The Art of the Helicopter John Watkinson - Karatunov.net

30 The Art of the Helicopter
reversible. Work is done winding the spring or charging the battery and this is turned
into stored energy, most of which can later be released to do work.
Energy can also be stored in the position and motion of objects. If a weight is lifted
against gravity, it stores potential energy that can be released when the weight is lowered
again. Potential energy is proportional to the height through which the object is lifted.
If a weight is accelerated, the resultant force acting on it moves through a distance
and does work which is stored as kinetic energy. Figure 2.10 shows a mass being
accelerated from rest by a constant force F over a distance s in time t up to a velocity v.
The kinetic energy of the mass is equal to the work done on it. This is equal to the
product of force F multiplied by distance s.
Since F = m × a, then KE = m × a × s.
Acceleration is the rate of change of velocity, thus a = v/t. Since the velocity increases
uniformly then distance s is the time multiplied by the average speed, thus s = 1
v × t. 2
KE = m × a × s = m × v v · t m · v2
× =
t 2 2
Kinetic energy is proportional to the square of the velocity. Power is the rate at which
work is done or the rate at which energy is released, which is the same thing. Thus a
high powered engine will burn fuel at a higher rate in order to release more energy in
a given time.
The final quantity to be considered is momentum. This is equal to the mass multiplied
by the velocity. The use of momentum will better be explained when the topic of lift
generation is dealt with in Chapter 3.
A helicopter in flight has both kinetic and potential energy. This energy was stored
in the helicopter by doing work against the earth’s gravitational field. Thus the helicopter’s
potential and kinetic energy exists with respect to the earth and Newton’s laws
determine what the helicopter will do with respect to the earth when forces act upon it.
The earth is the inertial frame of reference.
Other than gravity, the forces when airborne can only come from the movement of
the machine and its rotors with respect to the air. In still air the aerodynamic frame
of reference and the earth’s frame of reference are the same and this simplifies matters.
However, when considering a machine flying in the presence of a wind, it is important
to realize that the wind means that the aerodynamic frame of reference is moving with
respect to the inertial frame of reference.
The reader is cautioned against texts that erroneously claim that the helicopter flies
only with respect to the air because it doesn’t know what the ground is doing and that
all that matters is airspeed. If this were true artificial horizons and inertial navigators
wouldn’t work.
Fig. 2.10 A mass being accelerated will gather kinetic energy (KE) as derived here.