Wendy Okolo

Application of Sweet Spot Determination to a Conventional Pair of Aircraft

of the trail aircraft at all points in the grid. The location of highest lift-to-drag ratio is then designated as the sweet spot based on the static simulation. A dynamic simulation is then used to determine if the sweet spot remains the same after considering the eects of trimming the aircraft. The trail KC-135R thrust required, along with the magnitudes of its control eectors, were investigated in the dynamic study, using the same grid as in the static case. The metric for sweet spot location in the dynamic case is the location of the least thrust required for the trail KC-135R. The results showed that the location of the sweet spot remains the same as that obtained using the static simulation. The eect on the static sweet spot, of varying the mass of the leader was also studied. It was observed that increasing the mass of the leading KC-135R aircraft aected only the aerodynamics of the trail aircraft and not the location of the sweet spot.

Effect of Trail Aircraft Trim on Optimum Location in Formation Flight

Aircraft flight generates vortices that induce nonuniform wind distribution in their wake. A trailing/follower aircraft will experience induced wind components and gradients with various magnitudes and directions, depending on its location relative to the leader. This paper explores two methods of determining the relative location for optimum formation flight, termed the sweet spot. The relative location with the highest lift-to-drag ratio on the follower is denoted as the static sweet spot. In the second method, the trail aircraft is trimmed by adjusting the thrust and control surfaces to maintain its commanded position relative to the lead. The relative location requiring the least thrust is then assigned as the dynamic sweet spot. The results showed that, depending on the trail aircraft size, the static sweet spot might differ from the dynamic sweet spot. The effect of the leader weight and follower size on both static and dynamic sweet spot was also studied. It was discovered that the static and dynam...

Determination of Sweet Spot for Trailing Aircraft in Formation Flight

of the EQ-II at all points in the grid. A dynamic simulation was then used to determine if the sweet spot remained the same after considering the eects of trimming the aircraft. The EQ-II thrust required, along with the magnitudes of its control eectors were investigated in the dynamic study in the same grid as the static case. The results showed that the sweet spot changes and the optimal location to place the EQ-II diers from that obtained using the static simulation. The eect of the leader mass and follower size on the sweet spot was also studied. It was observed that increasing the mass of the leading KC-135 aected the aerodynamics of the follower but not the sweet spot location. It was also seen that changing the size of the follower changed both the aerodynamics of the follower and the location of the sweet spot.

Modified Study of Trail Aircraft Trim Effect on Sweet Spot in Formation Flight

Aircraft flight generates vortices that induce nonuniform wind distribution in their wake. A trailing/follower aircraft will experience induced wind components and gradients with various magnitudes and directions, depending on its location relative to the leader. This paper explores two methods of determining the relative location for optimum formation flight, termed the sweet spot. The relative location with the highest lift-to-drag ratio on the follower is denoted as the static sweet spot. In the second method, the trail aircraft is trimmed by adjusting the thrust and control surfaces to maintain its commanded position relative to the lead. The relative location requiring the least thrust is then assigned as the dynamic sweet spot. The results showed that depending on the trail aircraft size, the static sweet spot might differ from the dynamic sweet spot. The effect of the leader weight and follower size on both static and dynamic sweet spot was also studied. It was discovered that the static and dynamic sweet spot location changed when the size of the trail aircraft was modified. It was also observed that the static sweet spot remained the same but the dynamic sweet spot changed when the lead aircraft weight was modified. This study, as opposed to the previous work of the authors, utilizes a different and improved aerodynamic coupling technique to model the effect of the lead on the trail aircraft.

A modified analysis of alternate lateral trimming methods for flying wing aircraft at sweet spot in formation flight

In the wake of an aircraft in flight, the trailing vortices generate a nonuniform wind field. Another aircraft flying within the nonuniform wind field experiences varying aerodynamic forces and moments depending on its location relative to the lead aircraft. As a result, there is an optimal location, termed the ”sweet spot”, within the nonuniform wind field for the trail aircraft to have the largest lift to drag ratio. At this sweet spot, the trail aircraft should have the largest formation benefit in terms of the largest thrust reduction. However, at the sweet spot, the trail aircraft is also subject to aerodynamic moments induced by the nonuniform wind field. This requires additional control surface deflections to trim the aircraft at the sweet spot. Since control surface deflections induce drag, this causes lower thrust reduction or may even cause higher thrust requirement than that of solo flight. To obtain the full benefits of formation flight, this paper investigates two alternative trim mechanisms that generate moments to trim without causing additional drag: (i)internal fuel transfer between fuel tanks primarily to generate rolling moment and (ii) differential thrust between the left and right engines to generate yawing moment. Simulation results showed that the full benefit of formation flight can be obtained if the combination of these two alternative trim mechanisms are employed. This study utilizes a different and improved aerodynamic coupling technique to model the effect of the lead on the trail aircraft as compared to the previous work of the authors.

Ride quality within trail aircraft in formation flight

This paper investigates the ride quality for persons located within a trail aircraft flying in formation with a lead to obtain fuel savings. As the trail aircraft flies at the optimum location with the largest fuel-saving benefits of formation, also termed the ”sweet spot”, it is subjected to a non-uniform induced wind field generated by the wingtip vortices of the lead. Different trail aircraft are utilized and analyses of ride quality/comfort levels are done using ISO 2631-1 standards for persons located at various points within the trail aircraft. It is shown that if a trail aircraft flies at the sweet spot and is subjected to the non-uniform induced wind field and/or atmospheric turbulence, the comfort levels are comparable to solo flight. The performance of formation flight is not degraded once ride quality is implemented as a metric in the formation performance and there is no additional detrimental impact to a person on board a trail aircraft in formation with a lead.

Development of an aerodynamic model for a delta-wing equivalent model II (EQ-II) aircraft

An aerodynamic model is developed for an aircraft to represent the performance and maneuvering capabilities of a delta-wing subsonic long range tailless aircraft. This aerodynamic model is implemented into an integrated simulation environment for the purpose of aerial refueling and formation flight simulation. The aerodynamic coefficient data of the Equivalent Model II (EQ-II) aircraft and damping derivative data were estimated using vortex lattice methods with empirical corrections for the EQ-II configuration. Control surface effectiveness of the EQ-II which utilizes clamshells and elevons for pitch, roll, and yaw control, was also estimated using the same methods. This paper presents the aerodynamic force and moment coefficients in the form of polynomial expressions fitted into these data points.

Effect of trail aircraft size on sweet spot location for a conventional aircraft pair in formation

This paper studies the optimum fuel-saving locations for a pair of different-sized conventional aircraft flying in formation. The optimum location is studied based on methods previously defined by the authors, a static and a dynamic study. The static sweet spot, is the relative location of the trail aircraft where the lift-to-drag ratio is the highest and the dynamic sweet spot is the relative location with the least thrust required for the trail. It was seen that for a smaller conventional trailing aircraft, the static and dynamic sweet spots coincide but for a larger conventional trail, the two sweet spots differ. This is in agreement with prior work done by the authors using different-sized unconventional deltawing trailing aircraft. The results of this study lead to the conclusion that the relative sizes of the aircraft in the formation are the main factor on whether or not the location of highest lift-to-drag matches the location with the least required thrust for the trail aircraft.

Aircraft Input Prediction in the Presence of Spatially Varying Wind Field

This paper presents a method of input prediction for an aircraft flying in spatially and/or temporally varying wind field. Input prediction is done using inverse simulation to compute the required control variables (control surface deflections and thrust level) for an aircraft to fly through a prescribed trajectory. Various simulation cases are presented to demonstrate the feasibility of input prediction method and the importance of including wind field information in inverse simulations.

Benefits of Formation Flight of Extended Duration Considering Fuel Burn

This paper investigates the effect of fuel consumption by a lead aircraft on the benefits of flying in formation. As an aircraft flies, it generates wingtip vortices that a trail aircraft, within the wake, can utilize for fuel-saving benefits. The strength of the wingtip vortices generated by the lead depend on the weight of the lead aircraft. Thus, as the weight of the lead decreases due to fuel consumption, the strength of the wake vortices and corresponding fuel savings for the trail aircraft decrease. To analyze this effect, formations of extended duration are simulated, in which fuel consumption leads to significant weight reductions for the lead and the trail aircraft. This paper confirms that as the weight of the lead aircraft decreases, the benefit to the trail aircraft decreases. This decrease is not significant enough to nullify the fuel-saving benefits of extended-duration formations even in turbulent atmospheric conditions.