The novel aerodynamics of insect flight: applications to micro-air vehicles

The first appearance of winged insects is shrouded in the past, but they probably took to the air almost 350 million years ago (Wootton, 1981; Ellington, 1991a). Wingspans of the early fossils ranged from 10 to 710 mm, and the form of the wings suggests a variety of adaptations in flight style. The Protodonata, which were the ancestors of dragonflies, were among the early fliers; their wings were similar enough to modern forms to suggest comparable flight capabilities, although perhaps with less refinement. Through natural selection, the insects have been experimenting successfully with wings, kinematics, aerodynamics, control and sensory systems for hundreds of millions of years.

Much more recently, interest has developed in small autonomous flying vehicles, largely motived by the need for aerial reconnaissance robots inside buildings and confined spaces. Industry, commerce and the military have all identified potential roles for such micro-air vehicles (MAVs). Research on MAVs is primarily conducted by aerodynamic and robotic engineers who are attempting to improve the performance at small sizes of conventional fixed wings and rotary wings. However, there already exists a very successful design for intelligent MAVs with much better aerodynamic performance than conventional wings and rotors: the insects. When contemplating the design of small flying machines, therefore, we would be well advised to consider them.

There are some general, simplifying trends in insect evolution. For example, early insects had two pairs of wings, but most modern forms have either lost one pair or coupled the fore-and hindwings together into a single functional pair. This simplification is in stark contrast to the elaborate and idiosyncratic wing designs found in some insects: e.g. wing ornamentation and special motions for courtship and mating displays; thickening of the forewings into hard protective shells; modification of the hindwings of flies into distinctive sensory organs, the halteres. Such aerodynamic oddities are of little interest here. Small flying machines are in their infancy, and the purpose of this paper is to identify general-purpose designs that have survived the testbed of insect evolution. Furthermore, these designs should be reduced to their simplest features, such as only one pair of wings.

The smallest flying insects that have been studied weigh 20–30 μ g and the largest approximately 2–3 g. Over this 100 000-fold size range, the design is very close to isometric: wing area is proportional to m^2/3 on average, where m is body mass. Wingbeat frequency increases as size decreases, scaling as m^−1/4 (Dudley, 2000). There is very considerable scatter in such scaling relationships; individual species can compensate for a relatively small wing area, for example, by a higher wingbeat frequency. However, the general trends confirm that the insects do follow a basic pattern.

The wing motion in free flight has been described for insects with wingspans from approximately 1 to 100 mm, covering the wide range of Re discussed above. Most of the wing motions are rather similar and constitute a picture of ‘normal’ flight that is probably a good starting point for the design of insect-based flying machines. Other wing motions offer special advantages that might prove useful for some purposes. In general, the flapping motion is approximately confined to a ‘stroke plane’, which is at a nearly constant orientation with respect to the body for most insects.

Studies on bumblebees offer one of the most complete kinematic descriptions of free flight (Dudley and Ellington, 1990a,b; Cooper, 1993) and will be used to illustrate the main points of this section. Bumblebees vary considerably in size; I shall refer to an individual with a mass of 0.175 g, a wing length R of 13.2 mm, a wingbeat frequency n of 149 Hz and a wingbeat amplitude Φ of 114 °. Recent work on the large hawkmoth Manduca sexta provides an interesting comparison (Willmott and Ellington, 1997a,b); the individuals were more uniform in size, with masses of 1.6–2.0 g, R=51 mm, N=25–26 Hz and Φ ranging from approximately 115–120 ° during hovering to 100–105 ° at top speeds. Although much larger, the hawkmoth has disproportionately longer wings and hence a lower wing loading: 9 N m⁻² compared with 36 N m⁻² for bumblebee queens. Both species use what might be called ‘normal’ flight.

Fig. 1 shows the path of the wing tip through the air for a bumblebee worker hovering and at speeds up to 4.5 m s⁻¹, which is close to the maximum flight speed of 5–6 m s⁻¹. The wingtip path would look much the same for an insect with twice the flapping velocity flying twice as fast, so it is more useful for comparative purposes to introduce a dimensionless measure of speed: the flight velocity divided by the flapping velocity. By analogy to propeller theory, we call this the advance ratio J. The flapping velocity varies linearly along the wing, and some representative value must be chosen to calculate an advance ratio. Again, we choose the mean wingtip flapping velocity, and the advance ratio J is then:

where V is the flight velocity. The advance ratio is zero during hovering and rises to approximately 0.6 for bumblebees at high speed. It may be useful to think of J as the forward speed in wing lengths per wingbeat (=V/nR) divided by 2 Φ.

The wingtip path is determined by the vector sum of the flight, flapping and downwash velocities; the all-important velocity of the wing relative to the air is given by the tangent to the path. Lift and drag are therefore perpendicular and parallel to the path, respectively, and the resultant force vectors are drawn to scale for each half-stroke in Fig. 1. During hovering, the stroke plane is horizontal, and the wingtip path is determined only by the flapping velocity and the downwash. The downstroke and upstroke are nearly symmetrical, providing weight support but no net horizontal thrust. The wing rotates through approximately 120 ° between the half-strokes, so the leading edge always leads, and the anatomical lower surface of the wing becomes the aerodynamic upper surface on the upstroke. In effect, the wing oscillates between positive and negative angles of attack, 90 ° out of phase with the flapping motion.

As flight speed and advance ratio increase, the body tilts nose-down, and finally becomes horizontal; body drag is therefore minimised at high speeds, where it is increasingly important. The stroke plane rotates with the body orientation and eventually reaches an inclination of approximately 40 ° to the horizontal. As advance ratio increases, the downstroke increasingly dominates the force balance; the downstroke path becomes relatively longer, indicating a higher velocity and thus larger forces. At high J, the asymmetry is very pronounced, with the powerful downstroke responsible for weight support and some thrust, but the direction of the feeble upstroke force is suitable for thrust only. The required thrust is never very large for insect flight, and even at high speeds it is only some 10–20 % of the weight. The net aerodynamic force is therefore nearly vertical, tilted forwards by less than approximately 10 °. Between hovering and fast flight, the stroke plane tilts by almost 40 ° for the bumblebee, but the net force vector tilts by only 8 °.

The geometry of the wingtip path is of paramount importance; it fixes the direction and relative magnitude of the wing forces on the downstroke and upstroke. This geometry is determined mainly by the advance ratio, then by the stroke plane angle, and finally to a small extent by the relative magnitude of the downwash. The advance ratio fixes both the relative wavelength of the wingpath (=V/nR) and, through Φ, its baseline amplitude. The stroke plane angle then controls the symmetry of the half-strokes and the inclination of their respective paths. Fig. 1 shows clearly that, as advance ratio increases, the tilt of the stroke plane ensures that the inclination of the downstroke path changes but little over the forward speed range. For a given downstroke lift-to-drag ratio, which will presumably be at some optimal value, the stroke plane angle must be such that the inclination of the downstroke path produces the almost vertical net aerodynamic force. At lower advance ratios, the geometry is not so constrained and the downstroke path can be somewhat less inclined, because the increasing upstroke forces will cancel the slightly backwards direction of the downstroke forces.

Maximum flight speeds seem to be reached at the advance ratio and stroke plane angle combination giving a nearly vertical upstroke path and a downstroke path inclination consistent with the lift-to-drag ratio. For bumblebees over a large size range (Dudley and Ellington, 1990a; Cooper, 1993) and for hawkmoths (Willmott and Ellington, 1997b), this corresponds to J around 0.6–0.9. Hawkmoths seem able to exceed this limit slightly by not reversing the angle of attack on the upstroke at the highest speeds. The upstroke therefore provides some weight support but a negative thrust, and the insect struggles to produce a net positive thrust over the cycle. This is a highly unusual kinematic adaptation, however, and needs further study. Advance ratios in excess of 1 have also been reported for some butterflies and a day-flying moth (Betts and Wootton, 1988; Dudley, 1990; Dudley and DeVries, 1990). It is not yet known whether these slightly higher values are correlated with their low aspect-ratio wings and low wingbeat frequencies.

An upper limit to the advance ratio of around unity determines the maximum flight speed for a given flapping velocity. Dreams of very high speed insect-based micro-air vehicles (MAVs) will simply not be realised; top speeds are limited by the advance ratio, just as with propellers.

The most obvious kinematic changes with increasing speed can be seen with the naked eye: the concomitant tilting of the body and stroke plane. The relationship is approximately linear with speed. At top speed, the body is close to horizontal, and the stroke plane angle reaches approximately 40 ° for the bumblebee and 50–60 ° for the hawkmoth. For both insects, the wingbeat frequency is rather constant, although with large sample sizes Cooper (1993) found a shallow U-shaped relationship between wingbeat frequency and speed for bumblebees.

Wingbeat amplitude Φ tends to decrease with speed: by 20–30 ° for bumblebees (Cooper, 1993) and by approximately 15 ° for hawkmoths (Willmott and Ellington, 1997a). Results for other insects either support this trend or else suggest that amplitude remains constant.

Bumblebees and the hawkmoth are the only insects in which angle of attack has been measured over the entire speed range. It has already been stated that the angle is reversed on the downstroke and upstroke, except for the hawkmoth at the highest speeds. The geometric angle of attack α relative to the stroke plane varies with speed, with the end result that the effective angle of attack α_r relative to the wingtip path remains fairly constant at around 30 ° during most of the downstroke. The negative α_r on the upstroke is of similar magnitude for the bumblebee, but smaller for the hawkmoth. It would be reasonable to assume that the changes in geometrical angle of attack, particularly on the more important downstroke, ensure that the wings are always operating close to some optimal angle relative to the airflow. At 30 °, α_r seems very high compared with that of conventional wings, but it is quite characteristic of insect wings at their lower Re.

The wings are also twisted by 10–20 ° along their length, rather like propellers, with a higher angle of attack at the wing base than at the tip. Fruit-fly wings, however, show a negligible twist; these small wings appear relatively stiffer than those of larger insects and hence more resistant to torsional twisting (Vogel, 1967; Weis-Fogh, 1972; Ellington, 1984b).

Many insects are capable of remarkable controlled manoeuvres. High-speed films of them flying slowly inside chambers sometimes reveal horizontal thrusts up to five times their weight (Ellington, 1984b). More gentle manoeuvres, however, are simply controlled by tilting the stroke plane, as for a helicopter. Horizontal changes in flight direction and velocity are always preceded by a tilt of the stroke plane: the tilt is increased as the insects accelerate forward, and decreased, usually becoming negative, as they decelerate or begin backward flight. Similarly, accelerations in lateral directions are accompanied by a roll of the stroke plane. Roll can be effected by increasing the flapping amplitude and/or angle of attack of the outside wing. Pitching results from a fore/aft shift of the centre of lift, which pitches the body and hence the stroke plane. The shift can be realised by changing the fore/aft extent of the flapping motion and/or the angle of attack over a half-stroke. Studies on bumblebees and the hawkmoth suggest that a backward shift of the flapping motion is partly responsible for the increasing tilt of the stroke plane with forward speed (Dudley and Ellington, 1990b; Willmott and Ellington, 1997a). A nose-down pitching moment from body lift, which is typically less than 10 % of the weight and thus a small component in the force balance, also contributes significantly to the body and stroke plane inclination at forward speeds.

Changes in angle of attack have been observed to initiate accelerations at low speeds (Ellington, 1984b). To accelerate into forward or backward flight, insects increase the angle of attack to large values on the upstroke or downstroke, respectively, and use the increased drag to initiate acceleration. The angle of attack on the drag-producing half-stroke often approaches 90 ° and provides large horizontal accelerations. This ‘paddling’ or ‘rowing’ motion also rotates the body (and the stroke plane) in the correct direction because the drag force is applied above the centre of mass. As the stroke plane tilts, the increased drag would detract from weight support, and the insects revert to more normal angles of attack after only one or two wingbeats.

During hovering and slow flight, the body hangs below the wing bases, and the insect benefits from passive pendulum stability. The centre of mass typically lies close to the junction between the thorax and abdomen, and this will produce a nose-up pitching moment even at the large body angles observed for slow flight. The wings must therefore produce a compensatory nose-down pitching moment about their bases, and this is accomplished by locating the centre of lift aft of the body; the mean flapping angle of the wings in the stroke plane is typically directed 20–30 ° backwards during hovering (Ellington, 1984b). Thus, the insects can control the mean pitching moment, and hence the mean body angle, simply by changing the mean flapping angle of the wings.

Whether passive pendulum stability applies to faster flight speeds has not been addressed. I suspect that the flight becomes unstable to some extent, but it is difficult to investigate experimentally. Indeed, it is likely that we will learn more about the stability of flapping flight from future work on machines than on insects.

Tilting the stroke plane offers a very simple method of control. It is not suitable for brisk manoeuvres, however, when coupled with pendulum stability. With a fixed orientation of the stroke plane relative to the body, the body’s moment of inertia will prevent rapid changes in attitude and hence in the stroke plane tilt. The sluggishness of the response is particularly evident for bumblebees, whose large pendulum-like body can be seen swinging around as they manoeuvre. Highly manoeuvrable insects such as hoverflies circumvent this problem in two ways (Ellington, 1984a,b). Their centre of mass is closer to the wingbases, reducing their moment of inertia. In addition, they can hover and fly at low speeds with the body horizontal and the stroke plane inclined (Fig. 2). This requires very large downstroke forces to support the weight, because the direction of the upstroke path makes it suitable only for horizontal forces. The inclined downstroke path is necessary for its resultant aerodynamic force to be nearly vertical, and the weight-supporting role of the upstroke is sacrified to provide large thrusts when needed. Because the body is already horizontal, the hoverfly can then accelerate rapidly without waiting for the body angle to tilt. Other flies (Ennos, 1989) can also vary the relative lift on the half-strokes, tilting the net force vector without tilting the stroke plane for rapid manoeuvres. Hovering with an inclined stroke plane has been suggested for dragonflies (Weis-Fogh, 1973), but recent studies have shown that they can hover and manoeuvre much like other insects (Wakeling and Ellington, 1997b,c).

Yaw control has received little attention for insects in free flight. In some of my high-speed films of slow flight, yawing motion is caused by a large drag force on one wing operating at a very high angle of attack; in effect, the insect paddles on one side. At higher flight speeds, tethered locusts are known to use ruddering – lateral deflections of the abdomen – during steering and yaw control (Dugard, 1967; Camhi, 1970).

The flight of tiny insects, with wingspans of less than approximately 1 mm, deserves special mention because of interest in micro-robots. At a Reynolds number of the order of 10, the wings of these insects should have lift-to-drag ratios of unity or less. Horridge (1956) suggested ‘that they have abandoned altogether the aerofoil action and that they literally ‘swim’ in the air.’ However, Weis-Fogh (1973) later discovered that the parasitic wasp Encarsia formosa indeed relies on lift, and not drag: its mass is 25 μ g, its wingspan 1.5 mm and its wingbeat frequency 400 Hz. Its wing motion is broadly similar to that of most insects, except that the left and right wings come together at the dorsal end of the wingbeat. They ‘clap’ together at the end of the upstroke and ‘fling’ apart for the beginning of the downstroke. The fling motion is of great conceptual interest. As the wings fling open, air is sucked over their upper surfaces into the widening gap, creating a vortex around each wing (Fig. 3). The vortex functions as a ‘bound vortex’ when the downstroke motion begins, increasing the air velocity over the upper surface and decreasing it over the lower surface, respectively. This velocity difference causes a pressure difference across the wing by Bernoulli’s theorem and thus generates lift.

A ‘bound vortex’ exists for any wing that produces lift; it is simply a description of the velocity difference over the wing. The strength of the vortex is called its circulation, and it is directly proportional to the lift force. During normal translational or flapping motion, a wing creates a bound vortex by shedding a ‘starting vortex’ of equal but opposite strength from its trailing edge. The secret of the fling mechanism is that the bound vortex of each wing acts as the starting vortex for the other and that the circulation is determined by the rotational motion. With a high angular velocity of rotation, the fling circulation can be larger than the wing would normally experience, and thus the downstroke lift can be larger than expected.

The other tiny insects that have been filmed to date rely on the fling mechanism for enhanced lift production: the greenhouse white-fly Trialeurodes vaporariorum (Weis-Fogh, 1975b) and thrips (Ellington, 1984b). On a slightly larger scale, the fling is observed for the fruit-fly during tethered flight (Götz, 1987; Zanker, 1990) and occasionally during hovering (Ellington, 1984b; Ennos, 1989). The fling is also found in some medium/large insects, most notably in butterflies and moths, and typically produces some 25 % more lift than ‘normal’ wing motions (Marden, 1987).

The fling mechanism of lift generation provides an important lesson in the aerodynamics of flapping flight: wing performance can be better than the Re might suggest. The Reynolds number is a steady-state characterisation of the flow regime, but it takes time for thick, viscous boundary layers to develop. Rapid changes in the wing velocity during the flapping cycle should keep boundary layers thinner and effectively raise the Reynolds number above steady-state considerations. Creation of the bound vortex by the rotational motion also illustrates that novel lift mechanisms might apply and that the lift predicted by steady motion may not be appropriate to flapping flight.

Although many insects take advantage of the circulation created by the fling, most seem to shun the mechanism in spite of the aerodynamic benefits. If nothing else, there must be significant mechanical wear and damage to the wings caused by repeated clapping. A fling motion might be thought advantageous for micro-robots, because all tiny insects seem to have converged on it, but it is likely to prove impractical. Extra lift can be gained instead by relatively larger wings or by a higher wingbeat frequency.

One method of applying the blade-element analysis rests on successive stepwise solutions of equations 3 and 4. Complete kinematic data are necessary for this approach: the motion of the longitudinal wing axis, the geometric angle of attack and the section profile must all be known as functions of time and radial position. Combined with an estimate of the downwash, the effective angle of attack can then be calculated, and appropriate values of C_L and C_D,pro selected from experimental results. However, this approach is very prone to error: angles of attack and profile sections cannot be measured with great accuracy, and the downwash estimate is crude at best. The ‘mean coefficients method’ is normally used instead. By treating the force coefficients as constants over a half-stroke, they can be removed from the double integrals resulting from manipulations of the equations, and mean values found that satisfy the net force balance. The kinematic detail required for this method is greatly reduced since only the motion of the longitudinal wing axis is needed. The mean lift coeffient is particularly interesting because it is also the minimum value compatible with flight; if C_L varies during the wingbeat, then some instantaneous values must exceed the mean.

Maximum lift coefficients for insect wings in steady airflow in a windtunnel are typically 0.6–0.9 (reviewed in Willmott and Ellington, 1997b), although dragonflies show values up to 1.15 (Wakeling and Ellington, 1997a). Most modern applications of the mean coefficients method have concluded than the mean C_L required for weight support exceeds the maximum for steady flow, sometimes by factors of 2 or 3 (for reviews, see Ellington, 1995; Wakeling and Ellington, 1997c; Willmott and Ellington, 1997b). These results show that insects cannot fly according to the conventional laws of aerodynamics and that unsteady high-lift mechanisms are employed instead. The fling is one such mechanism, but it is not widely used.

Recently, flow visualization studies on the hawkmoth and a 10 × scale mechanical model – the flapper – have identified dynamic stall as the high-lift mechanism used by most insects (Ellington et al., 1996; van den Berg and Ellington, 1997a,b; Willmott et al., 1997). During the downstroke, air swirls around the leading edge and rolls up into an intense leading-edge vortex, LEV (Fig. 4). A LEV is to be expected at these Re for thin wings with sharp leading edges operating at high angles of attack. The circulation of the LEV augments the bound vortex and hence the lift. This is an example of dynamic stall, whereby a wing can travel at high angles of attack for a brief period, generating extra lift before it stalls.

Dynamic stall has long been a candidate for explaining the extra lift of insect wings, but two-dimensional aerodynamic studies showed that the lift enhancement is limited to approximately 3–4 chord lengths of travel (Dickinson and Götz, 1993); the LEV grows until it becomes unstable at that distance and breaks away from the wing, causing a deep stall. The wings of hawkmoths and bumblebees travel twice that far during the downstroke at high speeds, which should rule out dynamic stall as the high-lift mechanism. However, a strong spanwise flow in the LEV was discovered for the hawkmoth and the flapper; when combined with the swirl motion, it results in a spiral LEV with a pitch angle of 46 °. The spanwise flow convects vorticity out towards the wing tip, where it joins with the tip vortex and prevents the LEV from growing so large that it breaks away. The spanwise flow therefore stabilises the LEV, prolonging the benefits of dynamic stall for the entire downstroke. The spiral LEV is a new aerodynamic phenomenon for rotary and flapping wings, and the exact conditions for establishing spanwise flow in the LEV are not yet understood. However, the mechanism appears to be robust to kinematic changes, and it generates sufficient lift for weight support.

The picture of normal insect flight presented in this paper provides a minimal design for flapping machines capable of controlled flight over a range of speeds. In this section, we summarise the kinematics necessary for the design and then calculate the load-lifting capacity, power requirement and top speed for machines over a wide size range.

The simplest implementation of the design is likely to need independent adjustment of the flapping amplitude and mean flapping angle for each wing. Furthermore, the angle of attack must change with forward speed for the wings to operate at an optimal angle relative to the wing path. Angles of attack could also be varied for manoeuvres, but it might be easier to control them with amplitude and mean flapping angle adjustments. The wing design should incorporate a twist from base to tip, like a propeller, but this twist must reverse between the half-strokes. There has not been time in this paper to consider the mechanical design of insect wings, but Wootton (1990) provides an excellent introduction to the subject. Insect wings are elegant essays in small-scale engineering. They are deformable aerofoils whose shape is actively controlled by the wingbase articulation while the wing area is subject to inertial, elastic and aerodynamic forces. For the first generation of flapping machines, however, a simple sail-like construction will probably suffice: a stiff leading edge supporting a membrane, further braced by a boom at the base. Movement of the boom will control the angle of attack at the wing base, and billowing of the sail will provide the necessary twist along the span. The fan-like hindwings of some insects, such as locusts, provide a more sophisticated variant on the sail design that might prove useful (Wootton, 1995).

How much weight can be supported by the wings of an insect-based flapping machine, and how much power is needed? For five reasons, I shall use hovering flight as a convenient benchmark for these calculations. First, the lift and power equations are particularly simple because the added complication of the flight speed is absent. Second, as with insects, hovering flight will be easier to study for flapping machines, providing a practical testbed for designs. Third, pendulum stability will minimise control problems. Fourth, lift coefficients decline with increasing speed, showing a maximum somewhere between hovering and approximately 2m s⁻¹ (Dudley and Ellington, 1990b; Cooper, 1993; Willmott and Ellington, 1997b). And fifth, the power requirement of hovering is also adequate for flight at speeds approaching the maximum speed (Dudley and Ellington, 1990b; Ellington et al., 1990; Cooper, 1993; Willmott and Ellington, 1997b). Thus, if we can design an insect-based machine that hovers, it will also be able to support its weight and power the wings over virtually the entire speed range. The maximum flight speed can even be estimated from the flapping velocity in hovering, using a maximum advance ratio of approximately unity.

Full equations for the aerodynamic analysis of hovering flight are derived in Ellington (1984c). I shall simplify them here by incorporating minor variables into numerical constants to emphasize the important design parameters. For example, simple harmonic motion will be assumed for the flapping velocity. The centroid of wing area will be taken at half the wing length; the wing planform influences the calculations, but for a range of insects the mean position of the centroid is very close to 0.5R. Standard values for air density and gravitational acceleration are also absorbed into the constants.

The first specification in a design study is probably the mass to be supported, and this is likely to prove a difficult target. Equation 6 shows that the mass is proportional to n²R⁴, so increases in R will be more effective in achieving the required mass than increases in n; e.g. doubling R will increase mass support 16-fold, whereas doubling n will increase it only fourfold. Therefore, within any limitations imposed by the design specifications, longer wings rather than higher frequencies offer a better route for mass support, as shown in Fig. 5.

The aerodynamic power per unit mass is proportional to nR. To support the same target mass, R has to be increased much less than n, and hence the mass-specific power will be lower. The power saving can be very substantial, as shown in Figs 5 and 6: e.g. to support 200 mg with R=10 mm and n=200 Hz requires an order of magnitude more power than with R=100 mm and n=2 Hz. Therefore, a given mass will be supported with less power by using a longer wing length and lower wingbeat frequency. The only disadvantage is that the maximum flight speed is 10 times lower for the larger design (Fig. 7). Flight speed is proportional to the flapping velocity and hence to nR. If mass support is achieved by small increases in R rather than larger ones in n, the speeds will necessarily be smaller.

Mass, power and maximum speed are likely to be major design constraints for insect-based flapping machines. Small power plants with a high output per unit mass are a severe limitation at present, but internal combustion engines and lithium batteries can provide sufficient power for many of the examples given here. Longer wings are clearly advantageous for mass support and for power savings. Maximum speeds would be low but, because of their larger size, fabrication would be easier and they would offer a more convenient testbed for the development of control systems.

This research is supported by the BBSRC and DARPA.