EXAM I REVIEW
Format
 Administered in a few minutes more than one hour
 20 questions
o 15 objective (multiple choice / true-false)
o 5 short answer/calculations
 MUST show work on short answer problems
 Can receive ½ credit on show work problems with an incorrect numeric
answer if you
o Write the correct equation
o Substitute correct numeric values in the equation
Allowed Materials
 Pencil/eraser—NO INK PENS PLEASE
 Blue-covered gathering from bookstore
o many questions can’t be answered without access to this
information--YOU MAY NOT BORROW A FRIEND’S COPY
o Nothing may be written in the gathering—NOTHING!!! If you
have already written in your copy with ink or cannot completely
erase anything you have written in pencil, please purchase a
second copy for use exclusively in exams
o You may put tabs on pages to help locate information if you wish
 Electronic calculator
o but not one that is on a cell phone or other device with Internet
connectivity
o If you have an aviation calculator, you may not use aviation
functions
o If you have a programmable calculator, you may not store
information in the instrument’s programmable memory
 8.5” x 11” study sheet, written on both sides
o You must make your own—don’t copy a friend’s or share yours
with someone else
o Study sheets must be submitted with the exam
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 Draftsman’s triangle
 NOTHING ELSE MAY BE ON YOUR DESKTOP DURING THE
EXAM—this includes food and drinks
Time Constraints
 The exam will start as soon as we have access to the room,
o ABSOLUTELY NO TALKING IN THE CLASSROOM AFTER
YOU ENTER—RESPECT YOUR FELLOW STUDENTS WHO
MAY ALREADY BE AT WORK
o Please don’t enter the classroom unless you are ready to sit down
and start the exam
o Please sit down promptly and quietly once you enter the
classroom
o Organize your materials BEFORE you come to class
o Once you are seated with a clear desk (except for materials you
will use on the exam), I will give you an exam booklet and you
may start the exam.
o To respect the class entering after our class period, the exam will
end PROMPTLY at the scheduled end of class. THERE CAN BE
NO EXCEPTIONS TO THIS TIME CONSTRAINT—
ANOTHER CLASS USES THE ROOM AFTER WE LEAVE IT.
What information will be queried by the exam questions?
 If a topic is covered in lectures or on a quiz or a quiz worksheet, it may
appear on the exam
 Exam questions in format are similar to quiz questions
 To review for the exam, use the course lecture notes, quizzes, and quiz
worksheets.
 If you can explain to someone who hasn’t taken the course the subjects
covered in the course lecture notes/quiz worksheets, you are ready to
take the exam. If there is a topic you don’t understand well enough to
explain to someone else, you might have trouble answering a related
exam question
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Hints for getting the highest possible grade
 Prepare carefully. Small study efforts tend to lead toward mediocre
exam results
 Remember—this is only an exam, not a Level D simulator flight that
will determine whether or not you will get an airline job. Keep calm
and cool—your mind works better when you are calm.
 What you know about the course content when you walk through the
door is what you know. Not everyone will know enough to answer every
exam question correctly. DO NOT WASTE TIME DELIBERATING
OVER A QUESTION THAT PERPLEXES YOU IN THE VAIN
HOPE THAT THE GODS WILL MIRACULOUSLY SEND YOU THE
ANSWER. YOU NEED THAT TIME TO WORK ON QUESTIONS
THAT YOU DO KNOW THE ANSWERS TO.
 Answer the 15 objective questions first—they count 75% of your grade
but take less than half the exam time to answer
o You will answer objective question first on the exam booklet.
When you are satisfied with your answers, you will then copy
them to a Scantron form. Be sure to allow enough time to do this
BEFORE the end of the exam arrives
o Go through the questions systematically 1-15
o Eliminate answers that are clearly incorrect
o If you aren’t sure about the correct answer, make your BEST
GUESS among the remaining distracters WITHOUT UNDUE
DELAY
o Don’t waste time: go on to the next question agonizing over a
question you aren’t sure about
o Don’t change an answer once you record it unless something later
in the exam reminds you of something you didn’t recall when you
made your first answer. Studies show that your are more likely to
change from wrong to wrong or from right to wrong than from
wrong to right
o If you follow these guidelines, you will finish the objective
questions in about ½ hour or less
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 Next answer the 5 show-work/fill in the blank questions—they count
25% of your grade but take almost as long to complete as the objective
questions
 If time allows, review your answers to make sure you haven’t made a
careless mistake. However—as indicated previously—beware of
changing answers to objective questions, as you are statistically more
likely to lose than to gain points when you do, assuming of course that
your first guess was really a considered “best” guess
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Review Quiz 1 Material
Standard Atmosphere:
 Pressure Ratio:  = P / P0 (14.69444 #/in2; 29.92” Hg)
 Temperature Ratio:  = T / To (59o F, 15o C). Must use absolute T.
 Density Ratio:  =  /  0 (0.002377 slugs/fat3)
18000  22000  0.5.
From universal gas law,  =  / .
 and  have an inverse non-linear relationship with altitude.
 has an inverse linear relationship with altitude.
Indicated Altitude IA = on cockpit instrument
Pressure Altitude PA = IA corrected for non-standard pressure.
1” Hg  1000’ in lower atmosphere.
Suppose 30.22 at 4000’ elevation. 30.22 – 29.92 = 0.30. (0.30) 1000 = 300.
Since high pressure is associated with low altitude (inverse relationship), we
must subtract the correction: 4000 – 300 = 3700’ PA.
Density Altitude DA = PA corrected for non-standard temperature.
DA = IA corrected for non-standard density because ρ  P/T
Can use Figure 2.5 to find DA and SMOE (must know PA and T in degrees
C):
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Temperature Ram Rise:
 IOAT is indicated outside air temperature (on cockpit instrument)
 AAT is ambient air temperature (actual outside air temperature in
vicinity of aircraft)
 IOAT  AAT due to ram air heating effect caused by dynamic
pressure q =  V2 /2
 Theoretical difference IOAT – AAT is called Temperature Ram Rise
TRR
 TRR  M2, where M is mach number (recall q =  V2 /2 is also a
parabolic relationship)
 Recovery Coefficient (RC  1.0) is the proportion of TRR which
must be subtracted from IOAT to get AAT:
1. AAT = IOAT – RC (TRR)
2. If RC < 1.0, IOAT is sometimes called Ram Air Temperature
(RAT)
3. If RC = 1.0, IOAT is sometimes called Total Air Temperature
(TAT) or just Total Temperature.
 RC is aircraft dependent.
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Figure 11.3 for Boeing 737-300 allows computing AAT from IOAT (total
temperature). The fact that the figure requires TAT input implies that RC =
1.0.
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Review Quiz 2 Material
IAS = read on cockpit instrument
CAS = IAS corrected for pitot-static system error (aircraft dependent)
EAS = CAS corrected for compressibility effect (aircraft independent)
TAS = EAS corrected for non-standard density (SL density on a standard
day)
Figure 3.1 is an example of a chart to correct IAS to CAS (note: aircraft
dependent):
Figure 3.2 and Figure 3.4 can be used to correct CAS to EAS (note: aircraft
independent):
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The same information is available in table form in the blue-covered booklet:
Pres.
Alt.
SL
2000
4000
6000
8000
1000
12000
14000
16000
18000
20000
22000
24000
26000
28000
30000
32000
34000
36000
TAS =
EAS

150 kts
CAS
0
0
0
0.5
0.5
0.5
0.5
1.0
1.0
1.0
1.0
1.5
1.5
1.5
2.0
2.0
2.5
3.0
3.0
200 kts
CAS
0
0
0.5
0.5
1.0
1.0
1.5
1.5
2.0
2.5
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.5
7.0
250 kts
CAS
0
0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
5.0
5.5
6.5
7.5
8.0
90.
10.0
11.5
12.5
300 kts
CAS
0
0.5
1.0
1.5
2.5
3.5
4.0
5.0
6.0
7.0
8.0
9.0
10.5
12.0
13.5
15.0
17.0
18.5
20.5
350 kts
CAS
0
0.5
1.5
2.5
4.0
5.0
6.0
7.5
9.0
10.5
12.5
14.0
16.0
18.0
20.5
22.5
25.0
28.0
= EAS  SMOE.
Direct non-linear relationship between SMOE and altitude.
M=
TAS EAS EAS 
EAS 
EAS




a
a 
a 
a0   a0 
Example: CAS =350 kts at 32,000’ PA. Find EAS, TAS, and Mach number.
1. From Figure 3.2 or Figure 3.4, EAS = CAS – 25 = 325 kts.
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2. In standard atmosphere, SMOE32,000 = 1.6968; TAS = EAS (SMOE) =
325 (1.6968) = 551.46 kts.
3. From standard atmosphere table, M = TAS /a32000 = 551.46 / 584.43 =
0.944.
Or M = EAS / (a0 32000) = 325 / (661.7 
.27090) = .944.
Or there are other
comparable ways to compute the same value.
Use Figure 3.6 (and related figures) to find TAS and Mach number for F14
Tomcat. Must know CAS and PA. Note that the figure has dark example
lines to show algorithm for using the chart.
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Airspeed Envelop for B767 (dependent on gross weight and G factor safety
margin):
1. VS – minimum 1 G EAS; i.e., stall speed (invariant with altitude)
2. VMO – maximum operating EAS due to structural integrity
(invariant with altitude)
3. MMO – maximum operating Mach due to high speed buffet (invariant
with altitude)
4. VMMO – airspeed associated with MMO (decreases as altitude
increases)
5. MDF – maximum demonstrated flight Mach (invariant with altitude)
VS is low speed buffet airspeed; MMO (VMMO) is high-speed buffet airspeed.
Key Terms/Concepts (refer to Figure 3.12 below):
1. VS gives low speed buffet.
2. Crossover altitude: MMO (VMMO) = VMO.
3. Coffin corner altitude: MMO (VMMO) = VS (low speed and high
speed buffet)
4. Below crossover altitude, upper speed limit is VMO (structural
integrity).
5. Above crossover altitude, upper speed limit is MMO (VMMO)
(high speed buffet)
6. Allowable airspeed range is upper speed limit – VS.
Figure 3.12 gives Airspeed Envelop for B767 at 300,000# gross and 2G safety
margin.
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Use Figure 3.13 to find high /low airspeeds (and allowable IAS range) for
B737 at various gross weights.
Aerodynamic Force is resolved into Lift and Drag. Drag includes both
parasite and induced drag, assuming the existence of wingtip vortices, which
are a fact of life for all real world fixed wing airplanes.
L
AF

D
relative wind

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Factors influencing life (and drag):
 Dynamic pressure =  V2 /2 in #/ft2 (V is TAS in ft/sec).
 Air density ratio  (dimensionless)
 Planform wing area S in ft2
 Shape of airfoil section, especially camber
 Air viscosity
 Compressibility effect
 AOA  (for a given configuration, an airplane always stalls at same
AOA)
Lift and Drag Formulae:
L = CL q S = C L V
2
S
295 .37
D = CD q S = C D V
2
S
295 .37
(V is TAS in kts)
Also, since EAS2 = V2, the lift and drag formulae may be written:
C L EAS 2 S
L=
295.37
C D EAS 2 S
D = CD q S =
295.37
(EAS in kts)
Solving the lift formula for TAS V (and assuming L = W in 1G level flight)
gives:
V
295 .37 L

CL S
295 .37 W
CL S
From this we may conclude that to maintain L = W:
 Doubling W requires that V be increased by 2.
 Doubling CL, , or S allows decreasing V by 2.
 Doubling V allows increasing W by a factor of four.
 Doubling V allows decreasing one of {CL, , S} by a factor of four.
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CL is a linear function of AOA  for airspeeds above VS.
Quiz 3 Review
True Airspeed as a Function of Gross Weight, Density Ratio, Coefficient of
Lift, and Bank Angle.
These equations reflect the fact that TAS (e.g. stall speed, max range cruise
speed, &c.) varies directly with gross weight, bank angle, and G force and
inversely with density ratio and coefficient of lift. EAS varies directly with
gross weight, bank angle, and G force and inversely with coefficient of lift.
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Body Attitude (Deck Angle). A given airspeed (e.g. stall speed, max
endurance speed, max range speed) typically corresponds in steady state flight
to a given AOA. Since most airliners don’t have AOA indicators, body attitude
is used as an equivalent indicator. By body attitude, we mean simply the pitch
angle shown on the attitude indicator. There is a direct mapping between
pitch angle and angle of attack in steady state flight. The vector diagram
below shows how velocity (airspeed and vertical speed), flight path angle,
angle of incidence, angle of attack, and pitch angle (body attitude) are related.
Angle of
Attack
Pitch Angle =
Body Attitude
Angle of
Incidence
Body AOA
Velocity
Flight Path Angle
Body attitude together with vertical speed, altitude, and power setting can be
used to maintain safe flight with an unreliable airspeed indictor.
Factors Affecting EAS. Assuming W = L, the following equation shows that
equivalent air speed is dependent only on weight, coefficient of lift, and
planform area. In particular, EAS is not dependent on density altitude
(reflected by density ratio ), while TAS is. Thus, for example, a plane in
steady state 1G flight at a given configuration and gross weight always stalls
at the same EAS.
EAS 
295.37 L

CL S
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295.37 W
CL S
Induced, Parasite, and Total Drag. Recall from AS309 that induced drag
decreases non-linearly as AOA decreases and airspeed increases, while
parasite drag increases polynomially. (The latter fact is predictable from the
formula for dynamic air pressure, q =  V2 / 2.) The scalar sum of induced
and parasite drag at various TASs gives the Total Drag Curve. Such a curve
applies to a given aircraft in a given configuration operating at 1G steady
state flight at a given gross weight and density altitude.
Some important facts about the Total Drag Curve:
 Applies to a given a/c in 1G steady state flight at fixed gross weight,
density altitude.
 Lowest point on curve corresponds to (L/D)max, hence gives the
airspeed for best glide.
 Value of (L/D)max gives the best glide ratio, but can’t be computed
from Total Drag Curve).
 Sharp increase in total drag at high TAS is due to compressibility
effect in the transonic flight regime.
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POWER OFF GLIDING FLIGHT





AA is absolute altitude; GD is glide distance; a = glide angle.
Glide ratio GR = GD / AA
Tan a = AA / GD, so GD / AA = 1/tan a
L = W cos a is the component of weight supported by lift.
D =W sin a is the component of weight that propels the aircraft down the
glide path at a constant glide speed.
 For a given AA, GD is maximum when the glide angle a is minimum
 The small right and large right triangular above are similar (same angles):
this implies that the ratios of any two corresponding sides are equal. Thus:
GR =
GD W cos a
1
L


 . Thus GD = GR (AA) = (L/D) (AA) = (AA) / tan a
AA W sin a tan a D
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Key Points
 Glide angle a is minimum and glide distance GD is maximum at
DMIN, i.e. when drag is minimum (proven in text).
 Thus best glide speed GS is obtained at the airspeed corresponding
to (L/D)MAX, because this is where D is minimum on the DT curve.
 Best glide airspeed is affected by weight changes according to the
formula V2 = V1 (W2 / W1). However, AOA αBG for best glide is
invariant for fixed configuration.
 A pilot who deviates from best glide speed shortens glide distance,
appreciably if the deviation is large (which results in drag
significantly higher than DMIN).
 AA is often specified in feet and GL in nautical miles (nm) or statute
miles (sm). To use the formula GR = GD/AA or any related formula,
GD and AA must be in the same units.
 A nautical mile has 6076 feet, and a statute mile has 5280 feet. To
convert feet to nm (or sm), divide by 6076 (or 5280).
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Drag Polar. Drag polars are plots of cL vs. cD for various AOAs. Data on an
individual curve are gathered in fixed configuration in SS SL flight over the
airspeed range of the airplane. The shape of a drag polar reveals that at high
AOAs, lift increases more rapidly than drag as AOA increases. However, at
high AOAs, the reverse holds true. The transition point on the curve occurs
where line drawn from the origin tangent to the curve intersects the curve.
This point corresponds to (CL / CD)max = (L / D)max, as illustrated below on the
low speed cruise drag polar for the B767. (L / D)max  19.4 for this curve
shows that the B767 can glide approximately 19 nm horizontally for each 1
nm of absolute altitude.
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Changes in configuration affect the drag polar, as reflected in the following
plot for the B767 at Flaps 15. Here (L/D)max is less than 15, and the a/c glides
less far than in clean configuration.
Note: x-axis scale: 0.01, 0.02, 0.03 ; y-axis scale: 0.1, 0.2, 0.3 …
Note: Origin not always at intersection of figure axes
Note: to find GR, find points on the tangent line, not on the drag polar curve
Some important facts about the drag polar:




Applies to a specific airplane in a specific configuration.
Affected by compressibility.
Can determine value of (L / D)max, but not the corresponding TAS.
The point on the curve corresponding to (L / D)max divides curve
regions where lift increases faster than drag, and drag increases
faster than lift, as AOA increases.
 Many drag polars may exist for the same airplane, and each one
reveals a unique (L/D)max value. However, only one of these values
gives the best glide ratio for the airplane, and that is the one that is
maximum over all of these curves.
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Review of Jet Engines
Important Facts about Jet Engines:
 The thrust developed by a jet engine is given by F = (m/t) V, where m
is mass, t is time, and V is the velocity change of the air mass. The
term m/t is known as mass flow. Since the density of air (hence mass
per unit volume) changes drastically with altitude, more thrust is
developed on cold days at lower density altitudes, and vice versa.
 Jet engines may be divided into two categories: 1) pure jets; and 2)
Turbofans. Both types of engines have a compressor, combustion,
and turbine section. However, turbofans bypass some of the air
moved by the compressor around the combustion section, while pure
jets do not.
 Both type of engines may have dual stage compressors, so a turbofan
may have as many as three stages in the compressor, including the
fan bypass section.
 The symbols N, N1, N2, and N3 denote the RPM (measured as percent
of maximum allowable RPM) of various compressor section stages
 RPM is one important measure of engine performance, and most of
an engine’s thrust is developed at higher RPM, e.g., 80% - 85% and
above. (Turbofans tend to produce a higher percentage of maximum
thrust than pure jets running at the same RPM.)
 Other important measures of engine performance are EGT (exhaust
gas temperature), fuel flow (usually measured in pounds of fuel per
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hour), and EPR (exhaust pressure ratio), the ratio of total air
pressure at the exhaust to total air pressure at the engine intake.
 Thrust produced by jet engines is fairly constant over the mid
velocity range of TAS. So is power produced. (Power is work per
unit time, or force times distance divided by time, which in the case
of a jet engine is thrust times distance divided by time).
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 Thrust specific fuel consumption (TSFC) is fuel flow (in pph) divided
by thrust produced (#). Both thrust and TSFC for a turbojet engine
decrease as density altitude increases, so range improves with
altitude
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 Counter-intuitively, for a given density altitude, TSFC decreases as
engine rpm increases.
 Efficient fuel management for jet engines (climb, cruise, descent) is a
complex issue. For example, before climbing to get better (i.e. lower)
TSFC in a holding pattern, must be sure that the fuel expended in
the climb will be saved during the wait in the higher-altitude holding
pattern.
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