The mythical flying horse Pegasus lead me to consider power requirements for sustained hover. It is not clear to me that Pegasus ever sustained a hover, but simple analysis yields some interesting results.
From momentum theory, the minimum power required to maintain hover out of ground effect is:
Where:
- T is vertical thrust
- is air density
- A is the area of rotating or flapping surface
Assuming the mass of a horse to be roughly 500 kg, air density at sea level, and a wing area of 6 m2, the required hover power is:
P = 121 Horsepower
Given the definition of Horsepower, we can make several conclusions:
- Pegasus cannot sustain hover out of ground effect
- Pegasus is more powerful than the average horse by at least two orders of magnitude
- Pegasus is much lighter than the average horse
- The drawings of Pegasus' wings are not to scale
Consider power requirements for a hummingbird with a wing area of 0.003 m2:
P = 0.059 Watts
This is roughly six orders of magnitude less than that required by Pegasus. This is due the non-linear increase in power requirement as a function of thrust. Note that hovering insects and animals found in nature tend to be quite small. This is due to relatively low power density of organic muscles compared with man made engines.
From a historical perspective, helicopter development had to wait for power plants with sufficient power density. This is part of the reason helicopters were developed many years after fixed wing aircraft. Much of the increase in engine power density is due to dramatic improvements in fuels and oil refineries during the first half of the 20th century. The power density of gasoline engines roughly doubled between 1900 and 1940. Development of gas turbine engines increased power density by roughly another factor of two in the second half of the 20th century.