Re: Hamiltonian for flight?

[John Peterson <jaypee@netcom.com>]

On Tue, Apr 06, 1999 at 05:45:43PM +0000, Digital ChoreoGraphics wrote:
> At 07:14 PM 4/5/99 -0400, you wrote:
> >Aeronautical physicists,
> >
> >	I am looking for the physics formula that demonstrates that
> >unpowered aerodynamic flight is characterized by a constant glide
> >ratio (as opposed to the parabolic curve of ballistic flight).
> >
> >[...]
> >
> >Bob
> >
> 
> Bob - 
> 
> I am not familiar with the formula in question, but you have the 
> Kinetic and Potential Energies, and the drag.  All that is missing is 
> an expression for Lift as a function of 'v'. 
> 
> However, I cannot find, in my physics texts, such an expression.  Perhaps 
> an associate with an aerodynamics background (or textbook).  The following 
> is the lift as a function of the 'circulation' about the airfoil:
> 
> F = p v L Gamma
> p is fluid density
> v is velocity of undisturbed fluid flow 
> L is length of wing
> Gamma is the fluid circulation above & below the wing.
> 
> I have seen Hamiltonians used for the equations of motion when there
> is no dissipation.  I suppose it will work in the glider scenario if 
> you assume negligable drag, in which case you could determine the 
> limits of motion. 
> 
> Let me know what you work out.
> - Don Black
> 

   I've never seen a variational solution of this problem, and I
suspect one would be rather messy. Both C_l and C_d (the coefficents of
lift and drag) for a whole aircraft (as opposed to just a wing) are
difficult to express in closed form. They are usually determined
experimentally (e.g. from a wind tunnel).

   The "proofs" I've seen simply equate the total force (the sum
of gravitational, lift and drag forces) to zero. The argument for the
existance of a stable solution (or extrema) is based on the observation
that in a power law representation, the exponent for rate of growth of
drag forces is larger than for lift forces, (with respect to both flow
velocity and angle of attack). [Similar to how you show a falling body
reaches some terminal velocity when you include aerodynamic drag].

   You might find one of the cheap Dover texts to be of some help. I
have "Theoretical Aerodynamics", by Milne-Thomson for when I need a
refresher.

   By the way, I'm not trying to play bandwidth cop, but the post
seems a little off topic. Is this for a Linux sim project? Or were you
just guessing you'd get a better answer than from the MS Windows
Aviation mailing list?

Regards, JOhn

-- 
 ___|___  | John C. Peterson, KD6EKQ | Micro$oft free since 1987!!!
  -(*)-   | mailto:jaypee@netcom.com | Where would you like to go tomorrow?
  o/ \o   | San Diego, CA   U.S.A    | See http://www.linux.org/ for info!
-
Archives of linux-aviation: http://mail.nl.linux.org/lists/linux-aviation/
To unsubscribe: send the command "unsubscribe linux-aviation" in the body
of a mail message to <Majordomo@mail.nl.linux.org>.