Administered in a Few Minutes More Than One Hour

EXAM I REVIEW

Format

• Administered in a few minutes more than one hour
• 20 questions
• 15 objective (multiple choice / true-false)
• 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
• Write the correct equation
• Substitute correct numeric values in the equation

Allowed Materials

• Pencil/eraser—NO INK PENS PLEASE
• Blue-covered gathering from bookstore
• many questions can’t be answered without access to this information--YOU MAY NOT BORROW A FRIEND’S COPY
• 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
• You may put tabs on pages to help locate information if you wish
• Electronic calculator
• but not one that is on a cell phone or other device with Internet connectivity
• If you have an aviation calculator, you may not use aviation functions
• 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
• You must make your own—don’t copy a friend’s or share yours with someone else
• Study sheets must be submitted with the exam
• 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,
• ABSOLUTELY NO TALKING IN THE CLASSROOM AFTER YOU ENTER—RESPECT YOUR FELLOW STUDENTS WHO MAY ALREADY BE AT WORK
• Please don’t enter the classroom unless you are ready to sit down and start the exam
• Please sit down promptly and quietly once you enter the classroom
• Organize your materials BEFORE you come to class
• 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.
• 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

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
• 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
• Go through the questions systematically 1-15
• Eliminate answers that are clearly incorrect
• If you aren’t sure about the correct answer, make your BEST GUESS among the remaining distracters WITHOUT UNDUE DELAY
• Don’t waste time: go on to the next question agonizing over a question you aren’t sure about
• 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
• If you follow these guidelines, you will finish the objective questions in about ½ hour or less
• 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

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):

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.

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.

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):

The same information is available in table form in the blue-covered booklet:

TAS = = EAS  SMOE.

Direct non-linear relationship between SMOE and altitude.

M =

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.
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.

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.

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.

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 = D = CD q S = (V is TAS in kts)

Also, since EAS2 = V2, the lift and drag formulae may be written:

L = D = CD q S = (EAS in kts)

Solving the lift formula for TAS V (and assuming L = W in 1G level flight) gives:

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.

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.

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.

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.

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.

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 = . ThusGD = GR (AA) = (L/D) (AA) = (AA) / tan a

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).

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.

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.

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 hour), and EPR (exhaust pressure ratio), the ratio of total air pressure at the exhaust to total air pressure at the engine intake.