Transcript Engineering 310

Aero Engineering 315
Lesson 21
GR#2 Review
GR Breakdown
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150 points total
25 multiple choice/matching
 Mostly conceptual
 3 short work outs
2 long work outs worth 46 pts total
 Hand graded with partial credit
available
General strategy
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Prior to class
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Work your GR review handout
Review reading for lessons 12 – 20
Work all problems through #25
Review slides and handouts
 Lift and drag summary
 NACA Airfoils
 Mach effects
Know your memory equations—including GR#1
equations (especially dynamic pressure, q)
Be familiar with applicable supplemental data info
In class
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Bring calculator, straight edge, pencils
2-D Airfoils
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two-dimensional
An airfoil is a __________________
cross-section of a wing. It
infinitely
2-D object, an _____________
may be thought of as a _____
long
object, or an object that completely _______
spans the width of the
test section of a wind tunnel, such that no _________
effects
wingtip
influence the flowfield
The forward-most point on an airfoil is called the
leading edge
______________,
and the rear-most point is called the
_________________
trailing edge
A straight line that connects the leading edge and the trailing
chord line
edge is called the ___________;
the length of this line is
chord (or _______________),
chord length
c
_______
abbreviated ___
A curved line drawn from the leading edge to the trailing edge so
as to be midway between the airfoil’s upper and lower surfaces is
mean camber line
called the ____________________
The maximum distance between the mean camber line and the
max camber
chord line is called the airfoil’s _________________
(or just
camber
__________)
2-D Airfoils
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A symmetrical airfoil has _______
zero
camber
For NACA 4-digit series airfoils, the first digit represents
_______________
in _________
max camber
percent of chord, the second digit
tenths
location of max camber
represents ___________________________
in _________
of
chord, and the third and fourth digits together represent
max thickness
percent
__________________
of the airfoil, in __________
of chord.
By definition, the first two digits for a symmetric airfoil are
00
_____.
The length (tip-to-tip) of an airfoil model tested in a wind tunnel
b
is its ______,
span abbreviated ___
Planform
__________area
(___)
is the area of a projection of the airfoil’s
S
b•c
shape onto a horizontal surface beneath it; S = _______
The direction of the freestream velocity is the
relative wind
___________________;
the angle between the relative wind
angle of attack
a
and the chord line is __________________
(___),
with leading
edge ____
up being the positive direction
2-D Airfoils
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The AOA at which an airfoil produces no lift is the
al=0
0
________________________________
(______);
al=0 = ___
zero-lift angle of attack
for symmetric airfoils
The aerodynamic force acting on a wing is created by the
___________
and _______________
distributions over the wing
shear stress
pressure
surface
The aerodynamic force can be resolved into _____,
the
lift
component perpendicular to ________________,
and _____,
relative wind
drag
the component parallel to _______________
relative wind
Summing upper and lower surface forces, we find the existence
of a pitching moment; this moment is positive in the L.E.- ____
up
direction
center of pressure
The ____________________
is the location on an airfoil at
which the pitching moment is zero; this location can change with
AOA
_________
The ____________________
is the location on an airfoil at
aerodynamic center
which the pitching moment is constant (i.e. doesn’t change with
_________);
for subsonic flight, the aerodynamic center is
AOA
located at approximately the ________________
point (x =
quarter-chord
____)
c/4
2-D Airfoils
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At the aerodynamic center, the moment is __________
negative for positively
zero for symmetric airfoils
cambered airfoils and is _____
L/(q•S) drag coefficient Cd =
We define lift coefficient Cl = _______,
D/(q•S) moment coefficient Cm = _________;
M/(q•S•c) these coefficients
_______,
M
are _______________
a ____,
Re and ____
nondimensional and can vary with ____,
The NACA airfoil data is for ____,
2-D ________________
incompressible flow
The slope of the linear part of the lift curve is the lift curve slope,
Cla Cla ≈ _____/deg
_____;
for thin airfoils
0.11
airfoil stall
The top of the lift curve rolls off due to _________________;
the
astall
AOA where the curve peaks is _______,
and lift coefficient is
Clmax
_______
To determine drag coefficient (Cd) at a given a, we must first
Cl
determine ___
Know how Reynolds number, camber, flaps, and boundary layer
control affect the lift and drag curves!
Know how to find lift coefficient, drag coefficient, quarter-chord
moment coefficient, and moment coefficient at the aerodynamic
center from the NACA airfoil data charts!
3-D Wings
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The length (tip-to-tip) of a wing is the ______
span (___)
b and its
projected area is the _______________
(___)
planform area
S
Aspect ratio (AR) = _______
and describes whether the wing is
b2/S
long and skinny
“_____________________”
or “_______________________”
short and stubby
tip chord
Taper ratio (__)
to
l is the ratio of _____________
______________,
or ct/cr
root chord
L is the angle between the wing’s
Leading edge sweep angle (__)
leading edge and a line _______________
to the root chord line
perpendicular
To delay stall near the wingtips, we can use ___________
geometric twist
(wingtip twisted ______)
twist (different
down or ______________
aerodynamic
airfoil)
Due to the top surface-to-bottom surface pressure imbalance on
a wing, rotating ____________
form at the wingtips
vortices
Wingtip vortices form a downward velocity component, or
_________,
downwash on the wing’s upper surface, deflecting the local
e and
flow velocity downward by the _________
downwash angle (___)
reducing the effective angle of attack (aeff = _______),
causing a
a-e
_____________
in lift
reduction
3-D Wings
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lower than the 2-D lift curve slope,
The 3-D lift curve slope is _______
but the zero-lift AOA (aL=0) is ____________(a
the same
= al=0)
L=0 ___
Wingtip vortices also cause a spanwise flow component: root-totip on the _______
lower surface, tip-to-root on the _______
upper surface
Wingtip vortices also tilt the net force vector back by the
_________
downwash angle, causing an increase in drag; this “drag due to
lift” is called __________
drag. Physically, this drag results
induced
because the energetic vortices are “robbing” energy from the
plane’s __________.
engines
The span efficiency factor (___)
is 1 for __________
elliptical wings, and
e
________
than 1 for all other types of wings
less
We can minimize induced drag by using ___________
wings,
elliptical
high-_____________
wings, _________
winglets on the wingtips,
aspect ratio
________
drooped wingtips, or wingtip ________
stores (i.e. air-to-air missile)
3-D Wings
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profile drag
Total drag for a 3-D wing is the sum of _________
skin friction
(composed of _____________drag
and __________
pressure drag)
and __________
drag
induced
Know how to calculate lift for straight-and-level flight
(L = W), how to calculate 3-D lift coefficient (CL = L/qS),
how to calculate induced drag coefficient (CDi = CL2/peAR),
how to calculate total drag coefficient (CD = Cd + CDi,
where Cd is found in the NACA airfoil charts), and how to
calculate 3-D wing total drag (D = CD•q•S)
Or alternately, know how to calculate 3-D lift curve slope
(CLa = Cla /[1+57.3°•Cla /peAR]) and then calculate 3-D lift
coefficient (CL = CLa (a-aL=0), where aL=0 = al=0, found in
the NACA airfoil charts)
High-Lift Devices
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For straight level unaccelerated flight (______),
lift __
SLUF
= weight,
2W
and velocity required to maintain lift is V∞ = ____________
ρSC
2W
The stall velocity, Vstall, occurs at ______:
CLmax Vstall =___________;
ρSC
2W
in equivalent airspeed, Ve-stall = ____________
ρ SC
takeoff and
We must fly at relatively slow airspeeds during _________
_________;
takeoff speed is limited by ________
landing
runway length and
available engine ________,
while landing speed is limited by
thrust
_________
braking effectiveness, ______
tire specifications, and runway
____________
condition
For a given aircraft weight, if you want to fly slower, you must
increase ____,
CL so we use __________
high-lift devices to improve CL
Trailing edge flaps increase wing ________,
camber thereby increasing
CL (the lift curve is shifted ___
up and to the ______)
left
Flaps also increase ______
drag (the drag polar is shifted ___
up and to
the ______)
right
A plain flap’s effectiveness can be reduced because of flow
___________;
split flaps and slotted flaps attempt to overcome
separation
this problem
L
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L max
SL
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L max
High-Lift Devices
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Fowler flaps help delay flow
Similar to slotted flaps, _______
separation, but also increase wing _________________,
further
surface area
increasing lift
Like a trailing edge flap, a leading edge flap can increase CL by
increasing wing ________
camber
Boundary layer control devices, such as a fixed _____,
slot a leading
edge _____,
slat upper surface ________,
suction and upper surface
_________
blowing increase CLmax by helping keep the boundary layer
_________,
attached delaying stall
Another approach to supplementing lift is _________
vectored thrust,
such as that used by the AV-8B Harrier and the Marine Corps JSF
Leading edge strakes produce strong _________
vortices and direct
them over the top of the wing; the very low _________
pressure in the
core of the vortices augments the _____
lift produced by the wing—
especially at high _________________
angles of attack
Strakes cause the lift curve to rotate ___
up and _______
extend
Whole Aircraft Lift and Drag
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When determining whole aircraft lift, the lift of the wing is
modified by the __________,
________
fuselage
strakes and other high-lift
devices, and the ____________
tail and/or ________
horizontal
canard
The general form for the whole aircraft drag coefficient is
linear term is generally
CD = CDo + k1CL2 + k2CL, but the _______
CDo + kCL2
negligible and can be ignored; we use CD = _____________,
an
equation known as the whole aircraft ____________
drag polar
k1 (often referred to simply as k) = 1/peoAR, where eo is
_________
Oswald’s efficiency factor, which will be ______
lower than span
efficiency factor e
CDo, which represents _________
parasite drag, is _________
constant and
includes the following drag contributions: ______________
skin friction
drag, _________
pressure drag at zero lift, _____________
interference drag from
wing/fuselage coupling, and ______
wave (supersonic) drag
Whole Aircraft Lift and Drag
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kCL2 represents drag due to _________
and includes the
lift
following drag contributions: wingtip _______-induced
vortex
drag, __________
pressure drag that varies with lift, and any other
drag that varies with lift (due to leading edge _________,
strakes
for example)
Similar to 3-D wing calculations, know how to calculate lift
for straight-and-level flight (L = W), how to calculate
whole aircraft lift coefficient (CL = L/qS), how to calculate
whole aircraft drag coefficient (CD = CDo + kCL2, where CDo
will be given, k may be given or may be calculated by
k = 1/peoAR), and how to calculate whole aircraft drag
(D = CD•q•S)
Supersonic Flow
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a varies only with temperature: a =
Speed of sound (__)
γ RT
_________;
the ratio of specific heats g = 1.4 for air
M is the ratio of freestream velocity and
Mach number (__)
v/a
speed of sound: M = ______
m represents how steeply a Mach wave
The Mach angle (__)
1/M
sweeps back, and sin m = _____
Mcrit
Critical Mach number (______)
is the freestream Mach
number at which the flow somewhere on the airplane first
1
reaches M = __
shock waves
As Mach number increases beyond Mcrit, ____________
form on aircraft surfaces, which can cause flow
separation
lift and increasing _____;
____________,
reducing _____
drag
the additional drag resulting from shock-induced
wave drag
separation is called ______
Supersonic Flow
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The different flight regimes are __________
subsonic flight, at Mach
Mcrit
numbers below ______,
where the flow is everywhere
__________
than the speed of sound; ___________
slower
transonic flight, at
Mach numbers above Mcrit and below about ____,
1.3 where regions
of both ____________
and ___________
subsonic
supersonic flow exist;
____________
faster
supersonic flight, where the flow is everywhere ________
than the speed of sound; and ___________
hypersonic flight, at Mach
numbers above about __,
5 where extreme high _____________
temperatures
significantly change the chemical properties of air
As flow crosses a _______
normal shock (perpendicular to flow
direction), ________________and
__________
fall, while
total pressure
velocity
_________________,
_____________,
and _________
temperature
density rise
static pressure
When the freestream exceeds Mach 1, _____________shocks
bow wave
will form in front of bodies with blunt leading edges, while
____________
shocks will attach to bodies with sharp leading
oblique
edges
Supersonic Flow
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In the airfoil lesson, we discussed the fact that lift and drag
coefficients vary with a, Re, and __;
M to predict the variation (due
to compressibility effects) of lift coefficient with Mach numbers
between 0.3 and 0.7, we use the ______________________
Prandtl-Glauert
correction
shock stall causes a large
Cl ______
rises with Mach number until ___________
drop in Cl; once the shock moves to the trailing edge, Cl
_________
recovers
CDo remains essentially constant below Mcrit, but begins to
_________
Mach
increase rapidly above the __________________
drag divergence
number, MDD
When M∞ > 1, the wing’s aerodynamics center shifts back from
the ________-chord
point (c/4) to the _______-chord
point
quarter
half
(c/2)
If we want to fly at high subsonic speeds while avoiding wave
Mcrit
drag, we want to increase ______;
strategies for doing so
include the use of _____
thin wings; less _________
cambered wings;
_________
wings; ______,
sharp ________
swept
slender leading edges; and
_______________
airfoils
supercritical
Supersonic Flow
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increases Mcrit by decreasing the velocity
Wing sweep __________
L although wing
component the airfoil “sees” by 1/cos __,
decreasing aspect ratio
sweep increases induced drag by __________
reducing
and ___________
span efficiency factor
If we want to fly at supersonic speeds, we want to
wave drag; strategies for doing so include the
minimize _____
use of a _________
blended wing-body; an ____________
area-ruled
fuselage (Coke-bottle shape or “wasp waist”); offsetting
tailplane
the ___________
above or below the main wing; sharp,
slender _________
(causing oblique shocks, which
wings
bow wave
produce less wave drag than ______________
shocks);
and ____________-geometry
wings
variable
Next Lesson (T22)
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Prior to class
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Read
Study
Homework problems
EI
In class
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GR#2