WT1 Aerodynamic Analysis and Energy Balance

Having completed the conceptual design of the WT1 configuration, we proceeded with the project design. In particular, we focused on a more accurate aerodynamic analysis of the aircraft. The WT1 concept is shown in Figure 1.

Figure 1. WT1

By that time, I had available only 2D X-FOIL viscous results for the LEMFEV airfoil.

We also had some aircraft CFD data, but its reliability seemed questionable.

The conventional analytical approach to adjusting airfoil characteristics to a finite wing with a given aspect ratio is only valid if the wing is expected to feature a linear lift curve. In the case of the LEMFEV, that is, at a Reynolds number of the order of 100 000, the wing is going to produce a laminar bubble, that is, the lift curve may be more or less non-linear. For this reason, based on the general trend for the airfoil lift curve slope and the maximum lift coefficient to decrease when installed on a wing, I reduced the two by 10 %, maintaining the non-linearity of the slope. 10 % from all perspectives is a very optimistic guess. Figure 2 compares the WT1 airfoil and wing lift curves.

Figure 1. WT1 airfoil and wing lift curves

---

The minimum aircraft drag was predicted based on the aircraft wetted area and equivalent skin friction coefficient by Raymer, p. 280 [1]. I used a conventional parabolic drag polar to predict the aircraft's total drag. The Oswald factor for this low-Reynold number condition was calculated based on [2]. Figure 3 gives a sense of the magnitude of the Oswald factor expected for the LEMFEV.

Figure 3. Oswald factor vs wing aspect ratio for Re = 60 000 - 120 000. Wing taper ratio is 0.5

The result shown in Figure 4 terrified me.

Figure 4. WT1 airfoil and aircraft drag coefficient variation with angle of attack

Even more striking was the WT1 polar, Figure 5.

Figure 5. WT1 airfoil and aircraft drag polar

And, of course, the lift-to-drag ratio, Figure 6.

Figure 6. WT1 airfoil and aircraft lift-to-drag ratio

Initially, we designed WT1 to fly at a high lift coefficient of 0.85 at an angle of attack of 5.5 degrees, since a large wing increases the airplane weight and drag therefore calls for more power for flight. Actually, my MATLAB design code didn't return any feasible configurations at a design lift coefficient lower than 0.65. In addition, for airfoil, the maximum lift-to-drag ratio is achieved at an angle of attack of 5.5 degrees. At this lift coefficient, the airplane induced drag is skyrocketing. Therefore, the angle of attack where the airplane achieves its maximum lift-to-drag ratio reduces to 2 degrees. The magnitude of the maximum lift-to-drag ratio, which is 10, is typical for flying models operating under similar Reynolds numbers, but it can only be achieved at a lift coefficient of 0.5. For flying models, it is not uncommon to fly at a lift coefficient of 1 [3].

The high induced drag makes the day-night flight of our airplane on Mars impossible.

---

In our study, the data on the Martian climatological system were retrieved from the Mars Climate Database (MCD) [4], [5]. The MCD is a database of meteorological fields derived from General Circulation Model numerical simulations of the Martian atmosphere and validated using available observational data.

According to the standard solar average MCD scenario, the highest solar flux to surface expected on Mars amounts to approximately 450 W/m^2 (Figure 7). In this case, the maximum power available for a day-night solar airplane with a wing area of 5 m^2 from the sun is approximately 263 W. In the case of a planetary dust storm, the maximum solar flux reduces to 220 W/m^2 (Figure 8) and the available power falls to 82 W, and the wing area must be no smaller than 15 m^2. WT1 requires at least 18 N to maintain a level flight, while for the airplane with the selected propeller and wing area, only 12 N are available from the sun.

Figure 7. MCD - solar flux to surface. Climatology average solar scenario [4], [5]

Figure 8. MCD - solar flux to surface. Dust storm minimum solar scenario [4], [5]

References

[1] D. P. Raymer, Aircraft Design: A Conceptual Approach, 6th edition, AIAA Education Series, 2018

[2] G. Ananda, P. Sukumar and M. Selig, "Measured aerodynamic characteristics of wings at low Reynolds numbers," Aerospace Science and Technology, pp. 392-406, 2015.

[3] А. Болонкин. Теория полета летающих моделей. - Издательство ДОСААФ, Москва, 1962

[4] E. Millour and e. al., "THE MARS CLIMATE DATABASE (VERSION 5.3)," in ESAC Madrid, Madrid, 2018.

[5] F. Forget and e. al., "Improved general circulation models of the Martian atmosphere from the surface to above 80 km," JOURNAL OF GEOPHYSICAL RESEARCH, vol. 104, no. E10, pp. 155-175, 1999.