Power required for helicopter to hover.

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SUMMARY

A helicopter requires a specific power output, denoted as P, to hover. When a second helicopter is created with linear dimensions half that of the original, the power required for it to hover is one-eighth of the original helicopter's power. This conclusion is based on the relationship between volume, mass, and lift area, where volume and mass decrease by a factor of eight and lift area decreases by a factor of four. Therefore, the second helicopter can hover with only 0.5P of power, confirming that power scales with mass.

PREREQUISITES
  • Understanding of basic physics principles, particularly volume and mass relationships.
  • Knowledge of lift dynamics and how rotor area affects helicopter performance.
  • Familiarity with scaling laws in physics, especially in relation to geometric shapes.
  • Basic mathematical skills for manipulating equations related to volume and area.
NEXT STEPS
  • Research the principles of fluid dynamics as they relate to rotorcraft lift.
  • Study the effects of rotor diameter and rotation speed on helicopter performance.
  • Explore scaling laws in physics, particularly in mechanical systems.
  • Investigate the relationship between power output and mass in various aircraft types.
USEFUL FOR

Aerospace engineers, physics students, and anyone interested in helicopter design and performance optimization will benefit from this discussion.

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Homework Statement



A helicopter can hover when the output of its engines is P. A second helicopter, an exact copy of the first one, but its linear dimensions are half of those of the original. What power output is needed to enable this second helicopter to fly?


Homework Equations



The teacher describes this problem as being "maximum physics and minimum maths" so I am modeling the helicopter as a sphere for simplicity and working from there.


The Attempt at a Solution



If the helicopter is a sphere then decreasing the radius of the sphere by a half will decrease the volume by an eighth (V is proportional to radius cubed).
If the volume is decreased by an eighth then the mass is decreased by an eighth.

The lift of the blades if proportional to area of the circle they sweep out so decreasing their length by a half will decrease the area of the circle by a quarter (area is proportional to r squared).

So if the weight is decreased by an eighth and the lift from the blades is decreased by a quarter then half of the power of the original helicopter will suffice for this one to hover.

Am I missing anything?
Is this solution plausible?
Thanks for the help.
 
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Honestly I think you went further.
The power needed is just one eight of the bigger helicopter.
 
It is all about scaling. Power scales with mass (you better try to prove it).

Rotor diameter doesn't matter, as amount of air moved depend not only on rotor diameter, but also on the rotation speed - and it doesn't have to be constant.
 

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