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.