AERO 2200: INTRODUCTION TO AEROSPACE ENGINEERING I
TAKE-HOME PORTION OF FINAL EXAM
PERFORMANCE ANALYSIS OF THE DIAMOND DA-40
Due in class, Monday, December 2, 2013
Turn-in Instructions
Both steps must be completed in order to receive credit
1. Turn in a printed hard copy of your report in class
2. Upload an electronic copy (PDF only) of your report to the Carmen dropbox
This portion of the final is worth 50 points (10% of your final grade), while the in-class portion of the final is worth 100 points (20% of your final grade). The in-class portion of the final exam will be given at 10:00 am on Thursday, December 5, 2013 in Lazenby 0021 (our normal classroom). This project for the take-home portion of your final exam is open book and open notes. It is an INDIVIDUAL effort.
The project involves performance evaluation of the Diamond DA-40. The DA-40 is a 4-seat general aviation aircraft with a low wing and T-tail. Your performance evaluation is to be based ONLY on the geometry, aerodynamics, and propulsion characteristics noted below. The results of your analysis are to be presented in a formal report, following the format of the accompanying guidelines. Each major section (e.g., Power Required, Climb Performance, etc.) is to be clearly presented.
Diamond DA-40 Specifications:
Maximum Weight: 2,645 lbs Engine: Lycoming IO-360-M1A
air-cooled, 4-cyl, horizontally-opposed
Wing Area: 145.7 ft2 Maximum Shaft Horsepower:
Wing Span: 39.17 ft Sea Level 180 hp
Parasitic Drag: CD0 = 0.0300 5,000 ft 150 hp
Span Efficiency: e = 0.75 10,000 ft 120 hp
Maximum Lift (clean): CLmax = 1.90 Cruise SFC: 0.49 (lb/hr)/shp Usable Fuel Volume: 50 gal
Density of 100LL Fuel: 6 lbs/gal
Propeller Efficiency:
235
1
78
.
0
V
(where units of V are in knots) Task I: Drag PolarEstimate the parasitic drag coefficient (CD0) and Oswald efficiency factor (e) for the aircraft, using the methods developed in class. Plot the drag polar as CD vs. CL and clearly mark CD0 on the polar. Create a separate plot of L/D vs. CL and determine (L/D)max.
Task II: Power Required
Determine the Power required as a function of velocity for flight at three altitudes: sea level, 5000 ft, and 10000 ft. Present the data on a single graph. Locate the stall speed, speed for minimum PR, and speed for maximum lift-to-drag ratio on this graph for each altitude. The graph should cover the speed range from 40 to 150 knots. Units of velocity must be knots, and units of power must be horsepower.
Task III: Power Available
Using the engine data provided, along with the propeller efficiency data, determine the maximum power available at the three altitudes. (This will be a “thrust horsepower”, or the power imparted to
the air by the propeller). On the same graph as the one developed in Task II, plot PA as a function of velocity. In your report include a table replicating the table below, with all values filled in. Units of velocity must be knots, and units of power must be horsepower.
Minimum Speed Speed for (L/D)max Maximum Speed
Altitude V PR PA V PR PA V PR PA
Sea Level 5,000 ft 10,000 ft
Task IV: Climb Performance
a.) Prepare a graph of rate of climb (ft/min) vs. V (knots) for the three altitudes. Note the
maximum rate of climb and the true airspeed (V) that corresponds to the maximum rate of
climb.
b.) Plot the results of (a) on an altitude vs. R/C graph and extrapolate the results to estimate the absolute and service ceilings.
c.) Use the results of (b) to determine the time to climb from sea level to an altitude of 10,000 ft. d.) Develop a climb hodograph for sea level climb at maximum takeoff weight to determine the true
airspeeds (V) for best angle of climb and best rate of climb. Complete the table below.
Rate of Climb (ft/min) Climb Angle (degrees) Velocity (knots) Best Rate of Climb Condition
Best Climb Angle Condition
Task V: Range and Endurance
Use the Breguet Range and Endurance relations to determine the maximum range and endurance for the DA-40 while cruising at 10,000 ft and using 90% of the fuel on board. For this cruise flight, consider the specific fuel consumption and propeller efficiency to be constant:
SFC = 0.49 (lb/hr)/shp and = 0.78
Note the airspeed(s) that the pilot must maintain during these flights in order to maintain the optimum conditions assumed in the Breguet equations. Range values should be reported in nautical miles and endurance values should be reported in decimal hours.
Task VI: Gliding Flight
a.) Develop a glide hodograph, with VH and VV in ft/s for the DA-40 at maximum takeoff weight at sea level.
b.) Assuming engine failure at a pressure altitude of 5,000 ft at maximum takeoff weight, determine the maximum distance (in nmi) that the aircraft can glide to reach an airfield situated at a pressure altitude of 1,000 ft. What indicated airspeed (in knots) should the pilot fly in order to maximize glide distance? If the pilot instead wants to remain over a certain location during the descent, what airspeed should be used in order to maximize time aloft? How long would it take for the aircraft to descend from 5,000 ft to 1,000 ft if the flight speed is maintained at the optimum for maximum time aloft?
Task VII: Turning Flight
Create a V-n diagram for the DA-40 if the “never exceed” airspeed is 178 knots, the maximum positive load factor is 3.8, and the maximum negative load factor is -1.52. Clearly define the maneuver point on
the diagram. What is the minimum turn radius and the maximum turn rate for the DA-40 at maximum takeoff weight at standard sea level conditions?
Task VIII: Takeoff and Landing Performance
Estimate the following for the DA-40:
a.) Takeoff ground roll distance at maximum takeoff weight at standard sea level conditions. b.) Takeoff ground roll distance at maximum takeoff weight at a high altitude airport (5000 ft). c.) Takeoff ground roll distance at a takeoff weight of 2400 lbs at standard sea level conditions. d.) Landing ground roll distance at maximum weight and standard sea level conditions.
