Task 2

Aerodynamic performance prediction:

Density and dynamic viscosity of air were assumed to be constant, ρ = 1.225 kg/m^3 and μ = 1.812E-5 kg/(ms) at sea level. For the Bixler 2, the characteristic length was chosen as the root chord of the main wing L = 0.2032 m.

Based on the flight data from PS1, the cruise speed varied from 7 m/s to 17 m/s. The Reynolds number is then between 0.96E5 and 2.34E5. In this regime, the drag depends on the Reynolds number significantly. Therefore, to improve drag estimates, the CDCL option was used in AVL to model rapid drag rise after stall. Additionally, in every analysis, level-flight conditions were imposed to calculate aerodynamic performances.

See figures for Cl vs alpha, drag polars and L/D vs airspeed. For the Drag polar and L/D vs. Airspeed plots, velocity was discretized into 7 points, ranging from 7 to 17 m/s.

Reasonable correlation between measured flight data and computed values from AVL was found, and the team could proceed forward that a "good" initial aerodynamic estimation for the prototype aircraft could be computed.

Stability and control derivatives:

For a given aircraft, AVL returns stability and control derivatives.

For these results, the team concluded that they are as accurate as the choice of NACA profile selected.

Frequency and damping ratios:

The above figures show frequency and damping ratio of the Bixler 2 as a function of airspeed. For low airspeed such (e.g. 7 m/s), the Phugoid mode is unstable. This is because the AVL model underestimated the drag of the Bixler 2. The average airspeed of the Bixler 2 during the mission, however, is above 12m/s which gives stable a Phugoid mode.

Spaero 1

Modelling in AVL:

Below figures are isometric view, top-view and side-view of the Spaero 1.

Aerodynamic performance prediction:

For Spaero 1, the characteristic length was chosen as the root of the chord at the main wing which was 0.196 m . Using the same range of velocities as the Bixler 2, Reynolds numbers ranging from 0.922E5 to 2.241E5 were determined. Again, there is a strong Reynolds number dependence on drag coefficient for this design.

See below Cl vs alpha, drag polars and L/D vs airspeed

.

When the AG 35 stalls, the cross section provides a lift coefficient of 1.235. From this information, Spaero 1 will stall when the angle of attack is 12 degrees as 40% of the main wing exceeds the lift coefficient of 1.235. Therefore, C_{L max} = 1.2362. The overall weight and reference area of the design are below

W = (0.600 kg)(9.81 m/s²) = 5.886N

S = 0.2004

Which yields a stall speed

Stability and control derivatives:

From AVL, stability derivatives can be seen below

Frequency and damping ratios:

Comments about above stability and control derivatives, frequency and damping ratios are in the comparison section below.

Estimate of the power consumption:

Instead of using the provided model, the team collected some data from the UIUC library and interpolated them to obtain a more accurate approach for the modelling of the propulsive system.

From this model, one can see the influence of cruise speed at constant altitude on the power drained from the battery. However, it is known that the maximal power from the battery is around 40W (result extracted from the test in the lab) which corresponds to a maximum cruise speed around 14 m/s.

Power requirements for several climb rates were also derived. Again, one can see that we have a strong dependence on the cruise speed for the power. The plots below allow the user to adjust climb speed to optimize battery usage.

Now consider the efficiency of the motor/propeller system. The efficiency for the motor is strictly increasing with the airspeed whereas the efficiency for the propeller reaches a maximum. Globally, in the range of airspeed considered (less than 14 m/s), the efficiency is strictly increasing: around the design cruise speed (12 m/s), there is a good compromise between almost the maximal efficiency and a power usage.

On the second plot, one can see an estimation of the duration of the mission. This estimation only considers a constant altitude cruise, neglecting turns and climb. One can see that for a cruise speed of 12 m/s, the aircraft can fly for nearly 10 minutes, which corresponds to the maximum mission time(this goal was met during the first flight).

Eventually, the following plot is the tool that will be used to improve the prototype aircraft and mission (the team might be considering another cruise speed for the mission). For a given airspeed, one can read on the left plot the value of the drag to define the value of the voltage needed for the thrust. Using this voltage, the right plot gives the current. In the end, this is a really efficient method to estimate the power needed at a given cruise speed.

Comparison between the Bixler 2 and Spaero 1

Aerodynamic performance prediction:

Performance characteristics for CL and CD can be seen below.

Spaero 1 has a lower total lift coefficient at all angles of attack. Also, it shows lower L/D throughout the whole speed range.

Stability and control derivatives:

For the Phugoid mode, the Bixler 2 and Spaero 1 show similar frequencies of oscillation but Spaero 1 has much larger damping ratio compared to the Bixler 2. Especially, for the Dutch roll mode, Spaero 1 exhibits a larger frequency as well as damping ratio. Large vertical tail of Spaero 1 provides better dynamics in the Dutch roll mode compared to the Bixler 2.

Note that above frequency and damping ratio analysis is based on modeling in AVL and should be verified with experiments.