Back at it. To summarize the Phugoid Mode - low freq (large period), lightly damped, alpha (AOA) assummed constant. Fn ~ 1/V , dp ~ Cd/Cl

Typical period ` 20+ sec, Houston's Magni ~ 18 - 19 sec (flt test). There is not much to "design" here. Easily controlled/trimmed in cruise fltt. No impact on Maneuver Flt.

**SHORT PERIOD**
This is the bread and butter of longitudinal stability. The same 2nd order eqns apply but the variables having strong influences on Fn and dsp (short pd damping ratio) are different. The static stability design factors have a large influence on short period characteristics.

**Variables** include AOA, deck angle, vertical g, and rotor rpm (rrpm). For simple testing, deck angle is the easiest to observe. Here's where rotor / airframe coupling discussions can enter. I will assume (?) for small pertubations about a trimmed condition, the rotor will follow the airframe with maybe some lag. For the math and flt test we define/set AS and Alt constant.

What are the variables?

Fnsp ~ Cma, 1/(Iyy)^0.5 , AS

dsp ~ Cmq, 1/(Cma)^0.5 , 1/(Iyy)^0.5

where

Fnsp - short pd. undamped natural freq.

Cma - restoring moment chg due to AOA chg, sign is neg by convention for statically stable AC. This is a strong term for both freq and damping and per static stability criteria affected by HS size and location as well as CG vs RLV

Iyy - here's your mom. of inertia about longit.

axis by convention.

Cmq - pitch rate damping - guys are getting creative naming this one. Moment change due to pitch rate or AOA rate chg (assuming rotor follows fuselage).

Changes in SP characteristics:

AS ^ - Fnsp v( v = down or lower)

Iyy ^ - Fnsp & dsp v Increassing mass about Y axis decreases damping &

freq

Cma ^ - Fnsp & dsp ^

Cmq ^ - Fnsp & dsp ^

Static Margin (cg vs RLV) v - Cma v and Fnsp v

Just like the Phugoid, thee characteristic eqn consists of a damping term

2 dps Fnsp and the frequency term Fnsp^2.

**dsp ** - damping ratio can be described by the number of overshoots of deck angle, vertical g, AOA, or rrpm. For dsp between 0.1 and 0.7, dsp can be approximated by dsp ~ 0.1 (7 - #peaks). These are peak overshoots until totally damped.

Here's some common terminology wrt damping ratios:

Overdamped - d > 1

Critically damped - d = 1

Underdamped - 0<d<1 this is where we'll usually operate ( 0.1 - 0.7)

Undamped - d = 0

Negatively damped d < 0

**2 dsp Fnsp ** - damping term which can be described as inversely proportional to the time to damp. We can measure this in flt test. Sometimes we refer

to what is called a time constant (Tau) = 1/dFn where one time constant = 63% of the final original value. Sometimes we use time to half amplitude -

T1/2 = .69/dFn.

I had an opportunity to fly a highly augmented Lear jet belonging to the Calspan Corp out of NY. We could "vary" many stability derivatives to see how flight characteristics changed. This was an outstanding teaching aid. Quoting from their manual:

*It is important to remember iin stability and control work that neither frequency nor damping ratio, nor time to damp *__alone__, will be sufficient to predict handling qualities. It is the combination of Fn and d and consequently 2*Fn* (time to damp) that is meaningful
It's difficult, if not impossible for specific cookbook numbers to apply to the LSA standards but we CAN talk about ranges of damping ratios and natural frequencies which are based on a large data base of pilot surveys while flying this augmented airplane. These same "goodness" ratings were bounded and put on a logarithmic chart with Fn vs d. The best tested boundary had d varying from 0.4 to 1.2 and Fn varying from 0.5 to 1.2 cycles per sec. More qualitative descriptions of these damping and freq ranges later.

I will try to get this graph thrown up on this forum. I contend the same favorable goodness, or pilot in the loop, ranges apply to sport gyros.

I'll later try to discuss simple FTTs for the short period including what some may be seeing as periods less than the phugoid but longer than a "typical" short period response.

I will also try to tie it all up in a Man. Flt discussion. Like Greg G. said all we may find is we need an adequate tail, reasonable cg wrt rlv and thrust line. I'm just trying to help put some #s (or reasonable ranges of numbers)on values we're not too used to defining. When all is said and done, it will be flt test and the inputs of many gyro pilots to come to a consensus. It will be as much qualitative as quantitative.