Derivation of the equations:

The vehicle is moving as shown in Figure 1:

Figure 1

We consider a coordinate system fixed in the transverse plane, moving, but not rolling over with the vehicle (Figure 2):

Figure 2

The vehicle is presumed to be traveling away from the viewer. The point P represents the bottom of the tires on the right side of the vehicle. The vehicle will be rolling over about an axis through the point P.

The vehicle is initially presumed to be traveling in a straight line at time t=0, with a velocity V₀, when the driver suddenly and sharply turns the wheel to the right or left. We will thus consider a steering induced rollover, which is the most common kind. For the purposes of the analysis we will assume that the driver turns the wheel to the left, but we could just as well have assumed that the driver turns the wheel to the right. The analysis is the same either way.

If the speed is sufficiently high and the radius of curvature of the path of the vehicle is sufficiently small, the vehicle will begin to roll over; that is, rotate about an axis through the point P.

Figure 2 shows the vehicle after it has begun to roll over. The vehicle will experience a centrifugal force fc1 due to the curvature of the path of the vehicle. In addition, the vehicle will experience a centrifugal force fc2 due to the roll, and a force W due to the weight of the vehicle. r_cg is the distance from the point P to the center of gravity (cg) of the vehicle. Theta (q) is the angle between the radius vector r_cg and the x axis, thetao (q₀) is the angle between the radius vector r_cg and the bottom of the vehicle and c is the angle between the x axis and the bottom of the vehicle. Thus,

c = q - q₀

Newton’s second law of motion may be may be expressed as

(1)

where T is the torque, I the moment of inertia, and the angular acceleration. Applying this equation to the rotation of the vehicle about the axis through the point P we get,

(2)

where is the radius of gyration, M the mass of the vehicle, , r the radius of curvature of the path of the vehicle, w_c the angular velocity of the vehicle about the center of curvature of the path, r_cg the distance from the point P to the center of gravity of the vehicle and W the weight of the vehicle.

We assume that the driver is turning the steering wheel so that the angle of the front wheels, w_a, varies linearly with t; i.e., w_a=ct. We have taken the proportionality constant c as 7⁰ per second, based on our experience as to how fast the driver of a vehicle equipped with power steering can turn the steering wheel.

We assume the driving speed of the vehicle, V₀ to remain constant; that is, the rpm of the rear wheels is assumed to be constant with no longitudinal slip. In order to determine the actual path of the vehicle we have to take into account two other factors: slip and slide. Slip refers to the fact that in a turn the front wheels may not be traveling in the direction the wheels are pointed in due to the distortion of the tires. Slide refers to the sideways motion of the wheels due to the centrifugal force. Szostek et al (1) identify three regimes: slip in the absence of slide, pure slide, and a transition region where both slip and slide are present. In the present case, the vehicle can be expected to pass through all three regions as the driver turns the steering wheel.

Slip depends on numerous factors, (tire design, tire pressure, camber, etc.) and is extremely difficult to predict. Experimental results show that the slip angle may vary from 3⁰ to 8⁰ (1,2,3,4) but 8⁰ is likely to represent a very soft tire. Slip angle is of interest mainly in calculating the steering torque (the force needed to turn and hold the steering wheel) and even here, Hsu and Gerdes (2) suggest that good results may be obtained by assuming a uniform tire pressure distribution and a rigid tire carcass.

Szostek (1) suggests a formula for the coefficient of friction in the transition region,

m = m₀(1 - K_m sin a ) (3)

in the absence of longitudinal slide (skid), where m is the coefficient of friction and a is the slip angle. (Note: Szostek uses the traditional symbol for coefficient of friction, m, in his equation but elsewhere in this paper we shall use m (mu) to designate an angle of the path and c_f to designate the coefficient of friction.) Singh (4,5) suggests a value of 0.124 for K_m . Thus it may be seen that the correction is very small.

Once the vehicle enters pure slide, slip ceases to be relevant. A vehicle will enter pure slide when the sideways force is sufficient to cause the tires to “break loose”; that is, when the sideways force exceeds mF_y , where m is the coefficient of friction and F_y the normal force on the tire. As will be seen from the results of our calculations, this will be the case as soon as the vehicle begins to roll over. To be strictly accurate however, we need to define w_a as the effective wheel angle; that is, as the direction in which the tire is rolling as opposed to the direction in which the wheel is turned, prior to the onset of rollover.

The lateral coefficient of friction, c_f , may vary from 0.1 to 1.6 (3,4). 0.1 would represent an icy road and 1.6 would generally be encountered only on the finest kind of racing tires. For passenger car tires under normal conditions (dry pavement) the coefficient of friction will be in the range of 0.8 to 1.0 (2,3,4). Singh (4) suggests 0.85, Hsu and Gerdes (2) suggest 0.95, Smith (3) suggests 0.9. In our calculations we have assumed a value c_f = 0.9 but, like the other parameters in our computer program, c_f may be chosen by the user. In their analysis, as well as in their experimental results, Hsu and Gerdes (2) find that c_f is fairly constant once the vehicle enters the pure slide region (and even in the transition region).

Once the vehicle enters the pure slide region, the magnitude and direction of the velocity will be given by , where V_O is the wheel speed and v_n is the slide speed. V_o and v_n are assumed to be perpendicular. We define f_n as the net sideways force on the vehicle; that is,

f_n = fc1 – c_f f_y (4)

where fc1 is the centrifugal force on the vehicle due to the curvature of the path of the vehicle, c_f is the lateral coefficient of friction, and f_y the normal force on the tires. In the present analysis we will assume that the vehicle is aligned in the direction of V_0. Since this will not be exactly the case in practice, we need to consider this assumption more carefully.

For a wheel velocity of 73 fps we find a maximum v_n of 31 fps. The vehicle would thus be at an angle of 23⁰ to the direction of the velocity. Since the cosine of 23⁰ is 0.92, there would, briefly, be a maximum error of 8% in the component of the lateral force perpendicular to the velocity. Thus, the actual v_n would be less and the error would be less. This does not take into account understeer or oversteer, however. The typical SUV has a 55 : 45 weight distribution; that is, 55% of the weight is on the front wheels and 45% on the rear wheels. Other things being equal, this would lead to oversteer which would increase the centrifugal force on the vehicle and the occupants. Neglecting this factor would thus result in a lower force being predicted than would actually be the case.

If the lateral force on the vehicle is greater than c_ff_y there will be a net outward force and hence a net outward acceleration: In accordance with Newton’s second law of motion, , the outward acceleration would be given by

a_n = f_n/M (5)

where M is the mass of the vehicle and f_n is given by equation (4). The normal (downward) force on the tires (before the vault) is given by

f_y = W sin²q - fc2 sinq (6)

(see Figure 2). The lateral velocity v_n is given by

(7)

The distance travelled by the vehicle in time dt will thus be

ds = [(V₀dt)² + (v_ndt)²]^1/2 (8)

The change in the direction of motion in time dt, in the absence of any change in the front wheel angle w_a and in the absence of slide, is given by

dm = w_a V₀dt/w_b (9)

where dm represent the change in the direction of motion (not the change in viscosity) and w_b is the wheel base. To get the actual change in the direction of motion we have to add the change in the wheel angle, dw_a, and the change in the direction of the outward velocity vector, v_n/V₀.

dw_a =0.122dt (10)

assuming a rate of change of the wheel angle of 7⁰ per second. The change in the direction of motion, dn, in time dt, is thus given by,

dn = dm + dw_a - d[arctan (v_n/V₀)] (11)

The radius of curvature of the path is given by

r =ds/dn (12)

The velocity of the vehicle is given by

V = [V₀² + v_n²]^1/2 (13)

Equation (3) may be written in the form

(14)

Given V₀, r_cg, and , we may thus integrate forward from the initial condititons t=0, v_n = 0, m = 0, n = 0, and = 0. Since, initially, the centrifugal force will not be enough to roll the vehicle, will initially be negative. We must thus step forward in time until is positive before we can generate a meaningful solution.

The suspension: In a real vehicle, the body will lean and the roll rate would already have some positive value before the wheels on the left (or right) side start to lift. That is, the springs and shock absorbers will extend on one side of the vehicle and compress on the other side. The extent of this lean and the initial angular velocity will depend on the suspension - less for a stiff suspension, more for a soft suspension. In the present analysis, we have ignored this effect; that is, we have assumed initial values of q = q₀ and = 0.

Referring to Figure 2, fc1 is given by

fc1 = MV²/r (15)

and fc2 is given by

fc2 = Mr_cg (16)

where M is the mass of the vehicle and is obtained by integrating equation (14). The vertical force on the wheels, f_y, will be given by

f_y = W sin²q - fc2 sinq (17)

where W is the weight of the vehicle, and hence the lateral force will be given by

f_n = fc1 - c_ff_y (18)

where c_f is the lateral coefficient of friction of the tires. We define fnet2 as

fnet2 = W sinq - fc2 (19)

Once fnet2 becomes negative, the center of gravity can no longer maintain a circular path. Strictly speaking, the tires will not actually lose contact with the ground until q reaches 90⁰ so that if fnet2 becomes negative before then there may be some slight further increase in . In practice the effect would be small so we have taken constant from the moment fnet2 becomes negative.

The force on the child: The child may be sitting either on the inside or the outside of the rotation. We consider first the child sitting on the inside of the rotation; that is, to the right of the cg in Figure 2. Figure 3 shows the position of the child.

Figure 3

fch is the force on the child, fch2 is the centrifugal force component on the child due to the rotation of the vehicle, fch1 is the centrifugal force component on the child due to the curvature of the path of the vehicle, wch is the weight of the child, rchv is the distance between the center of gravity of the vehicle and the center of gravity of the child, rch is the distance from the center of gravity of the child to the point P, Dq is the angle between r_cg and rch, fxch is the horizontal component of the force on the child, and fych is the vertical component of the force on the child. We define the angle s as arctan(fych/fxch). Thus, s may be either positive or negative. rchv is given by

rchv = [r_cg + rch² - 2r_cgrch cos(Dq)]^1/2 (20)

Note that c =q - q₀ and g = q + Dq (21)

W is the angle between the perpendicular to the side of the car and the force vector on the child. This is important not only in helping us to determine the force against the booster seat straps but also in evaluating claims of ejection through a car window. Clearly, the child, or an adult occupant, cannot be ejected through a window unless a) the force vector is in the direction of the window, b) the force vector is of sufficient magnitude, and c) the force is of sufficient duration in that direction.

In addition to the forces shown in Figure 3, the child will also experience a force which is approximately in the direction of motion of the vehicle, the so-called Coriolis force, due to the rotation of the coordinate system. This force, however, is spread over the back of the child by the padded seat back and will, therefore, not be as harmful as the force on the straps. In the present case the Coriolis force is given by

(22)

where is a unit vector perpendicular to the reference plane (moving coordinate system) and V_r the velocity of the center of gravity of the child in the moving coordinate system. Because the vehicle is sliding sideways, the vector will not be exactly in the direction of motion.

Referring again to Figure 3,

(21)

(22)

where mch is the mass of the child and rch is the distance from the center of gravity of the child to the point P. (Notice that we have ignored the fact that the center of gravity of the child does not coincide, exactly, with the center of gravity of the vehicle). The y component of the force on the child is given by

fych =(fch2)sin(g) - wch (23)

The x component of the force on the child is given by

fxch = fch1 - (fch2)cos(g) (24)

The total force on the child is given by

fch = [(fxch)² + (fych)²]^1/2 (25)

For the child sitting on the outside of the rotation we define W as the direction of the force on the child relative to the outward perpendicular to the left side of the car (Figure 4). If W is between 0 and p, (W positive), the force component perpendicular to the seat is upward relative to the seat, while if W is between 0 and -p, (W negative) the force component perpendicular to the seat is downward on the seat. Here the situation is a little more complicated than for the child sitting on the inside of the rotation because Dq can be either positive or negative. We need to define four cases:

1. Dq positive, before the vault (rotation about P).
2. Dq positive, during the vault (rotation about the cg).
3. Dq negative, before the vault (rotation about the point P).
4. Dq negative, during the vault (rotation about the cg).

Case 1. Referring to Figure 4,

Figure 4

we see that

W = p - (c + s) (26)

Case 2. Referring to Figure 5,

Figure 5

we see that if al < 90⁰, W = -(s + c). Notice that s is negative while c is positive so that W is positive upwards.

Referring to Figure 6,

Figure 6

we see that if al > 90⁰, W = p - (s + c). In practice, the vault usually occurs when al is at, or close to 90⁰ . Notice that s may be positive or negative.

Case 3. Dq < 0. Referring to Figure 7

Figure 7

we see that W = p - (s + c), as in the previous case.

Case 4. Referring to Figure 8,

Figure 8

we see that when Dq < 0, al must be defined as al = g - ap, where ap is always taken as positive. Here, al < p/2. Hence, s < 0 (fych >0, fxch <0) and hence W = -(s + c).

Integration of the equations and the computer programs.

The integration of the equations can perhaps be best understood by referring to the computer programs (appendixes 1, 2, and 3, p23 et. seq.). The computer programs are written in Fortran 77 and can be run on any computer with a Fortran 77 compiler. We present three different versions of the computer program. sideslip1 (appendix 1) is the full program with the child on the inside of the rotation. The program prints the solution for all the principal parameters at each step of the intergration. This results in approximately 22 pages of output for step size of 0.01. (appendix 4).

mensai (appendix 2)is the same as sideslip1 except that it prints out t, x, y, fch, W, q, and in tabular form which can readily be transferred to a spread sheet program such as Lotus 123 or Excel. mensao (appendix 3) is the same as mansai except that the program has been modified to generate the solution for the child sitting on the outside of the rotation. (sideslip1 can easily be modified the same way.)

Getting the solutions.

The first step is to select and enter the input parameters. In order to gernerate the path of the vehicle we have arbitrarily chosen the initial values of x and y as x=0, y=82. y=82 was chosen because it corresponded to the radius of curvature on some of our initial test runs. Other input and initial parameters which must be chosen are fnet2, V₀, a_n, f_n, w_a, w_b, v_n, M, W, w_ch, m_ch, t, c_f, y_cg, r_cg, Dq, m, n, q₀, dt, q, and q₁. Since Fortran 77 does not permit subscripts or greek letters, the following nomenclature has been used in the computer programs:

V₀ = Vo r_ch = rch r = rho f_ch=fch

a_n = an m_ch = mch = thetadd s = sigma

f_n= fn c_f = cf = theta3d c = chi

w_a = wa = rsqbar f_y = fy W = omega

w_b = wb y_cg = ycg f_x = fx r_chv = rchv

v_n = vn r_cg = rcg f_ycg = fycg r_ch = rch

m = mu q_o = thetao f = phi

n = nu dt = deltat b = beta

W = w q = theta g = gamma

Dq = dtheta = thetad f_ych = fych

w_ch = wch q₁ = theta1 f_xch = fxch

Since the vehicle is asssumed to be travelling in a straight line at time t = 0, the initital values of t, fnet2, an, fn, wa, vn, mu, nu, and thetad are all zero. wb is the wheel base and was taken as ten feet, which is the average wheel base of common SUVs. M is the mass of the vehicle which was chosen as 124.22 slugs (4000 pounds) for convenience. Full size SUVs tend to be slightly heavier while compact SUVs may be slightly lighter.

The location of the center of gravity of the child is specified in polar coordinates by the distance from the point P, rch, and the angle Dq (dtheta) from the center of gravity of the vehicle (Figure 2). For our example we have taken rch = 4.24 feet and dtheta = 0.436 radians. The weight of the child is assumed to be 40 pounds, the average weight for a four year old child (8).

The moment of inertia about the point P is given by

(27)

where is the radius of gyration. In the sample calculation we have taken as 4.9, giving a moment of inertia about P of 2981 slug-ft² for the assumed mass 124.22 slugs (4000 pounds). Yamaguchi (6) gives a moment of inertia of 2079.6 for a Toyota pickup truck where most of the mass would be concentrated lower down since the truck lacks an upper body except for the cab. For the distance of the center of gravity of the vehicle from the point P we have taken 4.24 feet. These figures are estimates. The actual values will depend on the particular vehicle. For a base width of six feet, q_o (thetao), the polar coordinate of the center of gravity of the vehicle works out to 0.785 radians (Figure 2) in the present case. Since the vehicle is initially level, the initial value of q is q_o.

Since we are concerned with the first 90⁰ of the roll in the present case, we set the final value of theta, theta1, as the initial value plus 90⁰. Thus,

theta1 = thetao + 1.57 (28)

This will be the point where the iteration stops but we could just as well have chosen some other value; for example, if the roof is narrower than the base, the vehicle would roll past 90⁰ before the first roof edge strike and we could choose an appropriate higher value, based on the dimensions of the vehicle.

Finally, we have to choose a step size, deltat, for the numerical integration. We chose an initial step size of 0.01 seconds. This turned out to give good results except near the discontinuity at the vault. This problem was overcome by using a smaller step size.

The equations were intergrated using the Euler method. The accuracy of the results may be tested by using the convergence method. This involves repeating the integration using progressively smaller step sizes and noting the change in the solution. If one plots the results one finds that the solution usually approaches an asymptote as the step size approaches zero. In this way it is possible to get quite accurate solutions as well as a good idea of the error involved for a particular step size. In the present case we found a maximum error of approximately 5.5% for a step size of 0.01.

The results.

The computer programs were used to find the solutions for a typical SUV rollover at speeds ranging from 40 to 65 mph. Since the number of solutions the program can generate is essentially unlimited, we present this sample solution and publish the program itself so that the reader may generate his own solutions. The program can be run on any computer with a Fortran 77 compiler. No special skill is required. Anyone not having a Fortran compiler can obtain one free of charge from http://www.geocities.com/Athens/Olympus/5564 or http://kkourakis.tripod.com .

Sample numerical outputs of sideslip1.for, mensai.for and mensao.for are given in appendixes 4, 5, and 6 (pp. 31 et. seq.). To save space, and for clarity, the remainder of the results are presented in graphical form. (To present the full results of our sample calculations in numerical form would run to over 400 pages.) If you look carefully you will note a few blips and wiggles in the in the solutions for the larger step sizes. These have been smoothed out in the charts to show the overall trend line. These blips and wiggles tend to disappear when one goes to smaller step sizes.

Looking at Figure 9, (page 15) we see the force on the child sitting on the inside of the rotation. The results are presented for both a 0.01 second and a 0.005 second step size. As may be seen, it makes little difference. The curves show the results for speeds of 59, 66, 73, 81, 88, and 95 feet per second (40, 45, 50, 55, 60 and 65 miles per hour). As may be seen, the maximum force on the child ranges from 80 to 93 pounds just prior to the vault. The solution clearly shows the sudden drop when the vehicle vaults.

Figure 10 shows the direction of the force. The angle omega is the angle is the angle the force vector makes with the outward perpendicular to the vehicle (see Figure 3). A positive value indicates an upward component away from the seat, a negative value indicates a downward component into the seat. Thus it may be seen that during the period of highest force, the force is upward and outward - that is, against the harness. The child would thus suffer severe, and probably fatal injuries even prior to the first roof edge strike.

Figures 11 and 12 show the magnitude and direction of the force on the child sitting on the outside of the rotation. Here we see that the maximum force ranges between 70 and 80 pounds. The direction of the force, omega, is defined in Figures 4 and 5. A value greater than p (3.1416) indicates a downward component of the force (into the seat) and a value of less than p indicates an upward component of the force; i.e., away from the seat and into the harness. Again we see that the maximum force occurs just before the vault and is directed against the straps. These results also enable one to calculate the distribution of the force between the hip and the neck (see the solution to puzzle no. 2, elsewhere on this web site).

Figure 13 show the path of the vehicle for the different speeds considered. The rate of change of the angle of the front wheels is the same in each case but the curvature needed for a vault is less at the higher speeds, as might be expected. Once the vehicle vaults, the wheels lose contact with the ground and hence the path becomes a straight line.

Figures 14(a) and (b) show the variation of q (theta) with time. Once the vehicle vaults, (thetad) becomes constant and hence the variation of theta with time must be a straight line of constant slope. Although it appears from the graphs that the value of q at the vault, q_v, may be independent of velocity, a closer look shows that this is not the case, at least based on the numerical solutions of the equations, as we may see when we consider the variation in angular velocity.

Figures 15 (a) and (b) show the angular velocity of the roll as a function of time. The results for the 0.01 step size appear to be somewhat erratic and even the results for the 0.005 step size did not seem satisfactory so we went to a 0.001 step size (Figures 15b). While the variation in the final angular velocity decreases with step size it is not a priori evident that it has to converge to zero. While the graphs show little difference, the numbers still reveal considerable variation:

59 66 73 81 88 95

2.7517 2.7488 2.7435 2.7308 2.7280 2.7165

q_v 1.4616 1.4365 1.4101 1.3785 1.3541 1.3286

(83.75⁰) (82.31⁰) (80.80⁰) (78.99⁰) (77.59⁰) (76.13⁰)

The critereon for the vault is

(29)

For an r_cg of 4.24, as chosen in our sample calculation,

(30)

Since sinq cannot exceed 1, must be 2.755. The value of q_v may be calculated from equation (30) for a given . Thus we find,

59 66 73 81 88 95

q_v from program: 83.75⁰ 82.31⁰ 80.80⁰ 78.99⁰ 77.59⁰ 76.13⁰

q_v from equation 30: 85.72⁰ 84.33⁰ 82.42⁰ 79.15⁰ 78.55⁰ 76.37⁰

Because the values of the sine are so close to 1.0 above 82⁰, it is likely that some round-off error is involved. These variations have no significant effect on the order of magnitude of the force on the child, however.

Figure 9a

Figure 9b

Figure 10a

Figure 10b

Figure 11a

Figure 11b

Figure 12a

Figure 12b

Figure 13a

Figure 13b

Figure 14a

Figure 14b

Figure 15a

Figure 15b

References:

1. Szostek, H.T., Allen, W.R., and Rosenthal, T.J. Analytical Modeling of Driver Response in Crash Avoidance Maneuvering. Volume II: An Interactive Tire Model for Driver /Vehicle Simulation. United States Department of Transportation DOT HS 807-271 Final Report, April, 1988.

2. Hsu, Judy Yung-Hsiang, and Gerdes, J. Christian: A Feel for the Road: A Method to Estimate Tire Parameters Using Steering Torque. Stanford University Department of Mechanical Engineering. Presented at the 8th International Symposium on Advanced Vehicle Control, AVEC '06,Tokyo, Japan, August 2006 http://www.jsae.or.jp/21jigu/2006/tsu601204.pdf

3. Smith, N.D. Understanding Parameters Influencing Tire Modeling. Formula SAE Platform, Dynamics. Department of Mechanical Engineering, Colorado State University Report, 2004.

4. Singh, Tarunraj, et. al., Tire Model in Driving Simulator. Department of Mechanical Engineering Report, State University of New York at Buffalo. http://code.eng.bufallo.edu/dat/sites/tire/tire.html

5. Telephone conversation with Professor Singh.

6. Yamaguchi, G.T., et. al., Development of a Computational Method to Predict Occupant Motions and Neck Loads During Rollovers. SAE Technical Paper Series 2005-01-0300, 2005 SAE World Congress, Detroit Michigan, April, 2005.

7. Larsen, R. E., et. al., Vehicle Rollover Testing. Methodologies in Recreating Rollover Collisions. SAE Technical Paper Series 2000-01-1641. Proceedings of the Automotive Dynamics Conference, Troy, Michigan, May, 2000.

8. United States Center for Disease Control (CDC): Weights and Dimensions of Children. http://www.cdc.gov

APPENDIX 1

program sideslip1

real M, rsqbar, rcg, theta, thetad, thetadd, theta3d, theta1, x,

+ y, rho, V, t, thetao, deltat, kone, ktwo, alpha, a, ycg, fycg,

+ fc1,fc2,fy,fn,fx, beta, phi, nu, mu, muav, dmu, dnu, dr,rchv,

+ gamma,sigma, fch1, fch2, wch, fych, fxch, dtheta, w, fch, omega

+ r, wa, vn, an, wb, vn1, ds, dwa, vnav, fnet2, cf, chi,rch,mch,

+ q, al, aq, Vo

fnet2=0.0

Vo=73.0

x=0.0

y=82.0

an=0.0

fn=0.0

fnet2=0.0

wa=0.0

wb=10.0

vn=0.0

mu=0.0

nu=0.0

M=124.22

w=32.2*M

dtheta=0.436

wch=40.0

rch=4.24

mch=wch/32.2

t=0

alpha=0.0

a=6.0

cf=0.9

rsqbar=(a**2)*((2.0-1.33*alpha)/(3.0-alpha))

ycg=a*(1.0-alpha)/(2.0-alpha)

rcg=SQRT(ycg**2+a**2/4.0)

thetao=ATAN(2.0*ycg/a)

deltat=0.01

theta=thetao

thetad=0.0

theta1=thetao+1.57

PRINT 5, M, rsqbar, rcg, Vo, deltat

5 FORMAT(1X,'M=',F6.2,3X,'rsqbar=',F4.1,3X,'rcg=',F4.2,3X,

+ 'Vo=',F5.1,3X,'deltat=',F4.2)

PRINT 6, thetao, a, ycg, alpha

6 FORMAT(1X, 'thetao=', F5.3, 3X, 'a=', F3.1, 3X, 'ycg=',

+ F5.3, 3X, 'alpha=', F3.1)

10 IF(theta.LE.theta1) THEN

IF(fnet2.GE.0.0) THEN

an=fn/M

wa=wa+0.122*deltat

r=wb/wa

dr=0.8197/(1+t)**2

vn1=vn+an*deltat

ds=SQRT((Vo*deltat)**2+(vn1*deltat-dr)**2)

dmu=wa*Vo*deltat/wb

dwa=0.122*deltat

dnu=dmu+dwa-ATAN(vn1/Vo)+ATAN(vn/Vo)

rho=ds/dnu

V=SQRT(Vo**2+vn1**2)

kone=rcg*(V**2)/(rsqbar*rho)

ktwo=32.2*rcg/rsqbar

thetadd=kone*sin(theta)-ktwo*cos(theta)

IF (thetadd.LT.0.0) THEN

t=t+deltat

GO TO 10

ELSE

ENDIF

theta3d=thetad*(kone*cos(theta)+ktwo*sin(theta))

thetad=thetad+thetadd*deltat+(theta3d/2.0)*(deltat**2)

theta=theta+thetad*deltat+(thetdd/2.0)*(deltat**2)

fc1=M*(V**2)/rho

fc2=M*(thetad**2)*rcg

fy=w*(sin(theta))**2-fc2*sin(theta)

fn=fc1-cf*fy

fnet2=w*sin(theta)-fc2

fx=fc1-fc2*cos(theta)

fycg=fc2*sin(theta)-w

phi=ATAN(fycg/fx)

beta=(3.1416-theta)-phi

gamma=(theta+dtheta)

fch2=mch*(thetad**2)*rch

fch1=fc1*(wch/w)

fych=fch2*sin(gamma)-wch

fxch=-fch2*cos(gamma)+fch1

fch=SQRT(fxch**2+fych**2)

sigma=ATAN(fych/fxch)

chi=theta-thetao

omega=chi+sigma

t=t+deltat

muav=mu+dmu/2.0

vnav=(vn1+vn)/2.0

dx=ds*cos(nu)

dy=-ds*sin(nu)

x=x+dx

y=y+dy

vn=vn1

mu=mu+dmu

nu=nu+dnu

PRINT 20, t, theta, thetad, thetadd

20 FORMAT(// 1X,'t=',F6.4, 2X,'theta=',F6.4, 2X,'thetad=',

+ F6.4, 2X,'thetadd=',F7.4)

PRINT 25, theta3d, rho, nu

25 FORMAT(' ',1X,'theta3d=',F8.4,2X,'rho=',F7.3,2X,'nu=',F6.3)

PRINT 30, fc1, fc2, fy, fn, mu

30 FORMAT(' ',1X,'FC1=',F7.1,2X,'FC2=',F8.2,2X,'FY=',F9.2,

+ 2x,'FN=',F8.2,2X,'mu=',F6.3)

PRINT 40, fx, phi, beta, x, y

40 FORMAT(' ',1X,'FX=',F9.2,2X,'PHI=',F7.4,2X,'BETA=',F6.4,

+ 2X,'x=',F8.5,2X,'y=',F8.5)

PRINT 50, fch, omega, fch1, fch2, fnet2

50 FORMAT('',1X,'FCH=',F6.1,2X,'OMEGA=',F6.4,2X,'FCH1=',

+ F6.1,2X,'FCH2=',F6.1,2X,'fnet2=',F8.2)

PRINT 60, r,wa,vn,an,dnu,dmu

60 FORMAT(' ',1X,'r=',F7.2,2X,'wa=',F6.4,2X,'vn=',F5.2,2X,

+ 'an=',F6.2,2X,'dnu=',F6.4,2X,'dmu=',F6.4)

PRINT 65, sigma, gamma, chi, fych, fxch

65 FORMAT(' ',1X,'sigma=',F7.4,2X,'gamma=',F6.4,2X,'chi=',

+ F6.4,2X,'fych=',F6.2,2X,'fxch=',F6.2)

GO TO 10

ELSE

theta=theta+thetad*deltat

fc1=0.0

gamma=(theta+dtheta)

rchv=SQRT(rcg**2+rch**2-2.0*rcg*rch*COS(dtheta))

q=((rchv**2+rcg**2-rch**2)/(2.0*rch*rchv))

aq=ACOS(q)

al=aq-theta

fch1=0.0

fch2=mch*(thetad**2)*rchv

fych=fch2*SIN(al)-wch

fxch=fch2*COS(al)

fch=SQRT(fxch**2+fych**2)

sigma=ATAN(fych/fxch)

chi=theta-thetao

omega=chi+sigma

t=t+deltat

ds=V*deltat

dx=ds*cos(nu)

dy=-ds*sin(nu)

x=x+dx

y=y+dy

PRINT 70, t, theta, thetad, nu

70 FORMAT(// 1X,'t=',F6.4,2X,'theta=',F6.4,2X,'thetad=',F6.4,

+ 2X,'nu=',F6.3)

PRINT 90, x, y

90 FORMAT(' ',1X, 'x=',F8.5,2X,'y=',F8.5)

PRINT 95, fch, omega, fch1, fch2

95 FORMAT('',1X,'FCH=',F6.1,2X,'OMEGA=',F6.4,2X,'FCH1=',

+ F6.1,2X,'FCH2=',F6.1)

PRINT 100, sigma, gamma, chi, fych, fxch

100 FORMAT(' ',1X,'sigma=',F7.4,2X,'gamma=',F6.4,2X,'chi=',

+ F6.4,2X,'fych=',F6.2,2X,'fxch=',F6.2)

ENDIF

GO TO 10

ELSE

ENDIF

STOP

END

APPENDIX 2

program mensai

real M, rsqbar, rcg, theta, thetad, thetadd, theta3d, theta1, x,

+ y, rho, V, t, thetao, deltat, kone, ktwo, alpha, a, ycg, fycg,

+ fc1,fc2,fy,fn,fx, beta, phi, nu, mu, muav, dmu, dnu, dr,rchv,

+ gamma,sigma, fch1, fch2, wch, fych, fxch, dtheta, w, fch, omega

+ r, wa, vn, an, wb, vn1, ds, dwa, vnav, fnet2, cf, chi,rch,mch,

+ q, al, aq, Vo

fnet2=0.0

Vo=59.0

x=0.0

y=82.0

an=0.0

fn=0.0

fnet2=0.0

wa=0.0

wb=10.0

vn=0.0

mu=0.0

nu=0.0

M=124.22

w=32.2*M

dtheta=0.436

wch=40.0

rch=4.24

mch=wch/32.2

t=0

alpha=0.0

a=6.0

cf=0.9

rsqbar=(a**2)*((2.0-1.33*alpha)/(3.0-alpha))

ycg=a*(1.0-alpha)/(2.0-alpha)

rcg=SQRT(ycg**2+a**2/4.0)

thetao=ATAN(2.0*ycg/a)

deltat=0.001

theta=thetao

thetad=0.0

theta1=thetao+1.57

PRINT 5

5 FORMAT(' ',T6,'t',T15,'x',T23,'y',T31,'fch',T39,

+ 'omega',T47,'theta',T54,'thetad')

10 IF(theta.LE.theta1) THEN

IF(fnet2.GE.0.0) THEN

an=fn/M

wa=wa+0.122*deltat

vn1=vn+an*deltat

ds=SQRT((Vo*deltat)**2+(vn1*deltat)**2)

dmu=wa*Vo*deltat/wb

dwa=0.122*deltat

dnu=dmu+dwa-ATAN(vn1/Vo)+ATAN(vn/Vo)

rho=ds/dnu

V=SQRT(Vo**2+vn1**2)

kone=rcg*(V**2)/(rsqbar*rho)

ktwo=32.2*rcg/rsqbar

thetadd=kone*sin(theta)-ktwo*cos(theta)

IF (thetadd.LT.0.0) THEN

t=t+deltat

GO TO 10

ELSE

ENDIF

theta3d=thetad*(kone*cos(theta)+ktwo*sin(theta))

thetad=thetad+thetadd*deltat+(theta3d/2.0)*(deltat**2)

theta=theta+thetad*deltat+(thetdd/2.0)*(deltat**2)

fc1=M*(V**2)/rho

fc2=M*(thetad**2)*rcg

fy=w*(sin(theta))**2-fc2*sin(theta)

fn=fc1-cf*fy

fnet2=w*sin(theta)-fc2

fx=fc1-fc2*cos(theta)

fycg=fc2*sin(theta)-w

phi=ATAN(fycg/fx)

beta=(3.1416-theta)+phi

gamma=(theta+dtheta)

fch2=mch*(thetad**2)*rch

fch1=fc1*(wch/w)

fych=fch2*sin(gamma)-wch

fxch=-fch2*cos(gamma)+fch1

fch=SQRT(fxch**2+fych**2)

sigma=ATAN(fych/fxch)

chi=theta-thetao

omega=chi+sigma

t=t+deltat

muav=mu+dmu/2.0

vnav=(vn1+vn)/2.0

dx=ds*cos(nu)

dy=-ds*sin(nu)

x=x+dx

y=y+dy

vn=vn1

mu=mu+dmu

nu=nu+dnu

PRINT 60, t, x, y, fch, omega, theta, thetad

60 FORMAT(' ', 1X, F6.4, 2X, F7.3, 2X, F7.3, 2X, F7.3,

+ 2X, F6.4, 2X, F6.4, 2X, F6.4)

GO TO 10

ELSE

theta=theta+thetad*deltat

fc1=0.0

gamma=(theta+dtheta)

rchv=SQRT(rcg**2+rch**2-2.0*rcg*rch*COS(dtheta))

q=((rchv**2+rcg**2-rch**2)/(2.0*rch*rchv))

aq=ACOS(q)

al=aq-theta

fch1=0.0

fch2=mch*(thetad**2)*rchv

fych=fch2*SIN(al)-wch

fxch=fch2*COS(al)

sigma=ATAN(fych/fxch)

chi=theta-thetao

omega=chi+sigma

fch=SQRT(fxch**2+fych**2)

t=t+deltat

ds=V*deltat

dx=ds*cos(nu)

dy=-ds*sin(nu)

x=x+dx

y=y+dy

PRINT 70, t, x, y, fch, omega, theta, thetad

70 FORMAT(' ', 1X, F6.4, 2X, F7.3, 2X, F7.3, 2X, F7.3,

+ 2X, F6.4, 2X, F6.4, 2X, F6.4)

ENDIF

GO TO 10

ELSE

ENDIF

STOP

END

APPENDIX 3

program mensao

real M, rsqbar, rcg, theta, thetad, thetadd, theta3d, theta1, x,

+ y, rho, V, t, thetao, deltat, kone, ktwo, alpha, a, ycg, fycg,

+ fc1,fc2,fy,fn,fx, beta, phi, nu, mu, muav, dmu, dnu, dr,rchv,

+ gamma,sigma, fch1, fch2, wch, fych, fxch, dtheta, w, fch, omega

+ r, wa, vn, an, wb, vn1, ds, dwa, vnav, fnet2, cf, chi,rch,mch,

+ q, al, aq, Vo, p, ap

fnet2=0.0

Vo=95.0

x=0.0

y=82.0

an=0.0

fn=0.0

fnet2=0.0

wa=0.0

wb=10.0

vn=0.0

mu=0.0

nu=0.0

M=124.22

w=32.2*M

dtheta=0.14

wch=40.0

rch=5.20

mch=wch/32.2

t=0

alpha=0.0

a=6.0

cf=0.9

rsqbar=(a**2)*((2.0-1.33*alpha)/(3.0-alpha))

ycg=a*(1.0-alpha)/(2.0-alpha)

rcg=SQRT(ycg**2+a**2/4.0)

thetao=ATAN(2.0*ycg/a)

deltat=0.01

theta=thetao

thetad=0.0

theta1=thetao+1.57

PRINT 5

5 FORMAT(' ',T6,'t',T15,'x',T23,'y',T31,'fch',T39,

+ 'omega',T47,'theta',T54,'thetad')

10 IF(theta.LE.theta1) THEN

IF(fnet2.GE.0.0) THEN

an=fn/M

wa=wa+0.122*deltat

vn1=vn+an*deltat

ds=SQRT((Vo*deltat)**2+(vn1*deltat)**2)

dmu=wa*Vo*deltat/wb

dwa=0.122*deltat

dnu=dmu+dwa-ATAN(vn1/Vo)+ATAN(vn/Vo)

rho=ds/dnu

V=SQRT(Vo**2+vn1**2)

kone=rcg*(V**2)/(rsqbar*rho)

ktwo=32.2*rcg/rsqbar

thetadd=kone*sin(theta)-ktwo*cos(theta)

IF (thetadd.LT.0.0) THEN

t=t+deltat

GO TO 10

ELSE

ENDIF

theta3d=thetad*(kone*cos(theta)+ktwo*sin(theta))

thetad=thetad+thetadd*deltat+(theta3d/2.0)*(deltat**2)

theta=theta+thetad*deltat+(thetdd/2.0)*(deltat**2)

fc1=M*(V**2)/rho

fc2=M*(thetad**2)*rcg

fy=w*(sin(theta))**2-fc2*sin(theta)

fn=fc1-cf*fy

fnet2=w*sin(theta)-fc2

fx=fc1-fc2*cos(theta)

fycg=fc2*sin(theta)-w

phi=ATAN(fycg/fx)

beta=(3.1416-theta)+phi

gamma=(theta+dtheta)

fch2=mch*(thetad**2)*rch

fch1=fc1*(wch/w)

fych=fch2*sin(gamma)-wch

fxch=fch1-fch2*cos(gamma)

fch=SQRT(fxch**2+fych**2)

sigma=ATAN(fych/fxch)

chi=theta-thetao

omega=3.1416-(chi+sigma)

t=t+deltat

muav=mu+dmu/2.0

vnav=(vn1+vn)/2.0

dx=ds*cos(nu)

dy=-ds*sin(nu)

x=x+dx

y=y+dy

vn=vn1

mu=mu+dmu

nu=nu+dnu

PRINT 60, t, x, y, fch, omega, theta, thetad

60 FORMAT(' ', 1X, F6.4, 2X, F7.3, 2X, F7.3, 2X, F7.3,

+ 2X, F6.4, 2X, F6.4, 2X, F6.4)

GO TO 10

ELSE

theta=theta+thetad*deltat

fc1=0.0

fc2=M*(thetad**2)*rcg

fy=w*(sin(theta))**2-fc2*sin(theta)

fn=fc1-fy

fnet2=w*sin(theta)-fc2

fx=fc1-fc2*cos(theta)

phi=ATAN(fy/fx)

beta=(3.1416-theta)+phi

gamma=(theta+dtheta)

rchv=SQRT(rcg**2+rch**2-2.0*rcg*rch*COS(dtheta))

q=((rchv**2+rcg**2-rch**2)/(2.0*rch*rchv))

aq=ACOS(q)

p=(rch**2+rchv**2-rcg**2)/(2.0*rch*rchv)

ap=COS(p)

fch1=0.0

fch2=mch*(thetad**2)*rchv

chi=theta-thetao

IF(dtheta.LE.0.0) THEN

al=gamma-ap

ELSE

al=gamma+ap

ENDIF

fych=fch2*SIN(al)-wch

fxch=-fch2*COS(al)

sigma=ATAN(fych/fxch)

IF(al.LE.1.571) THEN

omega=-(sigma+chi)

ELSE

omega=3.1416-(sigma+chi)

ENDIF

fch=SQRT(fxch**2+fych**2)

t=t+deltat

ds=V*deltat

dx=ds*cos(nu)

dy=-ds*sin(nu)

x=x+dx

y=y+dy

PRINT 70, t, x, y, fch, omega, theta, thetad

70 FORMAT(' ', 1X, F6.4, 2X, F7.3, 2X, F7.3, 2X, F7.3,

+ 2X, F6.4, 2X, F6.4, 2X, F6.4)

ENDIF

GO TO 10

ELSE

ENDIF

STOP

END

APPENDIX 4

M=124.22 rsqbar=24.0 rcg=4.24 Vo= 73.0 deltat=0.01

thetao=0.785 a=6.0 ycg=3.000 alpha=0.0

t=0.4300 theta=0.7844 thetad=0.0000 thetadd= 0.0006

theta3d= 0.0000 rho=165.471 nu= 0.005

FC1= 4000.5 FC2= 0.00 FY= 1995.91 FN= 2204.20 mu= 0.004

FX= 4000.52 PHI=-0.7853 BETA=3.1425 x= 0.83556 y=82.00000

FCH= 56.6 OMEGA=-.7863 FCH1= 40.0 FCH2= 0.0 fnet2= 2825.50

r= 190.62 wa=0.0525 vn= 0.00 an= 0.00 dnu=0.0050 dmu=0.0038

sigma=-0.7853 gamma=1.2204 chi=-.0010 fych=-40.00 fxch= 40.01

t=0.6800 theta=0.7834 thetad=0.0007 thetadd= 0.0717

theta3d= 0.0001 rho=162.276 nu= 0.010

FC1= 4079.3 FC2= 0.00 FY= 1991.91 FN= 2286.57 mu= 0.010

FX= 4079.30 PHI=-0.7756 BETA=3.1338 x= 1.62183 y=81.99603

FCH= 57.1 OMEGA=-.7776 FCH1= 40.8 FCH2= 0.0 fnet2= 2822.66

r= 120.54 wa=0.0830 vn= 0.18 an= 17.74 dnu=0.0048 dmu=0.0061

sigma=-0.7756 gamma=1.2194 chi=-.0020 fych=-40.00 fxch= 40.79

t=0.6900 theta=0.7824 thetad=0.0014 thetadd= 0.0724

theta3d= 0.0059 rho=161.929 nu= 0.015

FC1= 4088.1 FC2= 0.00 FY= 1987.94 FN= 2298.96 mu= 0.016

FX= 4088.11 PHI=-0.7745 BETA=3.1337 x= 2.40612 y=81.98827

FCH= 57.2 OMEGA=-.7775 FCH1= 40.9 FCH2= 0.0 fnet2= 2819.85

r= 118.79 wa=0.0842 vn= 0.36 an= 18.41 dnu=0.0048 dmu=0.0061

sigma=-0.7745 gamma=1.2184 chi=-.0030 fych=-40.00 fxch= 40.88

t=0.7000 theta=0.7814 thetad=0.0028 thetadd= 0.1386

theta3d= 0.0119 rho=159.056 nu= 0.020

FC1= 4162.1 FC2= 0.00 FY= 1984.03 FN= 2376.47 mu= 0.022

FX= 4162.09 PHI=-0.7655 BETA=3.1257 x= 3.18844 y=81.97675

FCH= 57.7 OMEGA=-.7695 FCH1= 41.6 FCH2= 0.0 fnet2= 2817.07

r= 117.10 wa=0.0854 vn= 0.55 an= 18.51 dnu=0.0049 dmu=0.0062

sigma=-0.7655 gamma=1.2174 chi=-.0040 fych=-40.00 fxch= 41.62

t=0.7100 theta=0.7805 thetad=0.0043 thetadd= 0.1440

theta3d= 0.0233 rho=158.554 nu= 0.025

FC1= 4175.5 FC2= 0.01 FY= 1980.16 FN= 2393.32 mu= 0.029

FX= 4175.46 PHI=-0.7639 BETA=3.1251 x= 3.96881 y=81.96140

FCH= 57.8 OMEGA=-.7689 FCH1= 41.8 FCH2= 0.0 fnet2= 2814.32

r= 115.45 wa=0.0866 vn= 0.74 an= 19.13 dnu=0.0049 dmu=0.0063

sigma=-0.7639 gamma=1.2165 chi=-.0049 fych=-40.00 fxch= 41.76

t=0.7200 theta=0.7795 thetad=0.0063 thetadd= 0.2063

theta3d= 0.0355 rho=155.943 nu= 0.030

FC1= 4245.6 FC2= 0.02 FY= 1976.38 FN= 2466.87 mu= 0.035

FX= 4245.60 PHI=-0.7556 BETA=3.1177 x= 4.74726 y=81.94226

FCH= 58.3 OMEGA=-.7615 FCH1= 42.5 FCH2= 0.0 fnet2= 2811.63

r= 113.84 wa=0.0878 vn= 0.93 an= 19.27 dnu=0.0050 dmu=0.0064

sigma=-0.7556 gamma=1.2155 chi=-.0059 fych=-40.00 fxch= 42.46

t=0.7300 theta=0.7786 thetad=0.0085 thetadd= 0.2156

theta3d= 0.0527 rho=155.328 nu= 0.035

FC1= 4262.8 FC2= 0.04 FY= 1972.68 FN= 2487.34 mu= 0.042

FX= 4262.73 PHI=-0.7536 BETA=3.1166 x= 5.52380 y=81.91929

FCH= 58.5 OMEGA=-.7604 FCH1= 42.6 FCH2= 0.0 fnet2= 2808.98

r= 112.28 wa=0.0891 vn= 1.13 an= 19.86 dnu=0.0050 dmu=0.0065

sigma=-0.7536 gamma=1.2146 chi=-.0068 fych=-40.00 fxch= 42.63

t=0.7400 theta=0.7777 thetad=0.0113 thetadd= 0.2750

theta3d= 0.0713 rho=152.936 nu= 0.040

FC1= 4329.8 FC2= 0.07 FY= 1969.08 FN= 2557.67 mu= 0.048

FX= 4329.80 PHI=-0.7458 BETA=3.1097 x= 6.29846 y=81.89249

FCH= 58.9 OMEGA=-.7535 FCH1= 43.3 FCH2= 0.0 fnet2= 2806.41

r= 110.77 wa=0.0903 vn= 1.33 an= 20.02 dnu=0.0051 dmu=0.0066

sigma=-0.7458 gamma=1.2137 chi=-.0077 fych=-40.00 fxch= 43.30

t=0.7500 theta=0.7768 thetad=0.0141 thetadd= 0.2877

theta3d= 0.0946 rho=152.239 nu= 0.045

FC1= 4350.1 FC2= 0.11 FY= 1965.59 FN= 2581.10 mu= 0.055

FX= 4350.06 PHI=-0.7435 BETA=3.1082 x= 7.07123 y=81.86184

FCH= 59.1 OMEGA=-.7520 FCH1= 43.5 FCH2= 0.0 fnet2= 2803.90

r= 109.29 wa=0.0915 vn= 1.54 an= 20.59 dnu=0.0051 dmu=0.0067

sigma=-0.7435 gamma=1.2128 chi=-.0086 fych=-40.00 fxch= 43.50

t=0.7600 theta=0.7760 thetad=0.0176 thetadd= 0.3449

theta3d= 0.1197 rho=150.029 nu= 0.050

FC1= 4414.8 FC2= 0.16 FY= 1962.23 FN= 2648.77 mu= 0.062

FX= 4414.66 PHI=-0.7361 BETA=3.1017 x= 7.84216 y=81.82734

FCH= 59.6 OMEGA=-.7455 FCH1= 44.1 FCH2= 0.0 fnet2= 2801.47

r= 107.85 wa=0.0927 vn= 1.74 an= 20.78 dnu=0.0051 dmu=0.0068

sigma=-0.7361 gamma=1.2120 chi=-.0094 fych=-40.00 fxch= 44.15

t=0.7700 theta=0.7752 thetad=0.0212 thetadd= 0.3608

theta3d= 0.1494 rho=149.275 nu= 0.055

FC1= 4437.7 FC2= 0.24 FY= 1959.00 FN= 2674.65 mu= 0.068

FX= 4437.58 PHI=-0.7335 BETA=3.0999 x= 8.61123 y=81.78896

FCH= 59.7 OMEGA=-.7437 FCH1= 44.4 FCH2= 0.0 fnet2= 2799.12

r= 106.45 wa=0.0939 vn= 1.96 an= 21.32 dnu=0.0052 dmu=0.0069

sigma=-0.7335 gamma=1.2112 chi=-.0102 fych=-40.00 fxch= 44.38

t=0.7800 theta=0.7744 thetad=0.0254 thetadd= 0.4165

theta3d= 0.1815 rho=147.220 nu= 0.060

FC1= 4500.4 FC2= 0.34 FY= 1955.91 FN= 2740.12 mu= 0.075

FX= 4500.19 PHI=-0.7266 BETA=3.0937 x= 9.37849 y=81.74670

FCH= 60.2 OMEGA=-.7375 FCH1= 45.0 FCH2= 0.0 fnet2= 2796.87

r= 105.09 wa=0.0952 vn= 2.17 an= 21.53 dnu=0.0052 dmu=0.0069

sigma=-0.7266 gamma=1.2104 chi=-.0109 fych=-40.00 fxch= 45.00

t=0.7900 theta=0.7737 thetad=0.0297 thetadd= 0.4351

theta3d= 0.2178 rho=146.426 nu= 0.065

FC1= 4525.7 FC2= 0.47 FY= 1952.99 FN= 2768.01 mu= 0.082

FX= 4525.36 PHI=-0.7238 BETA=3.0917 x=10.14392 y=81.70052

FCH= 60.4 OMEGA=-.7354 FCH1= 45.3 FCH2= 0.0 fnet2= 2794.71

r= 103.76 wa=0.0964 vn= 2.39 an= 22.06 dnu=0.0052 dmu=0.0070

sigma=-0.7238 gamma=1.2097 chi=-.0117 fych=-40.00 fxch= 45.26

t=0.8000 theta=0.7731 thetad=0.0347 thetadd= 0.4899

theta3d= 0.2572 rho=144.504 nu= 0.071

FC1= 4586.9 FC2= 0.63 FY= 1950.23 FN= 2831.65 mu= 0.090

FX= 4586.41 PHI=-0.7171 BETA=3.0857 x=10.90756 y=81.65044

FCH= 60.9 OMEGA=-.7294 FCH1= 45.9 FCH2= 0.0 fnet2= 2792.65

r= 102.46 wa=0.0976 vn= 2.62 an= 22.28 dnu=0.0053 dmu=0.0071

sigma=-0.7171 gamma=1.2091 chi=-.0123 fych=-39.99 fxch= 45.87

t=0.8100 theta=0.7725 thetad=0.0398 thetadd= 0.5112

theta3d= 0.3006 rho=143.684 nu= 0.076

FC1= 4614.1 FC2= 0.83 FY= 1947.65 FN= 2861.22 mu= 0.097

FX= 4613.51 PHI=-0.7142 BETA=3.0833 x=11.66941 y=81.59643

FCH= 61.1 OMEGA=-.7271 FCH1= 46.1 FCH2= 0.0 fnet2= 2790.71

r= 101.19 wa=0.0988 vn= 2.84 an= 22.80 dnu=0.0053 dmu=0.0072

sigma=-0.7141 gamma=1.2085 chi=-.0129 fych=-39.99 fxch= 46.14

t=0.8200 theta=0.7719 thetad=0.0455 thetadd= 0.5655

theta3d= 0.3475 rho=141.876 nu= 0.081

FC1= 4674.1 FC2= 1.09 FY= 1945.26 FN= 2923.34 mu= 0.104

FX= 4673.30 PHI=-0.7078 BETA=3.0775 x=12.42948 y=81.53848

FCH= 61.5 OMEGA=-.7212 FCH1= 46.7 FCH2= 0.0 fnet2= 2788.87

r= 99.96 wa=0.1000 vn= 3.07 an= 23.03 dnu=0.0054 dmu=0.0073

sigma=-0.7077 gamma=1.2079 chi=-.0135 fych=-39.99 fxch= 46.74

t=0.8300 theta=0.7714 thetad=0.0514 thetadd= 0.5895

theta3d= 0.3984 rho=141.041 nu= 0.087

FC1= 4703.1 FC2= 1.39 FY= 1943.08 FN= 2954.31 mu= 0.111

FX= 4702.08 PHI=-0.7048 BETA=3.0749 x=13.18779 y=81.47657

FCH= 61.7 OMEGA=-.7186 FCH1= 47.0 FCH2= 0.0 fnet2= 2787.15

r= 98.76 wa=0.1013 vn= 3.31 an= 23.53 dnu=0.0054 dmu=0.0074

sigma=-0.7047 gamma=1.2074 chi=-.0140 fych=-39.99 fxch= 47.03

t=0.8400 theta=0.7710 thetad=0.0578 thetadd= 0.6438

theta3d= 0.4534 rho=139.334 nu= 0.092

FC1= 4762.1 FC2= 1.76 FY= 1941.11 FN= 3015.15 mu= 0.119

FX= 4760.88 PHI=-0.6986 BETA=3.0692 x=13.94434 y=81.41069

FCH= 62.2 OMEGA=-.7129 FCH1= 47.6 FCH2= 0.0 fnet2= 2785.55

r= 97.58 wa=0.1025 vn= 3.55 an= 23.78 dnu=0.0055 dmu=0.0075

sigma=-0.6985 gamma=1.2070 chi=-.0144 fych=-39.98 fxch= 47.62

t=0.8500 theta=0.7706 thetad=0.0646 thetadd= 0.6703

theta3d= 0.5122 rho=138.492 nu= 0.098

FC1= 4792.7 FC2= 2.20 FY= 1939.36 FN= 3047.30 mu= 0.126

FX= 4791.15 PHI=-0.6954 BETA=3.0664 x=14.69914 y=81.34081

FCH= 62.4 OMEGA=-.7101 FCH1= 47.9 FCH2= 0.0 fnet2= 2784.08

r= 96.43 wa=0.1037 vn= 3.79 an= 24.27 dnu=0.0055 dmu=0.0076

sigma=-0.6953 gamma=1.2066 chi=-.0148 fych=-39.98 fxch= 47.92

t=0.8600 theta=0.7703 thetad=0.0718 thetadd= 0.7250

theta3d= 0.5757 rho=136.874 nu= 0.103

FC1= 4851.1 FC2= 2.72 FY= 1937.84 FN= 3107.07 mu= 0.134

FX= 4849.17 PHI=-0.6895 BETA=3.0607 x=15.45220 y=81.26694

FCH= 62.9 OMEGA=-.7044 FCH1= 48.5 FCH2= 0.0 fnet2= 2782.73

r= 95.31 wa=0.1049 vn= 4.03 an= 24.53 dnu=0.0055 dmu=0.0077

sigma=-0.6893 gamma=1.2063 chi=-.0151 fych=-39.97 fxch= 48.50

t=0.8700 theta=0.7701 thetad=0.0794 thetadd= 0.7541

theta3d= 0.6430 rho=136.029 nu= 0.109

FC1= 4883.1 FC2= 3.32 FY= 1936.57 FN= 3140.22 mu= 0.142

FX= 4880.75 PHI=-0.6862 BETA=3.0577 x=16.20354 y=81.18904

FCH= 63.1 OMEGA=-.7013 FCH1= 48.8 FCH2= 0.0 fnet2= 2781.51

r= 94.22 wa=0.1061 vn= 4.28 an= 25.01 dnu=0.0056 dmu=0.0077

sigma=-0.6860 gamma=1.2061 chi=-.0153 fych=-39.97 fxch= 48.82

t=0.8800 theta=0.7700 thetad=0.0875 thetadd= 0.8096

theta3d= 0.7155 rho=134.490 nu= 0.114

FC1= 4941.1 FC2= 4.04 FY= 1935.54 FN= 3199.09 mu= 0.150

FX= 4938.18 PHI=-0.6805 BETA=3.0521 x=16.95315 y=81.10711

FCH= 63.5 OMEGA=-.6956 FCH1= 49.4 FCH2= 0.0 fnet2= 2780.42

r= 93.14 wa=0.1074 vn= 4.54 an= 25.28 dnu=0.0056 dmu=0.0078

sigma=-0.6802 gamma=1.2060 chi=-.0154 fych=-39.96 fxch= 49.40

t=0.8900 theta=0.7700 thetad=0.0960 thetadd= 0.8415

theta3d= 0.7918 rho=133.649 nu= 0.120

FC1= 4974.4 FC2= 4.86 FY= 1934.79 FN= 3233.09 mu= 0.158

FX= 4970.91 PHI=-0.6772 BETA=3.0488 x=17.70105 y=81.02112

FCH= 63.8 OMEGA=-.6923 FCH1= 49.7 FCH2= 0.0 fnet2= 2779.46

r= 92.10 wa=0.1086 vn= 4.79 an= 25.75 dnu=0.0056 dmu=0.0079

sigma=-0.6768 gamma=1.2060 chi=-.0154 fych=-39.95 fxch= 49.73

t=0.9000 theta=0.7700 thetad=0.1050 thetadd= 0.8982

theta3d= 0.8739 rho=132.181 nu= 0.126

FC1= 5032.1 FC2= 5.81 FY= 1934.29 FN= 3291.21 mu= 0.166

FX= 5027.90 PHI=-0.6715 BETA=3.0431 x=18.44724 y=80.93106

FCH= 64.2 OMEGA=-.6866 FCH1= 50.3 FCH2= 0.1 fnet2= 2778.63

r= 91.07 wa=0.1098 vn= 5.06 an= 26.03 dnu=0.0057 dmu=0.0080

sigma=-0.6711 gamma=1.2060 chi=-.0154 fych=-39.95 fxch= 50.30

t=0.9100 theta=0.7701 thetad=0.1144 thetadd= 0.9328

theta3d= 0.9598 rho=131.347 nu= 0.132

FC1= 5066.6 FC2= 6.90 FY= 1934.08 FN= 3325.95 mu= 0.174

FX= 5061.67 PHI=-0.6682 BETA=3.0396 x=19.19173 y=80.83691

FCH= 64.5 OMEGA=-.6830 FCH1= 50.7 FCH2= 0.1 fnet2= 2777.94

r= 90.07 wa=0.1110 vn= 5.32 an= 26.49 dnu=0.0057 dmu=0.0081

sigma=-0.6677 gamma=1.2061 chi=-.0153 fych=-39.94 fxch= 50.64

t=0.9200 theta=0.7704 thetad=0.1244 thetadd= 0.9911

theta3d= 1.0521 rho=129.942 nu= 0.137

FC1= 5124.2 FC2= 8.15 FY= 1934.15 FN= 3383.44 mu= 0.182

FX= 5118.33 PHI=-0.6627 BETA=3.0339 x=19.93453 y=80.73866

FCH= 64.9 OMEGA=-.6772 FCH1= 51.2 FCH2= 0.1 fnet2= 2777.36

r= 89.09 wa=0.1122 vn= 5.59 an= 26.77 dnu=0.0058 dmu=0.0082

sigma=-0.6621 gamma=1.2064 chi=-.0150 fych=-39.92 fxch= 51.21

t=0.9300 theta=0.7707 thetad=0.1347 thetadd= 1.0286

theta3d= 1.1483 rho=129.118 nu= 0.143

FC1= 5159.9 FC2= 9.56 FY= 1934.53 FN= 3418.80 mu= 0.190

FX= 5153.02 PHI=-0.6593 BETA=3.0302 x=20.67563 y=80.63628

FCH= 65.2 OMEGA=-.6734 FCH1= 51.6 FCH2= 0.1 fnet2= 2776.93

r= 88.14 wa=0.1135 vn= 5.86 an= 27.24 dnu=0.0058 dmu=0.0083

sigma=-0.6587 gamma=1.2067 chi=-.0147 fych=-39.91 fxch= 51.57

t=0.9400 theta=0.7712 thetad=0.1457 thetadd= 1.0888

theta3d= 1.2517 rho=127.772 nu= 0.149

FC1= 5217.5 FC2= 11.18 FY= 1935.19 FN= 3475.79 mu= 0.199

FX= 5209.45 PHI=-0.6539 BETA=3.0243 x=21.41505 y=80.52977

FCH= 65.6 OMEGA=-.6674 FCH1= 52.2 FCH2= 0.1 fnet2= 2776.60

r= 87.20 wa=0.1147 vn= 6.14 an= 27.52 dnu=0.0058 dmu=0.0084

sigma=-0.6532 gamma=1.2072 chi=-.0142 fych=-39.90 fxch= 52.14

t=0.9500 theta=0.7717 thetad=0.1570 thetadd= 1.1295

theta3d= 1.3588 rho=126.960 nu= 0.155

FC1= 5254.3 FC2= 12.99 FY= 1936.18 FN= 3511.71 mu= 0.207

FX= 5244.96 PHI=-0.6504 BETA=3.0203 x=22.15279 y=80.41909

FCH= 65.9 OMEGA=-.6633 FCH1= 52.5 FCH2= 0.1 fnet2= 2776.40

r= 86.28 wa=0.1159 vn= 6.42 an= 27.98 dnu=0.0059 dmu=0.0085

sigma=-0.6496 gamma=1.2077 chi=-.0137 fych=-39.88 fxch= 52.50

t=0.9600 theta=0.7724 thetad=0.1690 thetadd= 1.1921

theta3d= 1.4740 rho=125.666 nu= 0.161

FC1= 5312.0 FC2= 15.05 FY= 1937.46 FN= 3568.30 mu= 0.216

FX= 5301.23 PHI=-0.6451 BETA=3.0143 x=22.88885 y=80.30424

FCH= 66.4 OMEGA=-.6572 FCH1= 53.1 FCH2= 0.2 fnet2= 2776.30

r= 85.38 wa=0.1171 vn= 6.70 an= 28.27 dnu=0.0059 dmu=0.0085

sigma=-0.6442 gamma=1.2084 chi=-.0130 fych=-39.86 fxch= 53.07

t=0.9700 theta=0.7732 thetad=0.1814 thetadd= 1.2361

theta3d= 1.5930 rho=124.868 nu= 0.167

FC1= 5349.9 FC2= 17.35 FY= 1939.08 FN= 3604.70 mu= 0.224

FX= 5337.45 PHI=-0.6417 BETA=3.0101 x=23.62324 y=80.18518

FCH= 66.7 OMEGA=-.6528 FCH1= 53.5 FCH2= 0.2 fnet2= 2776.31

r= 84.50 wa=0.1183 vn= 6.99 an= 28.73 dnu=0.0060 dmu=0.0086

sigma=-0.6406 gamma=1.2092 chi=-.0122 fych=-39.84 fxch= 53.44

t=0.9800 theta=0.7741 thetad=0.1945 thetadd= 1.3014

theta3d= 1.7208 rho=123.624 nu= 0.173

FC1= 5407.9 FC2= 19.95 FY= 1941.00 FN= 3661.00 mu= 0.233

FX= 5393.64 PHI=-0.6364 BETA=3.0039 x=24.35595 y=80.06191

FCH= 67.1 OMEGA=-.6465 FCH1= 54.1 FCH2= 0.2 fnet2= 2776.40

r= 83.64 wa=0.1196 vn= 7.28 an= 29.02 dnu=0.0060 dmu=0.0087

sigma=-0.6352 gamma=1.2101 chi=-.0113 fych=-39.81 fxch= 54.01

t=0.9900 theta=0.7752 thetad=0.2081 thetadd= 1.3489

theta3d= 1.8525 rho=122.841 nu= 0.179

FC1= 5446.8 FC2= 22.83 FY= 1943.26 FN= 3697.83 mu= 0.242

FX= 5430.46 PHI=-0.6329 BETA=2.9993 x=25.08700 y=79.93440

FCH= 67.4 OMEGA=-.6417 FCH1= 54.5 FCH2= 0.2 fnet2= 2776.59

r= 82.80 wa=0.1208 vn= 7.57 an= 29.47 dnu=0.0060 dmu=0.0088

sigma=-0.6316 gamma=1.2112 chi=-.0102 fych=-39.79 fxch= 54.39

t=1.0000 theta=0.7764 thetad=0.2224 thetadd= 1.4173

theta3d= 1.9938 rho=121.641 nu= 0.185

FC1= 5505.2 FC2= 26.07 FY= 1945.84 FN= 3753.92 mu= 0.251

FX= 5486.58 PHI=-0.6278 BETA=2.9929 x=25.81639 y=79.80264

FCH= 67.8 OMEGA=-.6352 FCH1= 55.1 FCH2= 0.3 fnet2= 2776.82

r= 81.97 wa=0.1220 vn= 7.87 an= 29.77 dnu=0.0061 dmu=0.0089

sigma=-0.6262 gamma=1.2124 chi=-.0090 fych=-39.76 fxch= 54.96

t=1.0100 theta=0.7778 thetad=0.2372 thetadd= 1.4688

theta3d= 2.1392 rho=120.875 nu= 0.191

FC1= 5545.0 FC2= 29.65 FY= 1948.76 FN= 3791.16 mu= 0.260

FX= 5523.92 PHI=-0.6242 BETA=2.9880 x=26.54410 y=79.66659

FCH= 68.1 OMEGA=-.6301 FCH1= 55.5 FCH2= 0.3 fnet2= 2777.13

r= 81.16 wa=0.1232 vn= 8.17 an= 30.22 dnu=0.0061 dmu=0.0090

sigma=-0.6225 gamma=1.2138 chi=-.0076 fych=-39.72 fxch= 55.35

t=1.0200 theta=0.7793 thetad=0.2527 thetadd= 1.5407

theta3d= 2.2952 rho=119.718 nu= 0.197

FC1= 5603.9 FC2= 33.66 FY= 1951.99 FN= 3847.14 mu= 0.269

FX= 5579.98 PHI=-0.6191 BETA=2.9814 x=27.27016 y=79.52625

FCH= 68.6 OMEGA=-.6232 FCH1= 56.0 FCH2= 0.3 fnet2= 2777.45

r= 80.36 wa=0.1244 vn= 8.48 an= 30.52 dnu=0.0062 dmu=0.0091

sigma=-0.6172 gamma=1.2153 chi=-.0061 fych=-39.68 fxch= 55.92

t=1.0300 theta=0.7810 thetad=0.2688 thetadd= 1.5962

theta3d= 2.4552 rho=118.970 nu= 0.203

FC1= 5644.8 FC2= 38.08 FY= 1955.56 FN= 3884.76 mu= 0.278

FX= 5617.72 PHI=-0.6156 BETA=2.9762 x=27.99455 y=79.38158

FCH= 68.9 OMEGA=-.6177 FCH1= 56.4 FCH2= 0.4 fnet2= 2777.81

r= 79.58 wa=0.1257 vn= 8.79 an= 30.97 dnu=0.0062 dmu=0.0092

sigma=-0.6134 gamma=1.2170 chi=-.0044 fych=-39.64 fxch= 56.32

t=1.0400 theta=0.7829 thetad=0.2857 thetadd= 1.6721

theta3d= 2.6269 rho=117.852 nu= 0.210

FC1= 5704.2 FC2= 43.01 FY= 1959.43 FN= 3940.71 mu= 0.287

FX= 5673.72 PHI=-0.6105 BETA=2.9692 x=28.71729 y=79.23257

FCH= 69.3 OMEGA=-.6105 FCH1= 57.0 FCH2= 0.4 fnet2= 2778.14

r= 78.81 wa=0.1269 vn= 9.10 an= 31.27 dnu=0.0063 dmu=0.0093

sigma=-0.6080 gamma=1.2189 chi=-.0025 fych=-39.60 fxch= 56.90

t=1.0500 theta=0.7849 thetad=0.3031 thetadd= 1.7321

theta3d= 2.8027 rho=117.121 nu= 0.216

FC1= 5746.0 FC2= 48.42 FY= 1963.64 FN= 3978.73 mu= 0.297

FX= 5711.74 PHI=-0.6069 BETA=2.9636 x=29.43836 y=79.07919

FCH= 69.6 OMEGA=-.6046 FCH1= 57.5 FCH2= 0.5 fnet2= 2778.45

r= 78.06 wa=0.1281 vn= 9.41 an= 31.72 dnu=0.0063 dmu=0.0094

sigma=-0.6041 gamma=1.2209 chi=-.0005 fych=-39.55 fxch= 57.30

t=1.0600 theta=0.7871 thetad=0.3214 thetadd= 1.8124

theta3d= 2.9913 rho=116.041 nu= 0.222

FC1= 5806.1 FC2= 54.44 FY= 1968.13 FN= 4034.74 mu= 0.306

FX= 5767.63 PHI=-0.6018 BETA=2.9563 x=30.15777 y=78.92142

FCH= 70.1 OMEGA=-.5971 FCH1= 58.1 FCH2= 0.5 fnet2= 2778.67

r= 77.33 wa=0.1293 vn= 9.74 an= 32.03 dnu=0.0063 dmu=0.0094

sigma=-0.5987 gamma=1.2231 chi=0.0017 fych=-39.49 fxch= 57.88

t=1.0700 theta=0.7895 thetad=0.3403 thetadd= 1.8772

theta3d= 3.1842 rho=115.330 nu= 0.229

FC1= 5848.8 FC2= 61.04 FY= 1972.94 FN= 4073.15 mu= 0.316

FX= 5805.81 PHI=-0.5982 BETA=2.9503 x=30.87552 y=78.75923

FCH= 70.4 OMEGA=-.5907 FCH1= 58.5 FCH2= 0.6 fnet2= 2778.83

r= 76.60 wa=0.1305 vn=10.06 an= 32.48 dnu=0.0064 dmu=0.0095

sigma=-0.5947 gamma=1.2255 chi=0.0041 fych=-39.43 fxch= 58.28

t=1.0800 theta=0.7921 thetad=0.3601 thetadd= 1.9623

theta3d= 3.3909 rho=114.285 nu= 0.235

FC1= 5909.5 FC2= 68.35 FY= 1978.00 FN= 4129.33 mu= 0.325

FX= 5861.53 PHI=-0.5931 BETA=2.9427 x=31.59161 y=78.59261

FCH= 70.8 OMEGA=-.5826 FCH1= 59.1 FCH2= 0.7 fnet2= 2778.82

r= 75.90 wa=0.1318 vn=10.39 an= 32.79 dnu=0.0064 dmu=0.0096

sigma=-0.5893 gamma=1.2281 chi=0.0067 fych=-39.36 fxch= 58.87

t=1.0900 theta=0.7949 thetad=0.3806 thetadd= 2.0324

theta3d= 3.6020 rho=113.594 nu= 0.242

FC1= 5953.2 FC2= 76.35 FY= 1983.34 FN= 4168.17 mu= 0.335

FX= 5899.71 PHI=-0.5894 BETA=2.9362 x=32.30603 y=78.42153

FCH= 71.1 OMEGA=-.5757 FCH1= 59.5 FCH2= 0.8 fnet2= 2778.67

r= 75.20 wa=0.1330 vn=10.72 an= 33.24 dnu=0.0065 dmu=0.0097

sigma=-0.5852 gamma=1.2309 chi=0.0095 fych=-39.28 fxch= 59.28

t=1.1000 theta=0.7979 thetad=0.4020 thetadd= 2.1228

theta3d= 3.8282 rho=112.584 nu= 0.248

FC1= 6014.6 FC2= 85.19 FY= 1988.91 FN= 4224.63 mu= 0.345

FX= 5955.16 PHI=-0.5844 BETA=2.9281 x=33.01879 y=78.24596

FCH= 71.6 OMEGA=-.5672 FCH1= 60.1 FCH2= 0.9 fnet2= 2778.26

r= 74.52 wa=0.1342 vn=11.06 an= 33.55 dnu=0.0065 dmu=0.0098

sigma=-0.5797 gamma=1.2339 chi=0.0125 fych=-39.20 fxch= 59.87

t=1.1100 theta=0.8011 thetad=0.4242 thetadd= 2.1985

theta3d= 4.0588 rho=111.913 nu= 0.255

FC1= 6059.2 FC2= 94.85 FY= 1994.71 FN= 4263.94 mu= 0.355

FX= 5993.17 PHI=-0.5806 BETA=2.9211 x=33.72987 y=78.06588

FCH= 71.9 OMEGA=-.5597 FCH1= 60.6 FCH2= 0.9 fnet2= 2777.62

r= 73.84 wa=0.1354 vn=11.40 an= 34.01 dnu=0.0066 dmu=0.0099

sigma=-0.5754 gamma=1.2371 chi=0.0157 fych=-39.10 fxch= 60.28

t=1.1200 theta=0.8046 thetad=0.4474 thetadd= 2.2947

theta3d= 4.3059 rho=110.936 nu= 0.261

FC1= 6121.4 FC2= 105.49 FY= 2000.68 FN= 4320.81 mu= 0.365

FX= 6048.27 PHI=-0.5755 BETA=2.9125 x=34.43929 y=77.88126

FCH= 72.3 OMEGA=-.5506 FCH1= 61.2 FCH2= 1.1 fnet2= 2776.61

r= 73.18 wa=0.1366 vn=11.74 an= 34.33 dnu=0.0066 dmu=0.0100

sigma=-0.5698 gamma=1.2406 chi=0.0192 fych=-39.00 fxch= 60.87

t=1.1300 theta=0.8083 thetad=0.4714 thetadd= 2.3764

theta3d= 4.5575 rho=110.287 nu= 0.268

FC1= 6166.8 FC2= 117.11 FY= 2006.82 FN= 4360.65 mu= 0.375

FX= 6085.89 PHI=-0.5717 BETA=2.9050 x=35.14703 y=77.69209

FCH= 72.6 OMEGA=-.5425 FCH1= 61.7 FCH2= 1.2 fnet2= 2775.26

r= 72.54 wa=0.1379 vn=12.09 an= 34.78 dnu=0.0066 dmu=0.0101

sigma=-0.5654 gamma=1.2443 chi=0.0229 fych=-38.89 fxch= 61.29

t=1.1400 theta=0.8123 thetad=0.4964 thetadd= 2.4790

theta3d= 4.8269 rho=109.343 nu= 0.275

FC1= 6229.8 FC2= 129.87 FY= 2013.04 FN= 4418.05 mu= 0.385

FX= 6140.45 PHI=-0.5665 BETA=2.8959 x=35.85309 y=77.49832

FCH= 73.0 OMEGA=-.5328 FCH1= 62.3 FCH2= 1.3 fnet2= 2773.40

r= 71.90 wa=0.1391 vn=12.44 an= 35.10 dnu=0.0067 dmu=0.0102

sigma=-0.5596 gamma=1.2483 chi=0.0269 fych=-38.77 fxch= 61.89

t=1.1500 theta=0.8165 thetad=0.5223 thetadd= 2.5672

theta3d= 5.1007 rho=108.716 nu= 0.281

FC1= 6276.0 FC2= 143.79 FY= 2019.36 FN= 4458.55 mu= 0.395

FX= 6177.50 PHI=-0.5626 BETA=2.8877 x=36.55747 y=77.29993

FCH= 73.3 OMEGA=-.5239 FCH1= 62.8 FCH2= 1.4 fnet2= 2771.05

r= 71.28 wa=0.1403 vn=12.79 an= 35.57 dnu=0.0067 dmu=0.0102

sigma=-0.5550 gamma=1.2525 chi=0.0311 fych=-38.64 fxch= 62.31

t=1.1600 theta=0.8210 thetad=0.5494 thetadd= 2.6766

theta3d= 5.3939 rho=107.806 nu= 0.288

FC1= 6339.7 FC2= 159.06 FY= 2025.65 FN= 4516.63 mu= 0.405

FX= 6231.31 PHI=-0.5573 BETA=2.8780 x=37.26017 y=77.09691

FCH= 73.7 OMEGA=-.5135 FCH1= 63.4 FCH2= 1.6 fnet2= 2768.04

r= 70.66 wa=0.1415 vn=13.15 an= 35.89 dnu=0.0068 dmu=0.0103

sigma=-0.5491 gamma=1.2570 chi=0.0356 fych=-38.49 fxch= 62.91

t=1.1700 theta=0.8257 thetad=0.5774 thetadd= 2.7718

theta3d= 5.6914 rho=107.202 nu= 0.295

FC1= 6386.7 FC2= 175.69 FY= 2031.92 FN= 4557.93 mu= 0.416

FX= 6267.53 PHI=-0.5533 BETA=2.8691 x=37.96117 y=76.88921

FCH= 74.0 OMEGA=-.5039 FCH1= 63.9 FCH2= 1.8 fnet2= 2764.37

r= 70.06 wa=0.1427 vn=13.52 an= 36.36 dnu=0.0068 dmu=0.0104

sigma=-0.5442 gamma=1.2617 chi=0.0403 fych=-38.33 fxch= 63.33

t=1.1800 theta=0.8308 thetad=0.6066 thetadd= 2.8886

theta3d= 6.0097 rho=106.325 nu= 0.302

FC1= 6451.1 FC2= 193.90 FY= 2038.03 FN= 4616.87 mu= 0.426

FX= 6320.35 PHI=-0.5479 BETA=2.8587 x=38.66047 y=76.67681

FCH= 74.5 OMEGA=-.4926 FCH1= 64.5 FCH2= 1.9 fnet2= 2759.84

r= 69.46 wa=0.1440 vn=13.88 an= 36.69 dnu=0.0069 dmu=0.0105

sigma=-0.5380 gamma=1.2668 chi=0.0454 fych=-38.15 fxch= 63.93

t=1.1900 theta=0.8361 thetad=0.6368 thetadd= 2.9912

theta3d= 6.3323 rho=105.746 nu= 0.309

FC1= 6498.7 FC2= 213.71 FY= 2043.97 FN= 4659.13 mu= 0.437

FX= 6355.45 PHI=-0.5437 BETA=2.8491 x=39.35808 y=76.45969

FCH= 74.7 OMEGA=-.4821 FCH1= 65.0 FCH2= 2.1 fnet2= 2754.45

r= 68.88 wa=0.1452 vn=14.25 an= 37.17 dnu=0.0069 dmu=0.0106

sigma=-0.5329 gamma=1.2721 chi=0.0507 fych=-37.96 fxch= 64.36

t=1.2000 theta=0.8418 thetad=0.6683 thetadd= 3.1158

theta3d= 6.6771 rho=104.903 nu= 0.316

FC1= 6563.8 FC2= 235.37 FY= 2049.58 FN= 4719.14 mu= 0.448

FX= 6406.98 PHI=-0.5381 BETA=2.8379 x=40.05397 y=76.23780

FCH= 75.1 OMEGA=-.4700 FCH1= 65.6 FCH2= 2.4 fnet2= 2747.96

r= 68.31 wa=0.1464 vn=14.63 an= 37.51 dnu=0.0070 dmu=0.0107

sigma=-0.5264 gamma=1.2778 chi=0.0564 fych=-37.75 fxch= 64.96

t=1.2100 theta=0.8478 thetad=0.7009 thetadd= 3.2264

theta3d= 7.0259 rho=104.350 nu= 0.323

FC1= 6611.9 FC2= 258.91 FY= 2054.83 FN= 4762.60 mu= 0.458

FX= 6440.65 PHI=-0.5337 BETA=2.8275 x=40.74816 y=76.01113

FCH= 75.4 OMEGA=-.4585 FCH1= 66.1 FCH2= 2.6 fnet2= 2740.36

r= 67.74 wa=0.1476 vn=15.01 an= 37.99 dnu=0.0070 dmu=0.0108

sigma=-0.5209 gamma=1.2838 chi=0.0624 fych=-37.52 fxch= 65.39

t=1.2200 theta=0.8542 thetad=0.7349 thetadd= 3.3594

theta3d= 7.3983 rho=103.542 nu= 0.330

FC1= 6677.5 FC2= 284.61 FY= 2059.52 FN= 4823.96 mu= 0.469

FX= 6490.58 PHI=-0.5280 BETA=2.8154 x=41.44062 y=75.77965

FCH= 75.8 OMEGA=-.4453 FCH1= 66.8 FCH2= 2.8 fnet2= 2731.38

r= 67.19 wa=0.1488 vn=15.39 an= 38.34 dnu=0.0071 dmu=0.0109

sigma=-0.5141 gamma=1.2902 chi=0.0688 fych=-37.27 fxch= 65.99

t=1.2300 theta=0.8609 thetad=0.7700 thetadd= 3.4785

theta3d= 7.7744 rho=103.017 nu= 0.337

FC1= 6726.1 FC2= 312.50 FY= 2063.61 FN= 4868.86 mu= 0.480

FX= 6522.42 PHI=-0.5233 BETA=2.8040 x=42.13136 y=75.54331

FCH= 76.0 OMEGA=-.4327 FCH1= 67.3 FCH2= 3.1 fnet2= 2721.01

r= 66.64 wa=0.1501 vn=15.78 an= 38.83 dnu=0.0071 dmu=0.0110

sigma=-0.5082 gamma=1.2969 chi=0.0755 fych=-36.99 fxch= 66.42

t=1.2400 theta=0.8679 thetad=0.8067 thetadd= 3.6203

theta3d= 8.1755 rho=102.247 nu= 0.344

FC1= 6792.0 FC2= 342.93 FY= 2066.85 FN= 4931.87 mu= 0.491

FX= 6570.36 PHI=-0.5173 BETA=2.7910 x=42.82036 y=75.30210

FCH= 76.4 OMEGA=-.4184 FCH1= 67.9 FCH2= 3.4 fnet2= 2708.91

r= 66.10 wa=0.1513 vn=16.17 an= 39.20 dnu=0.0071 dmu=0.0110

sigma=-0.5009 gamma=1.3039 chi=0.0825 fych=-36.69 fxch= 67.02

t=1.2500 theta=0.8754 thetad=0.8446 thetadd= 3.7482

theta3d= 8.5796 rho=101.753 nu= 0.351

FC1= 6840.9 FC2= 375.92 FY= 2069.19 FN= 4978.58 mu= 0.502

FX= 6599.99 PHI=-0.5122 BETA=2.7785 x=43.50763 y=75.05598

FCH= 76.6 OMEGA=-.4046 FCH1= 68.4 FCH2= 3.8 fnet2= 2695.07

r= 65.57 wa=0.1525 vn=16.57 an= 39.70 dnu=0.0072 dmu=0.0111

sigma=-0.4945 gamma=1.3114 chi=0.0900 fych=-36.37 fxch= 67.45

t=1.2600 theta=0.8832 thetad=0.8840 thetadd= 3.8994

theta3d= 9.0099 rho=101.021 nu= 0.358

FC1= 6906.9 FC2= 411.85 FY= 2070.32 FN= 5043.63 mu= 0.514

FX= 6645.52 PHI=-0.5059 BETA=2.7643 x=44.19314 y=74.80492

FCH= 77.0 OMEGA=-.3890 FCH1= 69.1 FCH2= 4.1 fnet2= 2679.12

r= 65.05 wa=0.1537 vn=16.97 an= 40.08 dnu=0.0072 dmu=0.0112

sigma=-0.4868 gamma=1.3192 chi=0.0978 fych=-36.01 fxch= 68.05

t=1.2700 theta=0.8914 thetad=0.9248 thetadd= 4.0365

theta3d= 9.4424 rho=100.562 nu= 0.366

FC1= 6955.7 FC2= 450.78 FY= 2070.18 FN= 5092.52 mu= 0.525

FX= 6672.45 PHI=-0.5005 BETA=2.7506 x=44.87690 y=74.54888

FCH= 77.2 OMEGA=-.3737 FCH1= 69.6 FCH2= 4.5 fnet2= 2661.00

r= 64.54 wa=0.1549 vn=17.38 an= 40.60 dnu=0.0073 dmu=0.0113

sigma=-0.4798 gamma=1.3274 chi=0.1060 fych=-35.63 fxch= 68.47

t=1.2800 theta=0.9001 thetad=0.9673 thetadd= 4.1974

theta3d= 9.9020 rho= 99.873 nu= 0.373

FC1= 7021.7 FC2= 493.13 FY= 2068.38 FN= 5160.11 mu= 0.536

FX= 6715.15 PHI=-0.4937 BETA=2.7352 x=45.55889 y=74.28784

FCH= 77.5 OMEGA=-.3567 FCH1= 70.2 FCH2= 4.9 fnet2= 2640.31

r= 64.04 wa=0.1562 vn=17.79 an= 41.00 dnu=0.0073 dmu=0.0114

sigma=-0.4714 gamma=1.3361 chi=0.1147 fych=-35.21 fxch= 69.07

t=1.2900 theta=0.9092 thetad=1.0113 thetadd= 4.3439

theta3d= 10.3625 rho= 99.452 nu= 0.380

FC1= 7070.0 FC2= 538.97 FY= 2064.83 FN= 5211.68 mu= 0.548

FX= 6738.89 PHI=-0.4877 BETA=2.7201 x=46.23911 y=74.02177

FCH= 77.7 OMEGA=-.3399 FCH1= 70.7 FCH2= 5.4 fnet2= 2616.98

r= 63.54 wa=0.1574 vn=18.20 an= 41.54 dnu=0.0073 dmu=0.0115

sigma=-0.4637 gamma=1.3452 chi=0.1238 fych=-34.75 fxch= 69.50

t=1.3000 theta=0.9188 thetad=1.0570 thetadd= 4.5149

theta3d= 10.8509 rho= 98.807 nu= 0.388

FC1= 7135.6 FC2= 588.77 FY= 2059.08 FN= 5282.39 mu= 0.559

FX= 6778.30 PHI=-0.4804 BETA=2.7032 x=46.91754 y=73.75063

FCH= 78.0 OMEGA=-.3212 FCH1= 71.4 FCH2= 5.9 fnet2= 2590.53

r= 63.05 wa=0.1586 vn=18.62 an= 41.96 dnu=0.0074 dmu=0.0116

sigma=-0.4545 gamma=1.3548 chi=0.1334 fych=-34.25 fxch= 70.10

t=1.3100 theta=0.9288 thetad=1.1042 thetadd= 4.6711

theta3d= 11.3384 rho= 98.430 nu= 0.395

FC1= 7183.1 FC2= 642.62 FY= 2051.01 FN= 5337.21 mu= 0.571

FX= 6798.31 PHI=-0.4737 BETA=2.6865 x=47.59419 y=73.47438

FCH= 78.2 OMEGA=-.3026 FCH1= 71.8 FCH2= 6.4 fnet2= 2560.88

r= 62.57 wa=0.1598 vn=19.05 an= 42.52 dnu=0.0074 dmu=0.0117

sigma=-0.4460 gamma=1.3648 chi=0.1434 fych=-33.71 fxch= 70.52

t=1.3200 theta=0.9393 thetad=1.1534 thetadd= 4.8523

theta3d= 11.8541 rho= 97.835 nu= 0.403

FC1= 7247.8 FC2= 701.06 FY= 2040.07 FN= 5411.77 mu= 0.583

FX= 6833.98 PHI=-0.4656 BETA=2.6679 x=48.26904 y=73.19301

FCH= 78.5 OMEGA=-.2820 FCH1= 72.5 FCH2= 7.0 fnet2= 2527.48

r= 62.10 wa=0.1610 vn=19.48 an= 42.97 dnu=0.0075 dmu=0.0118

sigma=-0.4359 gamma=1.3753 chi=0.1539 fych=-33.13 fxch= 71.12

t=1.3300 theta=0.9504 thetad=1.2042 thetadd= 5.0181

theta3d= 12.3666 rho= 97.507 nu= 0.410

FC1= 7294.1 FC2= 764.17 FY= 2026.10 FN= 5470.57 mu= 0.595

FX= 6849.77 PHI=-0.4582 BETA=2.6494 x=48.94208 y=72.90646

FCH= 78.6 OMEGA=-.2614 FCH1= 72.9 FCH2= 7.6 fnet2= 2490.22

r= 61.63 wa=0.1623 vn=19.91 an= 43.57 dnu=0.0075 dmu=0.0118

sigma=-0.4263 gamma=1.3864 chi=0.1650 fych=-32.49 fxch= 71.54

t=1.3400 theta=0.9619 thetad=1.2569 thetadd= 5.2093

theta3d= 12.9068 rho= 96.968 nu= 0.418

FC1= 7357.3 FC2= 832.58 FY= 2008.47 FN= 5549.70 mu= 0.606

FX= 6881.13 PHI=-0.4492 BETA=2.6289 x=49.61331 y=72.61472

FCH= 78.8 OMEGA=-.2387 FCH1= 73.6 FCH2= 8.3 fnet2= 2448.49

r= 61.17 wa=0.1635 vn=20.35 an= 44.04 dnu=0.0075 dmu=0.0119

sigma=-0.4152 gamma=1.3979 chi=0.1765 fych=-31.80 fxch= 72.14

t=1.3500 theta=0.9740 thetad=1.3114 thetadd= 5.3848

theta3d= 13.4410 rho= 96.695 nu= 0.425

FC1= 7401.7 FC2= 906.37 FY= 1986.95 FN= 5613.49 mu= 0.619

FX= 6892.39 PHI=-0.4406 BETA=2.6082 x=50.28272 y=72.31775

FCH= 78.9 OMEGA=-.2158 FCH1= 74.0 FCH2= 9.1 fnet2= 2402.15

r= 60.72 wa=0.1647 vn=20.80 an= 44.68 dnu=0.0076 dmu=0.0120

sigma=-0.4044 gamma=1.4100 chi=0.1886 fych=-31.06 fxch= 72.57

t=1.3600 theta=0.9867 thetad=1.3680 thetadd= 5.5858

theta3d= 14.0016 rho= 96.220 nu= 0.433

FC1= 7462.9 FC2= 986.24 FY= 1960.81 FN= 5698.12 mu= 0.631

FX= 6918.99 PHI=-0.4305 BETA=2.5854 x=50.95030 y=72.01551

FCH= 79.2 OMEGA=-.1907 FCH1= 74.6 FCH2= 9.9 fnet2= 2350.50

r= 60.27 wa=0.1659 vn=21.25 an= 45.19 dnu=0.0076 dmu=0.0121

sigma=-0.3920 gamma=1.4227 chi=0.2013 fych=-30.25 fxch= 73.18

t=1.3700 theta=1.0000 thetad=1.4264 thetadd= 5.7703

theta3d= 14.5524 rho= 96.009 nu= 0.440

FC1= 7504.7 FC2= 1072.29 FY= 1929.77 FN= 5767.93 mu= 0.643

FX= 6925.32 PHI=-0.4206 BETA=2.5622 x=51.61604 y=71.70798

FCH= 79.3 OMEGA=-.1652 FCH1= 75.0 FCH2= 10.7 fnet2= 2293.40

r= 59.83 wa=0.1671 vn=21.71 an= 45.87 dnu=0.0076 dmu=0.0122

sigma=-0.3798 gamma=1.4360 chi=0.2146 fych=-29.38 fxch= 73.61

t=1.3800 theta=1.0138 thetad=1.4870 thetadd= 5.9805

theta3d= 15.1273 rho= 95.605 nu= 0.448

FC1= 7562.9 FC2= 1165.27 FY= 1892.99 FN= 5859.23 mu= 0.655

FX= 6946.93 PHI=-0.4090 BETA=2.5367 x=52.27994 y=71.39512

FCH= 79.5 OMEGA=-.1375 FCH1= 75.6 FCH2= 11.6 fnet2= 2230.05

r= 59.40 wa=0.1684 vn=22.18 an= 46.43 dnu=0.0077 dmu=0.0123

sigma=-0.3659 gamma=1.4498 chi=0.2284 fych=-28.44 fxch= 74.23

t=1.3900 theta=1.0283 thetad=1.5495 thetadd= 6.1735

theta3d= 15.6879 rho= 95.466 nu= 0.456

FC1= 7601.4 FC2= 1265.32 FY= 1850.11 FN= 5936.32 mu= 0.668

FX= 6948.17 PHI=-0.3974 BETA=2.5107 x=52.94200 y=71.07690

FCH= 79.5 OMEGA=-.1091 FCH1= 76.0 FCH2= 12.6 fnet2= 2160.28

r= 58.97 wa=0.1696 vn=22.65 an= 47.17 dnu=0.0077 dmu=0.0124

sigma=-0.3520 gamma=1.4643 chi=0.2429 fych=-27.43 fxch= 74.67

t=1.4000 theta=1.0434 thetad=1.6142 thetadd= 6.3919

theta3d= 16.2690 rho= 95.143 nu= 0.463

FC1= 7655.8 FC2= 1373.25 FY= 1800.18 FN= 6035.60 mu= 0.680

FX= 6964.67 PHI=-0.3839 BETA=2.4820 x=53.60220 y=70.75328

FCH= 79.8 OMEGA=-.0783 FCH1= 76.6 FCH2= 13.7 fnet2= 2083.21

r= 58.55 wa=0.1708 vn=23.12 an= 47.79 dnu=0.0077 dmu=0.0125

sigma=-0.3364 gamma=1.4794 chi=0.2580 fych=-26.33 fxch= 75.31

t=1.4100 theta=1.0592 thetad=1.6810 thetadd= 6.5920

theta3d= 16.8301 rho= 95.088 nu= 0.471

FC1= 7689.9 FC2= 1489.19 FY= 1742.79 FN= 6121.38 mu= 0.693

FX= 6960.87 PHI=-0.3702 BETA=2.4525 x=54.26056 y=70.42424

FCH= 79.8 OMEGA=-.0467 FCH1= 76.9 FCH2= 14.9 fnet2= 1998.64

r= 58.13 wa=0.1720 vn=23.61 an= 48.59 dnu=0.0077 dmu=0.0126

sigma=-0.3206 gamma=1.4952 chi=0.2738 fych=-25.16 fxch= 75.78

t=1.4200 theta=1.0757 thetad=1.7500 thetadd= 6.8173

theta3d= 17.4068 rho= 94.858 nu= 0.479

FC1= 7739.3 FC2= 1614.04 FY= 1676.83 FN= 6230.19 mu= 0.705

FX= 6972.53 PHI=-0.3544 BETA=2.4202 x=54.91706 y=70.08975

FCH= 80.1 OMEGA=-.0127 FCH1= 77.4 FCH2= 16.1 fnet2= 1905.62

r= 57.72 wa=0.1732 vn=24.10 an= 49.28 dnu=0.0078 dmu=0.0126

sigma=-0.3030 gamma=1.5117 chi=0.2903 fych=-23.90 fxch= 76.44

t=1.4300 theta=1.0929 thetad=1.8211 thetadd= 7.0231

theta3d= 17.9564 rho= 94.899 nu= 0.487

FC1= 7768.0 FC2= 1747.91 FY= 1601.85 FN= 6326.33 mu= 0.718

FX= 6964.17 PHI=-0.3380 BETA=2.3867 x=55.57172 y=69.74978

FCH= 80.2 OMEGA=0.0225 FCH1= 77.7 FCH2= 17.5 fnet2= 1803.92

r= 57.32 wa=0.1745 vn=24.60 an= 50.15 dnu=0.0078 dmu=0.0127

sigma=-0.2850 gamma=1.5289 chi=0.3075 fych=-22.55 fxch= 76.95

t=1.4400 theta=1.1109 thetad=1.8946 thetadd= 7.2533

theta3d= 18.5151 rho= 94.774 nu= 0.495

FC1= 7811.3 FC2= 1891.76 FY= 1516.62 FN= 6446.39 mu= 0.731

FX= 6971.64 PHI=-0.3193 BETA=2.3500 x=56.22452 y=69.40429

FCH= 80.5 OMEGA=0.0602 FCH1= 78.1 FCH2= 18.9 fnet2= 1692.49

r= 56.92 wa=0.1757 vn=25.11 an= 50.93 dnu=0.0078 dmu=0.0128

sigma=-0.2653 gamma=1.5469 chi=0.3255 fych=-21.10 fxch= 77.66

t=1.4500 theta=1.1296 thetad=1.9702 thetadd= 7.4626

theta3d= 19.0387 rho= 94.926 nu= 0.502

FC1= 7833.4 FC2= 2045.70 FY= 1420.65 FN= 6554.77 mu= 0.744

FX= 6959.74 PHI=-0.2996 BETA=2.3117 x=56.87548 y=69.05325

FCH= 80.6 OMEGA=0.0992 FCH1= 78.3 FCH2= 20.4 fnet2= 1571.11

r= 56.53 wa=0.1769 vn=25.63 an= 51.89 dnu=0.0078 dmu=0.0129

sigma=-0.2450 gamma=1.5656 chi=0.3442 fych=-19.56 fxch= 78.23

t=1.4600 theta=1.1490 thetad=2.0481 thetadd= 7.6954

theta3d= 19.5628 rho= 94.924 nu= 0.510

FC1= 7869.3 FC2= 2210.74 FY= 1312.59 FN= 6687.94 mu= 0.757

FX= 6964.28 PHI=-0.2774 BETA=2.2699 x=57.52462 y=68.69666

FCH= 81.0 OMEGA=0.1408 FCH1= 78.7 FCH2= 22.1 fnet2= 1438.65

r= 56.14 wa=0.1781 vn=26.16 an= 52.77 dnu=0.0078 dmu=0.0130

sigma=-0.2229 gamma=1.5850 chi=0.3636 fych=-17.91 fxch= 79.01

t=1.4700 theta=1.1693 thetad=2.1282 thetadd= 7.9055

theta3d= 20.0427 rho= 95.203 nu= 0.518

FC1= 7883.4 FC2= 2386.94 FY= 1191.93 FN= 6810.62 mu= 0.770

FX= 6950.59 PHI=-0.2538 BETA=2.2261 x=58.17193 y=68.33445

FCH= 81.3 OMEGA=0.1838 FCH1= 78.8 FCH2= 23.9 fnet2= 1294.89

r= 55.76 wa=0.1793 vn=26.70 an= 53.84 dnu=0.0078 dmu=0.0131

sigma=-0.2001 gamma=1.6053 chi=0.3839 fych=-16.16 fxch= 79.66

t=1.4800 theta=1.1904 thetad=2.2106 thetadd= 8.1378

theta3d= 20.5128 rho= 95.341 nu= 0.526

FC1= 7910.5 FC2= 2575.37 FY= 1057.24 FN= 6958.95 mu= 0.783

FX= 6954.30 PHI=-0.2273 BETA=2.1785 x=58.81744 y=67.96662

FCH= 81.8 OMEGA=0.2293 FCH1= 79.1 FCH2= 25.7 fnet2= 1138.62

r= 55.38 wa=0.1806 vn=27.25 an= 54.83 dnu=0.0078 dmu=0.0132

sigma=-0.1757 gamma=1.6264 chi=0.4050 fych=-14.30 fxch= 80.54

t=1.4900 theta=1.2124 thetad=2.2951 thetadd= 8.3458

theta3d= 20.9285 rho= 95.766 nu= 0.534

FC1= 7915.3 FC2= 2776.03 FY= 908.03 FN= 7098.12 mu= 0.796

FX= 6941.49 PHI=-0.1991 BETA=2.1283 x=59.46116 y=67.59314

FCH= 82.2 OMEGA=0.2763 FCH1= 79.2 FCH2= 27.7 fnet2= 969.65

r= 55.01 wa=0.1818 vn=27.81 an= 56.02 dnu=0.0078 dmu=0.0133

sigma=-0.1506 gamma=1.6484 chi=0.4270 fych=-12.34 fxch= 81.31

t=1.5000 theta=1.2352 thetad=2.3819 thetadd= 8.5741

theta3d= 21.3225 rho= 96.064 nu= 0.541

FC1= 7932.3 FC2= 2990.00 FY= 742.82 FN= 7263.77 mu= 0.810

FX= 6947.53 PHI=-0.1678 BETA=2.0742 x=60.10312 y=67.21398

FCH= 83.0 OMEGA=0.3257 FCH1= 79.3 FCH2= 29.9 fnet2= 786.71

r= 54.64 wa=0.1830 vn=28.38 an= 57.14 dnu=0.0078 dmu=0.0134

sigma=-0.1241 gamma=1.6712 chi=0.4498 fych=-10.27 fxch= 82.32

t=1.5100 theta=1.2589 thetad=2.4707 thetadd= 8.7763

theta3d= 21.6511 rho= 96.658 nu= 0.549

FC1= 7926.7 FC2= 3217.22 FY= 561.20 FN= 7421.59 mu= 0.823

FX= 6939.35 PHI=-0.1343 BETA=2.0171 x=60.74335 y=66.82911

FCH= 83.6 OMEGA=0.3766 FCH1= 79.3 FCH2= 32.2 fnet2= 589.66

r= 54.28 wa=0.1842 vn=28.96 an= 58.48 dnu=0.0077 dmu=0.0134

sigma=-0.0969 gamma=1.6949 chi=0.4735 fych= -8.09 fxch= 83.25

t=1.5200 theta=1.2835 thetad=2.5618 thetadd= 8.9968

theta3d= 21.9446 rho= 97.137 nu= 0.557

FC1= 7932.3 FC2= 3458.74 FY= 361.72 FN= 7606.75 mu= 0.837

FX= 6952.18 PHI=-0.0979 BETA=1.9560 x=61.38188 y=66.43851

FCH= 84.6 OMEGA=0.4293 FCH1= 79.3 FCH2= 34.6 fnet2= 377.18

r= 53.93 wa=0.1854 vn=29.56 an= 59.75 dnu=0.0077 dmu=0.0135

sigma=-0.0687 gamma=1.7195 chi=0.4981 fych= -5.81 fxch= 84.45

t=1.5300 theta=1.3090 thetad=2.6548 thetadd= 9.1892

theta3d= 22.1616 rho= 97.922 nu= 0.564

FC1= 7915.1 FC2= 3714.43 FY= 144.11 FN= 7785.38 mu= 0.850

FX= 6953.83 PHI=-0.0592 BETA=1.8918 x=62.01875 y=66.04214

FCH= 85.7 OMEGA=0.4835 FCH1= 79.2 FCH2= 37.1 fnet2= 149.20

r= 53.57 wa=0.1867 vn=30.17 an= 61.24 dnu=0.0077 dmu=0.0136

sigma=-0.0402 gamma=1.7450 chi=0.5236 fych= -3.44 fxch= 85.59

t=1.5400 theta=1.3355 thetad=2.7499 thetadd= 9.3979

theta3d= 22.3290 rho= 98.606 nu= 0.572

FC1= 7908.4 FC2= 3985.29 FY= -92.97 FN= 7992.04 mu= 0.864

FX= 6979.34 PHI=-0.0178 BETA=1.8239 x=62.65401 y=65.64000

FCH= 87.0 OMEGA=0.5390 FCH1= 79.1 FCH2= 39.8 fnet2= -95.61

r= 53.23 wa=0.1879 vn=30.80 an= 62.67 dnu=0.0076 dmu=0.0137

sigma=-0.0111 gamma=1.7715 chi=0.5501 fych= -0.97 fxch= 87.03

t=1.5500 theta=1.3630 thetad=2.7499 nu= 0.572

x=63.32021 y=65.21112

FCH= 43.7 OMEGA=-.5882 FCH1= 0.0 FCH2= 17.2

sigma=-1.1658 gamma=1.7990 chi=0.5776 fych=-40.20 fxch= 17.23

t=1.5600 theta=1.3905 thetad=2.7499 nu= 0.572

x=63.98642 y=64.78224

FCH= 44.2 OMEGA=-.5652 FCH1= 0.0 FCH2= 17.2

sigma=-1.1703 gamma=1.8265 chi=0.6051 fych=-40.68 fxch= 17.22

t=1.5700 theta=1.4180 thetad=2.7499 nu= 0.572

x=64.65262 y=64.35336

FCH= 44.6 OMEGA=-.5424 FCH1= 0.0 FCH2= 17.2

sigma=-1.1750 gamma=1.8540 chi=0.6326 fych=-41.15 fxch= 17.20

t=1.5800 theta=1.4455 thetad=2.7499 nu= 0.572

x=65.31882 y=63.92448

FCH= 45.0 OMEGA=-.5197 FCH1= 0.0 FCH2= 17.2

sigma=-1.1798 gamma=1.8815 chi=0.6601 fych=-41.62 fxch= 17.16

t=1.5900 theta=1.4730 thetad=2.7499 nu= 0.572

x=65.98503 y=63.49560

FCH= 45.4 OMEGA=-.4972 FCH1= 0.0 FCH2= 17.2

sigma=-1.1848 gamma=1.9090 chi=0.6876 fych=-42.09 fxch= 17.11

t=1.6000 theta=1.5005 thetad=2.7499 nu= 0.572

x=66.65124 y=63.06672

FCH= 45.8 OMEGA=-.4748 FCH1= 0.0 FCH2= 17.2

sigma=-1.1899 gamma=1.9365 chi=0.7151 fych=-42.56 fxch= 17.04

t=1.6100 theta=1.5280 thetad=2.7499 nu= 0.572

x=67.31744 y=62.63783

FCH= 46.3 OMEGA=-.4526 FCH1= 0.0 FCH2= 17.2

sigma=-1.1952 gamma=1.9640 chi=0.7426 fych=-43.03 fxch= 16.97

t=1.6200 theta=1.5555 thetad=2.7499 nu= 0.572

x=67.98365 y=62.20895

FCH= 46.7 OMEGA=-.4306 FCH1= 0.0 FCH2= 17.2

sigma=-1.2007 gamma=1.9915 chi=0.7701 fych=-43.50 fxch= 16.88

t=1.6300 theta=1.5830 thetad=2.7499 nu= 0.572

x=68.64986 y=61.78007

FCH= 47.0 OMEGA=-.4087 FCH1= 0.0 FCH2= 17.2

sigma=-1.2063 gamma=2.0190 chi=0.7976 fych=-43.96 fxch= 16.77

t=1.6400 theta=1.6105 thetad=2.7499 nu= 0.572

x=69.31606 y=61.35118

FCH= 47.4 OMEGA=-.3869 FCH1= 0.0 FCH2= 17.2

sigma=-1.2120 gamma=2.0465 chi=0.8251 fych=-44.42 fxch= 16.66

t=1.6500 theta=1.6380 thetad=2.7499 nu= 0.572

x=69.98227 y=60.92230

FCH= 47.8 OMEGA=-.3652 FCH1= 0.0 FCH2= 17.2

sigma=-1.2179 gamma=2.0740 chi=0.8526 fych=-44.87 fxch= 16.53

t=1.6600 theta=1.6655 thetad=2.7499 nu= 0.572

x=70.64848 y=60.49342

FCH= 48.2 OMEGA=-.3437 FCH1= 0.0 FCH2= 17.2

sigma=-1.2238 gamma=2.1015 chi=0.8801 fych=-45.33 fxch= 16.39

t=1.6700 theta=1.6930 thetad=2.7499 nu= 0.572

x=71.31468 y=60.06454

FCH= 48.6 OMEGA=-.3223 FCH1= 0.0 FCH2= 17.2

sigma=-1.2299 gamma=2.1290 chi=0.9076 fych=-45.78 fxch= 16.24

t=1.6800 theta=1.7205 thetad=2.7499 nu= 0.572

x=71.98089 y=59.63565

FCH= 48.9 OMEGA=-.3010 FCH1= 0.0 FCH2= 17.2

sigma=-1.2361 gamma=2.1565 chi=0.9351 fych=-46.22 fxch= 16.07

t=1.6900 theta=1.7480 thetad=2.7499 nu= 0.572

x=72.64709 y=59.20677

FCH= 49.3 OMEGA=-.2799 FCH1= 0.0 FCH2= 17.2

sigma=-1.2425 gamma=2.1840 chi=0.9626 fych=-46.66 fxch= 15.90

t=1.7000 theta=1.7755 thetad=2.7499 nu= 0.572

x=73.31330 y=58.77789

FCH= 49.6 OMEGA=-.2588 FCH1= 0.0 FCH2= 17.2

sigma=-1.2489 gamma=2.2115 chi=0.9901 fych=-47.09 fxch= 15.71

t=1.7100 theta=1.8030 thetad=2.7499 nu= 0.572

x=73.97951 y=58.34901

FCH= 50.0 OMEGA=-.2378 FCH1= 0.0 FCH2= 17.2

sigma=-1.2554 gamma=2.2390 chi=1.0176 fych=-47.52 fxch= 15.50

t=1.7200 theta=1.8305 thetad=2.7499 nu= 0.572

x=74.64571 y=57.92012

FCH= 50.3 OMEGA=-.2170 FCH1= 0.0 FCH2= 17.2

sigma=-1.2621 gamma=2.2665 chi=1.0451 fych=-47.95 fxch= 15.29

t=1.7300 theta=1.8580 thetad=2.7499 nu= 0.572

x=75.31192 y=57.49124

FCH= 50.7 OMEGA=-.1962 FCH1= 0.0 FCH2= 17.2

sigma=-1.2688 gamma=2.2940 chi=1.0726 fych=-48.36 fxch= 15.07

t=1.7400 theta=1.8855 thetad=2.7499 nu= 0.572

x=75.97813 y=57.06236

FCH= 51.0 OMEGA=-.1755 FCH1= 0.0 FCH2= 17.2

sigma=-1.2756 gamma=2.3215 chi=1.1001 fych=-48.78 fxch= 14.83

t=1.7500 theta=1.9130 thetad=2.7499 nu= 0.572

x=76.64433 y=56.63348

FCH= 51.3 OMEGA=-.1549 FCH1= 0.0 FCH2= 17.2

sigma=-1.2825 gamma=2.3490 chi=1.1276 fych=-49.18 fxch= 14.59

t=1.7600 theta=1.9405 thetad=2.7499 nu= 0.572

x=77.31054 y=56.20459

FCH= 51.6 OMEGA=-.1344 FCH1= 0.0 FCH2= 17.2

sigma=-1.2895 gamma=2.3765 chi=1.1551 fych=-49.58 fxch= 14.33

t=1.7700 theta=1.9680 thetad=2.7499 nu= 0.572

x=77.97675 y=55.77571

FCH= 51.9 OMEGA=-.1139 FCH1= 0.0 FCH2= 17.2

sigma=-1.2965 gamma=2.4040 chi=1.1826 fych=-49.97 fxch= 14.06

t=1.7800 theta=1.9955 thetad=2.7499 nu= 0.572

x=78.64295 y=55.34683

FCH= 52.2 OMEGA=-.0936 FCH1= 0.0 FCH2= 17.2

sigma=-1.3037 gamma=2.4315 chi=1.2101 fych=-50.35 fxch= 13.78

t=1.7900 theta=2.0230 thetad=2.7499 nu= 0.572

x=79.30916 y=54.91795

FCH= 52.5 OMEGA=-.0733 FCH1= 0.0 FCH2= 17.2

sigma=-1.3109 gamma=2.4590 chi=1.2376 fych=-50.73 fxch= 13.49

t=1.8000 theta=2.0505 thetad=2.7499 nu= 0.572

x=79.97536 y=54.48906

FCH= 52.8 OMEGA=-.0531 FCH1= 0.0 FCH2= 17.2

sigma=-1.3182 gamma=2.4865 chi=1.2651 fych=-51.09 fxch= 13.19

t=1.8100 theta=2.0780 thetad=2.7499 nu= 0.572

x=80.64157 y=54.06018

FCH= 53.0 OMEGA=-.0329 FCH1= 0.0 FCH2= 17.2

sigma=-1.3255 gamma=2.5140 chi=1.2926 fych=-51.45 fxch= 12.88

t=1.8200 theta=2.1055 thetad=2.7499 nu= 0.572

x=81.30778 y=53.63130

FCH= 53.3 OMEGA=-.0128 FCH1= 0.0 FCH2= 17.2

sigma=-1.3329 gamma=2.5415 chi=1.3201 fych=-51.80 fxch= 12.56

t=1.8300 theta=2.1330 thetad=2.7499 nu= 0.572

x=81.97398 y=53.20242

FCH= 53.6 OMEGA=0.0072 FCH1= 0.0 FCH2= 17.2

sigma=-1.3404 gamma=2.5690 chi=1.3476 fych=-52.14 fxch= 12.23

t=1.8400 theta=2.1605 thetad=2.7499 nu= 0.572

x=82.64019 y=52.77353

FCH= 53.8 OMEGA=0.0272 FCH1= 0.0 FCH2= 17.2

sigma=-1.3479 gamma=2.5965 chi=1.3751 fych=-52.47 fxch= 11.89

t=1.8500 theta=2.1880 thetad=2.7499 nu= 0.572

x=83.30640 y=52.34465

FCH= 54.0 OMEGA=0.0471 FCH1= 0.0 FCH2= 17.2

sigma=-1.3555 gamma=2.6240 chi=1.4026 fych=-52.80 fxch= 11.54

t=1.8600 theta=2.2155 thetad=2.7499 nu= 0.572

x=83.97260 y=51.91577

FCH= 54.3 OMEGA=0.0669 FCH1= 0.0 FCH2= 17.2

sigma=-1.3632 gamma=2.6515 chi=1.4301 fych=-53.11 fxch= 11.19

t=1.8700 theta=2.2430 thetad=2.7499 nu= 0.572

x=84.63881 y=51.48689

FCH= 54.5 OMEGA=0.0867 FCH1= 0.0 FCH2= 17.2

sigma=-1.3708 gamma=2.6790 chi=1.4576 fych=-53.41 fxch= 10.82

t=1.8800 theta=2.2705 thetad=2.7499 nu= 0.572

x=85.30502 y=51.05800

FCH= 54.7 OMEGA=0.1065 FCH1= 0.0 FCH2= 17.2

sigma=-1.3786 gamma=2.7065 chi=1.4851 fych=-53.70 fxch= 10.45

t=1.8900 theta=2.2980 thetad=2.7499 nu= 0.572

x=85.97122 y=50.62912

FCH= 54.9 OMEGA=0.1262 FCH1= 0.0 FCH2= 17.2

sigma=-1.3864 gamma=2.7340 chi=1.5126 fych=-53.99 fxch= 10.07

t=1.9000 theta=2.3255 thetad=2.7499 nu= 0.572

x=86.63743 y=50.20024

FCH= 55.1 OMEGA=0.1459 FCH1= 0.0 FCH2= 17.2

sigma=-1.3942 gamma=2.7615 chi=1.5401 fych=-54.26 fxch= 9.68

t=1.9100 theta=2.3530 thetad=2.7499 nu= 0.572

x=87.30363 y=49.77135

FCH= 55.3 OMEGA=0.1655 FCH1= 0.0 FCH2= 17.2

sigma=-1.4021 gamma=2.7890 chi=1.5676 fych=-54.52 fxch= 9.29

t=1.9200 theta=2.3805 thetad=2.7499 nu= 0.572

x=87.96984 y=49.34247

FCH= 55.5 OMEGA=0.1851 FCH1= 0.0 FCH2= 17.2

sigma=-1.4100 gamma=2.8165 chi=1.5951 fych=-54.77 fxch= 8.88

APPENDIX 5

t x y fch omega theta thetad

0.6300 0.730 82.000 56.666 -.7837 0.7854 0.0001

0.6400 1.460 81.997 57.004 -.7778 0.7854 0.0008

0.6500 2.190 81.990 57.242 -.7737 0.7854 0.0017

0.6600 2.920 81.980 57.584 -.7679 0.7855 0.0031

0.6700 3.650 81.967 57.824 -.7638 0.7855 0.0049

0.6800 4.380 81.951 58.170 -.7580 0.7856 0.0072

0.6900 5.110 81.931 58.414 -.7540 0.7857 0.0098

0.7000 5.839 81.908 58.764 -.7483 0.7858 0.0129

0.7100 6.569 81.881 59.011 -.7442 0.7860 0.0163

0.7200 7.299 81.851 59.366 -.7385 0.7862 0.0203

0.7300 8.028 81.817 59.616 -.7344 0.7864 0.0246

0.7400 8.757 81.779 59.975 -.7287 0.7867 0.0294

0.7500 9.487 81.738 60.229 -.7245 0.7871 0.0346

0.7600 10.216 81.694 60.592 -.7188 0.7875 0.0403

0.7700 10.945 81.646 60.849 -.7146 0.7879 0.0464

0.7800 11.673 81.594 61.216 -.7087 0.7885 0.0530

0.7900 12.402 81.538 61.477 -.7044 0.7891 0.0601

0.8000 13.130 81.479 61.849 -.6985 0.7897 0.0677

0.8100 13.859 81.415 62.113 -.6940 0.7905 0.0757

0.8200 14.587 81.348 62.488 -.6880 0.7913 0.0843

0.8300 15.314 81.277 62.756 -.6833 0.7923 0.0933

0.8400 16.042 81.203 63.135 -.6772 0.7933 0.1029

0.8500 16.769 81.124 63.406 -.6723 0.7944 0.1130

0.8600 17.496 81.041 63.788 -.6660 0.7957 0.1237

0.8700 18.223 80.955 64.062 -.6609 0.7970 0.1349

0.8800 18.949 80.864 64.448 -.6544 0.7985 0.1467

0.8900 19.675 80.769 64.724 -.6491 0.8001 0.1591

0.9000 20.401 80.670 65.112 -.6423 0.8018 0.1721

0.9100 21.126 80.567 65.390 -.6367 0.8036 0.1857

0.9200 21.851 80.460 65.780 -.6296 0.8056 0.2000

0.9300 22.576 80.348 66.060 -.6236 0.8078 0.2149

0.9400 23.300 80.233 66.451 -.6162 0.8101 0.2305

0.9500 24.024 80.113 66.732 -.6099 0.8126 0.2468

0.9600 24.747 79.989 67.122 -.6022 0.8152 0.2639

0.9700 25.470 79.860 67.403 -.5954 0.8180 0.2816

0.9800 26.193 79.727 67.793 -.5872 0.8210 0.3001

0.9900 26.914 79.590 68.073 -.5800 0.8242 0.3194

1.0000 27.636 79.448 68.461 -.5714 0.8276 0.3396

1.0100 28.357 79.301 68.738 -.5636 0.8312 0.3605

1.0200 29.077 79.150 69.122 -.5545 0.8350 0.3823

1.0300 29.797 78.995 69.396 -.5461 0.8391 0.4050

1.0400 30.516 78.835 69.774 -.5364 0.8434 0.4287

1.0500 31.235 78.670 70.042 -.5274 0.8479 0.4532

1.0600 31.952 78.500 70.413 -.5170 0.8527 0.4788

1.0700 32.670 78.326 70.674 -.5072 0.8578 0.5054

1.0800 33.386 78.147 71.035 -.4961 0.8631 0.5330

1.0900 34.102 77.964 71.286 -.4855 0.8687 0.5617

1.1000 34.817 77.775 71.635 -.4735 0.8746 0.5916

1.1100 35.532 77.581 71.874 -.4620 0.8808 0.6225

1.1200 36.245 77.383 72.208 -.4491 0.8874 0.6547

1.1300 36.958 77.180 72.431 -.4366 0.8943 0.6881

1.1400 37.670 76.971 72.748 -.4226 0.9015 0.7228

1.1500 38.381 76.758 72.954 -.4089 0.9091 0.7588

1.1600 39.092 76.539 73.250 -.3938 0.9170 0.7961

1.1700 39.801 76.315 73.437 -.3788 0.9254 0.8348

1.1800 40.510 76.087 73.709 -.3623 0.9341 0.8750

1.1900 41.217 75.853 73.873 -.3458 0.9433 0.9166

1.2000 41.924 75.613 74.119 -.3278 0.9529 0.9598

1.2100 42.629 75.369 74.259 -.3096 0.9630 1.0044

1.2200 43.334 75.119 74.478 -.2899 0.9735 1.0508

1.2300 44.037 74.864 74.593 -.2699 0.9844 1.0987

1.2400 44.740 74.603 74.784 -.2483 0.9959 1.1484

1.2500 45.441 74.337 74.874 -.2262 1.0079 1.1997

1.2600 46.141 74.065 75.039 -.2023 1.0205 1.2529

1.2700 46.840 73.788 75.108 -.1779 1.0335 1.3078

1.2800 47.538 73.506 75.252 -.1516 1.0472 1.3646

1.2900 48.235 73.218 75.307 -.1245 1.0614 1.4233

1.3000 48.930 72.924 75.438 -.0954 1.0763 1.4839

1.3100 49.624 72.624 75.490 -.0654 1.0917 1.5464

1.3200 50.317 72.319 75.624 -.0333 1.1078 1.6109

1.3300 51.009 72.008 75.690 0.0000 1.1246 1.6773

1.3400 51.699 71.692 75.848 0.0354 1.1421 1.7458

1.3500 52.388 71.369 75.956 0.0723 1.1602 1.8162

1.3600 53.076 71.041 76.169 0.1112 1.1791 1.8887

1.3700 53.762 70.707 76.355 0.1518 1.1987 1.9631

1.3800 54.447 70.367 76.663 0.1945 1.2191 2.0396

1.3900 55.131 70.022 76.974 0.2388 1.2403 2.1181

1.4000 55.813 69.670 77.430 0.2852 1.2623 2.1985

1.4100 56.494 69.313 77.925 0.3333 1.2851 2.2808

1.4200 57.174 68.949 78.593 0.3831 1.3088 2.3650

1.4300 57.853 68.580 79.337 0.4344 1.3333 2.4510

1.4400 58.530 68.204 80.288 0.4872 1.3587 2.5387

1.4500 59.206 67.823 81.355 0.5411 1.3849 2.6282

1.4600 59.880 67.436 82.661 0.5960 1.4121 2.7193

1.4700 60.554 67.042 84.125 0.6515 1.4402 2.8119

1.4800 61.225 66.644 45.751 -.4859 1.4684 2.8119

1.4900 61.895 66.245 46.188 -.4634 1.4965 2.8119

1.5000 62.566 65.847 46.619 -.4410 1.5246 2.8119

1.5100 63.237 65.449 47.045 -.4188 1.5527 2.8119

1.5200 63.907 65.050 47.464 -.3967 1.5808 2.8119

1.5300 64.578 64.652 47.876 -.3747 1.6090 2.8119

1.5400 65.248 64.253 48.282 -.3529 1.6371 2.8119

1.5500 65.919 63.855 48.682 -.3312 1.6652 2.8119

1.5600 66.590 63.457 49.074 -.3097 1.6933 2.8119

1.5700 67.260 63.058 49.460 -.2882 1.7214 2.8119

1.5800 67.931 62.660 49.838 -.2669 1.7496 2.8119

1.5900 68.602 62.261 50.209 -.2457 1.7777 2.8119

1.6000 69.272 61.863 50.573 -.2245 1.8058 2.8119

1.6100 69.943 61.465 50.929 -.2035 1.8339 2.8119

1.6200 70.613 61.066 51.278 -.1826 1.8620 2.8119

1.6300 71.284 60.668 51.619 -.1618 1.8902 2.8119

1.6400 71.955 60.270 51.952 -.1410 1.9183 2.8119

1.6500 72.625 59.871 52.277 -.1203 1.9464 2.8119

1.6600 73.296 59.473 52.594 -.0998 1.9745 2.8119

1.6700 73.967 59.074 52.903 -.0793 2.0026 2.8119

1.6800 74.637 58.676 53.203 -.0588 2.0307 2.8119

1.6900 75.308 58.278 53.496 -.0385 2.0589 2.8119

1.7000 75.979 57.879 53.779 -.0182 2.0870 2.8119

1.7100 76.649 57.481 54.054 0.0020 2.1151 2.8119

1.7200 77.320 57.082 54.321 0.0222 2.1432 2.8119

1.7300 77.990 56.684 54.578 0.0423 2.1713 2.8119

1.7400 78.661 56.286 54.827 0.0624 2.1995 2.8119

1.7500 79.332 55.887 55.067 0.0824 2.2276 2.8119

1.7600 80.002 55.489 55.298 0.1023 2.2557 2.8119

1.7700 80.673 55.090 55.520 0.1222 2.2838 2.8119

1.7800 81.344 54.692 55.733 0.1421 2.3119 2.8119

1.7900 82.014 54.294 55.937 0.1619 2.3401 2.8119

1.8000 82.685 53.895 56.132 0.1817 2.3682 2.8119

APPENDIX 6

t x y fch omega theta thetad

0.6300 0.730 82.000 56.666 3.9253 0.7854 0.0001

0.6400 1.460 81.997 57.004 3.9194 0.7854 0.0008

0.6500 2.190 81.990 57.242 3.9153 0.7854 0.0017

0.6600 2.920 81.980 57.584 3.9095 0.7855 0.0031

0.6700 3.650 81.967 57.824 3.9054 0.7855 0.0049

0.6800 4.380 81.951 58.170 3.8996 0.7856 0.0072

0.6900 5.110 81.931 58.414 3.8956 0.7857 0.0098

0.7000 5.839 81.908 58.764 3.8899 0.7858 0.0129

0.7100 6.569 81.881 59.011 3.8858 0.7860 0.0163

0.7200 7.299 81.851 59.365 3.8801 0.7862 0.0203

0.7300 8.028 81.817 59.615 3.8760 0.7864 0.0246

0.7400 8.757 81.779 59.973 3.8703 0.7867 0.0294

0.7500 9.487 81.738 60.227 3.8662 0.7871 0.0346

0.7600 10.216 81.694 60.589 3.8604 0.7875 0.0403

0.7700 10.945 81.646 60.846 3.8562 0.7879 0.0464

0.7800 11.673 81.594 61.212 3.8504 0.7885 0.0530

0.7900 12.402 81.538 61.471 3.8461 0.7891 0.0601

0.8000 13.130 81.479 61.841 3.8402 0.7897 0.0677

0.8100 13.859 81.415 62.103 3.8357 0.7905 0.0757

0.8200 14.587 81.348 62.476 3.8297 0.7913 0.0843

0.8300 15.314 81.277 62.741 3.8251 0.7923 0.0933

0.8400 16.042 81.203 63.117 3.8190 0.7933 0.1029

0.8500 16.769 81.124 63.384 3.8142 0.7944 0.1130

0.8600 17.496 81.041 63.761 3.8079 0.7957 0.1237

0.8700 18.223 80.955 64.030 3.8029 0.7970 0.1349

0.8800 18.949 80.864 64.409 3.7964 0.7985 0.1467

0.8900 19.675 80.769 64.679 3.7911 0.8001 0.1591

0.9000 20.401 80.670 65.059 3.7844 0.8018 0.1721

0.9100 21.126 80.567 65.328 3.7788 0.8036 0.1857

0.9200 21.851 80.460 65.708 3.7718 0.8056 0.2000

0.9300 22.576 80.348 65.976 3.7660 0.8078 0.2149

0.9400 23.300 80.233 66.354 3.7587 0.8101 0.2305

0.9500 24.024 80.113 66.620 3.7524 0.8126 0.2468

0.9600 24.747 79.989 66.995 3.7448 0.8152 0.2639

0.9700 25.470 79.860 67.257 3.7382 0.8180 0.2816

0.9800 26.193 79.727 67.627 3.7302 0.8210 0.3001

0.9900 26.914 79.590 67.884 3.7231 0.8242 0.3194

1.0000 27.636 79.448 68.246 3.7146 0.8276 0.3396

1.0100 28.357 79.301 68.495 3.7070 0.8312 0.3605

1.0200 29.077 79.150 68.847 3.6980 0.8350 0.3823

1.0300 29.797 78.995 69.086 3.6899 0.8391 0.4050

1.0400 30.516 78.835 69.425 3.6803 0.8434 0.4287

1.0500 31.235 78.670 69.651 3.6715 0.8479 0.4532

1.0600 31.952 78.500 69.974 3.6614 0.8527 0.4788

1.0700 32.670 78.326 70.183 3.6518 0.8578 0.5054

1.0800 33.386 78.147 70.486 3.6409 0.8631 0.5330

1.0900 34.102 77.964 70.674 3.6306 0.8687 0.5617

1.1000 34.817 77.775 70.953 3.6189 0.8746 0.5916

1.1100 35.532 77.581 71.115 3.6077 0.8808 0.6225

1.1200 36.245 77.383 71.365 3.5950 0.8874 0.6547

1.1300 36.958 77.180 71.496 3.5827 0.8943 0.6881

1.1400 37.670 76.971 71.711 3.5690 0.9015 0.7228

1.1500 38.381 76.758 71.807 3.5556 0.9091 0.7588

1.1600 39.092 76.539 71.981 3.5407 0.9170 0.7961

1.1700 39.801 76.315 72.035 3.5259 0.9254 0.8348

1.1800 40.510 76.087 72.162 3.5096 0.9341 0.8750

1.1900 41.217 75.853 72.168 3.4933 0.9433 0.9166

1.2000 41.924 75.613 72.241 3.4754 0.9529 0.9598

1.2100 42.629 75.369 72.194 3.4573 0.9630 1.0044

1.2200 43.334 75.119 72.209 3.4375 0.9735 1.0508

1.2300 44.037 74.864 72.103 3.4174 0.9844 1.0987

1.2400 44.740 74.603 72.054 3.3955 0.9959 1.1484

1.2500 45.441 74.337 71.886 3.3730 1.0079 1.1997

1.2600 46.141 74.065 71.771 3.3486 1.0205 1.2529

1.2700 46.840 73.788 71.539 3.3233 1.0335 1.3078

1.2800 47.538 73.506 71.359 3.2959 1.0472 1.3646

1.2900 48.235 73.218 71.068 3.2674 1.0614 1.4233

1.3000 48.930 72.924 70.829 3.2367 1.0763 1.4839

1.3100 49.624 72.624 70.488 3.2044 1.0917 1.5464

1.3200 50.317 72.319 70.205 3.1696 1.1078 1.6109

1.3300 51.009 72.008 69.834 3.1330 1.1246 1.6773

1.3400 51.699 71.692 69.533 3.0937 1.1421 1.7458

1.3500 52.388 71.369 69.165 3.0521 1.1602 1.8162

1.3600 53.076 71.041 68.888 3.0075 1.1791 1.8887

1.3700 53.762 70.707 68.574 2.9603 1.1987 1.9631

1.3800 54.447 70.367 68.380 2.9100 1.2191 2.0396

1.3900 55.131 70.022 68.194 2.8568 1.2403 2.1181

1.4000 55.813 69.670 68.166 2.8004 1.2623 2.1985

1.4100 56.494 69.313 68.202 2.7411 1.2851 2.2808

1.4200 57.174 68.949 68.449 2.6788 1.3088 2.3650

1.4300 57.853 68.580 68.824 2.6138 1.3333 2.4510

1.4400 58.530 68.204 69.470 2.5464 1.3587 2.5387

1.4500 59.206 67.823 70.314 2.4770 1.3849 2.6282

1.4600 59.880 67.436 71.489 2.4061 1.4121 2.7193

1.4700 60.554 67.042 72.929 2.3343 1.4402 2.8119

1.4800 61.225 66.644 32.036 3.8009 1.4684 2.8119

1.4900 61.895 66.245 32.294 3.7668 1.4965 2.8119

1.5000 62.566 65.847 32.558 3.7331 1.5246 2.8119

1.5100 63.237 65.449 32.829 3.6997 1.5527 2.8119

1.5200 63.907 65.050 33.104 3.6667 1.5808 2.8119

1.5300 64.578 64.652 33.386 3.6339 1.6090 2.8119

1.5400 65.248 64.253 33.672 3.6015 1.6371 2.8119

1.5500 65.919 63.855 33.962 3.5693 1.6652 2.8119

1.5600 66.590 63.457 34.257 3.5375 1.6933 2.8119

1.5700 67.260 63.058 34.556 3.5060 1.7214 2.8119

1.5800 67.931 62.660 34.858 3.4748 1.7496 2.8119

1.5900 68.602 62.261 35.163 3.4438 1.7777 2.8119

1.6000 69.272 61.863 35.471 3.4132 1.8058 2.8119

1.6100 69.943 61.465 35.782 3.3829 1.8339 2.8119

1.6200 70.613 61.066 36.095 3.3528 1.8620 2.8119

1.6300 71.284 60.668 36.410 3.3230 1.8902 2.8119

1.6400 71.955 60.270 36.726 3.2935 1.9183 2.8119

1.6500 72.625 59.871 37.044 3.2643 1.9464 2.8119

1.6600 73.296 59.473 37.363 3.2353 1.9745 2.8119

1.6700 73.967 59.074 37.683 3.2065 2.0026 2.8119

1.6800 74.637 58.676 38.004 3.1780 2.0307 2.8119

1.6900 75.308 58.278 38.324 3.1498 2.0589 2.8119

1.7000 75.979 57.879 38.645 3.1218 2.0870 2.8119

1.7100 76.649 57.481 38.965 3.0940 2.1151 2.8119

1.7200 77.320 57.082 39.285 3.0664 2.1432 2.8119

1.7300 77.990 56.684 39.605 3.0391 2.1713 2.8119

1.7400 78.661 56.286 39.923 3.0120 2.1995 2.8119

1.7500 79.332 55.887 40.240 2.9850 2.2276 2.8119

1.7600 80.002 55.489 40.556 2.9583 2.2557 2.8119

1.7700 80.673 55.090 40.870 2.9318 2.2838 2.8119

1.7800 81.344 54.692 41.182 2.9055 2.3119 2.8119

1.7900 82.014 54.294 41.492 2.8793 2.3401 2.8119

1.8000 82.685 53.895 41.800 2.8533 2.3682 2.8119