2 Experimental set-up

The two transfer functions are examined in two experimental set-ups. The oscillating airfoil is investigated in the TU Darmstadt open-return wind tunnel, comprising a pitch–plunge rig. The stationary airfoil encountering a sinusoidal vertical gust is investigated in the University of Oldenburg active-grid wind tunnel. An overview of the experimental set-ups is given below; a more detailed description of both set-ups can be found in Cordes (Reference Cordes2016).

2.1 Oscillating airfoil

Figure 1 shows a schematic of the experimental set-up of the TU Darmstadt open-return wind tunnel: a two-dimensional airfoil is oscillated in a steady flow, using a pitch–plunge rig. The airfoil has a Clark Y section, a chord length of $c=0.12~\text{m}$ , a span of $s=0.45~\text{m}$ and is mounted horizontally in a wind tunnel, covering the entire wind tunnel width. The wind tunnel has a closed test section of $0.45~\text{m}\times 0.45~\text{m}$ . A pitch–plunge rig, consisting of two linear actuators, is installed underneath the test section. The airfoil is mounted on the actuator pistons via aluminium adapters. The airfoil is oscillated around its leading edge at a mean angle of attack $\unicode[STIX]{x1D6FC}_{m}$ in a pure pitch motion $\unicode[STIX]{x1D6FC}_{p}=\widehat{\unicode[STIX]{x1D6FC}}_{p}\sin (2\unicode[STIX]{x03C0}ft)$ of amplitude $\widehat{\unicode[STIX]{x1D6FC}}_{p}$ and frequency $f$ , while the inflow velocity $U_{\infty }$ is kept constant. The dynamic pitch angle $\unicode[STIX]{x1D6FC}_{p}$ is obtained from the position of the linear actuators and can be calculated with an uncertainty of $u_{\unicode[STIX]{x1D6FC}_{p}}=\pm 8\times 10^{-2\circ }$ . The airfoil is equipped with three pressure taps at both the suction and pressure sides, to measure the pressure difference at three chord wise positions, $x/c=0.06$ , 0.11 and 0.14. Each pressure tap is connected to an HCL miniature pressure transducer. The coefficient of the pressure difference $C_{\unicode[STIX]{x0394}p}$ between the suction and pressure sides is obtained from $C_{\unicode[STIX]{x0394}p}=C_{p,SS}-C_{p,DS}$ , with an uncertainty of $u_{C_{\unicode[STIX]{x0394}p}}=\pm 4\times 10^{-2}$ .

Figure 1. Side view of the experimental set-up of the pitching airfoil in a steady air stream.

For each parameter set ( $U_{\infty }$ , $\unicode[STIX]{x1D6FC}_{m}$ , $\widehat{\unicode[STIX]{x1D6FC}}_{p}$ and  $f$ ), a phase averaged $C_{\unicode[STIX]{x0394}p}$ from approximately 15 continuously performed pitch cycles is derived. Damping effects in the pressure taps, tubes and sensors which cause a phase lag and a reduction of the pressure signal amplitude are accounted for by an additional dynamic calibration.

2.2 Sinusoidal vertical gust

Figure 2 shows a schematic of the experimental set-up in the University of Oldenburg wind tunnel: a stationary two-dimensional airfoil is submitted to a fluctuating inflow, generated by means of an active grid. The active grid allows the generation of sinusoidal modulated turbulent inflow conditions. The modulation is homogeneous $y$ -direction perpendicular to the profile. The resulting flow, from now on referred to as sinusoidal vertical gust $v_{g}=\widehat{v}_{g}\sin (2\unicode[STIX]{x03C0}f)$ , comprises a variable amplitude $\widehat{v}_{g}$ and variable frequency $f$ . More information about the active grid and its performance is given by Knebel, Kittel & Peinke (Reference Knebel, Kittel and Peinke2011). By varying either the inflow velocity $U_{\infty }$ or the frequency $f$ , velocity perturbations of different wavelengths $\unicode[STIX]{x1D706}=f/U_{\infty }$ are obtained. The velocity perturbations lead to a fluctuating gust angle $\unicode[STIX]{x1D6FC}_{g}=\widehat{\unicode[STIX]{x1D6FC}}_{g}\sin (2\unicode[STIX]{x03C0}f)$ on the airfoil with a reduced frequency $k=\unicode[STIX]{x03C0}fc/U_{\infty }=\unicode[STIX]{x03C0}c/\unicode[STIX]{x1D706}$ . A two-dimensional airfoil with a Clark Y profile, a chord length of $c=0.18~\text{m}$ and a span of $s=0.8~\text{m}$ is mounted vertically at a mean angle of attack mean $\unicode[STIX]{x1D6FC}_{m}$ approximately $\unicode[STIX]{x0394}x=1.1~\text{m}$ behind the active grid on a wind tunnel balance. The wind tunnel balance allows measurement of the lift $L$ with an uncertainty due to the accuracy of the force balance components of $u_{L}=\pm 0.12~\text{N}$ . The fluctuating angle of attack $\unicode[STIX]{x1D6FC}_{g}$ was measured prior to the airfoil experiments in the empty wind tunnel at the airfoil leading-edge position ( $x=0$ , $y=0$ , $z=h/2$ ) by cross wires and a Dantec Streamline anemometer with an estimated uncertainty of $u_{\unicode[STIX]{x1D6FC}_{g}}=\pm 0.2^{\circ }$ .

Figure 2. Top view of the experimental set-up of the fixed airfoil encountering a sinusoidal vertical gust.

For each parameter combination ( $\unicode[STIX]{x1D6FC}_{m}$ , $U_{\infty }$ , $\widehat{\unicode[STIX]{x1D6FC}}_{g}$ and $f$ ), a phase averaged lift response of approximately 200 cycles is derived.

3 Transfer functions

Traditionally, transfer functions relate an input to an output signal. Here, the input signal is the fluctuating flow and the output signal is the airfoil lift response $L_{dyn}$ . Adopting the approach of the theoretically derived first-order transfer functions, the dynamic airfoil response is not related to the fluctuating flow but to the corresponding quasisteady lift response $L_{qs}$ of the airfoil, which corresponds to a normalization of the transfer function  $h$ :

(3.1) $$\begin{eqnarray}h=\frac{L_{dyn}}{L_{qs}}=\frac{\widehat{L}_{dyn}}{\widehat{L}_{qs}}\frac{\text{e}^{\text{i}(\unicode[STIX]{x1D714}t-\unicode[STIX]{x1D711})}}{\text{e}^{\text{i}\unicode[STIX]{x1D714}t}}=\widehat{h}\text{e}^{-\text{i}\unicode[STIX]{x1D711}}.\end{eqnarray}$$

The transfer function $h$ is a complex function of the reduced frequency $k$ and comprises both magnitude and phase information. For purely harmonic excitations and responses, the magnitude corresponds to the ratio of the dynamic and quasisteady lift amplitudes,

(3.2) $$\begin{eqnarray}\widehat{h}=\frac{\widehat{L}_{dyn}}{\widehat{L}_{qs}}.\end{eqnarray}$$

For values of $\widehat{h}<1$ , the dynamic lift is smaller than its quasisteady value. The argument of the transfer function represents the phase between the input and output signals,

(3.3) $$\begin{eqnarray}\arg (h)=-\unicode[STIX]{x1D711}.\end{eqnarray}$$

For negative values of $\unicode[STIX]{x1D711}$ , the load response leads the excitation, while for positive values of $\unicode[STIX]{x1D711}$ , the load response lags the excitation. First-order transfer functions are functions of the reduced frequency $k$ only. They are independent of the mean angle of attack $\unicode[STIX]{x1D6FC}_{m}$ and the perturbation amplitude. The perturbation amplitude corresponds to the pitch amplitude $\widehat{\unicode[STIX]{x1D6FC}}_{p}$ in the case of the Theodorsen function and to the gust amplitude $\widehat{\unicode[STIX]{x1D6FC}}_{g}$ in the case of the Sears function.

3.1 Oscillating airfoil

The lift force is not directly accessible in the present experimental set-up. The coefficient of the pressure difference on the airfoil leading edge $C_{\unicode[STIX]{x0394}p}$ serves as an estimator for the lift, as proposed by Gaunaa & Andersen (Reference Gaunaa and Andersen2009). A closed-form first-order transfer function for the unsteady pressure distribution is given by Mateescu & Abdo (Reference Mateescu and Abdo2003). The unsteady pressure distribution is an intermediate result of the unsteady lift response, and integration of Mateescus and Abdo’s solution yields the Theodorsen function. It is assumed that validation of a first-order solution of the unsteady pressure is equivalent to validation of the Theodorsen function of the total lift. The transfer function of the coefficient of the pressure difference $h_{C_{\unicode[STIX]{x0394}p}}$ is defined as

(3.4) $$\begin{eqnarray}h_{C_{\unicode[STIX]{x0394}p}}=\widehat{h}_{C_{\unicode[STIX]{x0394}p}}\text{e}^{-\text{i}\unicode[STIX]{x1D711}}.\end{eqnarray}$$

The magnitude $\widehat{h}_{C_{\unicode[STIX]{x0394}p}}$ relates the amplitude of the coefficient of the dynamic pressure difference $\widehat{C}_{\unicode[STIX]{x0394}p,dyn}$ to its quasisteady counterpart $\widehat{C}_{\unicode[STIX]{x0394}p,qs}$ ,

(3.5) $$\begin{eqnarray}\widehat{h}_{C_{\unicode[STIX]{x0394}p}}=\frac{\widehat{C}_{\unicode[STIX]{x0394}p,dyn}}{\widehat{C}_{\unicode[STIX]{x0394}p,qs}}.\end{eqnarray}$$

The quasisteady value $\widehat{C}_{\unicode[STIX]{x0394}p,qs}$ is obtained by

(3.6) $$\begin{eqnarray}\widehat{C}_{\unicode[STIX]{x0394}p,qs}=\frac{\unicode[STIX]{x2202}C_{\unicode[STIX]{x0394}p,qs}}{\unicode[STIX]{x2202}\unicode[STIX]{x1D6FC}}\cdot \widehat{\unicode[STIX]{x1D6FC}}_{p},\end{eqnarray}$$

where $\unicode[STIX]{x2202}C_{\unicode[STIX]{x0394}p,qs}/\unicode[STIX]{x2202}\unicode[STIX]{x1D6FC}$ is the slope of the coefficient of the pressure difference in the region of attached flow, derived from quasisteady reference measurements, and $\widehat{\unicode[STIX]{x1D6FC}}_{p}$ is the amplitude of the pitching angle of attack. In the dynamic experiments, a purely sinusoidal excitation is realized. This corresponds to

(3.7) $$\begin{eqnarray}\displaystyle \text{Re}(C_{\unicode[STIX]{x0394}p,dyn}) & = & \displaystyle \text{Re}(\widehat{C}_{\unicode[STIX]{x0394}p,dyn}\text{e}^{(\text{i}\unicode[STIX]{x1D714}t-\unicode[STIX]{x1D711})})=\widehat{C}_{\unicode[STIX]{x0394}p,dyn}\cos (\unicode[STIX]{x1D714}t-\unicode[STIX]{x1D711})\nonumber\\ \displaystyle & = & \displaystyle \widehat{C}_{\unicode[STIX]{x0394}p,dyn}\sin (90^{\circ }-(\unicode[STIX]{x1D714}t-\unicode[STIX]{x1D711})).\end{eqnarray}$$

The amplitude $\widehat{C}_{\unicode[STIX]{x0394}p,dyn}$ and phase $\unicode[STIX]{x1D711}$ with respect to the pitching angle of attack $\unicode[STIX]{x1D6FC}_{p}$ are directly derived from phase averaged dynamic pressure measurements.

3.2 Sinusoidal vertical gust

In this experimental set-up, the lift force is directly accessible, and the experimental transfer function $h_{L}$ is

(3.8) $$\begin{eqnarray}h_{L}=\widehat{h}_{L}\text{e}^{-\text{i}\unicode[STIX]{x1D711}}.\end{eqnarray}$$

Here, $h_{L}$ corresponds to the Sears function. As above, the magnitude $\widehat{h}_{L}$ relates the dynamic lift amplitude to the corresponding quasisteady lift amplitude,

(3.9) $$\begin{eqnarray}\widehat{h}_{L}=\frac{\widehat{L}_{dyn}}{\widehat{L}_{qs}}.\end{eqnarray}$$

The quasisteady lift amplitude $\widehat{L}_{qs}$ is the product of the quasisteady lift curve slope and the amplitude of the oncoming gust,

(3.10) $$\begin{eqnarray}\widehat{L}_{qs}=\frac{\unicode[STIX]{x2202}L_{qs}}{\unicode[STIX]{x2202}\unicode[STIX]{x1D6FC}}\cdot \widehat{\unicode[STIX]{x1D6FC}}_{g}.\end{eqnarray}$$

The amplitude of the dynamic lift $\widehat{L}_{dyn}$ and phase $\unicode[STIX]{x1D711}$ are derived from phase averaged dynamic lift measurements, such that

(3.11) $$\begin{eqnarray}\displaystyle \text{Re}(L_{dyn}) & = & \displaystyle \text{Re}(\widehat{L}_{dyn}\text{e}^{(\text{i}\unicode[STIX]{x1D714}t-\unicode[STIX]{x1D711})})=\widehat{L}_{dyn}\cos (\unicode[STIX]{x1D714}t-\unicode[STIX]{x1D711})\nonumber\\ \displaystyle & = & \displaystyle \widehat{L}_{dyn}\sin (90^{\circ }-(\unicode[STIX]{x1D714}t-\unicode[STIX]{x1D711})).\end{eqnarray}$$

As the gust travels over the airfoil with $U_{\infty }$ , a reference point for the determination of the phase $\unicode[STIX]{x1D711}$ between the gust angle $\unicode[STIX]{x1D6FC}_{g}$ and the dynamic lift response $L_{dyn}$ has to be chosen. In the experiments, this reference point is set at the airfoil leading edge, as the preliminarily performed hotwire measurements are taken at this position. In the derivation of first-order transfer functions, the phase reference is traditionally set at the airfoil mid chord. This is accounted for by an additional phase shift of the Sears function.

4 Steady results

Figure 3 shows steady reference measurements of the coefficient of the pressure difference $C_{\unicode[STIX]{x0394}p,qs}$ (oscillating airfoil experiment) and the lift $L_{qs}$ (sinusoidal vertical gust experiment), from which the quasisteady responses are derived. Both measured variables have a similar dependence on the mean angle of attack $\unicode[STIX]{x1D6FC}_{m}$ . This confirms the assumption that the coefficient of the pressure difference $C_{\unicode[STIX]{x0394}p}$ at the airfoil leading edge is a good estimator for the total lift $L$ . In the region of attached flow, $C_{\unicode[STIX]{x0394}p}$ and $L$ are proportional to $\unicode[STIX]{x1D6FC}_{m}$ . This is the angle of attack range in which first-order transfer functions are supposed to be valid.

Figure 3. Quasisteady reference measurements of the lift $L_{qs}$ (sinusoidal vertical gust experiment) and the coefficient of the pressure difference $C_{\unicode[STIX]{x0394}p,qs}$ (oscillating airfoil experiment), exemplarily shown for $U_{\infty }=15~\text{m}~\text{s}^{-1}$ . The region of attached flow is highlighted with a grey background.

5 Unsteady results: oscillating airfoil

Figure 4 shows the influence of the mean angle of attack $\unicode[STIX]{x1D6FC}_{m}$ (figure 4 a) and the pitching amplitude $\widehat{\unicode[STIX]{x1D6FC}}_{p}$ (figure 4 b) on the experimental transfer function of the pressure difference $\widehat{h}_{C_{\unicode[STIX]{x0394}p}}$ of the pitching airfoil. Experimental values are compared with a first-order solution given by Mateescu & Abdo (Reference Mateescu and Abdo2003), which integrally yields the Theodorsen function.

Figure 4. The magnitude $\widehat{h}_{C_{\unicode[STIX]{x0394}p}}$ of the transfer function of the coefficient of the pressure difference $C_{\unicode[STIX]{x0394}p}$ . The airfoil is pitched continuously around its leading edge at the indicated mean angle of attack $\unicode[STIX]{x1D6FC}_{m}$ and pitch amplitude $\widehat{\unicode[STIX]{x1D6FC}}_{p}$ . An inflow velocity of $U_{\infty }=15~\text{m}~\text{s}^{-1}$ and pitching frequencies in the range $1~\text{Hz}<f<12~\text{Hz}$ yield reduced frequencies in the range $0.025<k<0.3$ . Experimental values, represented by marker symbols, are compared with a first-order solution given by Mateescu and Abdo. (a) Variation of $\unicode[STIX]{x1D6FC}_{m}$ ; $\widehat{\unicode[STIX]{x1D6FC}}_{p}=4^{\circ }$ . (b) Variation of $\widehat{\unicode[STIX]{x1D6FC}}_{p}$ ; $\unicode[STIX]{x1D6FC}_{m}=2^{\circ }$ .

A significant dependence of the experimental transfer function on the mean angle of attack $\unicode[STIX]{x1D6FC}_{m}$ is observed. At $\unicode[STIX]{x1D6FC}_{m}=-4^{\circ }$ , the experimental and theoretical values agree best. This is the angle of attack that produces zero mean pressure difference $C_{\unicode[STIX]{x0394}p,qs}=0$ under quasisteady conditions. With increasing $\unicode[STIX]{x1D6FC}_{m}$ , the difference between the experimental and theoretical values increases. At the highest mean angle of attack of $\unicode[STIX]{x1D6FC}_{m}=+8^{\circ }$ , significant differences are observed between the experimental values and the theoretical predictions. At this mean angle of attack, the total angle of attack $\unicode[STIX]{x1D6FC}=\unicode[STIX]{x1D6FC}_{m}+\unicode[STIX]{x1D6FC}_{p}$ exceeds the static stall angle during every pitch cycle. The magnitudes $\widehat{h}_{C_{\unicode[STIX]{x0394}p}}$ of the experimental and theoretical values show opposite frequency dependence and approach different values for $k\rightarrow 0$ .

From figure 4(b), we find that the pitching amplitude $\widehat{\unicode[STIX]{x1D6FC}}_{p}$ has no influence on the transfer function. This is in accordance with linear theory and in good agreement with the findings of Halfman (Reference Halfman1952) for a harmonically pitching NACA 0012 airfoil.

6 Unsteady results: sinusoidal vertical gust

Figure 5 shows the influence of the mean angle of attack $\unicode[STIX]{x1D6FC}_{m}$ (figure 5 a) and the gust amplitude $\widehat{\unicode[STIX]{x1D6FC}}_{g}$ (figure 5 b) on the magnitude of the experimental transfer function of the lift $\widehat{h}_{L}$ of an airfoil encountering a sinusoidal vertical gust. Experimental values are compared with the magnitude of the Sears function.

Figure 5. The magnitude $\widehat{h}_{L}$ of the transfer function of the lift  $L$ . The airfoil is submitted to a fluctuating inflow of gust amplitude $\widehat{\unicode[STIX]{x1D6FC}}_{g}$ with a gust frequency of $f=5~\text{Hz}$ . The free stream velocity is varied in the range $10~\text{m}~\text{s}^{-1}<U_{\infty }<25~\text{m}~\text{s}^{-1}$ , yielding different reduced frequencies  $k$ . Experimental values, indicated by marker symbols, are compared with the Sears function. (a) Variation of $\unicode[STIX]{x1D6FC}_{m}$ ; $\widehat{\unicode[STIX]{x1D6FC}}_{g}=2.7^{\circ }$ . (b) Variation of $\widehat{\unicode[STIX]{x1D6FC}}_{g}$ ; $\unicode[STIX]{x1D6FC}_{m}=2^{\circ }$ .

The experimental $\widehat{h}_{L}$ increases with increasing reduced frequency $k$ , while the Sears function predicts the inverse. This behaviour is observed for all parameter combinations, regardless of whether the total angle of attack $\unicode[STIX]{x1D6FC}=\unicode[STIX]{x1D6FC}_{m}+\unicode[STIX]{x1D6FC}_{g}$ stays completely in the attached flow region or exceeds the static stall angle cyclically. The mean angle of attack $\unicode[STIX]{x1D6FC}_{m}$ and the gust amplitude $\widehat{\unicode[STIX]{x1D6FC}}_{g}$ have no significant influence on  $\widehat{h}_{L}$ .

For $\unicode[STIX]{x1D6FC}_{m}=2^{\circ }$ and $\widehat{\unicode[STIX]{x1D6FC}}_{g}=5^{\circ }$ , additional experiments are carried out: the reduced frequency of the oncoming gust is varied by changing the gust frequency $2~\text{Hz}<f<6~\text{Hz}$ in steps of $\unicode[STIX]{x0394}f=1~\text{Hz}$ at five different free stream velocity values $U_{\infty }$ . Figure 6 shows the magnitude $\widehat{h}_{L}$ of the experimental transfer function for these parameter combinations. The experimental values of $\widehat{h}_{L}$ fall in line, regardless of whether $U_{\infty }$ or $f$ is varied to change the reduced frequency $k$ . This indicates that $k$ is the right parameter to describe the problem. The Sears function fails to capture the experimental values in terms of frequency dependence and limiting values. A different approach to model the unsteady lift response of an airfoil encountering a sinusoidal vertical gust as a function of $k$ is provided by Atassi (Reference Atassi1984). Atassi’s theory is nonlinear in the steady flow and linear in the dynamic perturbation. For an airfoil with zero thickness, Atassi (Reference Atassi1984) separates the effects of mean angle of attack, camber and transverse gust number, and shows their contribution to the total response function, which is obtained as a sum of the individual effects. Employing Atassi’s model with the parameters corresponding to the experimental set-up ( $\unicode[STIX]{x1D6FC}_{m}=2^{\circ }$ , camber $\unicode[STIX]{x1D702}=3.5\,\%$ , transverse wavenumber corresponding to wind tunnel width) yields the presented plots.

Figure 6. The magnitude $\widehat{h}_{L}$ of the transfer function of the lift $L$ . At $\unicode[STIX]{x1D6FC}_{m}=2^{\circ }$ , the airfoil is submitted to a fluctuating inflow with a gust amplitude of $\widehat{\unicode[STIX]{x1D6FC}}_{g}=5.5^{\circ }$ . The reduced frequency $k$ is varied by varying the gust frequency $f$ in the range $2~\text{Hz}<f<6~\text{Hz}$ at constant free stream velocity $10~\text{m}~\text{s}^{-1}<U_{\infty }<20~\text{m}~\text{s}^{-1}$ . Experimental values, indicated by marker symbols, are compared with the first-order solution by Sears (Reference Sears1938) and a second-order solution by Atassi (Reference Atassi1984).

Contrary to Sears’ first-order transfer function, which does not capture the experimental results, Atassi’s solution captures the experimental data well in terms of frequency dependence and limiting values.

7 Discussion and conclusions

In the case of the oscillating airfoil (Theodorsen function), experimental results agree reasonably well with theory if the airfoil is oscillated around small mean angles of attack. The unsteady load response is independent of the perturbation amplitude, which is in good agreement with theory. With increasing mean angle of attack, the frequency dependence is inverted and the limiting value for $k\rightarrow 0$ falls below 1. It can be concluded, that the Theodorsen function is a good approximation of the unsteady load response of an oscillating airfoil, if the assumptions leading to thin-airfoil theory (small mean angle of attack, attached flow) are fulfilled.

In the case of a fixed airfoil encountering a sinusoidal vertical gust (Sears function), the experimental results are not in agreement with the theoretical predictions. The experimental values are uninfluenced by the gust amplitude and the mean angle of attack. It is also irrelevant whether the reduced frequency is changed by changing the gust frequency or the inflow velocity. For all investigated parameter combinations, the unsteady lift amplitude increases with increasing reduced frequency, while the Sears function predicts the inverse. All experimentally derived transfer functions approach limiting values $h_{L}(k\rightarrow 0)<1$ , while the quasisteady value of the Sears function is $S(k=0)=1$ . The observed discrepancy between experimental and theoretic results is very similar to the observations for the oscillating airfoil under high mean angles of attack. The Sears function appears to be more sensitive to the physical reason that causes experimental values to deviate from the Theodorsen function at high mean angles of attack. This physical reason might be the distortion of the steady velocity field by the presence of an airfoil. Assumptions comprised in first-order theory allow the superposition of partial solutions to obtain a global solution of the flow field. This entails that the oncoming velocity perturbation is completely uninfluenced by the presence of the airfoil. In the experiment, we found this approximation to be violated when we tried to measure the fluctuating angle of attack at the airfoil leading edge with the airfoil present in the test section. A theory accounting for the presence of the airfoil by a distortion of the steady flow field is the second-order closed-form transfer function by Atassi (Reference Atassi1984). Experimental results show good agreement with this second-order theory.

It can be concluded that for the present experimental set-up the Sears functions is not a suitable tool to approximate the unsteady lift response, although the experimental set-up meets the assumptions usually required when applying thin-airfoil theory. Hence, the Sears function should be applied with caution. The Sears function still lacks a systematic verification in terms of frequency dependence. In future work, experiments with flat thin plates should be carried out, further approaching thin-airfoil assumptions. For flow situations corresponding to the current set-up (airfoil with thickness and camber), the second-order transfer function by Atassi appears to be a more appropriate approach.