect of profile
y
incidence
drag of the blade
II. Dimensionless Parameters:
J
: advanced ratio of a propeller
III. Variables:
V
freestream velocity
:
v :
incremental velocity
pA
:
p'
:
initial
pressure
incremental
pressure
HA : initial head flow
A
: area
E
:
energy
T
:
torque
Ta
:
torque available
a : scale
factor (Simplified Momentum
a : axial
interference flow (Blade Element
D
P
:
diameter
: power
Theory)
Theory)
Pa
: power available
r : radius
a'
interference flow
: rotational
Cd
: coefficient of
drag
Cl
: coefficient of
lift
M
: resultant
c : chord of
velocity
the airfoil shape
of
blade
s :
solidity
N
: number of
n :
frequency
blades
(Wright Brothers Theory)
L
: thrust
K
: air pressure coefficient
SWing
S
:
total wing area
: reference area
A
=
Ai
AR
: geometric aspect ratio
: effective aspect ratio
e : correction
b
: wingspan
h
:
height between
W
Q
factor
wings on a
: weight
:
torque
CT
: coefficient of thrust
CP
: coefficient of power
bi-plane
IV. List
Tables:
of
page
Table 1
:
Table
Table 2
:
Flyer Drag Coefficients
60
Table 3
:
B
Drag Coefficients
61
Table 4
:
B
Velocity/Drag Force
63
Table 5
:
B Power Required
V. List
of
of
Software Inputs
64
Graphs
Graph 1
:
Efficiency vs.
Graph 2
:
HP
Graph 3
:
Efficiency vs.
Graph 4
:
Thrust
vs.
Graph 5
:
Cp
Advanced Ratio
Graph 6
:
Ct
Graph 7
:
Flyer CLvs. Cd
Graph 8
:
B
Graph 9
:
Flyer CL
vs.
vs.
Speed
44
Speed
45
Advanced Ratio
Speed
(induced)
CL vs. Cd (induced)
vs.
Cd (induced/total)
Graph 10
:
B CL
Graph 1 1
:
Power Required
VI. List
vs.
of
46
47
Advanced Ratio
vs.
42
Cd (induced/total)
vs.
Power Available
48
49
59
59
60
62
65
Figures:
Figure 1
:
Wright Flyer
19
Figure 2
:
Wright Model B
20
Figure 3
:
Simplified Momentum Theory Diagram
25
31
Figure 4
:
Blade Element
Figure 5
:
Software Program Diagram
36
Figure 6
:
Aspect Ratio Diagram
57
Theory Diagram
10
Chapter 1
1.1
Brothers
order to understand the magnitude of the accomplishment that the
set out to
divulged to the
achieve,
reader.
a
brief description
At the time
action on aerial propellers.
In
of
the
marine
propeller
knowledge
Up to
would
of
contemporary
Brothers,
no one
had
history in
yet
Wright
aviation will
be impossible
Transferring
marine
be
determined the forces
propellers, most knowledge was empirical
needed experimentation to reach perfection.
of
Introduction
Contemporary History
In
in
:
knowledge into
and
aerial
and not reasonable.
this point in aviation, propellers were only about 40% efficient with some
the better designs and better craftwork reaching as high as 55%. These numbers might
seem
high, but the Wright Brothers
and goals.
wished
to go higher and surpass the previous designs
Settling for what other people had constructed was
Brothers. For example, Santos-Dumont's Bird of Prey,
airborne.
This relatively high
inefficient
and
the
motor capable of
ambition and
meant a
gain
in
small
plane was
weight
and
bigger
from the
motor, light in
motors
from
developed
probably
required
indicated that the
overweight.
The
losing
a
skill possessed
engine.
This, in turn,
motor alone.
weight.
lot
by the
Casting
of weight.
The
50 HP to become
propellers must
goal of
only 8 HP This tremendous difference in
engineering
larger
power number
to the
unacceptable
the Brothers
that the plane would
predicted weight of
processes of
the
to use a
the
instantly
automatically
the Flyer only allowed for a
day also prevented the
Propellers had to be
was
requirements exhibits
Brothers. More horsepower
meant
have been
more efficient
larger
than those
by Maxim and Langley. They merely attached large pushing surfaces to
a
11
central
hub
dictates the lift
and
For their
has
Brothers
in the
consideration the curvature of the upper surface which
case of a
achievement
Wright Brothers
reader
taking into
without
in aviation,
will
including the plane and the propellers,
were considered pioneers and
better understanding
a
propeller, the thrust.
be discussed,
as
innovators in their field. Now that the
in depth look
of the time period, a more
they
are
the
at
the Wright
the main focus of this document.
1.2 Background
In the early 1900's
a team of
two brothers would be the first to achieve the
unreachable goal of sustainable powered
revolutionize the
industry
But this tremendous
challenges that
unforeseen.
propulsion
system,
would prove
to
power
first
historic flight
obstacles and
engine
equipment
manufacturers and gave
time (these
at
Kitty Hawk.
technical
then one occasion, both anticipated and
or
forward
means
movement.
by which the engine
Both
of
these components
them all.
bicycle shop, the Wright Brothers had little to
building business. They had constructed
in their shop but that
was
for their plane, they
no
a one-cylinder engine
the extent of their expertise. When
they
contacted automobile engine
them their specifications,
numbers will
would
to be designed before the flight was the
obstacles of
and operators of a
considered powerplants
ahead of
its
Wilbur Wright
including the engine/motor itself and the
to be the largest
in the
the
aspect of the plane
and
plane and one
encounter on more
be transformed into thrust
Owners
experience
homemade
accomplishment was not without
they would
The last
power would
with a
flight. Orville
be discussed in
which
had been
chapters
calculated and checked
following). No
automobile
12
manufacturer at the time could meet the
engine would
Luckily one
have to be
of
almost single
constructed
demands
from
their employees, Charlie
of the
scratch and
Taylor, had
handedly built the brothers
a
four
a
brothers and; therefore, the
from the
be
purpose-built
bit
more engine experience and
cylinder engine
for their plane,
onset.
to
and
their specifications.
However,
made
by the brothers
propulsion.
engine
word.
once this problem was overcome, a
The
No
turn into a revolutionary idea
would
propellers required to transform the
into forward
one prior
seemingly
and
energy
at
premature assumption
design in the
the
flight
area of
output shaft of
the
through the air would be reinvented, in every sense of the
motion
to the Wright Brothers had
understood
the dynamics and design
of
propellers.
"
Maxim/Langley developed
great motors
flat-bladed
Most
of
the
work completed
not airplane propellers.
in this
but terribly inefficient
"
propellers
only in the
area existed
The brothers believed they
could
area of marine propellers and
just
substitute air pressure
place water pressure and achieve propeller performance predictions.
this
assumption proved
previous work
forced to
this
the first
method employed
large
and not
applicable
to their
quick
situation.
(Note that they did
had to be
not
correct and
part of their success or
look into
With
theoretical, the Wright Brothers
in
order
have the
all
were
to construct the correct
capital
to rely on the "cut
by other contemporary inventors.). With only one
their grasp, their calculations
propellers was a
be
equations and calculations
attempt
try"
and
would not
being entirely empirical
develop their own
propellers on
theory
A
in
predicting the efficiency
attempt at
of the
failure.
13
1.3
Wright
Brothers'
Experiments
and
Analysis
Before completing their design for the
conducted various experiments to
design.
tunnel
of
the Propeller
(Flyer)
propeller, the Wright Brothers
airfoil
help them determine
shapes, sizes, and speeds for their
Specifically they conducted fan screw and propeller experiments in a scaled wind
they had custom built for this
specific purpose.
These, along
with
the analysis of
their eventual propeller will be undertaken in this portion of the chapter.
For the first
of
their experiments,
their power equipment).
of
Pressure,
horizontal
employed
probably taken from their bicycle shop
motor was
Center
they
wing.
the hub. There
which
is defined
differently from the
as a
blade
measured or estimated
section
They used these crude blades
blades
them visualize
help
experiments and so
they
sophisticated and a
lot
The
how the prop
closer
to their
mainly due to
length to the fan
screw
a
failure
and a motor
it to drive
some of
paid close attention
meaning
located 5/6
contributed
as
of
the radius away from
rotational
velocity, and
should
finally appear.
These
were
only early
that eventually became a lot more
ultimate goal.
of
the same motor as the fan screw
the larger motor. The propellers were similar in
but differed in blade
the length of the blade
less to the performance,
to the
associated with a
width and
blade
angle.
The Brothers
these two variables to gain the best thrust/lift design that would suit their needs.
determined that
(the
to create early models of the propeller
moved onto propellers
propeller experiments again used
experiments,
used
blade angle, camber,
angle of attack.
and
they
During these experiments the brothers
This they defined
they
where
fan blades
and
increased,
the blade sections near the
altered
They
hub
the higher the efficiency of the propeller
14
became. The Brothers developed
appears as
an equation
for the thrust/lift
of the propeller and
it
follows:
L
(D
KxVxSxCL
=
A"
where
L is thrust,
blade area,
and
is
an air pressure
C/,is the lift
corresponds to thrust
for
a
coefficient, V is the velocity in mph, S is the total
coefficient.
By simply understanding that lift for a wing
propeller, the Brothers were able to apply this equation
directly to their designs.
Once they had finished these experiments, they
propeller
for the
the onset of the
plane
they
project
were
building based on
weight
performance as well as
kept
notebooks on
has been
the
excerpted
Efficiency,
=
correct
they had
made at
755 lbs
=
23
Engine & prop
=
200 lbs
design
requirements
weight
area
=
500
mph
ft2
dictated the
propeller's
design
and
its
the motor and other necessary components. The Wright Brothers
progression of
from Wilbur's
as
some assumptions
Min velocity for flight
Total wing
above mentioned
determine the
regarding their Flyer. These included:
Plane
They
could
defined
___
their
design
notebook
became the
PowerOutput
.
the
following analysis
H, 1902-1905.
by the Wrights,
Efficiency
and analysis and
following equation:
(2)
=
Powerlnput
15
Knowing this relationship,
velocity
of rotation
determine
one can
the input
by multiplying the
torque and
to obtain:
40lb xl2l ft/ s
=
4, S40 ft
lb/s
-
4,840
=
550
This
gives
output
is
S.13hp
the first part of the efficiency equation. Now
product of
by understanding that the power
the thrust and forward velocity, the second portion becomes:
90lb x 24 mi/'hr
=
2,160/m
-
Ib/hr
2,160
=
375
where
375
mi-lb/hr
is
to one horsepower. Once two out of three variables have
equal
been determined, the efficiency
of
the propeller as
equation can now
__,
Brothers'
for
5.76
PowerOut
.
propellers
undertaking been
to determine the performance
,,
x
=
=
propeller
they
a new era.
the propellers used on the
surpassed
Their
the achievements of past
analysis would serve as
for decades to follow. Never before in
accepted and
machine and
into
n
= 66%
1 00
8.73
Powerln
According to calculations they had
brought the
designing
flying
used
was the theoretical number associated with
Flyer.
aviators and
be
follows:
Efficiency
This
5J6hp
then overcome.
would prove that
aviation
had
The Brothers had the last
it did
work and
did
the basis
such an
piece
for their
fly at Kitty Hawk later that
16
year.
Some
were as
other critical numbers associated with the propellers of the
Flyer
and
the B
follows:
Flyer Data
Speed
Gross
of machine
(forward velocity
speed
of
Thrust
Area
of
Speed
of
Center
of
Angle
of
Normal
Weight
:
=
=
=
44 ft/s
5.4 sq ft
330
at
5/6
incidence
pressure
=
:
of
=
7
the total radius)
=
121 ft/s
deg
25.3 lbs
755 lbs (with
Wing area
air)
90 lbs
blades
Pressure (located
mph
relative to the
prop
=
RPM
23
=
500
one
pilot)
ft2
1911 Model B Data
Speed
of machine :
Gross
Weight
:
speed :
RPM
of
is the freestream velocity
thrust is the estimated
data,
58.6 ft/s
:
:
472
ft2
428
without the added
"suck"
velocity
and
90 lbs
drag of the Flyer according to the Brothers. Along with these
numbers were also quite a
drew coefficients,
mph
1250 lbs (with two pilots)
Wing area
where gross speed
40
few tables, graphs,
and
design ideas. This
and
diagrams from
which the
analysis constituted the
bulk
Brothers
of the
17
propeller
design, in
an
following two pages
engineering
show
sense of the word.
The figures (1
three view schematics of the
and
2)
on
the
aircraft.
18
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./,LU.-._
.
y
s
a
I--1
1
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f1
,
I
-L..A_i...L.,
i
^*i_
II
"^Vi
1
l
>
i
i
i
i
\
_______!$
n
i
r-#v\
j
_/
1
^
-f-h.
.
-.-__
.
1
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,
1
H
(U
GO
m
o
0\
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CO
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I
_.
pa
.
-8
I
On
~
5
CN
U
z
o
00
PL,
o
CN
1.4 Objective
Now that the background for the study has been documented, the
main purpose of
the study will be discussed. The overall objective of this study was to employ current
techniques of propeller design and efficiency calculation in order to predict the efficiency
of
the propeller used on the Wright Model B as
flight. This
computer
prediction would
in
of
in
the cruise speed of the plane in
a number of various
range of sources and
determining the
overall
efficiency
and power of
available would allow
Once this is complete, the
and
The
techniques.
the Wright Brothers design.
data to be inputted
software program would
be
calculations and simulations and output six performance graphs
Results
ways, both with a
these methods was to employ a propeller performance software
Having propeller drawings
software.
carried out
tool and analytically in order to capture a
The first
package
be
well as
directly into the
able to run
(can be
through its
in the
seen
Conclusions section)
second method of
analyzing
performance would
the overall
plane and use available equations
drag force.
The
drag
power available.
force
would
then be
plotted
From the thrust numbers,
directly determine the performance
to transform
drag study of
of power required against
be derived
and cruise speed of
conduct a
drag numbers into an overall
in the form
power can
be to
and this can
the aircraft,
be
used to
including max level
speed and max climb rate.
21
The third
source of
data
would
be the Wright Brothers
conducted an extensive analysis prior to
efficiency
was a critical part of
numbers will
be
Following data collection,
compared
created.
to the number obtained
The
results will
constructing the Flyer
this analysis. There
used as a comparison
to the two
and
They
the propeller
method of analysis and
resulting
aforementioned methods.
the efficiency and power
by the Wright Brothers
be discussed
themselves.
numbers were compiled and
at the
time the Flyer B was
and recommendations made
in
chapters
following.
22
Chapter 2
In
order to
better
understand
:
Propeller
how the efficiency
Theory
of a propeller
in depth
explanation of the employed theories will now
are used
in
determining
the
ideal efficiency
be
of a propeller.
given.
This
is determined,
a more
The first two theories
explanation
is necessary
to understand how the software program operates in the next chapter.
2.1 Simplified Momentum
As
of
evidenced
in the
the momentum as
in depth into
a
name
well as
detailed
assumptions attached
Theory
alone, this
(Rankine
theory
and
Froude)
of airscrews
the kinetic energy of the system
analysis of
this
depends
on a consideration
being studied.
theory however, it is necessary
Before going
to state the
to the theory.
Assumptions:
is
1. the
airscrew
2. the
generated
3. any
4. the
to
be
a
disc
(spinning in
the air)
thrust is distributed evenly over the disc
rotation of
axial
considered
the
velocity
slipstream
of
due to the
action of the torque
is ignored
the fluid is continuous as it passes through the disc
(this is necessary to
maintain
the continuity of the
flow)
23
Now that the
be
is
set
assumptions
forth. As the fluid
equal
have been categorically described, the theory
passes through the
disc,
an
incremental
to the thrust per unit area of the disc. This can be
following page.
Another
effect of the
disc is to form
velocity behind the disc. The fluid flow from
irrotational,
as
previously
stated
in the
these ideas have been established, it is
fluid flow. Bernoulli's Equation
for dynamic
pressure as
point
seen
pressure
in Figure 3
a slipstream of
A to
point
B is
applied
then
added which
on
the
increased
axial
regarded as
assumptions associated with
now proper
is
can
this theory. Once
to apply Bernoulli's Equation to the
to the diagrammed fluid flow yields an
equation
follows:
nA=pA+y2pv2=p+y2p{v+v)2
(3)
where
V is the freestream velocity
stream passes through
airscrew and
Further,
p is the
after
the
and v
airscrew.
pressure
just
is the incremental velocity
p0 is the initial pressure before
prior
to passing through the
p'
the
being effected by the
screw.
passing through the prop,
H =P,+/2P(V+\f =P+P +/2P(V+vf
where
added once
is the incremental
pressure added
by the
Ap-HB-HA_p(v +
By considering this Ap,
the disc. This is also an
the thrust,
expression
T
=
for the
A/7(V
+
T,
airscrew.
And,
^/vB)vB
(5)
then becomes the
rate of change
l/2vB)vB
(4)
in
following with A
=
area of
axial momentum:
(6)
24
Figure 3
Simplified Momentum Theory Diagram
25
And this indicates that half of the
Therefore
after the airscrew.
T
Here V can be
the
=
added
equation
2Ap(V
considered the
velocity
(6)
can
be
occurs
before the
rewritten
taking
airscrew and
half of it
this into consideration,
+ v)v
(7)
freestream velocity
or gross
velocity
and v can
be taken
as
"suck"
or the
velocity
An
in the fluid
velocity
examination of the
system
added
by the
kinetic energy
corresponding to the
airscrew.
of the system reveals an
increase
time
following equations:
(8)
E^A^V+v^V+vJ-V2)
Which
over
reduces to
E=2Ap(V+v)2v
(9)
Which
yields
the
following
after
using
equation
(7)
E_T(V+v)=QQ
where
Q is
airscrew.
to
equated
Now this
angular
velocity
expression can
the thrust.
Once the
efficiency
of the system can
be
ideal
actual and
be
of
(10)
the
used
(27if)
and
Q is
the torque of the
to define the total work done on the fluid
work are
written as
airscrew
both known,
an expression
by
for the
follows:
TV
<>
n=^Q
and where the total work
done is
nQ
=
T(V
+
v)
(12)
26
And if
(13)
y=aV
where a
here is
used
Then the ideal efficiency is then
to symbolize a
said to
be:
V
rj
By constructing
system
other
The
of
this
most
=
V
+ v
equation
of
which are
1
+ aV
the axial velocity in the slipstream. But there are
ignored in this theory
friction
b)
no
kinetic energy loss in the
c)
no
loss
frictional loss here
of thrust towards
the listed losses
depending
on
the
rotation of
efficiency
above
equation,
determining
will
be
which
almost
would
blade
versus power
input to
85% that
indicates that
airscrew
a
a
of
study
Another
actual efficiency.
power, speed, and the
surface material.
can
is in ft/s
with some
of
exists a
large
a quick and
amount
dirty
certainty that the
(#4, H. Glauert) from the
the ideal efficiency is a good guide to
the efficiency equation
be derived
involving
when one considers power output
being the following
2P
1-7
Note that the
For
the ideal efficiency
version of
diameter
the slipstream
be (a) because there
propeller, with the final result
rj
listed below.
the blade tips
the efficiency of a propeller, one can predict
actual
as
drag of the blades
no
of
(14)
+ a
the assumption is made that the only loss in the
a)
influential
estimate of
1
=
is due to the kinetic energy
losses in the system,
V
=
V
multiplier
(H. Glauert,
1983)
(15)
npND
value
for
and the value
power must
be in ft lb/s, the
value
for V
for D is in ft.
27
It
can
be deduced from this
coefficient
increases,
efficiency falls quickly
equation that the
such as
attempting to
lot
put a
of power
as
the power
through a relatively small
propeller.
2.2 Blade Element
As
a continuation of the simplified momentum
for
provides
by the
Theory (Extension of Momentum Theory)
a more
detailed
blade. As
airscrew
analysis of the propeller
with
The
.
element
by exploring the
forces
theory
experienced
the momentum theory, there are several assumptions made
by this theory in order to conduct
1
theory, the blade
rotational
an analysis and
velocity
of
they
are as
follows:
the tips of the blade does not approach the
speed of sound.
2.
The blade is
placed
in
a uniform stream of
velocity V
parallel
to the
axis of rotation.
There
exist also some
become
in
useful
Inflow
Outflow
Wake
-
helping one
Flow
-
-
terms that need to be defined in order for
Flow in
front
slipstream
-
some
screw
Velocity field of system of trailing vortices which
on
one, the blade is
propeller
blade
considered
acts as an
the blade elements
important terms have been defined for the reader,
the activity surrounding a
previous
screw
far behind the
interference
Now that
explanation to
of screw
immediately behind the
Interference Flow
full
analyze a propeller.
immediately in
Flow
a
can
a more
in depth look
be discussed. In this theory,
to be a two
dimensional
object
as
at
in the
in motion, but this
28
time it is subject to
interference flow
root
blade
and
the mean value is
elements.
represented
(In this case, the
exact effect of
not occur
in front
rotation then transforms
trailing
into
of
flow in the
vortices and circulation around
screw will
is understood, the
related
element
dr
have
inflow
This
the blades. Due to the
an angular
velocity in the
screw
and outflow.
be
blades
will
Once the flow
examined and
known
screw.
distance
at radial
variables and equations can
acceleration of
analyze
Note that this
boundary layer.
angular momentum of the outflow can
to the torque of the
Consider blade
following
and
examined and
the screw. The circulation around the
cause equal and opposite angular velocities of the
to be closely
by tip
is difficult to
slipstream.
the airscrew or outside the
vortices, the flow in the plane of the
same sense as the rotation of
motion
vortices
the airscrew must be
of
understood to create rotation about the axis of
does
the
created
generally substituted.)
To begin the analysis, the torque
rotation
by helical vortices
r
in the Figure 4. From this figure the
be derived. Equation (16)
shows that
the
the flow in the direction of the blade travel results in torque. Equation
is then the incremental thrust for
dQ
u
=
torque
axial
=
torque
dQ
=
^
=
=
(16)
rate
2-
=
this
of
along the
propeller
blade.
element
thru
the
increase
of
airscrew
angular
annulus
momentum
u-2--
r2dr
xp
4-
reduces
u
of
velocity
dr
Where Equation
an element
(17)
r> VQ(l +
to Equation
V(l + a)
a)a'
(17)
(17) if the following definitions
Qa'
and
ar
(16)
=
are used
(18) & (19)
29
and a
The
is the
interference flow
velocity is
axial
axial
axial
velocity
at
magnitude one
considered to
consider
important
surfaces of
continuous through the airscrew and u
assumption must
on
blade
experienced
The trailing
r
made: the
trailing vortices
at
distance
distances. For this
from the
vortices which
be
by the blades
elements at other
the blade element dr at
not present.
be
interference flow.
becomes the
the inflow and outflow. In estimating the axial interference flow
The interference flow
doesn't depend
while afis the rotational
center when
spring from the
the two circular cylinders of radius
the
from the
statement
the
in helices.
axis
to be true,
remainder of
ends of
r and r+dr.
r
move
the airscrew
element
The vorticity is
lie
on
is
the
resolved
into
two parts:
1
Axis
.
of
these
the
parts acts as a
cylindrical surfaces and
the
bearing between
general air.
of air cannot acquire circulation about
the
blade
rotational
cause
the
element
is
confined
be
to the
interference due to the
the rolling shell of air bounded
This translates into the fact that the
the
axis and
region
hence the
between the two
vortex system
is
rotation
only
general mass
due to the torque
cylinders.
experienced
by the
of
Therefore the
by those blades
that
vorticity.
Discovering this fact,
can
screw axis
Circumferential
2.
The first
parallel to
undertaken
a geometric analysis of
according to the Figure 4
on
the velocities and the overall effect
the next
page.
30
Figure 4
Blade Element
Theory Diagram
Resultant Force
M
Resultant
velocity
rQ(l-a').
Rotational velocity
V(l+a).
Axial velocity
31
where
V (1 + a)
a
tand
=
(20)
-
rQ(l-a')
Cl
and
Co
are
defined
in two-dimensional
as
the lift and
motion.
These
drag coefficients,
can
be
resolved
respectively.
into thrust
These apply to
and torque
airfoil
according to the
following equations:
\
/*2
The
elements of
chord of
=
=
expressions are
is
cos
(21)
(22)
tp
by the blade element of area cdr,
where c
is the
the airfoil shape, then become:
thrust and torque
which
CL sin <p + CD
thrust and torque given
dl
These
CLcost#-CDsin^
equal
then
for the
=
multiplied
(23)
AiyipM1cdr
by the
entire airscrew.
In
number of
place of c, s
blades to
is
used
obtain the elements of
for the
propeller
blades
to following:
(25)
Nc
s
=
2-r
where
N is the
the area of the
number of
blades in the
annulus at
distance
airscew. s represents
r and can
be known
as the
the ratio of blade elements to
solidity
of
the blade
element.
32
And the
advance ratio
for the
screw can
given as:
V
r
rjD
R
.
There
be
1-a'
V
r
(26)
,
R 1+a
rQ
two extremities for this analysis the first of which is the following:
exist
(27)
sCL=4^2
where
C_ is
taken at
positive value of </>
disappears
an angle of
for
incidence
a propulsive screw.
at a point given
by the
equal
The
to 0
-
second
<f>.
This
corresponds
extremity
occurs when
positive
but
the thrust
following:
(28)
CL=CDtan<*
The torque is
to a normal
vanishes at a
higher
rate of advance when
(29)
CL
Between these two points, the
torque is negative, the
airscrew
airscrew
an
incremental
method
_
rO.
\
^
as a
brake
and
beyond the
point where
as a windmill.
found in the Notes in the
element at
V
VdT
T,~
is acting
is then acting
For efficiency utilizing the
corresponding to
CD cot <j>
dr,
appendix and
the equation becomes the
tan^
following:
(30)
1 + a tan(0 +
y)
33
where
(31>
CD-CLtanr
Note
Profile
drag is
In the first
the
of
:
yis
blades
and
defined
as
as the effect of profile
drag of the
the skin
effect of rotation on the slipstream.
friction
and
induced
drag on
an airfoil shaped section.
these equations there are two additional sources of
energy loss and these are
following:
1
a'
The first loss is
: effect of rotation on
.
2.
.
defined
is the
a1
y
small over the
becomes important
when
employing the
program
order
need
working
drag of the blades
range of
the propeller, but the second loss
the blade element approaches the attitude
Now that the blade
that each blade
: effect of profile
the slipstream
element
element contributes
theory has been introduced
to the performance
of
account a number of
blade
lift.
explained, showing
the propeller, another technique
use of a computer software program will now
takes into
and
of no
be
elements and the
covered.
design
This
software
of the propeller
in
to predict the performance and efficiency of the overall prop. This eliminates the
to
perform
tedious hand
calculations
performance without construction of
points
along the
propeller
is know,
in
order
to get a faster estimate of the prop
the propeller itself. As
an
efficiency
long
as
geometry
and performance evaluation
at certain
is
possible.
34
Chapter 3
:
Propeller Software Program
3.1 Propeller Software Background
Modern
Prop and Duct Design, by Martin Hollmann and Mark Bettosini,
written guide that
first
explains the
proceeds to analyze potential
can
be properly utilized,
theory
designs
of
design behind
with an
included
and
discussed. The geometry
most
of the
to derive mathematic
basic
blade
of
section
these
understanding
quantities are more
understanding
quantity is
being that
of
given
quantities
easily
the
by
the
sum of
and
then
program
knowledge concerning
the
theory in
the software
blade to be
the
.
program
will
in
be divulged.
is based
be
explained
will now
be
fully described in
that pertain to thrust, power, and efficiency. The
If one
referenced.
be
manual will
used on the aircraft must
include the blade
the blade Q
is the free
the
on which
equations
It is
also
0
pitch angle
consults
relative wind speed seen
radius
Figure 5
R
on
,
of
the radius
blade,
the
r at which a
and
the
the next page, these
necessary to know
by both the plane
or
have
an
and the propeller.
This
:
v
V_
of
is described along the blade, the total
rotational speed of
where
But before the
then the relative inputs required for numeric predictions
The theoretical background
order
program.
ducts
a
authors'
a general
the subject must be undertaken. To this end, the
detail
propellers and
is
air
propeller
flow,
is
Vv>(nr)!
<32>
=
which
attached
in any
to the
case
plane.
is the
It
same
can also
for the prop
be
seen
and the plane
that the pitch angle is
two other angles as follows:
0
=
a +
O
(33)
35
Figure 5
Blade Element Diagram for Program Input
Blade
section
Direction
of
Airflow
Qr
J
-
<> +
<^
36
where
O
tan"1
=
-z-
(34)
Clr
It is
obvious that the pitch of the
each
blade
section
along the
better analysis), for
remains a constant
of power
Once
for
an
radius
a certain
wing
understanding
discuss efficiency 7
along the
varies
(note that it is
radius and so
recommended
and
4 degrees
which gives
O is determined
at
to use ten sections for a
speed, and certain free flow of air. The
between 2
certain
blade
however
variable a
the most lift for the least amount
sections.
these quantities has been acquired, it is
of
of a propeller which can
be defined
now relevant
to
as :
P
77
=
7"
(35)
In this equation, the efficiency is simply described
propeller over
system
with
the shaft
itself. But this
known
brake
power
as
delivered to the
equation needs
the power available from the
propeller
by the
the drive
engine or
to be broken down into a more descriptive equation
quantities and measurable values such as:
TV
77
"
(36)
p
where
the
by the
available
power available at
thrust.
From
the prop has been
past
determined that the efficiency is
ratio, (for a fixed
pitch
prop)
a
theory
and extensive
function
which
equated
of a
to the
free
stream
flow
multiplied
experimentation, it has been
dimensionless quantity J, the
is determined from the
advanced
following equation:
V
T
J~D
(37)
37
where n
is the frequency. A
various values of
cannot
be
used
J in
order to
program.
The
These include Ct, the
for
have
not
is
which
other quantities of
coefficient of thrust
depicting the efficiency versus
generated
directly read the efficiency number, but this
for blades that do
technique must be employed
Two
be
graph can
a
fixed
where
interest
pitch.
In this
case a more complex
the software program becomes most
are also analyzed and graphed
coefficient of
thrust,
depends
a propeller
technique
and
Cp,
by the
useful.
software
the coefficient of power.
on three separate
the shape of the propeller, the advance ratio, and the Reynold's
factors
number.
which
The
include
propeller
thrust is equal to the following:
T
where
d is the diameter
revolutions per second.
the thrust
of
it
be
The
Cq is the coefficient of torque.
P
and can
be
reduced
is the
equated to the
CP
where
n
power coefficient also
can
(38)
pnld*CT
the propeller and
The
coefficient and
=
=
=
rotational speed of
depends
on
the propeller in
the same factors affecting
following:
2nCQ
power equation starts as
pn3d527rCQ
(39)
the
following:
(40)
to the following:
P
=
pn3d5Cp
(4D
38
When calling
upon
the aid of a software
program
for
help
problem, it is always good practice to understand the inputs
corresponding
outputs to
be interpreted
by the user as
well.
in
an
engineering
required of
For this
the
computer
in
as well as
the environment in
determining a more
variables can
describe the
accurate result
be found in the Notes
analysis of the propeller can
actual
geometry
which
section.
be found
with
The
it
will operate.
in the
other
scheme of
inputs
the
particular program
there are a large number of inputs needed in order to correctly describe the
geometrically
user and
This
propeller
assists the
things. The list of
required
the Table of Inputs in the
for the
input
correct
next section.
These
of the propeller.
39
3.2 Selected Inputs For the Propeller Program (with
collaboration
from Ken
Blackburn)
After
defining and listing the inputs to the software program,
input the
correct values
This
tell the potential propeller designer and builder
will
enough
for the
purpose
for the
particular type of propeller
intended. For this
to determine the efficiency of the Wright
in existence, the
propeller
order
analysis, reverse engineering is
propeller.
simply be determined from the
used
Since the blade is already
sections provided on
required
for the
software
analyzed.
boundary layer program is employed.
Information
on the
distribution
for the
each
blade
analysis which occurs
analysis which
and pressure
looks
at
in two
used
boundary layer.
boundary layer solver that integrates
This is
a piecewise
inputs for the
sections
The
in the
The
the
The first
second
the
propeller
outputs will
be
of
is
produces a
an
velocity
note
is
the program is an
program can produce
following values
in the
transferred to
Important to
using the efficiency
examined
It
an
effects on small sections of the
integrator and, in the end, this
analysis of
For this task,
of these steps
airfoil.
step
program, the
drawing is
second step.
individual
according to Ken Blackburn, the
software program.
steps.
the air flow around the
distribution to be
that this program assumes no
required
to
the blades are adequate
be carefully
inviscid flow
these
whether
section must
this program
airfoil.
able
being used for the evaluation.
Brothers'
to acquire the necessary inputs
in turn
propeller and
integral
be
drawing itself.
In
Eppler
values must
particular
one must
program.
were
the
Analyzing
inputted into the
results portion of
the chapter.
40
M: 10
THETA75: 28.875
RPM: 428
rpm
VMPHBEGIN: 0
VMPHEND: 50
VMPHSTEP: 1
D:
8.5'
N:2
RHO:
.002378
CLP: 2.0
MINCL: 1.2
ALPHAMINCL: 22
The
propeller.
75%
describe the operating
aforementioned variables
out
retrieved
variable
from the
determine
Another
The
THETA75 specifically
center
all other
hub
values,
the analysis
a
propeller.
The
is the RPM of the
propeller rpm can
be
next set of variables
propeller
altered
characteristics and properties.
This
this vlaue to
twist as a function of radius is ideal.
propeller.
This
The
value of
rpm was
kept
turned at a constant rpm on the
account
Brothers'
to the angle of attack at the span
during flight but this is not the case
takes into
for the Wright
software program uses
angle of
drawing of the Wright propeller.
because the
design for the
the
assuming the
by
noticeable variable
from
of
refers
conditions
428
rpm was
constant throughout
Model B. Nowadays,
with
the Model B. The
the sections of the blade and their specific
will ensure
the program has the correct propeller
evaluation.
41
Table 1
Table
of
Inputs
Column
Column
Column
Column
Column
Column
1
2
3
4
5
6
.1
.1401
.0103
0
1.21
.2
.1401
.0103
0
1.21
.3
.1404
.0103
0
1.21
.4
.1594
.01
0
1.25
.5
.1805
.00935
0
1.295
.6
.21372
.0087
0
1.34
-5.91
.7
.2301
.0075
0
1.36
-6.345
.8
.2258
.0063
0
1.38
-6.78
.9
.2235
.00615
0
1.39
-6.6
.95
.2164
.0060
0
1.40
-6.42
Column 1
:
Mid
Column 2
:
Width
element spanwise
of the
blade
location
Width
Columns 3 & 4
Coefficients
:
of
the
=
.105
-8.89
.105
-8.89
.105
-8.89
-8.95
.11
as a percent of
airfoil section as given
Column 7
-7.43
the total
by the following
Chord/Radius
following equation
xa2
CD
where
=
A* is
A, +A3
by setting the angle of attack to
reading the corresponding CD and A3 is
obtained
and
obtained
known
CL for each
:
Max
Column 6
:
Lift
Column 7
:
Angle
Column 5
curve slope
of zero
zero
by reading the CD corresponding to a
angle of attack.
section
for
lift
each section
(entered
per
degree)
per section with respect to the chord of the airfoil.
42
The table
on
the
preceding
output of the graphs and
page completes the rest of the
efficiency
numbers
numbers, one can change the performance
plane to which the propeller will
order
be
by the propeller program. By
characteristics of
attached.
to obtain the correct traits of the Wright
representation of the results will
be
inputs necessary for the
presented
These
the
propeller and
numbers were
Brothers'
propeller.
in the
altering these
carefully
in turn the
calculated
in
Graphical
next section of this chapter.
43
3.3 Output Results from Software Program
Graph 1
-
428
Efficiency vs.
1
09
rpm
Speed
1
-
OR
^
07
-
n r
-
o
i>
_.
>>
c
05-
0)
'5
m
04-
i>
no
-
0< ?
10
15
25
20
Speed
?
30
35
40
45
(mph)
Efficiency
44
50
Graph 2
-
428
rpm
HP vs. Speed
18
16
<>
n
o
14
<>
12
o
10
a.
z
10
15
25
20
Speed
?
30
35
40
45
(mph)
HP
45
50
Graph 3
428
-
Efficiency vs.
rpm
Advanced Ratio
0.9
0.8
0.7
^
?
0.6
?
>>
c
a,
0.5
'5
UJ
0.4
?
0.3
0.2
?
0.1
<>
0.2
0.4
1
1
0.6
0.8
1.2
Advanced Ratio
?
Efficiency
46
Graph 4
-
Thrust
428
vs.
rpm
Speed
120
o
V.
100
a
<?
80
o
|
60
40
20
10
15
25
20
Speed
?
30
35
40
45
(mph)
Thrust
47
50
Graph 5
Cp vs,
-
428
rpm
Advanced Ratio
0.3
0.25
?
?
?
0.2
_
0.15
0.1
0.05
0.2
0.4
0.6
0.8
1.2
Advanced Ratio
?
Cp
48
Graph 6
CT
vs.
-
428
rpm
Advanced Ratio
0.2
0.18
?
0.16
?
?
0.14
?
0.12
0.1
<
0.08
0.06
0.04
0.02
0.6
0.4
0.2
0.8
Advanced Ratio
?
These
Model B
graphs can now
aircraft
in Chapter 5
be
used
in
CT
an overall performance evaluation of
in Chapter 4. Note that the discussion
of
the Wright
these six graphs will be undertaken
-Results
49
Chapter 4
Performance Evaluation
:
Now that the
computer software program
performance graphs, a
in
performance graphs
drag
will
study
be
has been
conducted to
be
utilized and produced
used
order to predict the cruise speed of the
this section, data from the Wright Flyer will be
Model B. This
the Wright Model B Aircraft
of
method was chosen
in
conjunction with
Wright Model B
used and corrected
due to the lack
of
data in
the
aircraft.
In
to fit the Wright
existence on
the Model B.
4.1 Drag Analysis Procedure of the Wright Model B
The first step in conducting
drawings
the
area of
reasons
for the
available of
plane.
a
drag study of the Wright Model
the plane in order to aid in the
In this
reader
to better
to obtain any
the equivalent frontal
the B were obtained (for
view
the
available material.
Once the
length,
strut
scale of
length,
the
and
2 in
order
drawing was
approximate engine
and approximate pilot size.
Following the
determined
with
measurements, a
help
from
a
strut coefficients were taken
calculated
using
was assumed
This
and
was
to be discussed later). These drawings were presented as Figures 1
established, measurements were taken of cable
size,
calculation of
both drawings for the Flyer
case
B
analysis will
equivalent
flat
determined
by
Fluid Dynamic
equivalent
be
plate
shown
data
provided
to the
in the
separate piece was
Drag textbook (Hoerner,S
directly from the book,
ejection seat
to be
drag coefficient for each
while a
Cd for the
pilot
in the book (Note: the frontal
ejection seat
because both
numerical results section.).
area, Cd*S (where S is the
adding the incremental
1965). Cable
were
a
had to be
area of
sitting
the pilot
position.
In the end, the total
reference area of
areas of each piece on
in
and
the part/wing/etc), was
the plane. From the total
50
flat
equivalent
plate
area, the
overall
drag coefficient of the plane was
then
calculated
according to the following:
(42)
C. plane
=
S.
wmg
where
Swing is the total
is
coefficient
not
area of the wing, not
totally
accurate so
coefficient to match wind tunnel
in the
be
wind
used
to
tunnel, the total
help
that the planes are relatively
was some
drag coefficients
number of
plane appeared similar enough
The first step
onto
flight. The total
was
to
pilots,
make
can
generated
by the wings
due to the
equivalent
due to the flat
and
flat
Flyer has been
already known. These
B.The inherent
data to date, this
area,
will
assumption
appears
is
to be a
too different in design. There
and
tail booms but the overall
coefficient of
drag of the plane
power required
to
in
order
keep the plane
to
in
be determined according to the following:
+
(43)
C. Induced
a
plate area and
the induced
drag is due to lift
the angle of attack of the plane. Since parasitic
plate
this
even
this assumption.
=
drag is
on
landing gear,
the final step of determining the
drag
are
of the model
to determine the total
coefficient of
Now
scale model of the
planes were not
Total
C'Parasitic
Cda
where parasitic
l/8th
a
in flight. Based
due to the fact that the
difference in the
further carry
data. Because
similar
area.
that a correction factor must be applied to boost the
drag coefficients of the plane
determine the
good assumption
just the frontal
which
drag is merely
has already been looked at, the induced
drag is
51
the only part
determine
requiring further
the induced
analysis.
The
following equation can be directly applied to
drag coefficient:
C2
C'induced
(^4)
=
-
where
Cl is
the lift coefficient,
Wright aircraft),
Cd, Cl is
known
values
over
is
aspect ratio
factor
for the
to be
(approximately equal to 0.9 for the
plane.
Since Cl
As
calculated.
be easily determined for
which were
bi-planes. In this
be known. Once the
on a graph
(can be
seen
to the corresponding Ai/A
determining
a correction
not needed
aspect ratio would
wings must
found
is
with
will
Cl,
be
plotted against
e and ;rare
already
leaving AR to be determined for each respective plane.
the Wright planes
between
was
AR is the
then given and
The
case of
and
e
(AR)
e
ratio of
in the Results
This
value.
the ultimate aspect ratio
-
was
Ai. The
a
monoplane, but changes for the
case
height to
and
wingspan was
determined, it
Discussion Chapter)
merely
value
the wingspan and height
an
AR
and
traced
intermediate step in
was then calculated
by the
following:
b2
AR
(45)
=
wing
where
b is
the
determined,
The
wingspan and
the
overall
next
step
Swing is the total
Ai for
was
to
each plane was
plot
the
induced
area of
the wings. Once this was
finalized.
drag coefficient on
a plot of
CL vs. Cd.
52
This step
for both the Flyer
was repeated
were created and these will
induced
plot
for the Flyer
means that the
the parasitic
induced
drag only,
be
shown
in the Results
be
plot could
which was
=
subtracted
between the Flyer
and
correction
B
models.
and
(Note that
Discussion
so
from the
separate plots
Chapter.) The
Cd for the Flyer. This
overall plot
in
order
to isolate
done according to the following:
Cdoverall
numbers were then adjusted
factor: (The
correction
B
was then combined with the overall
Cd parasitic
The resulting
and the
factor
-
Conduced
by multiplying them by the following
accounts
for
all of
the parasitic differences
CdB(parasitic) can be found.)
Y,CdS(B)
cf=
(47)
Y^CdS (Flyer)
CdB( parasitic)
where
CjS(B) is
equivalent
drag
flat
plate area
drag coefficient
new curve was
seen
for the Flyer. These
were
Cd (B
A
cfx
of
added
for the B
total)
then
in Section 4.2
then
=
plotted
(48)
CdFlyer{ parasitic)
the total equivalent flat plate area of B aircraft and
for the B plane,
combined
=
new
CdS(Flyer) is
the total
numbers, also known as the parasitic
to the induced curve for the B in order to get the
plane
according to the following:
Cd (B induced) + cf*Cd (flyer
to depict the
Cl vs. Cj
parasitic)
'4")
total for the B plane. This can be
Chapter 4.
53
One
of the
last
speeds on the plane.
plane was
steps of this analysis was to
This
was conducted
determine the
by first determining the
drag force
velocity
at certain
at which
the
flying according to the following equation:
W
CL=
(50)
,
y2pv2swing
where
W is the
weight of the plane,
total wing area.
Knowing Cl, W, S,
After rearranging the
equation the
p is the
and
air
density, V is
p, the only
velocity
can
the velocity, and
unknown value
is the
SWig is the
velocity.
be found from:
(51)
W
S1
V C
wing
Knowing this
calculated as
quantity
and
equation.
drag
at each
CL,
the
drag force was
then
follows:
Drag
where all of
the coefficient of
the
Force
above quantities
From here to the
1/
C,
x
V,
(52>
2
'
=
x pxV
x
5
have been previously defined
required power was
only
and are
a matter of
known in the
plugging into the
following equation:
Power
This
was then converted
omitted
for
required
=
Drag
Force x Velocity
into horsepower through
spatial reasons.
Now it
was
(")
a series of conversions which were
necessary to
plot
the power required vs.
velocity
54
on the plot of power available vs. speed obtained
obtained
from the
software program needed to
from the
software analysis.
be doubled in
order
to
The
account
power
for the two
propellers present on the plane.
The final step
was to
determine the
graph that corresponds to the
least
climb speed
amount of
HP
by reading the
required.
Then the
speed off of
rate of
climb,
the
R,
can
be found according to the following:
R
P
-P
=
Weight
where
and
Pa is
both
the available power and
are
Pr is
(54)
}
K
the required power at the climb speed.
in ft-lb/sec.
55
4.2
Drag Study Numerical Analysis and Results
According to the analysis description
drag
study
of
the Wright Brothers
completed and exhibited the
Planes,
proceeding
given
in the
Theory Chapter,
the Flyer and the
B,
the
following
was undertaken and
results.
Total Equivalent Flat Plate Area
Flyer
(wing)
+
:
2.69
6.48 (person
Model B
+.385
(cables)
(wheels)
:
+
+
13.54 (struts)
+ radiator +
fuel tank)
(1.91+.32) (cables)
7.08
(wing)
+
+
=
12.85
+
12.96 (pilot
planes was
was
the
(struts)
+
2.205 (engine)
2.21 (chain tubes)
-
fuel tank)
Dynamic
=
+
1.42
assumed and
the
there
area of
drag coefficient. The
drag coefficient was calculated
found in the book (the
was applied
Drag book and applied to the
was no clear-cut
example was
for
7.65
(motor)
39.135
the Wright
to find the total projected frontal area from the drawings. Then the
pilot
+
Drag Book)
determining the equivalent flat plate
found in the Fluid Dynamic
case of
+
34.365
+ radiator +
Cd of Person in Sitting Position (from Fluid
The first step in
1.8 (chain tubes)
frontal
frontal
area.
area
Cd
In the
had to
according to the information
an ejection seat
but the
drag coefficient
to the Wright pilot).
Drag
force
=
V~oV2SC
y2pV'SCd
(55)
56
where
5
=
V
=
p
6ft2(asumed)
500 knots
=
=
843.9-^/
.00238
Drag
force
=
5500lbs
Knowing this information, the Cd of the ejection
Aspect Ratio Determination (from Fluid
Figure 4
:
-
Dynamic
seat/person
is
equivalent
Drag book)
Aspect Ratio Diagram
ATA
(C^
()
>
a e a
(e,)
()
A
C I I
(C,)
(<)
A>
Gap
Ratio
=
=
Geometric Aspect Ratio
h is the height
area of
the
of
the
k/l
m
h/b
Effective Aspect Ratio
where
to 1.08.
Ai
=
A
=
y^
the total wingspan,
gap between wings, b is
and
S is the total
wings.
57
Flyer Analysis:
Gap Ratio
A
=
Ai
=
40Xio
=
h/
=
6/A40
=
=
n
0. 15
3-137
1.25x3.137
=
3.921
B Analysis:
Ratio
Gap
A/A
A
of
h/b=
=
'472
=
5'4%s 5
=
0.141
l.23
=
Ai
Plot
=
=
3.140
1.23x3.140
=
3.8622
Cd Induced
C
C,d induced
=
,
2
.
n{0.9)Ai
Once the
aspect ratio
has been determined from the
drag coefficient can be plotted versus
respective plots
following
the
previous
analysis, the induced
the coefficient of lift. The results can be seen in the
presentation of
the equations for each plane.
58
Flyer induced
C
C'
drag plot
.induced
=
.
,
^-(0.9)3.921
Graph 7
Flyer induced
-
drag
CL vs. Cd
Flyer
n
<
1
?
() 8
?
1 R
?
< 1 A.
?
*?
<1
n
?
i
0.01
-0.01
0.03
0.05
0.07
0.09
0.11
0.13
0.15
Cd
?
B induced
Cd induced
C,' induced
drag plot
C
=,
.
^-(0.9)3.3.8622
Graph 8
- -
Model B induced
CL
vs.
drag
Cd
B
r>
?
i
?
i p
( J.Q
?
1 fi
(1
?
A
?
i
I \J.c
fl
-0.
01
*
.
0.01
0.03
O.I35
0.07
0.09
0.11
0.13
0. 15
Cd
?
Cd induced
59
Plot
of
Flyer Induced
Drag + Parasitic Drag (taken from existing data)
Graph 9
Flyer induced
-
CL
vs.
and
total
drag
Cd
Ryer
1.2
?
?
0.8
?
0.6
0.4
0.2
1
*t
?
,
B
,
0.05
0.1
0.15
0.2
0.25
0.3
Cd
?
Parasitic
Cd induced
Drag Coefficient Determination of the Flyer
Cdparastic
Using the
above
section, the parasitic
placed
Cd induced+parasite
into the
described
=
Cd (measured)
equation and
-
Conduced
the curves presented in the previous
drag coefficient of the Flyer was determined
at each
data point
and
following table:
Table 2
Cd
-
Flyer
induced
Drag Coefficients
Cd total
Cd parasite
0
0.13
0.13
0.000902009
0.12
0.119097991
0.003608035
0.11
0.106391965
0.008118079
0.11
0.101881921
0.014432141
0.11
0.095567859
0.02255022
0.1125
0.08994978
0.032472317
0.115
0.082527683
0.044198431
0.12
0.075801569
0.057728563
0.13
0.072271437
0.073062713
0.145
0.071937287
0.09020088
0.18
0.08979912
0.109143065
0.24
0.130856935
60
Determination
of
the Parasitic
Now that the
applied to the
B
parasitic
with a
few
Cd for the B
drag coefficient has been determined for the Flyer, it can be
adjustments as
YC.S(B)
v
d
cf
=
coefficient of
drag
Cd(B total)
This
yields
the
=
=
following
=
(Flyer)
for the B is
as
-
Model B
Cd induced
1.1388
follows:
+
of values and
Table 3
factor:
34.365
Cd(B induced)
table
a correction
39.135
J
__^
2^CdS
The total
follows using
cf x.Cd
the
(flyer parasitic)
graph on
Drag
Cd
the
following page:
Coefficients
total
0
0.148044522
0.000915741
0.136545012
0.003662966
0.124822562
0.008241673
0.124265213
0.014651863
0.123484925
0.022893536
0.125328706
0.032966691
0.126949548
0.04487133
0.13119446
0.058607451
0.140910453
0.074175055
0.156097526
0.091574142
0.19383774
0.110804712
0.259825115
61
Graph 10
-
Model B induced
and
total
drag
CLvsCd
B
?
11
_
?
?
O
Ofi
\J.KJ
04
ut
?
OP
\J.C
A
n;
\
0
.
Q1
0.05
?
Cd induced
Q15
Q2
Q25
Q3
Cd irduced+parasite
62
Drag Force Determination for the B
Once the
the
above plot
has been completed,
a
drag force can be
obtained
by applying
from the
graphs and
following equations in the order presented:
W
V
=
/
Drag Force
In this
case
=
9
C.x
L
]/xpxV2xS
the unknown velocity is found first
then applying the second equation for
table was produced:
Table 4
-
wing
by pulling CL values
drag force.
Model B
From these two
equations
following
Velocity / Drag Force
cd
Velocity
drag force
CL
Total
ft/s
Lbs
18505.51
0
0.148045
471.747814
0.1
0.136545
149.179757
1706.808
0.2
0.124823
105.486018
780.1388
0.3
0.124265
86.1289731
517.7702
0.4
0.123485
74.5898787
385.8893
0.5
0.125329
66.7152157
313.3209
0.6
0.12695
60.9023809
264.4775
0.131194
56.3846484
234.2751
0.7
the
0.8
0.14091
52.743009
220.1719
0.9
0.156098
49.7265858
216.8015
1
0.193838
47.1747814
242.2965
1.1
0.259825
44.9793892
295.255
63
Power Required for Flight
Now that the
the plane in flight at
be
can
The
drag
force has been calculated, the
different
velocities can
power required can
be found
After the
via
HP
shows
the HP
required vs.
-
=
Drag
data in the
conversions to get to the ultimate goal,
Table 5
HP,
(mph)
previous
table and
drag force
Ft/s
Lbs
HP
471.747814
18505.51
15872.63
462.9482
power
produced:
req
149.179757
1706.808
105.486018
780.1388
149.6252
86.1289731
517.7702
81.08196
74.5898787
385.8893
52.33359
66.7152157
313.3209
38.00599
60.9023809
264.4775
29.28605
56.3846484
234.2751
24.01734
52.743009
220.1719
21.11372
49.7265858
216.8015
19.60148
47.1747814
242.2965
20.78236
44.9793892
295.255
24.14619
be
following some
Model B Required Power
Velocity
will
software program.
Force x Velocity
following table was
the
required against speed and
Speed
by the
the following:
required
equation was applied to the
keep
be determined. Once this has been found, it
plotted on the same graph as power available produced
Power
This
overall power required to
drag force.
presented
along
with
In the
next section
the plot of
the HP available vs.
Speed
(mph).
64
HP Required/Available
vs.
Speed
This is the last step in the
graph the stall speed can
overall
be determined
drag study of the Wright B
as well as regions of
lift
plane.
From this
and sinking.
The
following graph will be further discussed in the next section of this chapter.
Graph 11
Power Required / Power Available
60
'*-7<21.1vi.vc--.
A
50
40
A
/
_
/
/
30
*
20
10
30
20
10
Speed
Power Required B
Climb Speed
and
50
60
-
Power Available
Climb Rate
According to the graph above,
climb rate
40
(mph)
the climb speed is approximately 34 mph and the
is the following:
,,06107-107")
,,
1250
65
Chapter 5
5.1 Climb Speed
From the
and
Discussion
:
it
previous chapter
was shown
that the best climb speed occurred at 34
in ft/s is
often referred
differently then
power at
at
higher
As
altitudes.
compared to sea
due to the thinness
altitudes
it
air to maintain performance and therefore
The
at
this
255 ft/min. These
200 ft/min. The
period of
aircraft specific excess
advantage when
of
level,
the air. The
values
climb
aircraft performs
an aircraft's engine
engine cannot
ingest
loses
enough
cannot climb over a certain altitude.
CL Max
aircraft can still climb while on
use
or
to as the specific excess energy. At sea level an
higher
5.2 Performance
4.26 ft/s
known data from the Model B
the
with
closely
Results
Climb Rate
mph and this corresponded to a climb rate or almost
compare
of
energy
at
CL
max
the edge of a stall,
aborting
a
is 2.26 ft/s
which
is
a
.
This indicates that the
desirable trait. A
pilot can
landing or clearing high terrain.
5.3 Cruise Speed
The
power and
mph.
the
aircraft
closely to that
power curve which
required power at specific velocities.
This becomes the
Model B
from the
cruise speed was read
of
cruise speed of
indicate that its
the data
The two
curves
available
intersected
at
41
the aircraft. Available data from the period of the
cruise speed was around
generated
depicted the
by the
40
mph.
This
the
software program and
compares
drag
very
study.
5.4 Propeller Performance
Efficiency
take off and in
of a propeller
climbing.
the engine to the
If the
is
vital
to the performance of an aircraft in
propeller
propeller cannot
be
is inefficient, the
used
properly
and
is
power
flight both in
being transferred from
wasted.
The
goal of a propeller
66
is to
produce
thrust and act against
direction. The
a
body of air in order to propel the plane in
Wrights
propellers at the time of the
The
analysis of the propeller conducted
here
forward
hardly efficient and therefore
were
their goal of 66% seemed out of reach, but through perseverance
succeeded.
a
was
to
and
hard
confirm
they
work
their design and
their numerical outputs. Because the propeller turned at one speed most of the time, the
analysis was run at a constant rpm of 428,
Model B
(which is
graph
multiplied
confused with the power
power
a published number
propelling the
about right
transmission
for the
losses
aircraft
vertical
and
(2) from the
by 2
software program
for the dual
propeller
indicate the
set-up)
linked to the
power
and should not
resulting from the thrust. The efficiency factor
reduces
input to
be
the
forward.
As it turns out, the 428
is
is
aircraft.
The horsepower
propeller
being this
4
rpm results
engine.
in 28 total HP
This
required at the
engine was capable of
propellers, which
35 HP, but the
density of air will reduce this power.
Since the Wright Brothers first designed their propeller, there have been
enormous
improvements
efficiency
of
expected
to
the
and refinements made on propeller
propeller.
perform at
As
a result of
these
design itself,
improvements,
and
in turn the
today's propellers can be
85% efficiency (K. Blackburn).
67
Chapter 6
Conclusions & Recommendations
:
6.1 Conclusions
In the
previous
drag study were
chapter, the results
presented and
measurements obtained
conclusions
order
this
from these
their quest to
results and
of
the
for their
a propeller
area of concern was
their propeller performed
case
the
propeller.
in the
propeller and
The
itself. This
software was
Brothers. This
draw
make recommendations
in
to
efficiency
means
the
of
and
was
itself. From observing
Discussion Chapter, it is
conclude
it
propeller
that both
that their theories were correct and
intended.
data into the
designed to
clear
Taking the cross
sections and
software program was
conduct
efficiency
the ultimate
studies given the
the operating circumstances of the propeller, or in this
translates
the results can be
software came an
chapter will attempt to
the efficiency of the
manner
propeller as well as
plane
This
or
airplane.
inputting their corresponding geometrical
the
their correlation to the data
this subject matter. From the first chapter, the objective of
studies produce similar enough results
shape of
as
following chapter will
the presented data and graphs in the Results
test of the
far
through the software analysis and the
to determine the accuracy and correctness of the Wright Brothers in
design
The first
as
by the Wright Brothers.
to ease further study
research was
discussed
obtained
into
a
relatively
precise physical model of
considered as accurate as
70% that is
not
far
off of
model was a good one and
the
the inputted model. Out of the
the 66% predicted
by the Wright
the rest of the outputted data should
68
be
acceptable
in the Results
presented
completed
data
retrieved
from the
in the
each speed.
which
different
next
speeds
step
discovered.
closely
power curve
and
the
B,
Chapter (the
Theory
Using this
of
(
that was
a graph
the
analysis could
be
data
and
drag
be
the
be determined. From
was conducted
study
to
keep the
plotted against the predicted power
results of which can
the power
objective
equation
be
seen
scale
according to the
in the Results
in the
to
relatively
small amount of
knowledge
numbers were
at
only
presented, the
and
plane was constructed.
research and showed
actually
few
The
42
mph
combined
that the technique
produce viable numbers with a
the start. Even with
a
power-required curve
yielded a cruise speed of around
the time the
drag study could
employed
final
a
Overlaying both plots
fulfilled this
the planes, the
could
power required
drag study yielded both speeds and the drag force present at
matches that given at
conduct
data
determine
software and a cruise speed could
Discussion Chapter). This
was then
at
Discussion Chapter). The
calculated power
both the Flyer
of
procedure
and
horsepower
second objective of this research was to
in flight. The
drawings
available
knowing this information.
The
plane
including the
units off
only
from their
crude scale
supposed
drawings
of
targets (as set
by the Wright Brothers).
As
success.
mentioned
prior, the two
employed propeller and
early 1900's is
this research were met and with
this information it can be stated that the efficiency of the
Drawing upon
Brothers in their initial
objectives of
the
theory behind it
analysis.
still applied
airplane propellers were a
were
correctly
The theory developed
today
with
only
a
few
lot different from those
applied
by the Wright
by the Wright Brothers back in the
modifications.
used on
boats.
They understood that
Starting
from
scratch
69
they
engineering techniques to
used
was powerful enough to
develop a theory that would produce a propeller that
keep their creation in the air. They succeeded and their plane
took to flight. In the same manner, this research has proven successful and the
Concerning errors in the
interest to look
the software program.
became the
at
in
analysis of the
retrospect.
analysis.
The
drawings
of
in this
assumption.
original equivalent
Another
flat
include the blade
analyzed and
be too
great
an
Flyer
and
all cables or spars could
most
are a
section
input into
B
is in the
were
There
drag
be easily
likely off from the actual total
area of
the
error, but the relative difference between the B and the Flyer
if it is
assumed that the area missed
the drawings also hindered the
is approximately the
measuring the lengths
cables and
the spars. These are only a few of the errors that might have existed
analysis of
the plane, with some others going
Brothers
study
seen and
of
the
could
taken from
The detail
collected and
few
the rest of the data
possible area of error
plate areas of the
the planes themselves. Not
This introduces
might not
areas
Only every other section was
therefore the total area calculated was
plane.
These
Wright Brothers plane, there
average of the numbers on either side of the unanalyzed section.
exist some error
B
flight.
will soon take to
areas of
replica
original numbers
process of
unnoticed.
from the Wrights, the
But
by observing the
analysis seems
same.
of the
during
the
data
to match the
calculations.
70
6.2 Recommendations
From this step
B plane, there
and
its
from the B
of
of
be
areas of
study that
would aide
it
on a propeller
balance in
section
of
relying
which models
the B
blade. The
a propeller
hand
numbers
better data regarding
incomplete
full
flat
would
be
order
the Wright Brothers
to
from
the B using the
not account
In
addition
used
has been
scheduled
for
tunnel test could
a wind
to
to verify
constructed
to be tested in a
wind
1999.
would most
certainly have to be the
plate area as well as coefficients of
provide
Probably the best way to
does
a
directly from
data to be
a propeller
is
From
the plane itself. This model could provide
experimental
analysis at
of
further study
further
drag
at certain
then measuring distances off of an
more accurate
drawing. The
data in
scale replica of
in the fall
size model of
equivalent
This
scaled
calculated
sometime
product
actual propeller
scale wind tunnel.
and torque curves.
Currently
The finished
recommended area of
construction of a scaled or
angles of attack.
calculations.
propellers.
Langley, Virginia
Another
and
full
would also provide an alternate source of
software model and
tunnel at
a
on a computer software program which
that exists in
direct numbers, this
the
the Wright
the plane
studies of
this nature, torque and horsepower curves could be determined
directly transformed into power-available curves
the
in future
the most obvious areas of interest would be to construct an
plane and run
testing instead
every
further
speed of
propellers.
One
study
exist
by step analysis of the efficiency and cruising
data
collected could also
correlation
between the
be
compared to
present analysis
the turn of the century.
verify
some of
same materials
these results, would
be to
construct a
full
the Wright Brothers used to create their
71
original.
The
model could then
conditions as the original
be instrumented
B. This
would
and would provide the most accurate
plane
is
on or near the
of the
flight
opportunity to
anniversary
see what
flown approximately in the
certainly be the
data.
study through NASA. The
and
Currently there
expected to
of
closest
thing
are plans
be flown in the
to the
same
real plane
to conduct such a
summer of
the
year
2000,
the Wright Brothers. This would be the best
the Wright Brothers saw
when
they
were
in the
prime of their
aeronautical careers.
From this section, it
order to
should
be
clear
that there are further steps to be taken in
fully understand the engineering behind the
Wright B Plane. This study merely
scratched the surface on an otherwise tremendous accomplishment of two of the most
important
and significant
figures in
aviation
history.
72
VII. References
Books
Asselin, Mario. An Introduction
Institute
Bettosini, Mark
of
Aeronautics
and
to
Aircraft Performance. Reston, Virginia: American
Astronautics Inc., 1997.
and
Martin Hollman. Modern Propeller and Duct Design. Montery,
California: Martin Hollman, 1993.
Freedman, Russell. The Wright Brothers: How They Invented the Airplane. New York:
Holiday House, 1991
Glauert, H. The Elements of Aerofoil and Airscrew Theory. New York: Cambridge
University Press, 1947.
Hoerner, Sighard F. Fluid Dynamic Drag, June 1965.
Jakab, Peter L. Visions of a Flying Machine, The Wright Brothers and the Process of
Invention. Washington and London: Smithsonian Institute Press, 1990.
Jones, Robert T. Wing Theory. Princeton, New Jersey: Princeton University Press, 1990.
Kirk, Stephen. First in Flight : The Wright Brothers in North Carolina. Winston-Salem,
North Carolina : John F. Blair Publisher, 1995.
Wright, Orville. How We Invented the Airplane, An Illustrated History. Edited with
commentary by Fred C. Kelly. New York: Dover Publications, Inc., 1953.
Thurston, David. Design For Flying (Second Edition). New York: TAB Books, A
Division of McGraw-Hill Inc., 1995.
73
Papers
1.
"A
for the design and analysis of low speed airfoils".
Dan M. Somers, NASA Report No. NASA TM-80210,
computer program
Richard Eppler
August 1980
and
"On the Mechanical Principles of the Action of Propellers". W.J.M. Rankine,
Transactions Inst. Nav. Arch., vol 6, 1865, p. 13.
"On the
Elementary Relation Between Pitch, Slip and Propulsive Efficiency".
Wm. Froude, Transactions Inst. Nav. Arch., vol 19, 1878, p. 47.
Notebooks
1
3.
Wilbur Wright's Notebook H, 1902-1905
Orville
s Notebook K
Wilbur Wright's Notebook J, 1903-1909
4.
Wilbur
5.
Orville Wright's Notes, 1916-1917
.
2.
Wright'
and
Orville Wright's Notebook O, 1908-1912
Websites
www.pbs.org/wgbh/pages/amex/wright/index.html
www.wam.umd.edu/~stwright/WrBr/Wrights.html
www.alumni.caltech.edu/~johnlatz/1903.html
quest.arc.nasa.gov/aero/wright/
www.wright-b-flyer.org/
firstflight.open.ac.uk/
quest.arc.nasa.gov/aero/chats/
www.fi.edu/flights/
www.alwavs-
online.com/)avhawker/Pictures/Vriginia
Beach/Wright Bros/Wright Index.htm
www.first-to-fly.com/historv/1905.htm
sln.fi.edu/flights/first/flyer.html
www.lerc.nasa.gov/Other
Groups/IFND/airplane/propeller.html
Other
1
.
Conversations
with
Quentin Wald,
excerpts
from his book
and other
facts
74
VIII. NOTES:
1 Method for Calculation
Step
1 : Choose the
are all
Step
known
2:
or
Step 3:
a series of a
values of
Integration
due to the
by studying a
of a
Screw
along the blade for
which
r/R, s,
ty,
a,
Cd,
and
Cl
easily determined.
Note: It is
torque
Characteristics
number of elements
Starting with
corresponding
of
a, a',
J, dKj,
curves give
not possible
nature
for
of the
each element
and
it is
possible
to calculate the
JKq.
the total thrust and torque
for the
entire airscrew.
to obtain a simple analytical expression for the thrust and
blades, but in
general
the characteristic can
be
obtained
typical section.
2 Input Variables for Software Program
The
following is
a
list
of
the variables and their appropriate descriptions as necessary.
M: Number
of
blade
THETA75: Pitch
of
segments
to be used
-
the blade at 75% of the radius
RPM: Propeller
rpm
VMPHBEGIN:
Starting speed for analysis
VMPHEND:
(10 recommended)
Ending speed for analysis
VMPHSTEP: Incremental
(of plane)
(of plane)
speed change
between
start and end
75
D: Diameter
N: Number
RHO: The
CLP: The
of the propeller
of
air
blades
density in which the blade will most likely operate
peak
Q
MINCL: Min Ci
after
after
initial
ALPHAMINCL: Angle
The
aforementioned variables
initial
stall
stall
(recommended
(recommended
of attack that produces
describe the basic
propeller as well as
2.2)
1.4)
MINCL
the
operating
environment.
76