App-B Analysis Appendix.pdf

Appendix B to 20-0001 14 May 2020

A-1

MULTIVARIATE LANDING ANALYSIS

Initial Landing Conditions

The design envelope of initial landing conditions is based on the applicable parameters defined in this paragraph. The design envelope must be those determined by combinations of the variables specified in the form of a multivariate distribution. The distributions of each variable, independently, are defined by the normal or Gaussian distribution function for all variables.

The normal distribution function is defined by the mean and standard deviation.

The extreme values for each variable, independently, are those values corresponding to a probability of P0 of being greater than the maximum value or less than the minimum value.

Extreme conditions for each envelope are defined by those combinations of variables having a joint likelihood of occurrence equal to a constant, PT, as determined by the following equation:

Where:

a. The symbols > < denote greater than and less than, respectively.

b. Vai, Vei, Vvi, pi, ri, yi,, yi and di are the initial conditions for each variable.

c. P is the probability that the value of the variable under consideration is greater than and alternately, less than the given ith value of the variable.

d. The equation has the constraint that the symbol > is used with the ith values of the variable which are equal to or greater than the mean value and, alternately, the symbol < is used for the ith values of the variable which are less than the mean value.

e. The initial condition for each variable equals all values between the extreme minimum and extreme maximum.

f. Extreme values for each variable, independently, are those values corresponding to a probability of P0 of being greater than the maximum value and less than the minimum value. PT is the product of the probabilities P and is equal to a constant time P0.

Field Carrier Landing Practice on Prepared Runways

The total joint probability, PT, for field carrier landing practice or field landing without flare and the probability P0 is to be 7.8125 X 10-6 and 1.0 X 10-3, respectively. The variates and the associated values are defined in TABLE I.

TABLE I - Multivariate Parameters for Field Carrier Landing Practice on Prepared Runways

Shipboard Touch-and-Go

The total joint probability, PT, and the probability P0, for shipboard landings, is to be 7.8125

X 10-6 and 1 X 10-3, respectively. The variates and the associated values are defined in

TABLE II.

Symbol Variate Mean Value Standard Deviation σ Va Approach Speed (Kts) 1.05 Vpa 4.0 Ve Engaging Speed (Kts) Va-20 5.0 Vv Sink Speed (ft/s) 0.102 Ve 0.017 Ve +0.5 θp Air Vehicle Pitch Angle (deg.) Note a 2.25 Note b θr Air Vehicle Roll Angle (deg.) 2.0 2.5 θṙ Air Vehicle Roll Rate (deg./s) 0 3.0 θy Air Vehicle Yaw Angle (deg.) 0 3.0 d Off Center Engagement Distance

(ft)

0.0 6.0

Notes:

a. The multivariate mean pitch angle is specified as the on-speed carrier approach AoA corresponding to VPA minus with a glide slope angle of -3.5 deg., a lift to weight ratio of 1.0 and deck pitch angles of plus and minus deck pitch angle of 1.5 deg. at sea level on a tropical day.

b. Minimum pitch angle need not be less than that which produces a three point landing.

TABLE II - Multivariate Parameters for Shipboard Touch-and-Go Landings

Symbol Variate Mean Value Standard Deviation σ Va Approach Speed (kts) 1.05 Vpa 5.0 Ve Engaging Speed (kts) Va 8.0 Vv Sink Speed (ft/s) 9.00 (Note a) 2.20 θp Air Vehicle Pitch Angle (deg.) Note b 2.25 θr Air Vehicle Roll Angle (deg.) 2.0 2.5 θṙ Air Vehicle Roll Rate (deg./s) 0 3.0 θy Air Vehicle Yaw Angle (deg.) 0 3.0 d Off Center Distance (ft) 0.0 6.0

Notes:

a. Based on T-45 Fleet data. If candidate aircraft approach speed exceeds T-45, then respondent should assume a proportional increase in mean rate of descent (114≥Va≥133, avg 124 kts). No reduction should be assumed for approach speeds below that of T-45.

b. The multivariate mean pitch angle is specified as the on-speed FCLP approach angle of attack corresponding to VPA minus with a glide slope angle of -3.25 degrees, a lift to weight ratio of 1.0 at sea level on a tropical day.

c. FCLP design conditions do not include arrestments. Ve is utilized to calculate initial conditions for landings without arrestments. Ve for land based arrestment need not exceed 155 Knots Calibrated Air Speed (KCAS)

d. Minimum pitch angle need not be less than that which produces a three point landing.