Tailess aircraft - stability
Dave Pinella
to calculate the necessary stability derivatives for longitudinal and
lateral stability. In the case of longitudinal stability I've been
using approximate equations for Cmq (complete aircraft pitch damping)
and Cm-alpha-dot (damping due to to dAlpha/dt) which assume a
conventional tail type aircraft. These equations use dEpsilon/dt, and
Cl of the horizontal tail and other geometric parameters.
My question is this. I would like to study tailess aircraft. I'm at a
bit of a loss as to how to calculate these terms in a tailless
configuration. My references don't discuss this topic. If anybody
could point me to a reference or give any other input I'll greatly
appreciate it.
Thanks!
Dave P
Mark Drela
> I've been using panel methods (successfully!) for some time in order
> to calculate the necessary stability derivatives for longitudinal and
> lateral stability. In the case of longitudinal stability I've been
> using approximate equations for Cmq (complete aircraft pitch damping)
> and Cm-alpha-dot (damping due to to dAlpha/dt) which assume a
> conventional tail type aircraft. These equations use dEpsilon/dt, and
> Cl of the horizontal tail and other geometric parameters.
> My question is this. I would like to study tailess aircraft.
Cm-alpha-dot for a flying wing merely represents the Theodorsen lag effect.
This is normally negligible for alpha_dot c/2V < 0.05 or so, which is a
rather violent pitch motion. It can be ignored for most pitching situations.
The rate derivatives Cmq, Clp, Cnr, etc. can be computed with a modified
panel method. The modification is very simple: replace the freestream
velocity V at each control point location "r" with the local apparent
velocity due to both the freestream V and the aicraft rotation rate W.
V_local = V - W x r
V = (u,v,w) freestream velocities
W = (p,q,r) rotation rate
r = (x,y,z) of control point
All these must obviously be in the same set of axes.
By setting first W_1 = (0,0,0), then W_2 = (0,0.01,0), say,
Cmq is computed by finite difference:
Cmq = (Cm_2 - Cm_1) / (q_2 - q_1)
- Mark Drela
- MIT Aero & Astro
Jewel B. Barlow
Dave Pinella wrote:
> I've been using panel methods (successfully!) for some time in order
> to calculate the necessary stability derivatives for longitudinal and
> lateral stability. In the case of longitudinal stability I've been
> using approximate equations for Cmq (complete aircraft pitch damping)
> and Cm-alpha-dot (damping due to to dAlpha/dt) which assume a
> conventional tail type aircraft. These equations use dEpsilon/dt, and
> Cl of the horizontal tail and other geometric parameters.
>
> My question is this. I would like to study tailess aircraft. I'm at a
> bit of a loss as to how to calculate these terms in a tailless
> configuration. My references don't discuss this topic. If anybody
> could point me to a reference or give any other input I'll greatly
> appreciate it.
See Section 5.4 of Dynamics of Flight, Stability and Control, by
Bernard Etkin and Lloyd Reid, John Wiley & Sons, Inc., 1996. The
first order approximation is that a pitching airfoil generates a
normal flow along the chord line that is equivalent to the normal flow
distribution on a parabolicaly cambered mean line. This provides an
approximation to Cmq.
Jewel B. Barlow
Dr. Jewel B. Barlow
http://windvane.umd.edu
Director, Glenn L. Martin Wind Tunnel;University of Maryland
Jewel_...@umail.umd.edu
Tom Speer
>
> ...
> My question is this. I would like to study tailess aircraft. I'm at a
> bit of a loss as to how to calculate these terms in a tailless
Try Datcom (http://www.pdas.com/) for empirical methods. The
panel code should be able to calculate CMq for you; the main
question might be the wake shape (linear, circular, parabolic,
sinusoidal?). CMalpha-dot can probably be neglected, since the
time lag over the chord of the wing is probably insignificant at
the frequencies you'd be looking at for stability and control.
Cheers,
--
Tom Speer
tsp...@gte.net
http://home1.gte.net/tspeer
fax: +1 206 878 5269