Expert: Mark Janus - 5/26/2009

Question
QUESTION: Hi Mark,

In the midst of the great debate on downwind turns the following claim was
made:

"The inertial frame of reference for an aircraft is the ground, and it is the
aircraft's velocity relative to the ground which
determines its kinetic energy.  Hence if an aircraft is flying downwind with a
30 knot tailwind and 30 knot wind speed it has
kinetic energy but an aircraft flying upwind has zero kinetic energy!  If the
aircraft (read helicopter) then makes a downwind
turn it will lose height (after compensating for drag) whereas the helicopter
turning upwind will gain height because its
wind speed will rise from 30 knots to 90 knots due to conservation of kinetic
energy!

I an unqualified in this field but to my amateur way of thinking the assertions
made concerning kinetic energy and airspeed
are erroneous.  An aircraft's inertial frame of reference is the air mass in
which it is operating and hence both helicopters have
equal kinetic energy?

I would appreciate your assistance in explaining this concept and your
thoughts on upwind vs downwind turns and the power
required to maintain height in both instances.

Thanks

Steve

ANSWER: Hi Steve,

Sorry for the delay in getting to your question...
Kinetic energy is a relative property of a body (it depends on the reference frame).
The flight (or lift) of an aircraft depends on the relative velocity of the air to the vehicle (in the case of a helicopter it's the relative speed of the air to the rotor blade).
The kinetic energy of a body in an inertial frame of reference is simply a function of the speed of that body in that frame of reference. It's easier to explain with airplanes (since a helicopter's lift is more complicated since it does not require any horizontal motion).
An airplane must maintain a minimum relative airspeed to maintain lift.  When traveling downwind, the airplanes ground speed will be faster than when it is traveling upwind.  Recall it's the ground speed that determines the aircraft's kinetic energy relative to the ground (reference frame) and thus it's downwind kinetic energy will be greater than its upwind value.  
When a helicopter (in hover) turns downwind, the relative air velocity decreases and hence the lift is decreased whereas when turning upwind the opposite occurs (increased relative wind and hence more lift)....  

In steady level flight, relative to the air mass (reference frame) the kinetic energy would be the same (again when referenced to a coordinate system attached to the air mass (of steady velocity)....

Hope this helps,
mj

---------- FOLLOW-UP ----------

QUESTION: Dear Mark,

Thanks for your response.  I don't want  to take up your time in a prolonged
dialogue but I am puzzled.

You say:

"The flight (or lift) of an aircraft depends on the relative velocity of the air to
the vehicle (in the case of a helicopter it's the relative speed of the air to the
rotor blade)."

..and then:

"When a helicopter (in hover) turns downwind, the relative air velocity
decreases and hence the lift is decreased whereas when turning upwind the
opposite occurs (increased relative wind and hence more lift)...."  

If the helicopter turns, how does the "relative velocity of the air to the
vehicle" change?    Isn't a helicopter "in hover" merely maintaining airspeed at
the same rate as happens to be the wind's groundspeed?  So what's the
importance of groundspeed?

I note your final sentence: " In steady level flight, relative to the air mass
(reference frame) the kinetic energy would be the same (again when
referenced to a coordinate system attached to the air mass (of steady
velocity)....

Regards

Steve

Answer
A helicopter in hover is independent of the wind speed and yes it would be carried with the wind (at the wind's groundspeed), so both wind and helicopter would travel together (zero relative velocity for the most part).

For a helicopter to turn the rotor blade axis is "tilted" in the direction you want to go, by tilting "with the wind" (i.e. in the direction of the wind) the velocity through the rotor blade will decrease slightly and hence the lift will decrease...  for upwind turns the opposite occurs

groundspeed is only important when it comes to traveling somewhere, has no impact on the lift (flight) on the vehicle (unless maybe you're talking about spacecraft and launch locations/directions)

Hope this helps,
mj