Longitudinal static stability is an important aspect of an airplanes performance characterization as it plays a fundamental role in the operation of the plane. An airplane is statically stable when forces and moments exerted on the aircraft by a disturbance tend initially to return the airplane to its equilibrium position. For example, an airplane trimmed in level flight encounters an upward wind gust causing the nose of the airplane to pitch up; the statically stable planes nose will initially pitch back toward its original trim attitude, whereas the statically unstable airplane would continue to pitch up until countered by pilot input or a stall occurs when its critical angle-of –attack is exceeded. With this example in mind one might come to the conclusion that airplanes should be designed with as much static stability as possible to minimize overall pilot workload and aid in safe operation. Unfortunately it seems this line of reasoning rarely comes cheap as an excess of static stability comes with the price of reduced controllability. An airplanes degree of static stability will cause it to react to forces generated by control inputs in like manner to those of unwanted origin such as wind gusts; thus requiring greater control force to effect maneuvering flight. Greater control force causes increased pilot workload. The solution to this dilemma lies in compromise according to the designed mission of the airplane. A Kopp BD-4, does not need the maneuverability of a Navy SH-60B Seahawk attack helicopter (the pride of the fleet).

For an airplane to be statically stable (longitudinally) the following criteria must be met:

Positive zero lift moment coefficient, C_M,o
Negative change in moment coefficient due to a change in angle of attack

The term C_M,c.g. is the moment coefficient about the center of gravity of the airplane. is determined by the following equation:

, where h_c.g. and h_ac are locations of the c.g. and aerodynamic center of the aircraft measured with respect to the leading edge of the wing. This equation clearly shows the importance the location of c.g. has in static stability. The location of the c.g. (h_c.g.) such that = 0 is defined as the neutral point of the aircraft and is often used as an alternate measure of static stability. When the c.g. is forward of the neutral point (h_n) the aircraft is statically stable. Conversely when the c.g. is aft of the neutral point the aircraft is unstable. Therefore the difference between locations of neutral point and c.g. (h_n-h), defined as static margin, is a positive value for statically stable aircraft and negative for those that are unstable.

The purpose of flight test III is to determine the location of both stick fixed and stick free neutral points to further build upon the Kopp BD-4 performance summary table initiated in flight test I and expanded in flight test II. The current performance summary table is shown below.

Table 1 Performance Summary Table

Altitude / Weight	Max C_l/C_d	Min Thrust Required
3000 ft / 1950 lbs	8.8235	217.87 lbs
7500 ft / 2130 lbs	9.0329	229.63 lbs
Parameters	Drag Polar	Power Curve
C_do	0.0440	0.0425
e	0.7031	0.6507
Altitude	Minimum Thrust Horsepower Required
3500 ft 1950 lbs	52.33 HP
7500 ft 2130 lbs	60.59 HP
Standardized	59.16 HP
V_{ex (Ias)}	75 mph
V_{ie (ias)}	90 mph
R/C_max S.L max GW	799 fpm
AOC_max S.L. max GW	5.71°
Service Ceiling @ max GW	10,600 ft
Absolute Ceiling @ max GW	11,400 ft
Kopp BD-4 Summary Table Test I conducted 27 July, 2000 Test II conducted 12 Aug, 2000 Data to be added upon further testing

Part I – Flight Test

General Information

This test was conducted in the Kopp BD-4 on 24 Aug, 2000 departing from Monterey Peninsula Airport (MRY) at 10:00 am. Conditions at take-off were:

Wind: 290/8

Alt: 30.04

Sky Clear

Rwy: 28R

Crew and altitude assignments were as follows:

Table 2 Crew and altitude assignments

Crew – Stick free	Altitude	Gross Weight (approx)
LT Ken Kopp / Maj. Jim Hawkins	5500 ft	2025 lbs
Crew – Stick Fixed	Altitude	Gross Weight (approx)
LT Ken Kopp / Maj. Jim Hawkins	5500 ft	2025 lbs

The test area was restricted to Salinas Valley from Salinas to 15 miles South East of King City. Crew coordination and a thorough test procedures briefing preceded each flight. Data collection sheets were developed, printed and discussed in detail prior to flight as well. Specific responsibilities were delegated as follows:

Table 3 Flight Responsibilities

Responsibility	Pilot at the Controls	Pilot Not at the Controls
Flight Safety	Primary	Secondary
Airwork	Primary
Test Procedure		Primary
Data Recording		Primary
Communications	Primary	Secondary
Navigation	Secondary	Primary
Visual Lookout	Secondary	Primary
Emergencies	Primary	Secondary

ATC flight following was utilized to the maximum extent possible to aid in collision

avoidance. King City and Salinas Muni were designated primary diverts in the event an emergency due to mechanical failure or weather occurred.

To minimize parallax error the left seat pilot remained at the controls while the right seat pilot recorded data.

Flight Test Technique

Data necessary for determination of the stick fixed and free neutral points is obtained by measurement of stick (yoke) deflection and force throughout the aircrafts velocity range for different c.g. locations referenced to a nominal mid-range trim value. 120 mph was chosen as that trim airspeed for this aircraft. All yoke displacements and force measurements are made with respect to this initial position.

Four runs were completed at varying c.g. locations. The c.g. was changed by landing and rearranging previously measured ballast. Fuel was added as necessary to maintain a consistent gross weight between each run. In flight the aircraft was leveled at altitude, trimmed to 120 mph and the yoke displacement measured. Force measured at the trim airspeed is zero (by definition of “trim”). Airspeed was changed by climbing (diving) the aircraft while maintaining a constant power and trim setting. Once stabilized at the new airspeed the following parameters were recorded:

Airspeed
Altitude
Rate of Climb (descent) (based on timing between an initial and final altitude)
OAT
Stick Position
Stick Force

To obtain stick force a Wagner FDL force dial was used to push (pull) the yoke against trim. Once stabilized the dial reading was recorded.

Part II – Data Reduction

Stick Fixed

All recorded data was entered into an excel spreadsheet for data analysis. As was done in previous flight test all airspeeds and altitude measurements are corrected for static position errors. Center of Gravity locations are commonly referenced by the percent of the mean aerodynamic cord (%mac) the c.g. is aft of the leading edge of the aircraft. The Kopp BD-4’s MAC is 48” with the leading edge of the wing 75” aft of the nose cone, the reference point for all moment arms used in weight and balance determination. Subtracting the leading edge distance from c.g. locations and dividing the result by the MAC results in c.g. location in terms of %mac. The following table displays the c.g. locations flown during this test.

Table 4 c.g. Locations

c.g. Location
c.g. (inches)	%mac
85.63	22.15%
86.49	23.94%
87.2	25.42%
89.12	29.42%

The published c.g. limits for the Kopp BD-4 are 20.8% forward and 31.25% aft showing the values flown cover a large portion of the entire c.g. range permitted.

With recorded data for altitude, OAT, A/S and ROC (ROD) the aircrafts lift coefficient is determined by:

Because an increment in c.g. location causes a proportional increment in elevator position for a given airspeed (C_L) and the aircraft lift coefficient is proportional to angle of attack, determination of the c.g. location where is the also the c.g. location making =0 which is the neutral point. Plots of stick position vs. aircraft lift coefficient for each c.g. location are shown below.

Figure 1 Yoke Position vs. CL 22% c.g.

Figure 2 Yoke Position vs. CL 24% c.g.

Figure 3 Yoke Position vs. CL 25% c.g.

Figure 4 Yoke Position vs. CL 29% c.g.

Finding the values of is accomplished by taking the first derivative of the curve fit equations from the plots of yoke position vs. C_L above. Values of for each c.g. location and C_L are tabulated below.

Table 5

Stick Fixed Neutral Point (dyoke/dCL)
	c.g.	c.g.	c.g.	c.g.
CL	22.15	23.94	25.42	29.42
0.316	-5.36	-4.08	-4.70	-2.03
0.412	-4.15	-3.39	-3.71	-1.77
0.550	-2.73	-2.55	-2.57	-1.40
0.752	-1.31	-1.61	-1.48	-0.86
1.048	-0.62	-0.84	-1.12	-0.07

The stick free neutral point is determined by plotting the values of vs. c.g. for each C_L, curve fitting and extrapolating each line to zero. The intersection of these curves with zero (x axis) is the location of the neutral point for the given value of C_L. A linear airplane will have a single point of intersection indicating the neutral point is indeed a fixed point. A non-linear airplanes’ neutral point becomes a function of C_L. A plot of vs. c.g. is shown below.

A table of the neutral points for each C_Lalong with a corresponding plot are shown below

Table 6 Stick Fixed Neutral Points

Stick Fixed Neutral Point vs. Cl
CL	NP
0.3	34.5%
0.4	35.5%
0.5	37.5%
0.7	42.0%
1	33.0%

Figure 5 Stick Fixed Neutral Point vs. Cl

Stick Free

Stick free neutral point is determined in similar fashion. With corresponding plots shown below.

Figure 6 F/q vs. Cl

Once again to locate the neutral point requires a plot of the slopes of each of the curves above vs. c.g. position as shown below.

Figure 7 Stick Free NP

According to the above plot the stick free neutral point is 82% mac.

Part III – Conclusions

The results obtained for the stick fixed neutral point are reasonable in that the aircraft will remain stable throughout its published range of c.g. locations. However, the neutral points were determined through linear curve fit with chi square values of about 84%. The fourth data point (aft most c.g.) was recorded during an additional flight because the reduced data from the original three data points resulted in unstable neutral points. This occurred because the range of c.g.’s was not great enough to cause sufficient data spread. Having personally flown the test flight, I feel confident the data was collected consistently and following proper procedure. This particular airplane has a significant amount of stabilator area and is an all-flying stab configuration. Yoke position changes with airspeed are very small compared to airplanes of similar performance and weight causing the data to fall into very tight groups when c.g. positions are located at intermediate values. This makes curve fit extrapolation to zero very susceptible to errors in measurement, friction in the control system and round-off errors. Taking the average range of stick fixed neutral points results in a value of 36.5% giving the Kopp BD-4 a static margin of 5.25% at the aft c.g. and 16.5% at the forward c.g..

The result of 82% stick free neutral point must be discarded as invalid for two reasons. If the stick fixed results are accepted as valid then a more stable stick free neutral point does not make sense. Secondly, recording an accurate force measurement was extremely difficult because of variations in stick force required during flight to maintain a constant airspeed. It is very difficult to hold an airspeed against trim with a consistently constant force applied. The pilot is continually making small corrections thereby changing the reading on the force dial. Every attempt was made to determine the average reading during a particular run. Additionally, having recently spoken with the designer of the BD-4, Mr. Jim Bede, he felt strongly the BD-4 was designed with little difference in stick fixed and free neutral points. This is mostly due to the configuration of the anti-servo trim tab that prevents the stab from changing its trim position with hands free. This assertion has been confirmed by trimming the aircraft and displacing the yoke against trim and releasing the yoke. The yoke and airplane returns to its trim position indicating very little friction or free play in the longitudinal flight control system. The Kopp BD-4 summary table can now be expanded to include the stick fixed neutral points.

Altitude / Weight	Max C_l/C_d	Min Thrust Required
3000 ft / 1950 lbs	8.8235	217.87 lbs
7500 ft / 2130 lbs	9.0329	229.63 lbs
Parameters	Drag Polar	Power Curve
C_do	0.0440	0.0425
e	0.7031	0.6507
Altitude	Minimum Thrust Horsepower Required
3500 ft 1950 lbs	52.33 HP
7500 ft 2130 lbs	60.59 HP
Standardized	59.16 HP
V_{x (ias)}	75 mph
V_{y (ias)}	90 mph
R/C_max S.L max GW	799 fpm
AOC_max S.L. max GW	5.71°
Service Ceiling @ max GW	10,600 ft
Absolute Ceiling @ max GW	11,400 ft
Longitudinal Stability
Stick Free / Fixed Neutral Point	36.5% (mac)
Forward c.g. static margin	16.5% (mac)
Aft c.g. static margin	5.25% (mac)

Table 7 Kopp BD-4 Performance Summary Table

Altitude / Weight

Parameters

Drag Polar

Power Curve

Cdo

0.0440

0.0425

e

0.7031

0.6507