Feasibility discussion: Challenges anticipated with flight in transformed individuals

Lathreas and Zennith, 2023

The idea of giving people functioning wings, enabling flight, is alluring. In 2018, the Freedom of Form Foundation posted a whitepaper discussing some calculations that impact the feasibility of flight in people roughly the mass of humans. This document supercedes the corresponding sections in the 2018 whitepaper.

Here, we provide a more complete picture on the feasibility of flight by including new estimations of airspeed and wing loading, and also revisit old calculations. Our new estimates are unable to fully answer the question as to whether or not flight can be accomplished in humanoid-size animals through purely biological design. This suggests that the space of valid parameters is narrower than we previously appreciated. More intensive aeronautical modeling would be needed to understand the forces and mechanics involved (and thus, whether or not biological design is sufficient for flight). Nevertheless, based on our current calculations, there appears to be a meaningful likelihood that design may need to include components that are not biologically inspired. For example, flight may need novel tendons dissimilar from those in birds or bats.

When scheduling research projects, we aim to create synergies so they can proceed efficiently. Flight-associated challenges hold relatively less in common with other projects, and carry important technical risks. Therefore, research directed towards bodily modifications that enable flight, i.e. wings, currently appears unlikely to be included on our project schedule at least through 2043. Unfortunately, our previous decision to de-prioritize work on flight-associated anatomy in favor of other projects, and avoid commitments to specific wing-related research projects, seems to have been the right call so far.

If we learn new information, or gain access to appreciably greater resources, we may revisit this decision before that time. Note that cosmetic wings are not covered by this document, and may well be feasible.

Underlying biology and estimates

Bodily modifications that enable flight will be uniquely challenging. Unlike other anatomical goals, flight would need to succeed in the fields of both biomedical engineering and aeronautical engineering. It would involve the creation of new musculoskeletal systems, higher cardiovascular demands, and new neurological circuits. It would also require careful optimizations, namely in wingspan versus airspeed, muscle sizes that are sufficient for flight without being excessive or intrusive, and balancing tradeoffs between drag during flight versus the ability of a person to live normally terrestrially.

Here, we discuss the following:

  • Our understanding of working goals
  • Wingspan and airspeed
  • Force generation including flight muscle size
  • New anatomy needed
  • Metabolism

Assumed goals for flight and related anatomy

In order to ensure a precise discussion, we assume the following goals:

  • An anthropomorphic form preserving their existing forelimbs and hindlimbs and adding two new wings.
  • Wings should be consciously controllable as if they were naturally occurring limbs, and capable of sensory sensations such as touch.
  • Wings and associated anatomy should be capable of sufficient force generation for unassisted takeoff and sustained powered flight, i.e. not just gliding.
  • Wings and associated anatomy, when not being used for flight, should be sufficiently compact to avoid disruption with terrestrial life.
  • Implementations of associated anatomy should largely be biological, though occasional use of synthetic materials, e.g. for force generation or mass reduction, might be acceptable.

Wingspan and airspeed

Derivation of Force Balance

We will start by constructing a relationship between the lift force and the mass of a person. In principle, flight is the counteraction of gravity. To fly, the gravitational force and lift force must cancel out. Since these forces are vertical and opposite, we must satisfy the force balance:

\(F_{gravity} = F_{lift}\) (Equation 1)

The force of gravity is simply given by \(F_{gravity} = m * g\), where g is the gravitational constant.

The equation for lift is more complicated, and depends on the shape of the wings, the density of air, movement of the wings, and many more parameters. For this calculation, we will assume that the organism is using hovering flight, which means that the wings are fixed in a stationary position and provide an upward force by bending the airstream during flight. (For clarity, we are not referring to powered hovering, the type of hovering flight that hummingbirds use).

In this case, we can use the empirical lift formula, which assumes that the organism’s lift is only dependent on the horizontal air speed v, air density d, wing surface area A, and a nondimensional constant C that depends only on the shape of the wings. Dimensional analysis reveals that these factors relate as:

\(F_{lift} = C * A * v^{2} * d\) (Equation 2)

Substituting the equations for the lift and gravitational force into (Equation 1), we obtain:

\(m * g = C * A * v^{2} * d\) (Equation 3)

Scaling up a bird

Suppose we have a bird of size x = 2 m, y = 0.5 m, and z = 0.2 m, akin to a bald eagle. This gives us a mass of \(m_{bird} = c_{m} * x * y * z\), where \(c_{m}\) is the fraction of space inside the cuboid xyz occupied by the bird multiplied by the bird’s density. We assume that this fraction is a constant value. The wingspan of this bird is now given by \(A_{bird} = c_{A} * x * y\), where \(c_{A}\) is the fraction of the rectangle xy that the wing actually covers. As such \(c_{A}\) is a constant dependent only on the shape of the bird, and not its scaling.

This gives us a total bottom-facing surface area (the surface area that the bird uses to exert a vertical force onto the air) of:

\(A_{bird} = c_{A} * x * y = c_{A} × 1 m^{2}\) (Equation 4)

We take the bird’s mass to be \(m_{bird} = 5 kg\), as an estimated average for a bald eagle. Since this bird can glide, we will assume that a human would need similar efficiency.

Now suppose we scale up this bird-shaped creature to human proportions, by multiplying each axis with a scaling factor \(s\). In this case, \(m\) will scale cubically, while \(A\) will scale quadratically.

As such, we will see what happens to the wingspan if we increase the mass of this bird to \(m_{human} = 80 kg\) and require that the force balance is still satisfied.

In this case, \(m_{human} = 16 * m_{bird}\), so we have a sixteen-fold increase of the mass of the bird. Taking the mass balance again, and substituting the human mass \(m_{bird} = \frac{1}{16} * m_{human}\), we obtain:

\(\frac{1}{16} * m_{human} * g = \frac{1}{2} * C * A_{bird} * v^{2} * d\) (Equation 5)

\(m_{human} * g = \frac{1}{2} * C * (16 * A_{bird}) * v^{2} * d\) (Equation 6)

Since we do not allow for propelled flight, we will not change the velocity in the lift equation, instead assuming it to be constant. Assuming all other physical parameters remain constant, the equation above implies that:

\(A_{human} = 16 * A_{bird}\) (Equation 7)

This shows that humans would need at least sixteen times the wing area of a bird in order to keep the same gliding ability, assuming that the aerodynamics of the humanoid with wings are similar to those of a (highly optimized) bird.

A wing area of 16 m would correspond to a wingspan of 8 m with 2 m tall wings in the anterior-posterior axis. Most people are shorter than 2 m, though, so this would mean the wings are taller than the person themself, and still ridiculously sized. Alternatively, a 10 m wingspan with 1.6 m tall wings would produce the same wing surface area. However, this disregards the effects these alternative shapes will have on the aerodynamics, which may have additional impacts on flight performance.

Changing alternative parameters

Indeed, we can relax the constraint of the wingspan by instead changing one of the other parameters. C is the aerodynamic constant, and we can assume this to be close to optimized for birds. As such, we can safely assume we will not be able to increase this parameter further than that of a birds. In fact, it will likely be lower in practice for humanoids. The wings of a humanoid might very well have worse aerodynamics, due to a non-optimized shape of the head, neck, and shoulders, and non-retractable legs.

The parameter d is the parameter for the air density. Obviously, we cannot change this parameter in any reasonable scenario. The parameter v is the only remaining parameter that we can alter.

We take the average soaring speed to be approximately 50 km/h for eagles (American Eagle Foundation, 2021), again with an approximate mass of 5 kg.

Using the scaling factors established above, we can estimate the following tradeoffs between airspeed and wingspan for creatures with a mass of 80 kg:

  • A speed of 50 km/h with an 8 meter wingspan
  • A speed of 100 km/h with a 4 meter wingspan
  • A speed of 200 km/h with a 2 meter wingspan

Naively, 100 km/h (62 mph) and a 4-meter (13 feet) wingspan appears to be the most reasonable compromise. While it is not too difficult to imagine a creature flying at 100 km/h with a 4-meter wingspan, it is important to keep in mind that these numbers are within a system highly sensitive to input parameters.

A slight reduction in air pressure or effective wing area, slightly suboptimal aerodynamics, or slight reduction in possible speed (perhaps due to limited ability to produce forward thrust) could make this airspeed/wingspan system intractable. Even a draconic shape might have difficulties with drag in this case, all fins and horns considered.

As well, a heavier creature, perhaps heavier due to a need for more flight muscle, could also make this airspeed/wingspan system intractable. This point will become important in the next section.

Forces involved in flight

Force components

Flight involves competing forces: lift versus the animal’s weight, and thrust versus drag. When thrust is not provided, gliding occurs; the loss in a creature’s altitude compensates for energy lost to drag.

Thrust is relatively minor in magnitude compared to lift. To be more specific, when birds glide, their glide ratios vary by species, such as 11:1 in vultures or 22:1 in albatrosses – either 11 or 22 meters of distance covered for each meter of altitude lost (Doane, 2011; Parrott, 1970), meaning only 9% to 5% of the magnitude of lift force is needed for thrust while cruising.

On the other hand, while energy input is required for thrust, lift is a passive activity. Therefore, in an ideal system, the only necessary energy input is for thrust.

Pectoralis muscle forces

The pectoralis muscles are the major flight muscles of birds. Located on the torso, they pull each wing downwards, exerting force against the air. However, bird wings are like “bad” levers, where lift occurs far from the fulcrum (the shoulder), and the pectoralis muscles are much closer to the shoulder. Due to this lever effect, pectoralis muscles need to exert much larger force when contracting as compared to the ultimate force of lift. In addition, whereas the effect of gravity is constant, muscles apply varying force during the wingbeat.

We will use a study of ducks in flight for estimation of muscle force needs (Williamson et al., J Exp Biol, 2001). The ducks measured in the study had average masses of 0.995 kg, implying a lift requirement of 9.75 N in level flight. Since pectoralis muscles are working on a relatively short lever arm (compared to the size of the wingspan), pectoralis muscles need to exert more peak force than the force of lift. Each unilateral muscle exerts peak force of approximately 107.5 N in level flight. (Only slightly more force is exerted during takeoff and in ascending flight, so we will focus on level flight for ease of comparison). Bilaterally, 215 N of force is exerted, suggesting that the relation of pectoralis force to lift force can be estimated as 215 / 9.75 = 22 fold.

While the scales are different from the needs for an anthro, the basic relations between forces would be similar, as long as the relative positioning of the pectoralis along the wingspan is the same. Therefore, using the relation between total pectoralis force and lift force of 22 fold, we can estimate that a creature weighing 80 kg (necessitating lift of 80 kg * 9.8 m/(s^2) = 784 N) would need a bilateral pectoralis force specification of 17,248 N in level flight. (Note that this force specification is lower than the maximum force capacity of isotonic muscle. Therefore, when considering muscle cross-sectional area, it is important to distinguish whether forces are routine or maximum/isotonic per unit of cross-sectional area).

As well, ducks inform how a muscle’s cross-sectional area relates to this measure of pectoralis force. Measurements for ducks in Williamson et al 2001’s study give a unilateral myofibrillar area of around 5.47 cm^2. Myofibrillar area is approximately 60% of total muscle cross-sectional area (Dial and Biewener, J Exp Biol, 1993; Williamson et al., J Exp Biol, 2001), implying ducks have a total unilateral muscle cross-sectional area of 9.12 cm^2 per pectoralis (or 18.24 cm^2 for bilateral CSA). Therefore, in ducks, the relation is 215 N of force per 18.24 cm^2, or 11.78 N per cm^2 in level flight. Again, this is the force capacity of muscles in practice, in evolutionarily optimized animals. The isotonic force capacity of these muscles is higher (and would yield a higher N per cm^2 number), but not observed in living ducks.

Therefore, for equally optimized pectoralis muscles in anthro flyers, we would obtain 17,248 N / (11.78 N/(cm^2)) = 1,464 cm^2 of bilateral pectoralis muscle cross-sectional area (or 732 cm^2 per unilateral muscle). Simplistically, if the muscles are 60 cm (24 inches) along the torso (along the rostral-caudal axis), each muscle would be around 12 cm thick (4.7 inches). On the surface, this sounds reasonable.

Moreover, it is possible that muscle pennation would reduce the apparent cross-sectional area, but the literature of muscle anatomy requires close reading to make sure that we are not unfairly double-counting ‘discounts’ that would let us reduce apparent muscle size (existing literature tends to not give fully traceable inputs to published calculations). Therefore, to avoid the risk of double-counting pennation if it is already included in our muscle cross-sectional area calculations, we will not include a pennation correction factor here.

Pectoralis muscle length

We still need to estimate appropriate pectoralis muscle length. We will assume that muscle length will scale linearly with wingspan, since the muscle ultimately needs to span from places equivalent to a bird’s keel to where it inserts on the wing humerus. This is a fair assumption because muscle length needs to match the range of motion during a contraction, not the force being exerted. In other words, muscle length will not directly scale with body mass, nor with muscle cross-sectional area.

In the Williamson et al 2001 paper, ducks’ fascicle length, which we take as a proxy of overall muscle length (length from the muscle’s origin on the keel to its insertion on the wing humerus), is around 6.97 cm for animals with bilateral wingspans of 86.2 cm. This suggests that each pectoralis should have fascicle length of 0.081 cm per cm wingspan.

Similarly, in Silver King pigeons (a very large breed of pigeons), the relation is 5.5 cm of fascicle length for animals with wingspans of around 73.6 cm (calculated from “body mass” and “disk loading” in Table 1 of Biewener et al, J Exp Biol, 1998), yielding a ratio of 5.5 cm per 73.6 cm -> 0.074 cm per cm of wingspan, consistent with the above 0.081 cm per cm wingspan estimate.

If we take the slightly more conservative estimate of 0.81 cm/cm, and assume that the 4 m wingspan discussed in the “Wingspan and airspeed” section is reasonable, this would suggest that pectoralis fascicle length should be 0.081 (cm/cm) * 400 cm = 32.4 cm.

Estimating pectoralis muscle mass

We now have a cross-sectional area, as well as length, of pectoralis muscles. However, we are not yet ready to determine an overall mass of pectoralis, because pectoralis muscles have a shape very divergent from a rectangular prism volume with 90 degree angles. We will perform calculations that attempt to preserve the biological relations we have already established.

The pectoralis muscle in ducks has a unilateral mass of 0.067 kg (Williamson et al., J Exp Biol, 2001). Again, they also have a unilateral muscle cross-sectional area of 9.12 cm^2. Therefore, in ducks, pectoralis mass is 0.00735 kg per cm^2 for muscles with a fascicle length of 6.97 cm, or 0.00105 kg per cm^2 for 1 cm-long fascicles. Applying this to anthros, with muscles with a bilateral CSA of 1,464 cm^2 and an unrealistic fascicle length of 1 cm, we obtain muscles that are 0.00105 kg * 1,464 cm^2 = 1.54 kg in bilateral mass.

Finally, we need to lengthen the muscles from 1 cm to 32.4 cm, and we will simplistically use a linear multiplier of 32.4 cm/cm. Therefore, 1.54 kg * 32.4 = 50 kg of bilateral pectoralis mass. Ouch!

Possible adjustments to pectoralis mass while preserving nature-inspired anatomical design

50 kg of pectoralis mass is not practical to specify for anthro flyers, suggesting that it is not realistic to anticipate the use of biologically-inspired, bird-like pectoralis wing anatomy, while expecting similar levels of performance and comfort over long, sustained flight sessions.

If we reduce the performance demands, such as by allowing shorter-duration flight, it will be possible to reduce muscle mass below 50 kg.

For example, specifying that muscles should produce maximum forces of around 32.1 N/(cm^2) might be permissible, considering measurements in humans – though the measurements were for maximum strength, not over a longer span of time (de Monsabert et al, Med Biol Eng Comput, 2017). So, if we modify the force per CSA specification for flight muscles from 11.78 N/(cm^2) to 31.2 N/(cm^2), we could reduce bilateral muscle mass from 50 kg to perhaps 18.9 kg. These would still be very large muscles, and could be expected to be inconvenient for flyers when they are on the ground.

Still, for the sake of argument, let us propose the following parameters:

  • 17,248 N / (31.2 N/(cm^2)) = 553 cm^2 of bilateral pectoralis muscle cross-sectional area
  • Pectoralis muscles each 32.4 cm long
  • Bilateral mass of 18.9 kg

How about the lever arm? Above, we specified that the pectoralis would be acting at a proportionally identical region along the wing in anthros as in extant ducks. Per Williamson et al., 2001, the ratio between the lever arm of the pectoralis, versus the lever arm of air pressure acting upon the wing, is approximated by r_pectoralis/r_wing = 0.100. However, if we specify that the pectoralis inserts onto the humerus relatively more laterally than in ducks (e.g., by moving its joint with the wing-scapula more medially), we might obtain a ratio between the lever arms of 0.2, giving the pectoralis relatively higher mechanical advantage, though presumably incurring a need for a longer muscle to accomplish the same work.

Let us modify the specification, again for the sake of argument:

  • Bilateral pectoralis cross-sectional area = 553 cm^2 * 0.100 / 0.2 = 277 cm^2
  • Assuming fascicles 1 cm long: 0.00105 kg per cm^2 for 1 cm-long fascicles
  • Pectoralis muscle length = 32.4 cm * 0.2 / 0.100 = 64.8 cm
  • Muscle mass of 0.00105 kg/(cm^2_CSA * cm_fascicle_length) * 277 cm^2 * 64.8 cm = 18.8 kg.

In other words, the lever arm (of where the pectoralis meets the humerus) does not appear to impact the overall mass of the muscle.

Rationally designed structures, divergent from nature, appear crucial to satisfactory performance

Overall, these calculations suggest that relatively large pectoralis muscles would be needed if we were to pursue biologically inspired design. Pectoralis muscles likely still need to be large even if performance demands are reduced. As well, even if the mechanical advantage for pectoralis muscles is increased, this likely necessitates a longer muscle length to accomplish the same resulting movements of the wing. The use of biological muscles and biologically inspired flight anatomy appears difficult.

Still, it is important to remember that even though lift is the major force in flight, lift is a passive, rather than active, outcome of the mechanical system. Thrust is the force that overcomes drag (gliding does not require thrust input). Therefore, a ligament or tendon can substitute for much of the pectoralis muscle, in order to provide the cyclical force throughout wingbeats needed to hold wings downward against the force of air pressure. In fact, this is a strategy that albatrosses use: they lock their wings in place during gliding without muscle input.

Other energy input is of course required to overcome drag, and permit climbing rather than just level flight. But, this energy can be applied through muscles that are not already doing double-duty with holding the wings in position. Still, there is a caveat: we are not aware of any biological examples of tendons or ligaments that are used in parallel with muscles, rather than in series with them.

Conclusions about forces in flight

We come away with the following conclusions about forces involved in flight:

  • Lift and thrust (and weight and drag) are the major forces in flight. Lift/weight is larger than thrust/drag by between 11:1 and 22:1.
  • The vast majority of force experienced by flight muscles during wing beats goes towards providing lift, rather than thrust.
  • If using muscles in a similar biological design to natural birds, pectoralis muscles would need to be inconveniently large, especially for comfortably sustained flight.
  • The use of elastic structures to help support lift might dramatically reduce force demands on pectoralis and other flight muscles, allowing muscles to focus on providing energy input rather than both energy input and load. However, more detailed study would be needed.

New anatomy needed


The skeletons of birds and bats are well-adapted for flight. We can take some inspiration from their skeletons, without needing to copy all structures precisely. Bird and bat ribcages are strong, having thickened ribs and a modified sternum, the keel. In our designs, we specify a thickening of the ribs.

Another important structural feature of birds is the acrocoracohumeral ligament (Baier et al., 2007). This ligament is very small, but quite strong – able to withstand forces 39 times greater than the animal’s body weight. Without this ligament, the shoulder immediately dislocates if flight is attempted (Baier et al., 2007). It will be important to include an equally strong ligament for flight of any anthro or quad.

Of course, final anatomical decisions, especially those which may impact: (1) specific mechanical function of the diaphragm, (2) flexibility (bending forwards and backwards; side-to-side; and rotation) of the torso and abdomen, and (3) mechanical strength of flight-related structures, will only be made after thorough consultation and testing.

Muscles and force-generating structures

In nature, the most important muscles for providing lift in flight are the pectoralis muscles, as described above in “Forces involved in flight”. According to to our calculations, biological pectoralis muscles similar to those in birds would need to be inconveniently large if scaled up for an anthro flyer. Size reductions should be possible if rationally designed structures without natural homologs were used, such as energy-recovering tendons to help with each wing beat.

There are other muscles throughout the wing in both bats and birds, similar to the musculature of the human forelimb (Biewener, 2011; Than, 2007; Tian et al., 2006). These are used to shape the wing throughout the wingbeat, but undergo relatively small strains.

Birds have an additional flight muscle called the supracoracoideus (Biewener, 2011). This muscle pulls on the wing humerus during upstroke. However, this muscle is very small in albatrosses (Brooke, 2018), so the supracoracoideus may not be as necessary for larger fliers or those that tend to glide more frequently. Furthermore, bats (like any mammal) completely lack a supracoracoideus, instead using their deltoids for wing upstroke. Therefore, we suspect a traditional deltoid would be sufficient for our anthro flyer.

Additional musculature might be required, such as muscles in the torso, to help a modified individual with wings to maintain an aerodynamic posture in flight.

Sensory and motor innervation

New motor and sensory neurons would be needed to supply conscious control of the wings, as well as to detect sensory sensations. While these do not strictly need to exactly mimic naturally occurring patterns, at the minimum, new neurons will need to be introduced, potentially through intentionally introduced ectopic ganglia.


While the above sections bring up several challenges, metabolism at least appears to be of relatively lesser concern.

When animals fly, they use energy rapidly per unit of time, but the energy cost per distance traveled is actually 7.5-fold lower than for land-based animals (Butler, 2016). Moreover, the larger a flying animal is, the more energetically efficient it is: hummingbirds weighing 3.5 g burn energy in excess of 200 Watts per kg of body mass in level flight, whereas bar-headed geese, weighing nearly 1000x that (2.8 kg) consume around 48-50 W/kg of body mass in level flight (Butler, 2016; Ward et al., 2002).

Animals that tend to soar or glide are even more efficient. Black-browed albatrosses (around 4 kg) metabolize around 8.8 W/kg when actively flying, or only 2.4 W/kg when gliding (Scanes, 2014). Griffon vultures (around 7.5 kg) metabolize around 4.4 W/kg during take-off, and 2.03 W/kg while gliding (Duriez et al., 2014).

A creature, whether person-sized, or larger, should be able to actively fly for around the same metabolic effort as running, without including any enhancements to athletic performance. They should be able to glide for very little effort.

Let us assume again (setting aside the crucial concerns in previous sections) that an anthro with a tail, wings, and flight muscles might weigh 80 kg (176 pounds). Let’s say they are a bit less efficient than an albatross, and draw around 12 W/kg to actively fly. For 15 minutes of active flight, this anthro would consume 12 W/kg * 80 kg * 0.25 hour = 240 Watt-hours, or 206 Kilocalories. In comparison, healthy people can produce 11.73 W/kg when jogging at 2.75 m/s (6.2 mph). Also similar to the albatross, we can guess gliding costs 3 W/kg. This is slightly less effort than walking at 1.25 m/s (2.8 mph) (Farris and Sawicki, 2012).

It appears possible that human metabolism could power active flight without any athletic enhancements.

Findings and implications

In this discussion, we have obtained a first-order approximation of what wingspan, airspeed, flight muscle size, metabolism, and anatomical modifications would be required for flight. It is clear that more accurate modeling would be needed, and it is very possible that this modeling may confirm the need to use non-biologically-inspired design features.


  • Detailed aeronautical engineering is needed to better anticipate airspeed and wingspan needs.
  • Force estimates indicate that either a very large pectoralis is needed, or rationally engineered structures such as tendons (e.g. in parallel with muscles) are needed.
  • New flight-associated anatomy will include new musculoskeletal features as well as new motor and sensory innervation, presumably with a need for precise control in conscious movement.
  • Metabolism appears to be of relatively lower concern.


  • Uncertainty in our models for airspeed and wingspan as well as for pectoralis muscle size may have important and safety-critical impacts on anatomical decisions made.
  • The required anatomy, regardless of specifics, will have uniquely high performance demands in mechanical terms, as well as in terms of very large new tissues that would need to be created and added to a person’s body.
  • The engineering models as well as anatomical demands are generally divergent from other anatomical goals.
  • Metabolism is a lower concern and does not weigh against the preceding implications.

Due to the implications arising from this document, we have chosen to delay the next stages of engineering until the appropriate time later in our research schedule.

Sources cited and associated documents

Associated documents

Sources cited

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Brooke, M. (2018). Far from Land: The Mysterious Lives of Seabirds.

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