Piper Saratoga Lab Report

Numerous flight data has been collected on a Piper Saratoga while flying in different configurations. The data focuses on the coefficient of lift and the coefficient of drag while the aircraft is pitched at various angles of attack. This paper examines the research process and the data that was collected in order to determine the lift to drag ratio for various angles of attack.
Objectives
To experimentally determine both the coefficient of lift 〖(C〗_L) and the coefficient of drag (C_D) of a Piper Saratoga when it is flown at different angles of attack (α). This data will be used to calculate the lift to drag ratio (L/D) for various angles of attack (α).
Aircraft Description (aircraft and test system) The Piper Saratoga is a complex fixed-wing,
high-performance, single-engine, and all metal aircraft that holds six passengers, including the pilot (Piper Aircraft Corporation). Aboard the aircraft, there is an array of flight test equipment that uses the Data Acquisition System to collect data. The Data Acquisition System has probes located on the aircraft’s exterior that sends data to onboard computers (University of Tennessee Space Institute). The computer interprets the data and displays it on a tablet that the test pilot, and or test group can use to collect the data. Additionally, the Piper Saratoga has an air data boom on the right wing that collects data for the Data Acquisition System (University of Tennessee Space Institute). Not only does this help with providing accurate data for testing purposes, but the system also aids the test pilot because the information is more accurate that what the standard aircraft instruments would show.
Scope (to include date, time, location, test altitude, and atmospheric conditions) The flight test data was recorded on Thursday, March 23, 2017 around 13:45 CDT.
The test was conducted 13 miles southeast of Murfreesboro Municipal Airport. During the flight test the cloud coverage was reported as overcast at 7,000 feet, and the winds were reported to be calm with a temperature of 68°F. The flight test was conducted at the pressure altitude of 5,000 feet and the outside air temperature (OAT) was
52°F.
Method
Level Trim Shots After reaching the test altitude, pressure altitude (H_pi) and the outside air temperature (OAT) is recorded. When the first airspeed is reached, indicated airspeed (IAS) and angle of attack (α) is recorded as well. While maintaining the same altitude, the pilot will increase or decrease the airspeed in increments of 5-10 knots. Each IAS will be recorded along with the corresponding α reading at each of the testing points. The testing points should target various airspeeds to cover the airspeed range of the aircraft.
Rapid Deceleration At the same test altitude, the aircraft will be stabilized at the aircraft’s maximum allowable airspeed. The IAS will be recorded at the elapsed time (Δt) of 0. The test pilot will close the throttle and make an announcement that it has been done; the timer(s) will then be started. The pilot will maintain altitude by increasing α; this will cause a decrease in airspeed. Every five seconds, one member of the group is responsible for calling out the IAS for the other group members to record. The test is concluded when level flight can no longer be maintained.
Results and Discussion
Sample Calculation Coefficient of lift. To achieve the overall result of the lift to drag ratio of the Piper Saratoga, first it is necessary to calculate the coefficient of lift 〖(C〗_L), which will be plotted against the angle of attack (α). To begin this process, the total weight of the aircraft needs to be calculated. With the passengers loaded and the remaining fuel on board, the Piper Saratoga weighed 3,311 pounds. Next, the non-standard density of the air at 5,000 MSL feet must be calculated. In order to do this, non-standard pressure at 5,000 feet MSL must first be calculated. Within the equation is the standard day pressure at sea level 〖(P〗_0) 2116.2 psf, the standard lapse rate 〖(a〗_0)-.00356(°R)/ft, standard day temperature at sea level (T_0) 519°R, gravity (g) 32.2 ft/s, and the gas constant (IR) 1716(ft^2)/(S^2×°R). When calculated, the pressure at 5,000 feet MSL is 1,760.63 psf.
P_(ALT=) P_0 [1+(a_0 h)/T_0 ]^(((-g)/(a_0 IR)) ) (1)
With the calculated pressure at 5,000 feet MSL, it is possible to calculate the air density. To calculate this, the outside air temperature at 5,000 feet must be converted to Rankin from Fahrenheit.
°R=°F+460 (2)
Within the equation is non-standard pressure (P) at 5,000 feet MSL 1,760.63 psf, calculated using equation 1, divided by the gas constant (IR) 1716(ft^2)/(S^2×°R), multiplied by the outside air temperature (512°R), after being calculated using equation 2. When calculated the density (ρ) at 5,000 feet MSL is .00200 sl/(ft^3 ). ρ=P/RT (3)
The remaining factors within the coefficient of lift equation being related to the aspects of the flight data, it is possible to set up and solve the equation. Within this equation is lift (L)
(3,311 lbs), density (ρ) at 5,000 feet MSL .00200 sl/(ft^3 ), calculated using equation 3, velocity (v), and the plan form area (S) of 178.3 ft^2 (Piper Aircraft Corporation).
C_L=2L/(ρv^2 S) (4) When calculated using equation 4, the coefficient of lift 〖(C〗_L) can be plotted, along with the correlating angle of attack (α).
This concludes step one of the flight test. Coefficient of drag. The last step before determining the lift to drag ratio (L/D) is the calculation of the drag that is being produced by the aircraft, which will then be plotted against the correlating angle of attack (α). To determine the drag, the overall weight of the aircraft is needed, along with the gravity constant, and the total deceleration the plane was undergoing at the time the data was being recorded. Within this calculation are weight (w) 3,311 lbs, gravity (g) 32.2 ft/s, and the rate of deceleration (dec).
D=W/g dec (5) With the total amount of drag forces on the aircraft at various angles of attack, the coefficient of drag (C_D) can be calculated. This calculation process follows similar equation to the coefficient of lift (C_L) in equation 4; however, it includes the force of drag (D) instead of the force of lift (L). The information needed for this calculation was collected from the flight
data.
Within this equation is drag (D), calculated using equation 5, density (ρ) at 5,000 feet MSL .00200 sl/(ft^3 ), calculated using equation 3, velocity (v), and the plan form area (S) of 178.3 ft^2 (Piper Aircraft Corporation).
C_D=2D/(ρv^2 S) (6) When calculated using equation 6, the coefficient of drag (C_D) can be plotted, along with the correlating angle of attack (α), concluding the final step before determining the lift to drag ratio of the Piper Saratoga.

Lift to drag ratio. From the previous calculations in equation 4 and equation 6, the lift to drag ratio (L/D) of the Piper Saratoga can be calculated. To do this, the variations of coefficient of lift (C_L) that was calculated during different points in the flight will be divided by the variations of coefficient of drag (C_D) that the plane experienced during flight.
L/D=C_L/C_D (7) When the lift to drag ratio (L/D) is calculated using equation 7, it can be plotted against the angles of attack (α) in which the data was collected. This process determines the overall amount of lift that the aircraft generates compared to the amount of drag being generated. Aircrafts with higher lift to drag ratios are more efficient than aircraft with lower ratios (National Aeronautics and Space Administration). The maximum lift to drag ratio occurs at a specific point, where the total drag of the aircraft is at its lowest point (SKYbrary). While collecting flight data, the most efficient point that was recorded was an angle of attack (α) of 21.9 degrees. At this point in flight the lift coefficient (C_L) was 1.36 and the drag coefficient was (C_D) was 0.042.