Chapter 6

Chapter 6

• Some aspects of insect flight will be analyzed in this chapter.
• Many of the concepts introduced in the previous chapters will be used to calculate the hovering flight of insects.
• Most of the parameters required for the computations were obtained from the literature, but some had to be estimated because they were not readily available.
• The size, shape, and mass of insects can be different.
• The insect with a mass of 0.1 g is about the size of a bee.

• Birds and insects are a complex phenomenon.
• The changing shape of the wings at various stages of flight would be taken into account in a complete discussion of flight aerodynamics.
• There are differences in wing movements between insects.
• The following discussion shows some of the basic physics of flight.

• Many insects and small birds can beat their wings so fast that they can fly over a fixed spot.
• The lifting force needed to overcome the force of gravity is complicated by the wing movements in a hovering flight.

• The downward stroke of the wings results in the lifting force.
• The air on the wings creates a reaction force that pushes the insect up.
• The force on the wings of most insects is small during the upward stroke.

• The force of gravity causes the insect to fall.
• The upward force produced by the downward wing movement restores the insect to its original position.
• The vertical position of the insect is affected by the wingbeat.

• The distance between wingbeats depends on how quickly the insect's wings are beating.
• The time interval during which the lifting force is zero is longer if the insect flaps its wings at a slow rate.

• We can easily calculate the wingbeat Frequency for the insect to maintain its stability.
• Let us assume that the lifting force is zero while the wings are moving down and that it is zero while the wings are moving up.

• The insect is back to its original position after the upward stroke.

• Our example shows that the Frequency is over 100 wingbeats per second.
• This is a typical insect wingbeat, although some insects such as butterflies fly at a lower rate, about 10 wingbeats per second, and other insects produce as many as 1000 wingbeats per second.
• The average upward force on the insect is simply its weight, since the upward force on the insect is only applied for half the time.

• Different wing-muscle arrangements are found in insects.

• The force is applied to the wings with a Class 3 lever.
• The wing's length is assumed to be 1 cm.

• The flight muscles of insects are similar to those of humans.

• The muscles of the wing.

• The insect wing muscles are very strong.
• The wings have a lever arrangement.

• The period for one up-and-down motion of the wings is 9 x 10-3 seconds.
• Many types of muscle tissue can be seen contracting at such a rapid rate.

• The power required to maintain hovering will now be calculated.
• We can assume that the force generated by each wing acts through a single point at the midsection of the wings because the pressure applied by the wings is uniformly distributed over the total wing area.

• We can now look at where this energy goes.
• Each downstroke the mass of the insect has to be raised by 0.1mm.

• This is a small part of the total energy expenditure.
• Most of the energy is spent in other processes.
• The insect wing is moving.

• We neglected the energy of the wings in calculating the power used in hovering.
• The wings of insects, light as they are, have a finite mass.

• We will assume that the wing can be approximated by a thin rod pivoted at one end.

• At the beginning and the end of the wing stroke, the wings are not moving.
• The linear maximum velocity is higher than the average.
• The maximum speed is twice as high as the average speed if we assume that it varies along the wing path.

• The energy from the two wing strokes in each cycle is 2 x 43 86 erg.
• This is about the same amount of energy as hovering itself.

• The muscles provide the energy that the wings gain as they are accelerated.
• The energy must be dissipated when the wings are decelerated.
• The energy from the downstroke is dissipated by the muscles.

• Some insects are able to use the upward movement of their wings to aid in their flight.
• The resilin is stretched during the upstroke of the wing.
• The stretched Resilin stores the energy from the wing in a similar fashion to a spring.
• This energy is released when the wing moves down.

• The amount of energy stored in the stretched Resilin can be calculated using a few simple assumptions.
• We will assume that throughout the stretch the Resilin obeys Hooke's law.
• The area and Young's modulus change in the process of stretching as the resilin is stretched by a considerable amount.

• In an insect the size of a bee, the volume may be equivalent to a cylinder 2 x 10-2 cm long and 4 x 10-4 cm2 in the area.
• When stretched, the length of the rod is assumed to be increased by 50%.

• The upstroke of the wings has 36 erg of stored energy, which is the same as the stored energy in the two wings.
• Experiments show that 80% of the wing's energy can be stored in the Resilin.
• The use of Resilin is not limited to wings.

• The muscle should be parallel to the wing throughout the wing motion.

• A cylinder 2 x 10-2 cm long and 10-4 cm2 in area is equivalent to the shape of the flea's legs.
• The energy is stored in the resilin.

• A person with 50 kilograms of body weight could have Resilin pads in her joints.