*Article* **Numerical Investigation of Frequency and Amplitude Influence on a Plunging NACA0012**

#### **Emanuel Camacho, Fernando Neves, André Silva \* and Jorge Barata**

LAETA-Aeronautics and Astronautics Research Center, University of Beira Interior, 6201-001 Covilhã, Portugal; emanuel.camacho@ubi.pt (E.C.); fernandomneves@gmail.com (F.N.); jbarata@ubi.pt (J.B.)

**\*** Correspondence: andre@ubi.pt

Received: 27 February 2020; Accepted: 4 April 2020; Published: 11 April 2020

**Abstract:** Natural flight has always been the source of imagination for Mankind, but reproducing the propulsive systems used by animals that can improve the versatility and response at low Reynolds number is indeed quite complex. The main objective of the present work is the computational study of the influence of the Reynolds number, frequency, and amplitude of the oscillatory movement of a NACA0012 airfoil in the aerodynamic performance. The thrust and power coefficients are obtained which together are used to calculate the propulsive efficiency. The simulations were performed using ANSYS Fluent with a RANS approach for Reynolds numbers between 8500 and 34,000, reduced frequencies between 1 and 5, and Strouhal numbers from 0.1 to 0.4. The aerodynamic parameters were thoroughly explored as well as their interaction, concluding that when the Reynolds number is increased, the optimal propulsive efficiency occurs for higher nondimensional amplitudes and lower reduced frequencies, agreeing in some ways with the phenomena observed in the animal kingdom.

**Keywords:** energy saving and efficiency; aerodynamic coefficients; propulsive efficiency; bioenergetics; biomimetics

#### **1. Introduction**

When the flapping airfoil/wing mechanism was unveiled as a thrust production system, the scientific community foresaw the possibility to investigate new aerodynamic phenomena and develop newer systems that could improve substantially the way airplanes fly nowadays, which is today still rather conservative [1]. However, in the first part of the 20th Century, very little effort was made in terms of understanding and exploiting the aerodynamics of living beings.

Animals such as insects [2], birds, small fishes, and even the big blue whale are equipped with a spectacular propulsion system that was subjected to natural selection processes over millions of years, which inevitably offers a significant advantage [3,4].

Based on the phenomena seen in Nature, Micro Aerial Vehicles (MAVs) and Nano Aerial Vehicles (NAVs) with indispensable civil and military applications such as surveillance, espionage, atmospheric weather monitoring, and catastrophe relief purposes [5] are being developed to offer undeniable maneuverability and efficiency at lower length scales. The most advanced MAVs related research projects define these vehicles as vehicles with no length, width, or height larger than 15 cm, as declared in a Defense Advanced Research Projects Agency (DARPA) program [6].

The flapping airfoil was firstly studied by Knoller and Verein [7] and Betz [8] that found that while plunging an airfoil, an effective angle of attack, which changes sinusoidally over time, would be created. As a result, an oscillatory aerodynamic force normal to the relative velocity was generated which could be decomposed in lift and thrust forces. Katzmayr [9] experimentally verified the Knoller–Betz effect in an interesting way, by placing a stationary airfoil into a sinusoidal wind stream and measuring an average thrust.

However, the Knoller and Betz theory was only based on the airfoil motion and did not account for the vorticity shed downstream of the airfoil. Thus, later in 1935, Kármán and Burgers [10] successfully explained theoretically the thrust generation mechanism based on the vortex shedding on the downstream side of the airfoil and the orientation of the wake vortices, identifying the typical von Kármán vortex street which is always associated with the production of drag or an averaged jet-like flow that generates a propulsive force explained by Newton's third law of motion.

All these concepts were further studied by Freymuth [11] using flow visualization of both plunging and pitching motions. Firstly, studying the aerodynamics of plunging and pitching airfoils offered a better understanding regarding the flutter and gust-response effects, which are based only on the analysis of the lifting forces [12,13]. Oscillating airfoils also opened new ways to study the impact of the dynamic stall on helicopter and propeller blades performance and how impactful is the wake created by a foregoing blade on the following blades [14].

Plunging airfoils have been also analyzed by Lai and Platzer [15], Lewin and Haj-Hariri [16], and Young [17], where the wake structures were intensively studied, such as the vortex-pair shedding that represents the transition from the drag producing wake to the thrust producing inverted von Kármán vortex street. Young and Lai [18] concluded that this type of wake structure was caused by the interaction between bluff-body type natural shedding from the trailing edge and the motion of the airfoil and, more recently, Andersen et al. [19] suggested that a drag-thrust transition wake showing a two-vortex pair configuration per oscillation period is a characteristic of low frequencies and high amplitudes oscillations.

The plunging motion was further investigated by Young and Lai [20,21] who found the impact of the several parameters governing this problem, especially the Strouhal number, which showed that maximum thrust and optimum efficiency take place at the near dynamic stall boundary. However, for lower Reynolds numbers, the problem becomes more complicated because efficient lift and thrust generation is achieved by shedding the leading-edge vortex [22].

Interested in finding which flying conditions animals operate in, Taylor et al. [23] dedicated their studies to forty-two species of birds, bats, and insects in cruise flight and verified that these creatures fly within a limited range of Strouhal numbers between 0.2 and 0.4. Hence, this parameter is a possible indicator of the flapping conditions that provide the most efficient flight, being essential to characterize the flight of several natural flyers, regardless of their scale.

Natural flyers use these forces effectively where thrust and lift production means that energy is transferred from the wings to the fluid. However, the study of oscillating airfoils has undergone a drastic shift when researchers identified the potential of flapping airfoils to extract energy from the flow field [24]. Studies on energy harvesting efficiency over oscillating airfoils revealed that a harvester could achieve maximum efficiency of about 30% on sinusoidal motion for *Re* = 1000 and 40% to 50% on nonsinusoidal motion; other efficiency-enhancing mechanisms might include corrugations at the foil surface, its structural flexibility, and multiple foil configuration [25] such as the parallel foil configuration numerically investigated in [26].

Introducing structural flexibility, as studied by Zhu et al. [27], the airfoil shows a superior capability regarding energy extraction when comparing to the rigid case. The same conclusion is obtained by Jeanmonod and Olivier [28], who firmly stated that a foil with constant mechanical properties in the chordwise direction is far from being an optimal solution, demonstrating that a flexible plate can extract double the power of a rigid structure.

Another way to improve extraction efficiency can also be achieved by creating an effective camber which will produce a lift enhancement that is associated with the output power. This concept was studied by Bouzaher et al. [29], who added a Gurney flap at the trailing-edge that when synchronized with the flapping motion at a *Re* = 1100 created this virtual camber that improved the output power. The lift production can be further improved by controlling the development of the leading-edge vortex than, when attached to the airfoil surface, contributed to the improvement in lift generation which brings once again an increase in the energy harvesting magnitude [24]. The same concept may be

applied for thrust enhancement where camber morphing also reveals the potential to maximize the ratio of thrust to lift of flapping airfoils in several flight conditions [30].

Recently, Xia et al. [31] presented a wide range review on the fluid dynamics of flapping foils/wings where the authors reviewed the effects of some key parameters such as the Reynolds number, reduced frequency, and flapping amplitude. In addition, the intricacies of this problem are explored and the main challenges are identified, such as, highly efficient thrust mechanism, 3D flow control methods, and types of motion.

Regarding the type of motion, Boudis et al. [32] conclude that the sinusoidal waveform appears to favor the maximum propulsive efficiency notwithstanding the fact that nonsinusoidal trajectories can offer undeniable improvements, offering an increase up to 110% in terms of thrust production. At a Reynolds number of 5000, Dash et al. [33] also studied the influence of the airfoil motion concluding that, when at high frequencies, the thrust performance can be recovered when tweaking the effective angle of attack profile to a different type of wave, such as the square waveform.

The present work studied numerically the flapping airfoil problem, in particular, the plunging motion which has not been yet subjected to sufficiently detailed studies when compared with the combined plunging and pitching. Hence, the present work aims at studying the influence of flight velocity, the motion's frequency, and amplitude to fulfill this gap and help to understand the generation of thrust and what combinations in the operating domain are energetically adequate to a vehicle that uses the flapping mechanism as its mean of motion.

#### **2. Methodology**

The numerical methodology adopted for this paper is presented in this section. Firstly, the Reynolds-averaged Navier–Stokes (RANS) equations are selected as the governing equations, due to the unsteadiness of the current problem and the inherent turbulent phenomena seen in nature. The continuity and momentum averaged equations are written in a Cartesian tensor form as (e.g., ANSYS [34] or Lopes et al. [35]):

$$\frac{\partial \rho}{\partial t} + \frac{\partial (\rho u\_i)}{\partial x\_i} = 0 \tag{1}$$

and

$$\frac{\partial(\rho u\_i)}{\partial t} + \frac{\partial(\rho u\_i u\_j)}{\partial \mathbf{x}\_j} = -\frac{\partial p}{\partial \mathbf{x}\_i} + \frac{\partial}{\partial \mathbf{x}\_j} \left[ \mu \left( \frac{\partial u\_i}{\partial \mathbf{x}\_j} + \frac{\partial u\_j}{\partial \mathbf{x}\_i} - \frac{2}{3} \delta\_{ij} \frac{\partial u\_l}{\partial \mathbf{x}\_l} \right) \right] + \frac{\partial(-\rho \overline{u\_i' u\_j'})}{\partial \mathbf{x}\_j} \tag{2}$$

respectively.

The usage of an averaged formulation of the Navier–Stokes equations calls for the necessity of selecting a turbulence model that will model the velocity fluctuations as a function of the mean velocity field typically recurring to the Boussinesq hypothesis.

In the turbulence modeling field, some authors have studied the effectiveness of some turbulent models in representing the flow characteristics, but at the same time, some of the published research from other authors assumes the flow around flapping airfoils to be laminar. The Shear-Stress Transport *k* − *ω* model was selected to access its capability in predicting the flow surrounding a plunging airfoil since it shows a superior capability in representing the flow surrounding oscillatory airfoils [35].

In this study, the symmetrical airfoil NACA0012 is being used to simulate the plunging motion and analyze the flow configurations created by it. The airfoil's motion is described by the equation

$$y\left(t\right) = A\cos\left(2\pi ft\right)\tag{3}$$

and its velocity is given by

$$
\dot{y}\left(t\right) = -2\pi fA \sin\left(2\pi ft\right) \tag{4}
$$

where *A* and *f* are respectively the motion's amplitude and frequency, respectively.

Simulations were carried out using ANSYS Fluent with a mesh (Figure 1a) containing two main zones, which allowed the creation of a structured mesh around the airfoil (Figure 1b) and an unstructured grid in the airfoil's far-field. This mesh design effectively reduced the computational demand and time since only the outside part of the mesh was subjected to mesh update calculations such as deformation and remeshing.

The computational domain boundaries consisting of an inlet, an outlet, upper and lower walls, and the airfoil, is represented in Figure 2. The inlet was subjected to an inlet velocity boundary condition where the flow velocity was prescribed. On the outlet, the outflow boundary condition was applied, which is an extrapolation of the calculated variables on the interior. The remaining boundaries are walls, although with different characteristics, since the airfoil is treated as a wall where the no-slip condition is imposed, and the upper and lower walls are considered to have no shear stress which removes the boundary layer effects.

**Figure 2.** Computational domain.

The Least Squares Cell-Based scheme was selected as the gradients evaluation method, PREssure STaggering Option (PRESTO!) was chosen as the pressure interpolation arrangement, and the momentum, turbulent kinetic energy, and specific dissipation rate equations were discretized in a 2D space using the second-order accurate QUICK scheme. Regarding the transient formulation and knowing beforehand that the dynamic mesh feature was activated, the first order implicit method (in time) was the only scheme available. The pressure-velocity coupling algorithm used is the Pressure-Implicit with Splitting of Operators (PISO) that is highly recommended for all transient flow calculations.

After each initialization, the mesh was adapted to ensure that *y*<sup>+</sup> was between 0 and 1 (values up to 5 were acceptable), since when using the *k* − *ω* turbulence model, it is fundamental to guarantee that the effects of the flow close to the walls are well resolved. Due to the boundary conditions, solution initialization and nonlinearity, which characterizes the Navier–Stokes equations, it was observed that the flow configuration would stabilize after analyzing at least five periods, always maintaining all residuals below 10<sup>−</sup>3.

The processing and analysis of the data (drag and lift coefficients exported during simulations) were made recurring to in-house C-programs, whose aim was to obtain the averaged aerodynamic coefficients and propulsive efficiency.

As mentioned before, the flapping mechanism is typically correlated with thrust production since it can, in some conditions, positively change the wake momentum and because of that, it is important to evaluate not only the generated force but also the propulsive efficiency which is the ratio between the generated power, −*DU*∞, and the power supply is given by −*Ly*˙. The propulsive efficiency is then defined as

$$\eta = \frac{\overline{C\_t} \mathcal{U}\_{\infty}}{\overline{C\_P}} \tag{5}$$

where

$$\overline{\mathbf{C}\_{t}} = -\frac{1}{\Delta t} \int\_{t}^{t+\Delta t} \mathbf{C}\_{d} \, dt \tag{6}$$

and

$$\overline{\mathbb{C}\_{P}} = -\frac{1}{\Delta t} \int\_{t}^{t + \Delta t} \circ \mathbb{C}\_{I} \, dt \tag{7}$$

In these two last equations, *Ct* is the mean thrust coefficient, *Cd* is the drag coefficient, *Cl* is the lift coefficient, and *CP* is the mean power coefficient, which are parameters vastly used by researchers to evaluate the aerodynamic performance [24].

The influence of the mentioned parameters will be evaluated using the typical dimensionless quantities for a flapping airfoil: the reduced frequency, *k*, the nondimensional amplitude, *h*, Strouhal number, *St*, and the Reynolds number, *Re*, shown in Table 1 (see [31] for details). The variables *U*∞, *ρ*, *μ*, *c*, *f* , and *A* are the inlet speed, air density, air dynamic viscosity, aerodynamic chord, motion frequency, and amplitude, respectively, all in SI units.


**Table 1.** Dimensionless parameters.

The numerical validation started by performing a boundary location, mesh, and time step independence studies for a Reynolds number of 17,000, a nondimensional amplitude of 0.5, and a reduced frequency of 2.5. The boundary location study, presented in Figure 3, focused on the analysis of the blockage ratio influence on the drag coefficient over time. In this paper, the blockage ratio, *BR*, was defined as being the ratio between the wake dimension and the inlet height, and it is seen that no considerable influence is seen for the different cases tested.

**Figure 3.** Boundary location study.

The mesh independence study was conducted through the refinement of the internal zone of the mesh into several divisions (50, 71, and 100 divisions), as shown in Figure 4. It can be concluded that the mesh with 71 internal divisions holds an independent result that corresponds to a global mesh with 62,469 cells/52,394 nodes.

**Figure 4.** Mesh independence study.

The last phase focuses on the independence of the time step and for this study, three time steps were considered, calculated as *T*/100, *T*/200, and *T*/400 where *T* is the motion period. Figure 5 shows that a valid result is obtained for 200 points per oscillation period.

**Figure 5.** Time step independence study.

#### **3. Results**

This section shows the results concerning the influence of Reynolds number, motion's amplitude, frequency, and the Strouhal number on the flapping mechanism. Graphics of thrust and power coefficients, as well as propulsive efficiency, will be shown as functions of these relevant parameters. The pure plunging NACA0012 airfoil was firstly tested with a *Re* = 8500 with 1 ≤ *k* ≤ 5, 0.1 ≤ *St* ≤ 0.4, and *h* never surpassing 0.5.

In Figure 6, the thrust coefficient is shown in the *kh* plane. In the contour plot, it is noteworthy that the *Ct* value is growing faster than the Strouhal number with respect to *k*, a phenomenon that becomes evident for a nondimensional amplitude higher than 0.3. The same behavior is not exhibited by the power coefficient, which has its isolines almost parallel to the ones that represent a constant Strouhal number.

It is important to note that there is an intimate relationship between the Strouhal number and the maximum effective angle of attack to which the airfoil is subject, so it is expected that the required power (*CP*) and the maximum angle of attack also have one.

**Figure 6.** Mean thrust and power coefficients with *Re* = 8500.

Regarding the influence of the Strouhal number on the thrust and power coefficients, the following correlations are obtained:

$$\mathcal{C}\_{t}\left(St\right) = -0.051 + 0.462St + 2.668St^{2}\left(R^{2} = 0.87\right) \tag{8}$$

$$\mathcal{C}\_P\left(St\right) = 0.543 - 8.471St + 52.58St^2\left(R^2 = 0.96\right) \tag{9}$$

with 0.1 ≤ *St* ≤ 0.4. The coefficient of correlation for the *Ct* approximation is under 0.90 which once again reinforces the fact that the isolines of the thrust coefficient are not entirely parallel.

The consolidation of *Ct* and *CP* results in the propulsive efficiency shown in Figure 7, which has a peculiar distribution in the *kh* plane since it does not depend only on the reduced frequency or nondimensional amplitude alone but rather on the combination of both. Thus, the maximum efficiency region is encountered in the vicinity of a Strouhal number of 0.15 that unfortunately is incompatible with the maximum thrust coefficient area, reaching a maximum value of 0.23.

**Figure 7.** Propulsive efficiency with *Re* = 8500.

This, and the following propulsive efficiency graphics, are important to understanding how the energy given to the system is converted into the production of thrust (propulsive power) by an airfoil performing the plunging movement. Although it is already known that this sinusoidal movement may not represent the most efficient motion, it is nevertheless interesting to understand the regions where there is an optimal conversion of the input given to the system.

The airfoil was also tested with a Reynolds number of 17,000, keeping the previously mentioned parameters in the same range. The results show a similar distribution of the thrust coefficient, power coefficient (Figure 8), and propulsive efficiency, shown in Figure 9.

**Figure 8.** Mean thrust and power coefficients with *Re* = 17,000.

In respect to the influence of the Strouhal number on the thrust and power coefficients for a Reynolds number of 17,000, the following correlations were obtained:

$$\mathcal{L}\_t(St) = -0.029 + 0.312St + 3.584St^2 \, (R^2 = 0.88) \tag{10}$$

$$\mathcal{C}\_P(St) = 1.371 - 20.14St + 113.0St^2 \, (R^2 = 0.96) \tag{11}$$

with 0.1 ≤ *St* ≤ 0.4.

The propulsive efficiency increase is the major difference, which may indicate that the plunging movement tends to be more efficient at higher Reynolds numbers.

**Figure 9.** Propulsive efficiency with *Re* = 17,000.

In order to better interpret the evolution of propulsive efficiency for this specific case, propulsion efficiency curves are presented in Figure 10, considering the dimensionless amplitude (Figure 10a) and reduced frequency (Figure 10b) constant. When looking at the graphics, it is possible to verify that the maximum propulsive efficiency reached occurs at higher reduced frequencies when the dimensionless amplitude decreases. Regarding the graphic on the right, similar behavior is verified, since the highest propulsive efficiencies are detected at the highest reduced frequencies and lowest dimensionless amplitudes. However, a deeper comparison between both graphs concludes that the conversion of the required energy associated with the movement into propulsive energy is highly sensitive to the change in the nondimensional amplitude when a constant reduced frequency is considered, as observed by the higher slopes verified in the graphic on the right.

The Reynolds number was further increased to a maximum tested value of 34,000 (Figure 11). In this operating regime, the upper limit of the Strouhal range was limited to 0.2 since no clear advantage was seen in terms of achieving better aerodynamic performance. At this operating condition, an interesting fact is that the thrust coefficient isolines become equidistant to the constant *St* curves. In this situation, it becomes evident that the isolines of *Ct*, *St*, and *CP* are all doubtlessly parallel. Due to this turn of events, the maximum propulsive efficiency region was translated to the left, as seen in Figure 12 and, because of that, an additional zone (*k* < 1) was considered to understand the aerodynamic performance in low reduced frequencies.

**Figure 11.** Mean thrust and power coefficients with *Re* = 34,000.

The influence of the Strouhal number on the thrust and power coefficients for the actual number of Reynolds is also studied, obtaining the correlations:

$$\mathcal{C}\_{l}\left(St\right) = -0.059 + 0.671St + 3.643St^{2}\left(R^{2} = 0.96\right) \tag{12}$$

$$\mathbb{C}p\left(St\right) = 0.587 - 12.71St + 146.5St^2 \left(R^2 = 0.99\right) \tag{13}$$

with 0.1 ≤ *St* ≤ 0.2. The coefficient of determination regarding the *Ct* approximation improved (*R*<sup>2</sup> > 0.95) in comparison with the previously tested numbers of Reynolds, which corroborates the fact that the isolines of *Ct* became parallel with the Strouhal number.

**Figure 12.** Propulsive efficiency with *Re* = 34,000.

Overall, from a Reynolds number of 8500 to 34,000, the propulsive efficiency increased in comparison to the previous cases, which again suggests that the pure plunging motion is favored while operating at relatively high Reynolds numbers. Although animals use plunging and pitching combined, the results presented in this section are very much in concordance with what is seen in nature, considering that smaller animals tend to operate at high reduced frequencies and low nondimensional amplitudes. In comparison, bigger animals do the exact opposite.

#### **4. Conclusions**

Nature has been the main source of concepts that inspire the systems developed by engineers who, since the beginning of time, understood that it is powered by evolution mechanisms that tend to offer optimized solutions regarding the environmental conditions. These mechanisms directly affect animals, from the smallest insect to the big blue whale, that over millions of years, made them very well adapted to their habitat and to the way they move.

In this work, the flapping airfoil problem was investigated, utilizing a NACA0012, by studying the influence of several parameters such as motion frequency and amplitude, the Reynolds number, and the Strouhal number. Thrust, lift, and power coefficients, as well as the propulsive efficiency, were the selected parameters to analyze the aerodynamic performance.

The results indicate that the power coefficient isolines demonstrated to be almost parallel to the hyperbolas representing constant Strouhal numbers, a phenomenon not verified for the thrust coefficient, except for the *Re* = 34,000 case. It was also seen that higher frequencies and amplitudes propitiate higher thrust forces as well as required power while, in terms of propulsive efficiency, for the *Re* = 8500 and 17,000 cases, higher reduced frequencies and lower amplitudes are preferred and for the *Re* = 34,000 case, higher amplitudes and lower reduced frequencies are favored. The results highlight that although a constant *St* gives an infinity of combinations (*k*, *h*), it is seen as an interesting parameter that offers some correlations about the aerodynamic performance, especially at higher Reynolds numbers.

The physical phenomena underlying the flapping airfoil and flapping wing mechanisms were extensively studied in recent years, which resulted in a greater insight regarding the thrust generation. Nevertheless, much more investigation is needed to efficiently develop and produce vehicles with these propulsive systems for any stage of flight. Ways to improve knowledge should be focused on testing different geometries in order to understand how geometrical parameters such as the aerodynamic chord, camber, and thickness can influence the aerodynamic performance. Another way to boost the bio-inspired design is on the materials side, seeking innovative and different properties (flexibility, porosity) that may improve the flapping mechanism and bring us closer to developing animal-like propulsive/lifting systems and structures.

**Author Contributions:** Conceptualization, E.C. and J.B.; Data curation, E.C.; Formal analysis, E.C.; Methodology, E.C. and A.S.; Project administration, A.S. and J.B.; Resources, A.S.; Software, E.C.; Supervision, A.S. and J.B.; Validation, E.C. and A.S.; Visualization, E.C.; Writing—original draft, E.C. and F.N.; Writing—review & editing, A.S. and J.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** The present work was performed under the scope of the Aeronautics and Astronautics Research Center (AEROG) of the Laboratório Associado em Energia, Transportes e Aeronáutica (LAETA) activities and it was supported by Fundação para a Ciência e Tecnologia (FCT) through project numbers UID/EMS/50022/2019 and UIDB/50022/2020.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

#### **References**


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **Aircraft Propellers—Is There a Future? †**

#### **Pedro Alves \*, Miguel Silvestre and Pedro Gamboa**

C-MAST—Center for Mechanical and Aerospace Science and Technologies, University of Beira Interior, Rua Marquês d'Ávila e Bolama, 6201-001 Covilhã, Portugal; mars@ubi.pt (M.S.); pgamboa@ubi.pt (P.G.)


Received: 18 June 2020; Accepted: 7 August 2020; Published: 11 August 2020

**Abstract:** The race for speed ruled the early Jet Age on aviation. Aircraft manufacturers chased faster and faster planes in a fight for pride and capability. In the early 1970s, dreams were that the future would be supersonic, but fuel economy and unacceptable noise levels made that era never happen. After the 1973 oil crisis, the paradigm changed. The average cruise speed on newly developed aircraft started to decrease in exchange for improvements in many other performance parameters. At the same pace, the airliner's power-plants are evolving to look more like a ducted turboprop, and less like a pure jet engine as the pursuit for the higher bypass ratios continues. However, since the birth of jet aircraft, the propeller-driven plane has lost its dominant place, associated with the idea that going back to propeller-driven airplanes, and what it represents in terms of modernity and security, has started a propeller avoidance phenomenon with travelers and thus with airlines. Today, even with the modest research effort since the 1980s, advanced propellers are getting efficiencies closer to jet-powered engines at their contemporary typical cruise speeds. This paper gives a brief overview of the performance trends in aviation since the last century. Comparison examples between aircraft designed on different paradigms are presented. The use of propellers as a reborn propulsive device is discussed.

**Keywords:** propeller; aircraft; turboprop; flight efficiency; flight speed

#### **1. Introduction**

The propeller is a device that converts the rotary power of an engine or motor into a thrust force that pushes the vehicle to which it is attached. Comprised by one or more radial airfoil-section blades rotating about an axis, the propeller acts as a rotating wing. Aircraft propellers first emerged at the end of the 18th century; however, this study only discusses its history from the 20th century and beyond. See Ref. [1,2] for a historical review from the preceding decades. By the end of the 19th century, a feeling of disbelief on heavier-than-air manned flight was present [3]. The first controlled, powered flight, starred by the Wright Brothers in 1903, marked the turn of a page of skepticism concerning heavier-than-air manned flight. This remarkable achievement brought an increased excitement around the aviation community, and in the period 1905–1910, there was an impressive growth in the number of filed patents [4] (see Figure 1).

**Figure 1.** First patent filings by origin, 1900–1925. Between 1900 and 1970, patent filings relating to aviation tended to concentrate in the US, France, Germany, and the UK. Source: adapted from [4].

This pre-WWI (World War I) period was also responsible for a transition from individuals as hobbyists and enthusiasts, motivated by curiosity, pride, and fame, to institutions and governments acknowledging the airplanes as a strategic weapon to win wars. By the end of WWI, from the 1920s to the 1930s, designers, engineers, and inventors established new, active, and venturous aeronautic communities in Europe and North America. This prosperous era of innovation and technological growth of aviation extended its developments to all components of the airplane, including the propeller. Donald W. Douglas, head of the Douglas Aircraft Company, considered those communities of people responsible for helping change the world, acknowledging propeller makers and their creations indispensable for success [5]. The work on those propulsive devices joined the higher power outputs of the newer engines to the improved body aerodynamics resulting in higher performance aircraft capable of "climb quicker and cruise faster using less power and if need be, fly to safety on one engine" [3]. Since the first effective propellers powered by piston engines, through impressive supersonic aircraft and up to modern airliners, a lot has changed in aviation. The aircraft is now a balance between hundreds of different specifications. Some being improved at the cost of others. Today, the advent of electric multirotor vertical take-off and landing aircraft [6–11], starting as unmanned aerial vehicles but also aimed for personal transportation are bringing the assertion of the propeller as the main choice for low-speed, state-of-the-art efficient propulsion devices. Nevertheless, propellers are nothing more than a niche in commercial aviation commute aircraft. However, this century brought new challenges and priorities. Global warming, pollution, and sustainability are now serious concerns [12]. The present work shows the evolution of cruise speeds, especially on commercial aviation, in the past century to realize that the propeller comeback may be the next innovation towards more sustainable aviation. The trends are presented, and their motives are discussed. In the first section, a brief historical overview is presented. The second section introduces the influence of the cruise speed in the aircraft aerodynamic efficiency and engine fuel consumption. Then it discusses the evolution of the flight speed of the airliners since the jet age. The third section shows the relevance of bringing back the propeller and continue its development.

#### **2. Early Jet Age: The Race for Speed**

With the invention and development of the jet engine during WWII, gas turbine-powered aircraft expanded the whole flight envelope. Flying higher and faster, both commercial and military jet airplanes ruled the 1950s and 1960s, at what was called: The Jet Age [13]. Compared with piston airplanes, the speed and ceiling of these first jet-powered aircraft were incredible, and the race for flight speed became the leading trend [3]. The following years gave birth to a generation of even faster jet aircraft as the example of the Boeing 727, which had a maximum cruise speed of Mach 0.84. However, to overcome the speed of sound, a larger amount of power was required. This is due to the sharp rise in drag, experienced above a critical Mach number [14] (Figure 2). Also, supersonic flight introduced the need for pure jet engines since the propeller blades encounter the critical Mach number at smaller cruise speeds due to their additional rotation speed.

**Figure 2.** Drag rise due to cruise Mach and the effect of wing sweep. Adapted from [15].

Therefore, the race continued, and in the early 1960s, the Convair 990 could already fly at speeds up to Mach 0.87 [16]. At this time, in one of the test flights, Douglas company accelerated its DC-8 to Mach 1.01 in a 16-second dive. Nevertheless, commercial aviation did not stop there. Pursuing military achievements as the Lockheed SR-71 "Blackbird", that cruised at Mach 3.2, commercial aviation needed to rush forward. In the early 1970s, jet engine technology was developing at a tremendous pace. Commercial aircraft, characterized by sharp noses and high swept wings, also started breaking through the sound barrier. The Concorde and the Tupolev Tu-144 were developed to cruise at Mach 2. However, Mach 2 still seemed not enough, so, Boeing wanted to create an even faster commercial airplane [17–19], aiming to fly at Mach 3. Suddenly hypersonic transportation was the subject of research [20,21]. It seemed that there were no limits to the race for speed, but something went wrong, and the true supersonic age never came. The magnificence of supersonic airliners was comparable only to the horror of their ecology and economy. The supersonic engines roar was annoying to the cities' populations. Sound booms were destroying everything around [22], leading many countries to ban supersonic flights from their airspace [23]. In addition to that, the super-powerful afterburner engines were so hungry for fuel that airlines had to increase the cost of tickets to cover their expenses. Those facts, combined with the 1970s oil crisis, made the supersonic flight not to enter mass aviation. To transport ordinary travelers on such planes was the same as the average citizen commuting to work on supercars. One of the main reasons that made the airlines and manufacturers abandon the race for speed is also one of the main elements of the aircraft: the engine. The heart of most modern aircraft is a jet engine. The task of any jet engine (or reaction engine) is to convert the fuel's chemical energy

into the jet flow's kinetic energy. In practice, the fuel ignites, expands, accelerates, and pushes the machine forward. The jet engines used in aviation use not only their fuel but also the surrounding air, which is also heated up and accelerated to be ejected at high speed by a nozzle to create thrust. See Ref. [24] for further insights on jet engines. The Rolls-Royce / Snecma Olympus 593 that equipped the Concorde is a classic example turbojet engine. However, these engines were very greedy. With its small capacity, Concorde had a huge fuel consumption, resulting from the great increase in drag shown in Figure 2. The much larger Boeing 747, produced in 1968, turned out to be much more economical [25]. Despite that, new larger subsonic jet-powered airliners conquered the main long-haul routes, and smaller models were conquering the regional ones.

#### **3. Fuel Efficiency**

For commercial aircraft, fuel efficiency is usually regarded as the inverse of the fuel consumption, which is fuel quantity burned per unit traveled distance per unit passenger, normally, in *kmPax*/*LFuel*. When comparing different fuels, fuel mass is more meaningful than fuel volume. If, instead of mass or volume of fuel, the amount of energy consumed (or contained in that mass of fuel) was used, one could even compare different types of propulsion systems, e.g., the electric propulsion. Considering the propulsive system efficiency as *ηthηp*, where *ηth* is the thermal efficiency and *η<sup>p</sup>* is the propulsive efficiency, and that in cruise, the required thrust is:

$$F = \frac{W}{L/D} \tag{1}$$

where *F* is the propulsive thrust force, *W* is the aircraft weight, *L* and *D* are aircraft lift and drag, respectively.

Using Equation (1), the aircraft fuel efficiency can be regarded as:

$$
\eta\_{\text{Fuel}} = \frac{L}{D} \frac{\text{pax}}{\mathcal{W}} \eta\_{th} \eta\_{p} \tag{2}
$$

Therefore, the aircraft will be fuel-efficient if it has large aerodynamic efficiency (*L*/*D*) and low take-off weight per unit passenger (*W*/*pax*). The aerodynamic efficiency depends mostly on the airfoil design and wing design parameters: span; chord; sweep; etc., and all other elements of the aircraft that generate drag but not produce any lift. The weight per unit passenger depends mostly on the aircraft structure, materials, and design. The engine thermal efficiency has been improving in recent decades being close to its upper limits. Regarding the propulsive efficiency, to propel the aircraft, the propulsive system generates the thrust by accelerating the incoming air stream mass flow from *VCruise* to a propulsive stream with *VJet*, considering that the fuel mass flow is much smaller than this propulsive stream, we get Equation (3).

$$\eta\_p = \frac{2}{2 + \frac{F}{\dot{m}V\_{Cruise}}} \tag{3}$$

with *m*˙ being the propulsive stream mass flow rate.

According to Equation (3), the propulsive efficiency increases if *m*˙ is increased. This was accomplished in the jet engine by adding an external bypass outer stream of cold air mass flow. These engines were named turbofans and became a real classic solution in modern aviation. Since their birth, turbofan engines started to replace turbojets, becoming as fast as them, despite that the advantage of adding the bypass cold stream diminishes towards higher *VCruise*. Most modern fighters like the F-15, Eurofighter Typhoon, Sukhoi Su-30, and the newest F-22 and Sukhoi Su-57 are equipped with turbofan engines. At *VCruise* of current commercial aircraft, the bypass stream fan is in fact a ducted propeller. Figure 3 shows the typical propulsive efficiencies for the most common aircraft engine types. The influence in the propulsive efficiency of parameters such as the propeller

blade sweep and engine bypass ratio is also represented. It is clear that the bypass ratio of the turbofan increases the propulsive efficiency relative to the turbojet and that the propeller blade sweep extends the Mach cruise speed limit for propeller operation.

**Figure 3.** Propulsive efficiency for different engine types.

#### **4. Commercial Aviation—Higher and Faster! Or not?**

Although the aviation lemma has typically been higher and faster, in fact, slower commercial aircraft should lead to higher fuel efficiency [26]. Between 1990 and 2010, jet fuel prices have increased over five times, representing about 40 percent of a typical airline's total operating cost [27,28]. As a result, airlines are reviewing all phases of flight to determine how fuel burn savings can be gained in each phase and total.

It is noticeable that since the 1973 oil crisis, commercial airliners are losing their interest in speed from generation to generation (Figure 4). Today, short-haul airliners such as the Boeing 737 and Airbus A320 cruises at airspeeds lower than Mach 0.78. The giant, long-haul flagships like the Boeing 747-8 and the Airbus A380, equipped with four powerful engines, regularly fly at a non-impressing Mach 0.85. Moreover, even the most advanced planes of the modern age as the Boeing 787-Dreamliner and Airbus A350 XWB are not cruising at Mach higher than 0.85. Are the airliners, including the most sublime and advanced of our time, lagging behind the 50-year-old museum exhibits? In the last 50 years, the engines suffered the most noticeable change in aviation. Since the early jet age, engines' bypass ratios increased from 0 to 12.5 (Figure 5). This is easily explained through Equation (3) as engine manufacturers try to increase the engines' propulsive stream mass flow. Modern materials and processes also allowed for higher turbine inlet temperatures and overall pressure ratios. The increase in bypass ratios has been achieved by using bigger fans and fan ducts, which also led to increased empty-weight and parasitic drag. Those factors, associated with rising fuel prices and environmental concerns, are making higher cruise speeds less attractive. In [26], Torenbeek states that "Future long-range airliners optimized for environmentally friendly operation may cruise at no more than Mach 0.75".

**Figure 4.** Historical development in maximum cruise speeds for commercial aircraft.

**Figure 5.** Evolution on the Turbofan Bypass Ratio.

Another noticeable characteristic that confirms this trend of reduced interest in high cruise speeds is the wing design. A comparison of two airliners that operate in the same market segment is presented in Table 1. The wing of Boeing 727 is smaller and has a higher sweep angle than the 737 Max 7. The smaller wingspan and higher wing sweep allow the aircraft to fly faster. When flying near

the speed of sound, the airflow accelerates over the wing reaching supersonic speeds and slows down again to subsonic speeds towards the trailing edge of the wing, creating a shockwave and the resulting wave drag. Higher sweep angles delay this effect. The airflow over the wing consists of two components: chordwise flow (parallel to the chord line) and spanwise flow (perpendicular to the chord line). As the only component that suffers the acceleration is the chordwise flow, by reducing the amount of flow in this direction, the aircraft is able to fly faster for the same drag (see Figure 2). Like the newer Boeing 737 Max 7, many other modern airliners have lower wing sweep than their predecessors. This may also be, in part, due to the invention of the supercritical airfoil. However, if the intention were to fly faster, the wing would be kept with a lower span and higher sweep.


**Table 1.** Boeing 727-200 vs. Boeing 737 Max 7: Technical Specifications. Data from [29,30].

Lower speeds require smaller engine thrust, which represents lower fuel consumption, weight, and noise emissions. Improved efficiency not only allows airlines to save money on fuel but also enables airplanes to fly further. Comparing between the Boeing 727-200 and the 737 Max 7 (described in Table 1), both have similar payload capacities and mass, but the 727-200 has a range of 4500 km, while the 737 Max 7 has 7100 km, twice the range of the former one. In terms of power-plants, the 737 has two engines, while the 727 needed three. The improved take-off thrust of the high bypass turbofan engines was the key to the birth of wide-body airliners, which are the main element of global travel today. However, these high bypass turbofan engines have their drawbacks. All aircraft manufacturers face the same difficulty when upgrading their power-plants. These engines are huge. As the engine manufacturers are raising bypass ratios, the engines' diameter is getting larger, making them harder to fit under the wing of aircraft. The Pratt & Whitney JT8D installed on the 727-200 is much smaller than the CFM Leap-1B that equips the 737 Max 7 (Figure 6). The choice of the Leap-1B to equip the 737 Max 7 also required major upgrades to the landing gear, to maintain the required ground clearance and changes to the wing in order to compensate for the additional engine's weight and drag [31].

The problem is that to adapt the jet propulsion to operate efficiently at lower speeds, the propulsive jet must also have higher mass flow, as observed through Equation (3). Therefore, the turbofan bypass ratio must increase. However, several problems arise when trying to increase the fan size: the fan weight increases; fan noise increases steeply if the peripheral speed is increased to maintain the same shaft rotation speed; reducing the shaft rotational speed such that the noise does not increase, increases the number of stages required for the turbine and thus increases the weight of the core gas turbine. There are a lot more pros than cons to modern aircraft compared to the older airliners. It is a fact that they fly slower, but the rest of their performance is much better, not only due to modern technology but also because of such compromises. In Europe, according to [32], short-haul flights (up to 1500 km) within European Civil Aviation Conference (ECAC) bordering countries represented 78.5% of the total instrument flight rules (IFR) traffic in 2017. According to the same reference, in the United States, the share of short-haul flights reached 80.3% in the same period. Even with the technology that allows us to produce faster airplanes, at those distances, a small increase in speed may reduce flight time but has little impact on the journey. The journey is the wait at the airport, check-in, baggage check,

passport control, waiting at the terminal, flight, and again the passport control, baggage claim, and the way from the airport to the destination. All these journey stages will not be accelerated by a higher cruise speed, and all the advantages of flight speed can easily be lost by a traffic jam on the way to the airport. For airlines, the parameters of fuel consumption and life cycle of the aircraft are getting more critical than the cruise speed by the day. Also, fuel consumption is not only money. Fuel tanks on the aircraft remain the same, and flying faster may result in a reduction of range. It is cheaper for the airline to make the passenger more comfortable, show a couple of movies, or provide an extra meal in flight than to speed up the aircraft. From the passenger's point of view, such a deal is also attractive. The flight may be longer, but the level of comfort on those flights is not bad. Higher costs for speed will increase the cost of air tickets, and time is a more valuable resource than money just for a small group of people. The world is ruled by economically optimal airliners with economically optimal performance. A cheaper ticket is more important for a passenger and cheaper operation is more important for airlines. Modern airplanes pursue these goals.

**Figure 6.** Boeing 727-200 (**left**) side-by-side to a Boeing 737 Max 7 (**right**).

#### *4.1. Present-Day Airliner Speeds*

To understand how the typical cruise speeds from the manufacturer compares to the real flight speeds currently being used by airlines, a total of 80 flights were analyzed using Flightradar24. Flightradar24 is a flight tracking service that provides both real-time and stored information about aircraft flights around the world. Specific information such as atmosphere corrected Mach cruise speeds were used to perform this study. Two specific aircraft types were selected: the Boeing 737-800 and the Airbus A320neo. Both aircraft operate short- and medium-haul flights with similar cruise design speeds (with a design Mach cruise speed of 0.785). To compensate for different flight strategies of specific airlines (e.g., low-cost vs full-service), distinct airlines were analyzed for each aircraft type. In Table 2 a synopsis of the analysis is presented.


**Table 2.** Aircraft analyzed using Flightradar24.

<sup>1</sup> Design cruise speed announced by the manufacturer.

In Figure 7 the cruise speeds for the total analyzed 80 flights are plotted against aircraft manufacturer announced design cruise speed. From the analyzed flights, it is noticeable that the actual average cruise speed values are lower than the design cruise speed. Regarding the Boeing 737-800, Ryanair presented an average Mach of 0.758 and KLM 0.780. Furthermore, on the Airbus A320neo, Wizz Air average Mach was 0.775, while British Airways registered 0.761. The average Mach cruise speed for the total 80 presented flights is 0.769. Different dispersion can be attributed to distinct weather-related flight optimization, e.g., to account for head or tailwind. Parameters such as airport sockets, aircraft availability, and fuel prices influence each airline's fuel conservation strategies and cost index (CI) . By definition, cost index is the ratio between the time-related operational cost and the fuel cost of an airplane operation, reflecting the relative effects of fuel and time-related operating cost on overall trip cost.

**Figure 7.** Cruise flight speed from a total of 80 analyzed flights. Boeing 737-800 by Ryanair and KLM. Airbus A320neo by Wizz Air and British Airways. Data sourced from Flightradar24 [33].

From the exclusively propulsive efficiency point of view, referring to Figure 3, one can easily notice that for Mach values of 0.769 the aircraft may already be cruising in a condition where propeller-based propulsive systems, namely propfans, show competitive performance when compared to turbofans [34–36].

#### **5. Propellers Avoidance Phenomenon and the Oil Price Effect**

During the jet age, propeller specialists and companies struggled for their place in the industry. After a period of uncertainty, they found it with the development of the turboprop. Since they first emerged in the mid-1940s, turboprop engines were perceived as a temporary compromise between old piston engines and advanced jet engines (see Figure 4, bottom left). This fact resulted in scarce efforts towards technological developments in this type of power-plants and the few turboprop aircraft flying in the late 1960s were still the same built in the 1950s. Though considered rather obsolete, the industry, not seeing great prospects, was not particularly in a hurry to create a replacement for them. In the early 1970s, the use of propeller propulsion in large airframes was almost restricted to the military. However, in 1973, a severe oil crisis [37] started to affect the whole aviation industry. High fuel consumption of the jet engines previously perceived as a perfectly acceptable compromise for speed, associated with prohibitive fuel prices (Figure 8), turned out to be a severe problem. Long-range transportation by large aircraft remained profitable, but flights over short distances by regional vehicles were not often paying off [38]. For the first time in decades, the jet propulsion dominance was questioned, resulting in the industry and governments to chase for more efficient, alternative propulsive systems. This economic environment stimulated work towards a reinvention of the propeller for increased air transportation fuel efficiency.

**Figure 8.** Crude Oil Prices from 1960 to 2020, nominal and real (corrected by the 2019 U.S. inflation). 1960–1985: Arabian Light posted at Ras Tanura; 1986–2020: Brent Spot. Price data source: U.S. Energy Information Administration [39]. U.S. Consumer Price Index (CPI) to correct the prices for the 2019 inflation sourced from the U.S. Bureau of Labor Statistics [40].

#### *5.1. The Advanced Turboprop Project*

One of the most remarkable works for increased air transportation fuel efficiency was the Advanced Turboprop Project (ATP) [36]. The ATP was led by the National Aeronautics and Space Administration (NASA) in the 1980s and represented the most relevant and promising work in propeller propulsion up to date. NASA partnering with Boeing and General Electric developed a modern and advanced propeller propulsion system that demonstrated high efficient cruise at Mach 0.65 to 0.80, leading to an overall fuel consumption reduction of 40 to 50 percent relative to turbofans at the time. The flight tests were conducted in a modified B727-100 and McDonnell Douglas MD-80. Later, Pratt & Whitney, cooperating with Allison, developed an even more efficient geared propfan

unit that was tested in an MD-80 (Figure 9). In the 1980s, the Advanced Turboprop Project was developing rapidly, and several new aircraft concepts were being considered for the 1990s. Some of them were engine replacements in current aircraft, while others were new aircraft designs specifically for turboprop/propfan installations.

(**a**) (**b**) **Figure 9.** (**a**) Pratt & Whitney-Allison 578–DX geared propfan demonstrator engine, installed on an MD-80 testbed aircraft. (**b**) General Electric GE36 demonstrator engine installed on the Boeing 727 testbed for flight testing in 1986–1987.

In the meantime, new regional twin-engine turboprop aircraft started to appear to compete with the jets that were becoming too expensive to operate, and the interest for turboprop engines rose again (see Figure 4, bottom right). However, as those new turboprop aircraft started to claim the regional routes, a popular resistance, related to the idea of going back to propeller-driven airplanes, and what it represented in terms of modernity and security, started a propeller avoidance phenomenon on the travelers [3]. This negative perception affected the demand for these routes and impacted the economic viability of the turboprop operated routes. At the same time, a sharp drop in fuel prices (see Figure 8) put down all the research efforts in new and advanced propeller design programs like ATP. The turboprop market decreased, and the competition increased.

Jet planes were more expensive, consumed more fuel, and were more demanding on infrastructure but had better flight performance in factors such as cruise speed, range, and comfort, making them more attractive to operators. This fact led to the lowest demand for turboprop airplanes in the civil transportation market [41] making all those efforts to bring the propeller back to medium/long-haul airliners never materialize.

On the other hand, since its appearance, turboprop aircraft conquered the military and defense businesses. Models like the Lockheed C-130 Hercules and the Lockheed P-3 Orion, introduced in the late 1950s, counting with different variants and updated versions, remain in service up to the present. Their versatile airframe and unprecedented capability to use unprepared runways for takeoffs and landings, made those tactical airlifters to spread out among many military forces worldwide. In the 1970s, Lockheed proposed a C-130 variant with turbofan engines rather than turboprops, but the U.S. Air Force preferred the take-off performance of the existing aircraft [42]. Those characteristics associated with all the accumulated military operational experience and improved performance are demanding for the aircraft industry to come with civil, commercial variants. The Lockheed Martin's LM-100J is a civil derivative of the C-130J Super Hercules, the last major update to the military C-130 family. The LM-100J commercial freighter received its type certificate from the Federal Aviation Administration by the end of 2019, and it is expected to enter service by 2020. To answer the demand for the military tactical airlift and compete with C-130J Super Hercules, Airbus introduced the A400M Atlas in 2009. Equipped with four Europrop TP400-D6 turboprop engines, it has a maximum payload capacity of 37 tons, positioning itself between the C-130J Super Hercules and the larger turbofan Boeing C-17 Globemaster.

The growing concern on fossil fuel outage, combined with the global environmental strategy is increasing the oil price, forcing a paradigm shift in the whole transportation industry. New modern, propeller-powered, hybrid aircraft concepts are emerging. The usage of partial electric power-plants introduces part of the solution to one of the most significant handicaps of propellers in the last decades, the increased ground noise levels. Recently, the Electric Aviation Group (EAG) unveiled the HERA concept (see Figure 10), a Hybrid Electric Regional Aircraft with capacity for 70+ seats to be in service by 2028.

**Figure 10.** EAG Hybrid Electric Regional Aircraft (HERA) (Photo:PRNewsfoto/EAG).

Reinforcing the prominent comeback of the propellers, in 2008, within the Clean Sky program, the European Commission announced the Open Rotor demonstration program, targeting to reduce fuel consumption and associated CO2 emissions by 30% compared with current turbofans. Led by Safran (former Snecma), this program assembled a demonstrator in 2015 (see Figure 11), which performed the ground-testing in 2017 at the Istres site in southern France [43].

**Figure 11.** Open Rotor prototype by Safran.

In response, other companies, like Rolls-Royce, have also been resuming the work and progress from the 1980s ATP program to continue the development and testing on Open Rotor engines, recognizing a clear market opportunity for such technologies in the near future [44].

#### **6. Is There a Future for Aircraft Propellers?**

As seen in Section 3, on the one hand, the trend of increasing the bypass ratio in power-plants has been the way to increase the aircraft energetic and economic viability. It has ended up by introducing the gearbox turbofan (see Figure 5). On the other hand, the propeller (or propfan/open rotor fan) can be seen as an ultra-high bypass ratio propulsive device. The gearbox was perceived as a serious disadvantage that disappeared in relation to the recently introduced, geared turbofan. Nevertheless, other disadvantages concerning the use of propellers need to be addressed: higher noise levels and the maximum cruise speed limitation. In Section 4 is shown the acceptance in reducing the maximum cruise speed on consecutive turbofan airliners. On July 16, 2020, Israir, a fairly small Israeli airline with just seven planes in its fleet, including four Airbus A320 and three ATR 72-500, operated a flight from Tel Aviv to Kiev with one of its turboprop ATR 72-500 instead of the A320 (turbofan) [45]. Curiously, this route is stated at 1282 miles, considerably longer than the ATR 72-500 published range of 823 miles, which suggests a low flight load and velocity. The ATR 72-500 performed the flight in 4 h 55 min, while the A320 is capable of 3 h 25 min. Nevertheless, this shows that there are companies already willing to sacrifice flight speed by replacing turbofan aircraft with smaller, more economically viable, propeller-powered aircraft on considerably longer routes.

As stated in Section 5, since the 1970s, several factors were conditioning the broader use of propellers in the civil, commercial aircraft industry. However, the military never dropped the use of propeller aircraft. Their developments in the last decades, associated with current oil prices and ecology strategies, are re-introducing the turboprop aircraft in the civil market.

Finally, the recent developments in future hybrid and electric aircraft brought new challenges to the aircraft designer. When it comes to electric mobility, one of its most significant handicaps is the low energy density of current batteries. Although no disruptive progress is made in that area, the best approach to mitigate that obstacle is through better usage of the limited amount of energy that can be stored. This leads the design approaches back to propeller propulsive systems due to its, more efficient, ultra-high bypass ratios [46].

#### *6.1. Multirotor Drone Emergence and the Future Personal Aerial Mobility*

Multirotor drone emergence also re-introduced the propeller as the best-suited propulsion device for low-speed, low-cost, and accessible small aircraft. Furthermore, the enthusiasm for unmanned vehicles, alongside the broader access to technology, are accelerating the interest for personal aerial mobility and package delivery. The present reality of exploding numbers of electric multi rotary-wing drones is being followed by incorporating the fixed-wing flying mode into Vertical Take-off and Landing (VTOL) aircraft for range increase. It is likely that in the near future, electric VTOL (eVTOL) fixed-wing propeller aircraft will serve Uber-like personal mobility transportation systems. As a response to the rising thin-haul and on-demand transportation market, a growing number of startups, and more traditional companies like Airbus and Rolls-Royce are introducing smaller, mostly electric VTOL aircraft for urban air mobility applications. In [47], a review of the current technology and research in urban on-demand air mobility applications, including a comparison between 45 aircraft models, is presented. It is noticeable that in these categories, the propellers and jet propulsion still compete . However, the choice for the propeller-based propulsive systems is taking the lead. The higher efficiency that jet-powered ducted fans offer for high speed, high altitude cruise is not likely to be beneficial for urban applications, where lower speeds and altitudes are more common. In terms of safety, the usage of distributed propulsion is present in almost every new design, allowing improved propulsive efficiency and redundancy. The distributed propulsion takes advantage of typically smaller propellers, also reducing the overall noise with lower tip speeds. Figure 12 shows some of the relevant urban mobility contributions.

$$\mathbf{0}$$

(**c**) (**d**) **Figure 12.** Examples of VTOL aircraft demonstrator vehicles for personal transportation. (**a**) Airbus Vahana, by Airbus Urban Mobility. (**b**) Lilium Jet, by Lilium GmbH. (**c**) BlackFly, by Opener. (**d**) eVTOL, by Rolls-Royce.

#### **7. Conclusions**

Since the jet age, aircraft design aimed for speed and drove the airliners cruise speeds up to Mach 0.85. However, the 21st century brought a new sharp rise in energy prices [48], and consequently, a global economic crisis. At the same time, the global environmental consciousness is forcing the reduction of engine emissions, driving recent investigations to suggest that future airliners may have to reduce their design cruise Mach number [26]. Jet regional aircraft are, once again, becoming too expensive to operate, and the demand for turboprop engines rose again. Through the previous energetic crisis, the oil price has driven the progress and technological advance on propellers and their demise in favor of jets, feeding the race to fly higher and faster for decades. The race for speed reached its end, but the efforts to bring the propeller back to medium/long-haul airliners were abandoned as the oil prices dropped. Presently, the higher the oil price, the more likely the propeller comeback is becoming. The industry has played a more reactive than active role in this area. Nevertheless, beyond efficiency, propellers always offered benefits that the jet engine could not. Better take-off and landing performance allow transporting passengers to and from small regional airports. Also, its lower cost allowed enthusiasts and aviators to use them in their recreational, general aviation aircraft. In addition, the demand for turboprop aircraft increased due to a new wave of rising fuel prices, especially in countries that do not have a developed airfield infrastructure. At the very beginning of the 21st century, the propeller-driven airplane prevailed as a niche. However, this century brought new challenges and priorities. Recurrent oil crises are making propellers, and their specific advantages such as economic and environmental, the old answer to a prevailing problem. Therefore, propellers may have a role to play in progress again, even for commercial aviation. Nevertheless, the electric VTOL aircraft aimed for urban mobility seems like the new playground for propeller innovation. As noticed in the previous sections, the propeller has a future and we may be experiencing its rebirth in commercial aviation.

**Author Contributions:** All authors have contributed to this paper. Conceptualization, P.A. and M.S.; methodology, P.A. and M.S.; formal analysis, P.A. and M.S.; investigation, P.A.; writing—original draft preparation, P.A.; writing—review and editing, P.A., M.S. and P.G.; visualization, P.A., M.S. and P.G.; supervision, M.S. and P.G.; funding acquisition, M.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work has been supported by the project Centro-01-0145-FEDER-000017 - EMaDeS - Energy, Materials and Sustainable Development, co-financed by the Portugal 2020 Program (PT2020), within the Regional Operational Program of the Center(CENTRO 2020) and the European Union through the European Regional Development Fund (ERDF); and also the C-MAST - UID/EMS/00151 provided by FCT/MCTES through national funds (PIDDAC) and co-financed by the (European Regional Development Fund ERDF) through the Competitiveness and Internationalization Operational Program (POCI).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Abbreviations**

The following abbreviations are used in this manuscript:


#### **References**


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