Embry-Riddle Aeronautical University
Department of Aeronautical Science
AS-310 Aircraft Performance Course Plan (Section 2, 3 & 4)
Spring Semester 2015
MWF Section 2: 1030-1130 COA 259; Section 3: 1300-1400 COA-255 Section 4: MWF 1530-1639 COA-259
Credit Hours: 3 / Prerequisite: AS309 (implies PS104 and MA112)Instructor: Dr. R. Rogers / Office: COA-233 / Office Hours: available at
Phone: 386-226-6436 / email: / webfac.db.erau.edu/~rogers//Schedule.xls
Course Web Site: webfac.db.erau.edu/~rogers/as310 Dr. Rogers Home Page: webfac.db.erau.edu/~rogers
Course Text: Online at Course Web Site (webfac.db.erau.edu/~rogers/as310)
Required Course Materials: 1) Online Course Text (download from course web site links); 2) Supplemental Materials for AS310 Aircraft Performance (Dr. R. Rogers' Sections Only), available in ERAU bookstore; 3) Online Lecture Notes (download from course web site via Course Schedule / Links to Lecture Notes); 4) Current copy of course outline (download from course web site link); 5) Draftsman triangle, available in bookstore
Course Description: This course explores the performance of airplanes powered by reciprocating, turboprop, and/or jet turbine and turbofan engines. Topics studied include stability and control, weight and balance, and performance charts and graphs.
Goal: This course of study will provide the student with an understanding of the performance characteristics of modern reciprocating, turbo-prop, and/or jet-powered airplanes. Students will acquire a knowledge of weight and balance; takeoff and cruise control; and airplane performance charts and curves, from which they will extract data that maximize performance.
Learning Outcomes:
1. Analyze the variable factors affecting an aircraft’s performance.
2. Interpret basic performance curves and analyze performance data.
3. Perform weight and balance calculations and relate aircraft weight and weight distribution to aircraft performance and operational limitations.
4. Utilizing aircraft performance theory, explain the safe and efficient approaches to obtaining maximum performance from an airplane.
Grading: 3 tests (EA: 75%); 9 quizzes (QA: 25%). A: 90 and above; B: 80-89; C: 70-79; D: 60-69; F: 59 and below. Each quiz grade is an average of the Quiz Worksheet score submitted as homework and the Quiz Score resulting from in-class group work; however, if you fail to submit a substantially complete Quiz Worksheet, your Quiz Grade will be recorded as 0 because you came to class unprepared to participate in group work. Three bonus points for attending class (AB) are added to your course average. Initially AB = +3. For each absence from class, AB is decremented by 1 point, with negative values of AB resulting upon the 4th and subsequent absences. Two late arrivals to class are equivalent to an absence. . Your final numeric average is computed as 0.75*EA + 0.25*QA + AB. It follows that the highest possible numeric average is 103 (achievable only with 100% on time attendance). Note that absences in excess of 3 result in reducing the highest possible numeric average below 100.
Course Policies: available at http:// webfac.db.erau.edu /as310/AS310CoursePolicies.doc. Students are responsible for reading and understanding the contents of the Course Policies document and for abiding by its provisions.
Class Schedule: available at http://webfac.db.erau.edu/~rogers/as310/as310LectureNotes.htm
Class Schedule Including Reading Assignments and Work Due Dates
Unforeseen eventualities may require modifications to the following schedule.
http://pages.erau.edu/~rogers/as310/as310LectureNotes.htm
Note: the file found at the link above has links to online course lecture notes for each lecture!!!
Showing Work on Quizzes and Exams. To receive full credit for a quiz or exam answer that involves a calculation, you must show how you obtained the answer. A correct answer without substantiating work is awarded only half credit. (This requirement doesn’t apply for objective questions, i.e. questions where you pick the answer from a list.)
1. When an equation is used. If the answer involves using a formula or equation, you must
a. Write the equation with the unknown on the left hand side
b. Substitute full accuracy numeric values in the equation for each known in the equation
c. Use your calculator to determine and record the unknown value to the desired accuracy.
This is the minimum sufficient work required to receive full credit; additional work, if required, need not be written down. Steps a and b completed correctly receive half credit even if the answer in step c is incorrect.
Example: Suppose you are asked to calculate the height of a right cylinder of known volume V, where you also know the radius r of the cylinder’s base. The equation for the volume V of a cylinder with height h and radius of the base r is given by the equation
V = P r2 h (P r2 gives the area of the circular base of the cylinder).
If the volume of the cylinder V = 143.875 in3 and the radius of the base of the cylinder r = 2.12543 in, then the problem should be solved as follows. Note that we have solved algebraically for h in the volume formula and written the unknown h on the left hand side of the resulting equation.
h = V / (P r2)
h = 143.875 / (3.141592654 * 2.125432)
h = 10.13775640 in
2. When no equation applies. If the answer involves a calculation that does not derive from a formula, there is no equation to write. In that case, just show the numbers you used to calculate your answer, followed by the answer.
Example: suppose a performance table lookup results in two numeric values 143.75 and 21.2, where the smaller number must be subtracted from the larger number to produce the answer you are asked for. Then write
143.75 – 21.2 = 122.55
3. Inaccuracy due to rounding. You should always use values to the full accuracy of your calculator when making calculations. Otherwise, rounding may result in inaccuracy in your final answer, causing it to receive reduced credit even though your calculation method is correct.
Example: Suppose the desired accuracy in the problem in 1 above is 6 significant figures (i.e. accuracy to 4 decimal places). Then the desired answer is 10.1378 inches. Suppose we rounded P to two decimal places. Then the answer will be calculated as
h = V / (P r2)
h = 143.875 / (3.14 * 2.125432)
h = 10.14289842 in, which rounds to 10.1429, as opposed to 10.1378
If we rounded the radius to one decimal place with P at full accuracy, an even more serious inaccuracy would result.
h = V / (P r2)
h = 143.875 / (3.141592654 * 2.12)
h =10.38476981 in, which rounds to 10.3848 as opposed to 10.1378
PROPERTIES OF THE ATMOSPHERE
Standard Atmosphere
To facilitate the study of aircraft performance, atmospheric scientists have developed the notion of a standard atmosphere. There are several similar models; the differences between them minimal. Shown below and on the next page are the ICAO and NACA Standard Atmosphere Tables for altitudes between sea level and 100,000’. What follows explains the information in the tables.
ICAO Standard Atmosphere Table
Figure 2.1. NACA Standard Atmosphere Table
In AS30, always use the NACA table to obtain standard atmosphere values used in calculations.
Atmospheric Measurements: Pressure, Temperature, Density Ratios
Pressure. Always distinguish between static pressure and dynamic pressure. Naively, static pressure P results from the “weight”of air. Dynamic pressure q is created by relative motion between air and a body immersed in it and is a function of air velocity V and air density:
q = r V2/2 (where r is measured in (#-sec2)/ft4and V in ft/sec, so q is measured in #/ft2)
Total pressure is the algebraic sum of static and dynamic pressure i.e., T = P + q.
Static Pressure P is the force per unit area a column of air exerts on a surface At sea level on a standard day (15o C or 59o F),
P0 = 2116 #/ft2 = (2116 #/ft2) / (144 in2/ft2) = 14.69444 #/in2.
An alternative measure of static pressure is inches of mercury. Standard pressure at sea level is 29.92 inches of mercury (Hg). The millibar is a unit of static pressure used by meteorologists.
The pressure ratio d (small delta) at a given altitude with ambient pressure P is defined to be
d = P / P0.
For example, d18000’ = 0.49938 in a standard atmosphere, reflecting the fact that the standard pressure at 18,000 feet is about ½ the standard pressure at sea level.
In a standard atmosphere, pressure decreases as altitude increases, so 0 £ d £ 1 at sea level and above.
Approximate Lapse Rate for Pressure. When less than precise atmospheric measurements are required, pilots sometimes use the rule of thumb that pressure decreases in the atmosphere at 1” Hg / 1000 feet.
It is easy to verify that this approximate decrease is somewhat accurate in the lower standard atmosphere, up to say 10,000 feet, and that the rule of thumb in quite inaccurate as altitude decreases, For example, the rule predicts that d10,000’ = (29.92 – 10.0) / 29.92 – 19.92 / 29.29 ≈ 0.66578, whereas the value in the table is 0.68770, a small difference3. At 20,000 feet the approximated value is 9.92 / 29.92 ≈ 0.33155, whereas the “correct” value is 0.45954, a large difference.
If a lapse rate of 1” Hg /1000 ft of altitude were accurate, the atmosphere would end at 29,920 feet MSL.
Temperature: Absolute temperature (absolute zero = -273oC) must be use performance calculations. Since F = (9/5) C + 32, -273o C = 9/5(-273) + 32 = -459.4 » -460o F is absolute zero in Fahrenheit.
Add 273 (460) to centigrade (Fahrenheit) to get Kelvin (Rankine). K is the symbol for Kelvin, R for Rankine.
Sea level standard temperature:
T0 = 59o F = 59+460 = 519o R.
T0 = 15o C = 15 + 273 = 288o K.
Air temperature decreases with altitude until the tropopause (36, 089’), then stays constant at –69.7o F until about 85,000’.
Temperature ratio Q (theta) at a given altitude where the temperature is T is defined as
Q = T / T0.
For example, at the tropopause, Q = T / To = (-69.7+460) / (59 + 460) = ((5/9) (-69.7 – 32) + 273) / (15+273) = 0.752.
A common mistake in calculations involving Q = T / To is forgetting to use absolute T.
In a standard atmosphere, temperature decreases as altitude increases, so 0 £ Q £ 1at sea level and above.
Standard Lapse Rate for Temperature. The standard lapse rate for temperature in the earth’s atmosphere is 2o C (3.8o F) / 1000 feet. This lapse rate applies quite precisely up to the tropopause (the point where atmosphere temperature stops decreasing—between 36,000’ and 37,000’ feet), at which point the temperature stabilizes (remains the same) for many additional thousands of feet.
If Q is known, T in a standard atmosphere can be calculated. Suppose Q = 0.93125. Then
T = Q To = 0.93125 (15+273) = 268.2 K = (268.2 – 273)o C = -4.8o C.
This is a drop of approximately 20o C from standard temperature at SL. At a lapse rate of 2o C / 1000 feet, the altitude in a standard atmosphere should be about 10,000 feet. You can confirm this is the case from the NACA Standard Atmosphere Temperature, where T10,000’ = -0.4812
Density: Density r (rho) is mass per unit volume. Mass is
r = mass / unit volume = slugs/ft3 = (#-sec2/ft) / ft3 = (#-sec2)/ft4
The density at sea level on a standard day is r0 = 0.002377 slugs/ft3.
Density Ratio s (sigma) at an altitude where the density is r is defined to be
s = r / r 0
where r0 is as above. For example, r22000’ = 0.001183 slugs/ft3 in a standard atmosphere, so
s22000’ = r22000 / r 0 = 0.001183 /0.002377 = 0.497686159 » 0.5.
From this we may conclude only that, in a standard atmosphere, density at 22,000’ is ½ the density at sea level. (Compare this to 18,000’ for static pressure.)
In a standard atmosphere, density decreases as altitude increases, so 0 £ s £ 1 at sea level and above.
SMOE. The ICAO Standard Atmosphere Table has a Ös column. The corresponding NACA Standard Atmosphere column gives the reciprocal of this value, i.e., 1/Ös, referred to as SMOE, an acronym for standard means of evaluation.
In a standard atmosphere at sea level and above, s £ Ös £ 1.0, so SMOE ³ 1.0.
Relationship between Density, Pressure, and Temperature Ratios
From the universal gas law, density of a fixed volume of gas is proportional to P/T; i.e. r = k P / T for some k > 0, where the value of k depends on the properties of the gas. Thus
s = r / r 0 = (kP/T) / (kP0/T0) = (P/P0) / (T/T0) = d / Q.
This is a very important relationship, one that you will use frequently in calculations. In English, the equation says: “Density ratio is equal to pressure ratio divided by temperature ratio.” You should confirm this fact by performing the required calculation for several arbitrarily selected rows in the standard atmosphere table.
Note that the equation also reflects the fact that both temperature and pressure affect air density. As temperature increases (decreases), air density decreases (increases). As pressure increases (decreases), air density increases (decreases). That is, density is inversely proportional to temperature and directly proportional to pressure.
Speed of Sound in Air
As air temperature decreases, the speed of sound (a) in air decreases, from 661.74 KTS at sea level to 573.80 KTS at the tropopause. In other words, the speed of sound in air is a function of temperature only. This result is non-intuitive. An incorrect but common guess is that the speed of sound in air is a function of air density (i.e., of both pressure and temperature).