A key design requirement for bridled kites is longitudinal static stability . Stability is evaluated by considering the pitching moment about the bridle (tether attachment) point (B), which acts as the effective centre of rotation for a kite constrained by a tensioned tether (see Fig. , which illustrates the geometry of symmetric actuation). Longitudinal static stability implies the existence of a trim angle of attack, defined as the wing angle of attack at which the pitching moment around the bridle point vanishes. Small perturbations from this equilibrium generate restoring moments that return the kite towards the trim state. At trim, the resultant wing force is collinear with the force at the bridle point Fb, comprised of the tether force and any loads transmitted by a kite control unit (KCU), if present.

For a massless kite, the resultant wing force reduces to the aerodynamic force applied at the centre of pressure (CP). When mass is included, the same equilibrium condition holds but with a slightly different trim angle of attack such that the combined aerodynamic and gravitational forces remain aligned with the bridle resultant.

Numerical simulations of symmetric kites in virtual wind tunnels provide evidence of longitudinal static stability, consistently exhibiting convergence towards a unique trim angle of attack at which the net moment about the bridle point vanishes . Experimental measurements further confirm that the angle of attack remains relatively constant during flight .

The trim condition can be expressed geometrically by introducing the tow angle λb, defined as the angle between the front bridle line and the line from the bridle point (B) to the aerodynamic centre of pressure (CP). In the present formulation, variations in the centre of pressure near the trim point are assumed to be negligible, implying that, for a fixed depower setting, λb varies only weakly with angle of attack. This assumption is consistent with experimental observations showing that, for leading-edge inflatable (LEI) kites, the tension distribution between front and rear bridle lines remains approximately constant for a fixed depower setting .

To further substantiate this assumption, Fig. 3 plots the tow angle λb against the wing angle of attack αw for the TU Delft V3 kite, computed with the vortex step method (VSM), a lifting-line aerodynamic model tailored to soft kites . Shaded bands indicate the measured reel-out (powered) and reel-in (depowered) ranges . Across both operational regimes, λb varies by less than 1°. Thus, for a fixed depower setting, λb may be treated as approximately constant. Nevertheless, this assumption needs to be re-evaluated for each specific kite design.

Figure  also shows an apparent discontinuity near the zero-lift angle of attack, where the centre of pressure becomes mathematically undefined. As this angle is approached, the centre of pressure shifts aft, producing a nose-down moment that may lead to a front stall. This behaviour is not captured in the current model, as the kite is assumed to operate outside this regime.

To modify the mean trim angle during operation, the kite relies on depower control. Increasing the geometric depower angle θd pitches the wing relative to the front bridle lines (equivalent to increasing relative rear-line length) and reduces the trim angle of attack (see Fig. ). This reduction in angle of attack lowers both the lift-to-drag ratio and the resultant aerodynamic force, leading to reduced tether tension and tangential flight speed. As a consequence of the reduced tangential flight speed, the bridle angle of attack increases. The configuration with θd=0° defines a reference trim state in which the front bridle line is perpendicular to the local chord line, typical for powered LEI kites.

With the assumptions stated above – namely, a constant tow angle and geometric depower actuation – the angle between the resultant force at the bridle point B and the wing θb remains constant for a given depower configuration. The wing angle of attack αw can therefore be related to the bridle angle of attack αb by 1αw=αb-θb, where θb is defined as the sum of the tow angle λb and the depower angle θd, 2θb=θd+λb.

While symmetric actuation is used to control the trim angle and flight speed, asymmetric actuation is employed to generate turning manoeuvres by inducing lateral forces and moments. To initiate a turn, a force must be generated perpendicular to both the tether direction and the kite’s instantaneous velocity vector. This is achieved by rotating the aerodynamic lift vector towards the centre of the turn. For rigid or semi-rigid wings, this is typically accomplished by physically rolling the wing with respect to the tether axis . In contrast, soft kites often achieve this through a combination of body roll and asymmetric deformation .

Most bridled kites are designed to be directionally stable, i.e. they generate a restoring yawing moment in response to a sideslip . Unlike free-flying aircraft, a wing geometry that would appear unstable about its centre of mass can still be stable once tethered – provided the bridle point is positioned appropriately. In arched kites, this typically requires placing the bridle further forward, which ensures that the aerodynamic force distribution produces a restoring yawing moment about the bridle point in response to a sideslip.

In asymmetrically deformed kites, the steering input increases the angle of attack on the inner side of the wing relative to the outer side, generating both a side force and a roll moment. This asymmetry also produces an initial yawing moment that starts the turn. As the kite moves laterally, a sideslip develops. For directionally stable kites, the resulting sideslip produces a yawing moment that maintains the turn. For LEI kites, sideslip angles up to about 5° have been observed for Kitepower’s V9 . By contrast, in purely roll-driven steering, the roll induces a sideslip angle, which then generates a yawing moment via directional stability.

As the kite turns, the outer wing tip experiences a higher apparent velocity and lower effective angle of attack, while the inner wing tip experiences the opposite . This differential shortens the moment arm and produces a yaw-damping effect that resists further rotation, leading to the observed near-linear relation between steering input and yaw rate : 3ψ˙=kusva, where ψ˙ is the wing yaw rate, us is the dimensionless steering input (ranging from -1 to 1), va is the apparent wind speed at the kite, and k is an empirical gain. The good agreement with this simplified turn-rate law indicates a quasi-steady yaw response, where the yawing moment equilibrates rapidly and the yaw rate scales proportionally with the product of apparent wind speed and steering input.

The motion of the kite is described using the course reference frame (C-frame), illustrated in Fig. , which provides a natural decomposition of the velocity into radial and tangential components. The C-frame origin is located at the ground station, with the unit vectors eχ, en, and er corresponding to the course, normal, and radial directions, respectively.

The tangential plane, denoted as τ, contains eχ and en, and is perpendicular to er. The course angle χ defines the orientation of eχ within this plane, with χ=0 corresponding to motion directly towards the zenith .

A complete description of the additional reference frames and coordinate transformations is provided in Appendix .

The translational motion of the kite can be described using Newton's second law of motion, which states that the absolute acceleration d2rkdt2 of a point k is equal to the sum of all forces acting upon k, divided by its mass m: 4d2rkdt2=∑Fkm.

When analysed in a rotating reference frame, additional terms appear in the acceleration, commonly referred to as fictitious or inertial forces. Below, these quantities are derived in the chosen C-frame.

The external forces acting on the kite are the aerodynamic force Fa, the weight of the kite Fg, and the tether force Ft. These forces must be expressed in terms of the C-frame in accordance with the previous section.

Having defined the absolute acceleration and the external forces in the C-frame, the translational dynamics of a tethered kite follow from Newton’s second law: 28md2rkdt2=Fext=Fa+Ft+Fg.

The model is formulated as a system of differential-algebraic equations (DAEs): 29x˙=f(x,z,u)=vrvτcos⁡χrvτsin⁡χrcos⁡βχ˙v˙rv˙τ300=g(x,z,u)=md2rkdt2-Fext.

Here, x, z, and u denote the differential states, algebraic states, and control inputs, respectively. 31x=rβϕχvrvτ32z=v˙τχ˙Ft,g33u=v˙rusup.

In this work, us is the steering input (actuation that primarily sets the aerodynamic roll and thereby the course rate χ˙), and up is the depower input (actuation that changes the geometric pitch θb and thus affects the angle of attack αw).

To illustrate the governing balance in its simplest form, we first consider an idealised case in which the kite is positioned at the centre of the wind window (ϕ=0, β=0), with no tether dynamics included. In this scenario, the tangential acceleration v˙τ depends only on the tangential speed vτ, motion direction χ, reeling speed vr, and control inputs (depower up and steering us). The governing equation reduces to 34mv˙τ=12ρSvaCL(αw)cos⁡ϕa(vw-vr)-CD(αw)vτ-mgcos⁡χ.

The same interpretation applies at any position, although the explicit form of the aerodynamic terms is more complex.

Plotting v˙τ as a function of vτ in Fig.  shows that it typically crosses zero at two points, due to the nonlinear dependence of the aerodynamic forces on the angle of attack. These crossings correspond to candidate quasi-steady equilibria defined by 35v˙τ=0. However, only the equilibrium that satisfies the local stability criterion 36∂v˙τ∂vτ<0 is physically relevant. At this stable equilibrium, any perturbation in vτ is counteracted by the aerodynamic forces. An increase in vτ reduces the angle of attack, rotating the resultant force rearward and producing a decelerating tendency. A decrease in vτ has the opposite effect.

The effect of gravity appears as a vertical offset in Fig. . When the kite ascends (χ=0°), the gravitational component opposes the motion. To maintain equilibrium, the aerodynamic force must rotate forward, requiring an increase in the trim angle of attack. Conversely, during descent (χ=180°), gravity assists the motion, allowing the force vector to rotate backward and reducing the required trim angle. Because the trim angle of attack and tangential speed are linked by the aerodynamic equilibrium, a higher αw corresponds to a lower vτ, and vice versa. Consequently, changes in the gravitational component along the course lead to different equilibrium speeds, even under the quasi-steady assumption. The characteristic acceleration and deceleration in flight patterns typically attributed to gravity are thus captured implicitly within the quasi-steady solution, without the need for explicit modelling of dynamic inertial effects.

These observations support an interpretation of the kite dynamics as continuously converging towards a moving quasi-steady state, defined by the instantaneous position, motion direction, and control inputs. When aerodynamic forces dominate and the wing loading (m/S) is sufficiently small, this convergence is rapid enough to approximate the motion as a sequence of quasi-steady states. This assumption is further examined in Sect. , where dynamic and quasi-steady simulations are compared across a range of wing loadings.

This treatment differs from earlier implementations, where inertial accelerations were sometimes omitted entirely , or where tangential and radial accelerations were assumed to be negligible compared to aerodynamic contributions . In contrast, the present formulation retains the inertial terms and defines the quasi-steady equilibrium through the condition of zero tangential acceleration, corresponding to the trimmed state of the kite.

Following the definition of quasi-steady equilibrium, the dynamic DAE system in Eq. () can be reduced by eliminating the differential state associated with tangential acceleration, v˙τ. The resulting state vectors are 37xqs=rβϕχvr38zqs=vτχ˙Ft,g39uqs=v˙rusup, where xqs contains the remaining position and orientation variables; zqs indicates the algebraic variables associated with tangential speed, course rate, and tether force; and uqs is the control inputs.

The reduced quasi-steady formulation is thus expressed as a semi-explicit DAE system of index 1: 40dxqsdt=f(xqs,zqs,uqs)0=g(xqs,zqs,uqs), where f describes the reduced differential kinematics and g enforces instantaneous force balance.

The quasi-steady formulation is independent of the time history: at each instant, the state is obtained from the algebraic force balance g(x,z,u)=0 at the current position and inputs. By contrast, the dynamic formulation is history dependent and must be solved as an initial-value problem.

Aerodynamic modelling of flexible kites remains one of the most challenging aspects of kite design. The arched geometry and extensive recirculation zones induced by the unconventional leading-edge inflatable (LEI) airfoils complicate accurate aerodynamic simulation. Recent wind tunnel experiments with the V3 kite have demonstrated that neither CFD simulations nor simplified models based on lifting-line theory can reliably reproduce the aerodynamic behaviour of these kites. In particular, both the magnitude and slope of the drag coefficient are consistently underestimated, suggesting that neither parasitic nor induced drag components are captured adequately by current modelling approaches . Moreover, these discrepancies do not yet account for structural deformations, which further increase the gap between simulation and reality. Experimental observations have revealed significant deformation of the three-dimensional kite geometry, including bending of the inflatable struts, which directly affects aerodynamic performance. Additional phenomena such as trailing edge flutter and bridle line vibrations also contribute to deviations in aerodynamic characteristics.

Given these complexities, purely simulation-based aerodynamic identification often fails to accurately represent the true behaviour of deformable kites. Consequently, a semi-empirical approach combining both simulation data and experimental measurements is adopted to achieve a more reliable aerodynamic characterisation.

Experimental data obtained during flight tests allow the estimation of the mean lift and drag coefficients corresponding to three representative flight states: (i) powered and straight flight during reel-out, (ii) powered and steered flight during reel-out, and (iii) depowered flight during reel-in. The baseline aerodynamic polars are first computed using the vortex step method, a lifting-line-based model tailored to soft kites , suitable for low aspect ratio and curved geometries. Second-order polynomial fits are applied to both the lift and drag curves. The model was recently validated in wind tunnel experiments using a rigidised model of the TU Delft V3 kite , showing good agreement across the operating range, although with a tendency to underestimate the drag coefficient. Subsequently, for each of the three representative states, a parasitic drag offset is added to the drag curve such that the corresponding CL–CD polar intersects the experimentally identified coefficients for that state (see Fig. ).

The lift coefficient is modelled as a second-order polynomial function of the angle of attack 41CL(αw)=CL,0+CL,1αw+CL,2αw2.

The drag coefficient incorporates both the baseline drag curve and empirical corrections to account for control-induced effects. It is expressed as 42CD(αw,up,us)=CD,0+CD,1αw+CD,2αw2+CD,pup+CD,sus, where up and us are the depower and steering control inputs, respectively. The terms CD,p and CD,s introduce multiplicative corrections to capture the increase in drag associated with depower and steering, while CD,0 accounts for a baseline parasitic drag offset, representing the drag observed in straight powered flight. The polynomials for the TU Delft V3 kite can be found in Appendix .

The angle between the resultant bridle force and the wing θb, which effectively sets the trim angle of attack, is estimated separately for reel-out and reel-in. In each phase, θb is chosen such that, for a massless kite, the resulting lift coefficient matches the mean lift coefficient estimated in that phase.

Finally, the control-induced aerodynamic roll angle ϕa,w is empirically characterised as a linear function of the steering input us, based on flight test data: 43ϕa,w=kϕ,sus.

The resulting modified polars incorporate both the baseline aerodynamic behaviour and empirical corrections derived from flight tests, effectively accounting for the drag contributions of the bridle lines, KCU, and onboard turbine, used to power the KCU electronics. Similar correction strategies have been successfully employed in previous quasi-steady kite modelling studies , offering a practical compromise between model fidelity and computational tractability.

With the identified aerodynamic polars, assumed to be linearly dependent on steering and depower inputs, the quasi-steady model is used to retrace the force, tangential speed, and steering input required to sustain each measured state. This enables a direct comparison between the model predictions and experimental measurements at each point along the flown trajectory, under the assumption of instantaneous aerodynamic equilibrium.

Figure  shows segments of two representative flights, comparing measured and estimated tangential speed, tether force and steering input, as well as the pitch relative to the radial direction and bridle aerodynamic roll ϕa,b, against the corresponding pitch and roll relative to the radial direction calculated by the EKF , which employs a discretised tether model rather than the simplified model used here.

In the reel-out phase, the temporal response of the model is good, with the predicted peaks in tangential speed and tether force aligning closely with those measured. However, the estimated values appear noisier – particularly for the V9 kite – and some peaks are overestimated. The kite pitch with respect to the radial direction agrees well in both trend and magnitude with the estimations obtained from a discretised tether model. The roll is compared against the aerodynamic roll ϕa,b, which represents the effective rotation of the lift induced by KCU dynamics and tether direction. Although this quantity is not identical to the roll estimated by the EKF, the agreement in timing and order of magnitude indicates that the dominant roll response is well captured by the reduced-order model. Furthermore, the steering input us, which is directly associated with the steering-induced aerodynamic roll ϕa,w, shows a very similar temporal behaviour to the experimental input, indicating that the turn dynamics are correctly captured by the model.

For the V3 kite, which was equipped with a relatively large and heavy KCU, several states cannot be resolved in a quasi-steady manner – particularly during the lower part of the figure-eight, where the kite exits the turn and begins to climb. This explains the gaps observed in the corresponding model estimations. In these instances, no physical solution exists for the given measured state. The force balance equations yield no valid tangential speed or angle of attack, typically due to excessive inertial or gravitational loads that exceed what the aerodynamic force can support. As shown in Fig. , this corresponds to the absence of a zero crossing in the tangential acceleration. While the quasi-steady model fails under these conditions, the real kite continues the manoeuvre dynamically, as its inertia carries it through transient states that lie outside the quasi-steady trim envelope. Furthermore, wind estimation inaccuracies can increase the probability of encountering an infeasible state.

In the reel-in phase, the model reproduces the behaviour of the measured quantities reasonably well, provided that the depower setting is adjusted to yield a lift coefficient consistent with the values inferred from measurements. Under this condition, the magnitude variation of the tether force and tangential speed are in line with the measurements, although small discrepancies remain. For the V3 kite, the agreement in both roll and pitch with the EKF estimations is weaker, and consequently the steering input required by the model also shows larger deviations. This is partly attributed to inaccuracies in the tether model, which become more influential during reel-in, when fast turning manoeuvres are absent and KCU effects are less dominant.

The transition from reel-in to reel-out remains the most challenging phase for the model. In this regime, the predicted tether force often overshoots the measurements. These deviations arise from two main factors: the kite undergoes dynamic manoeuvres that violate the quasi-steady assumption, and the tether can exhibit significant sag under low tension, followed by a rapid transition to high tension that is not well captured by the simplified straight-line tether model. Together, these effects reduce the model’s accuracy during this phase. For the V9 kite, this behaviour appears at the beginning of the reel-out phase – immediately after transition – because of how the masks are defined, but it effectively corresponds to the first turn into reel-out.

The purpose of this comparison is to assess whether the overall behaviour and magnitude are consistent, rather than to achieve a direct point-by-point match, since the state variables used to reconstruct the quasi-steady equilibrium carry noise and inaccuracies. Moreover, the wind is not measured directly at the kite but either with lidar or estimated through an EKF, both of which introduce additional uncertainties.

The position of the kite within the wind window – that is, its azimuth and elevation relative to the wind direction – significantly influences the aerodynamic forces and resulting tangential velocity. As the kite moves away from the centre of the wind window, the component of the wind velocity perpendicular to the wing surface decreases. Consequently, the tangential speed vτ required to achieve a quasi-steady equilibrium (v˙τ=0) diminishes, since a lower apparent wind angle relative to the wing reduces the required flight speed to maintain the trim angle of attack.

This behaviour is illustrated in Fig. , which shows the non-dimensional tangential speed factor λ=vτ/vw as a function of the azimuth, elevation, and course angles, under the assumption of a constant course angle (χ˙=0).

As seen in Fig. a, the tangential speed decreases with the elevation of the kite; and as the elevation increases, the dependency on the course angle becomes greater, mostly due to the aerodynamic force getting closer to the weight. The tangential speed is maximal at χ=180°, where gravity assists the motion; and minimal at χ=0°, where it opposes it.

A similar dependency is observed with respect to the azimuth angle ϕ, where increasing misalignment reduces the tangential speed. The combined effect of azimuth and course angles shifts the location of maximum tangential speed. As shown in Fig. b, for ϕ=0°, the maximum occurs at χ=180°, but as ϕ increases, both the maximum and minimum shift towards χ=270°, where the kite points more directly into the centre of the wind window. This shift results from the interplay between the wind incidence angle and the tangential projection of gravity, which together influence the equilibrium speed.

The reeling speed plays a major role in determining both the tether force and the harvested power. It is well known that, for a simplified crosswind operation at the centre of the wind window and neglecting gravity, the optimal reeling speed is a fixed fraction of the wind speed, originally derived by to be vr=13vw. Extending this result to arbitrary positions within the wind window – while still neglecting gravity – the optimal reeling speed becomes dependent on both elevation and azimuth, and is given by 44vr,opt=vw3cos⁡ϕcos⁡β.

This positional dependency reflects the reduction in crosswind efficiency with increasing elevation β and off-centre azimuth ϕ.

These trends, now accounting for both gravitational effects and course angle, are illustrated in Fig. . The results show that maximum reeling speeds are obtained near χ=180°, where gravity assists the motion and increases tether force, whereas the optimal reeling factor decreases with increasing elevation or azimuth due to reduced tangential speed and diminished tether loading.

From Fig. , one can observe a consistent relationship between the optimal reeling speed and the corresponding tether force across different positions. This motivates the analytical derivation – under the assumption of quasi-steady flight and neglecting gravity – of a direct expression linking the two. Neglecting mass, the resultant tether force, can be expressed as 45Ft=12ρSCRva2, where CR=CL2+CD2, and the apparent wind speed va is given by triangle similarity with the aerodynamic force vector : 46va=vwcos⁡βcos⁡ϕ-vr1+CLCD2.

Substituting the optimal reeling speed from Eq. () into Eq. () yields va=2vr,opt1+CLCD2 and leads to the following position-independent relation between tether force and optimal reeling speed: 47Ft=2ρSCRvr,opt21+CLCD2.

This relation suggests a practical control strategy in which the winch reeling speed is regulated as a function of the measured tether force . Since Ft inherently captures the combined influence of wind speed and kite position, this enables an implicit adaptive reeling control scheme without the need for precise wind measurements or position-dependent logic.

The inclusion of gravitational effects alters the force equilibrium and shifts the aerodynamic trim, leading to deviations from the idealised relation in Eq. (). This displacement is illustrated in Fig. , where the optimal reeling speed is plotted as a function of tether tension for multiple positions and orientations in the wind window for different wind speeds. Nonetheless, for the wing loadings typical of soft kites, the deviation introduced by gravity remains relatively small, allowing the analytical relation in Eq. () to serve as an effective basis for reeling control.

It is important to note that while the analytical expression represents the instantaneous reeling speed that maximises power extraction, it does not necessarily correspond to the optimal reel-out speed over a full pumping cycle. The cycle-averaged optimum depends not only on the reel-out phase but also on the duration, dynamics, and efficiency of the reel-in phase. Consequently, an effective reeling strategy must take into account the full cycle for optimal power generation .

To analyse the system response along prescribed flight paths, the kite motion is parameterised using a scalar path coordinate s(t), which evolves in time. This formulation enables all state variables to be expressed as functions of s and its time derivatives, simplifying the comparison between dynamic and quasi-steady responses. The resulting velocity and acceleration components are derived analytically in terms of s, s˙, and s¨. The current parameterisation defines the kite trajectory on the wind window (elevation and azimuth) independently of its radial position, which makes it possible to specify the reeling strategy separately from the angular path. The complete formulation, including the path speed and kinematic derivatives in spherical coordinates, is provided in Appendix .

Two representative trajectories are considered for crosswind flight in the W-frame. The first corresponds to a circular path, whereas the second describes a Lissajous figure-eight. In both cases, the trajectory is parameterised by a shape parameter s and time t, allowing all state variables to be expressed as functions of t, s, its derivatives s˙ and s¨, the steering input us, and the tether force Ft,g. A constant reel-out speed is assumed for clarity of comparison between the dynamic responses: 48r(t)=r0+vrt.

The trajectories are defined as

Circular path:49β=βc+Δφ2sin⁡(s),ϕ=ϕc+Δφ2cos⁡(s).

Two integration schemes are applied. In the dynamic scheme, for each time step, the path acceleration s¨, the tether force Ft,g, and the steering input us are obtained by solving the force equilibrium given the current state (s,s˙) and are subsequently integrated to update s˙ and s. This is written as a differential-algebraic equation (DAE) system in semi-explicit form: 51ddtss˙=s˙s¨,0=g(s,s˙)︸x,(s¨,Ft,g,us)︸z, where the algebraic constraint g enforces instantaneous force balance along the prescribed trajectory.

In contrast, the quasi-steady scheme assumes that the tangential acceleration vanishes, i.e. v˙τ=0 such that s¨ need not be computed. In this case, only the path speed s˙ is obtained from the force equilibrium, and s is advanced using a single integration step. The system reduces to an algebraic-differential formulation: 52ddts=s˙,0=g(s)︸x,(s˙,Ft,g,us)︸z, where the algebraic equation determines the steady-state value of s˙ consistent with force equilibrium at each point along the trajectory.

Figure  compares dynamic, quasi-steady, and inertia-free simulations of a parameterised trajectory for two soft-kite configurations: the TU Delft V3 and the Kitepower V9. These systems represent typical soft-wing designs with moderate wing loading. The simulation setup reflects their real-world operation, with figure-of-eight trajectories, representative reeling speeds, and dimensions consistent with field-tested configurations. Both kite models correspond to systems used for validation in Sect. , and their aerodynamic and mass properties are summarised in Appendix .

The results in Fig.  show that for both the V3 and V9 soft kites, the quasi-steady approximation closely matches the dynamic simulation. For the V9 kite, the dynamic, quasi-steady, and inertia-free simulations are nearly indistinguishable in both mean values and time evolution, showing only a slight phase lag of the dynamic response relative to the quasi-steady and inertia-free results. For the V3 kite, the mean values of velocity and tether force remain comparable to those in the quasi-steady simulation (see Table ), but the temporal evolution exhibits larger deviations, with higher maximum speeds and a more damped tether-force behaviour. The dynamic simulation of the V3 also reveals stronger oscillations in the angle of attack, likely due to an oversized KCU, whereas the oscillations for the V9 remain below 3°. This difference is further reflected in the greater roll of the lift vector observed for the V3. Overall, the quasi-steady approximation reproduces the main dynamic behaviour of both kites with minor discrepancies in phase and amplitude, and with negligible differences in average power – below 1 % for both cases.