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Operation 31
a) Horizontal velocity Vh or vertical rate of climb Vz (times an input factor).
b) Aircraft altitude.
c) Aircraft angular rate, ˙ θ (pull-up) or ˙ ψ (turn).
d) Aircraft linear acceleration (airframe, inertial, or ground axes).
If the variable is velocity, first the velocity is found for the specified maximum effort; then the performance
is evaluated at that velocity times an input factor. For endurance, range, or climb, the slope of the quantity
to be maximized must be zero; hence in all cases the target is zero. The slope of the quantity is evaluated
by first-order backward difference. For the range, first the variable is found such that V/ ˙w is maximized
(slope zero); then the variable is found such that V/ ˙w equals 99% of that maximum. Two maximum
effort quantity/variable pairs can be specified, and solved in nested iterations. The secant method or
the method of false position is used to solve for the maximum effort. The task of finding maximum
endurance, range, or climb is usually solved using the golden-section method. A tolerance ɛ and a
perturbation Δ are specified.
Given the gross weight and useful load (from the flight condition or mission specification), the
performance is calculated for this flight state. The calculated state information includes weight, speed
and velocity orientation (climb and sideslip), aircraft Euler angles, rotor tip speeds, and aircraft controls.
The aircraft weight statement defines the fixed useful load and operating weight for the design
configuration. For each flight state, the fixed useful load may be different from the design configuration,
because of changes in auxiliary-fuel-tank weight or kit weights or increments in crew or furnishings
weights. Thus the fixed useful-load weight is calculated for the flight state; and from it the useful-load
weight and operating weight. The gross weight, payload weight, and usable-fuel weight (in standard
and auxiliary tanks) completes the weight information for the flight state.
4–5 Environment and Atmosphere
The aerodynamic environment is defined by the speed of sound cs, density ρ, and kinematic viscosity
ν = μ/ρ of the air (or other fluid). These quantities can be obtained from the standard day (International
Standard Atmosphere), or input directly. The following options are implemented:
a) Input the altitude hgeom and a temperature increment ΔT . Calculate the temperature
and pressure for the standard day, add ΔT , and then calculate the density from
the equation of state for a perfect gas. Calculate the speed of sound and viscosity
from the temperature.
b) Input the pressure altitude hgeom and the temperature τ ( ◦ For ◦ C). Calculate the
pressure for the standard day, and then the density from the equation of state for a
perfect gas. Calculate the speed of sound and viscosity from the temperature.
c) Input the density ρ and the temperature τ ( ◦ For ◦ C). Calculate the speed of sound
and viscosity from the temperature.
d) Input the density ρ, sound speed cs, and viscosity μ. Calculate the temperature
from the sound speed.
Here hgeom is the geometric altitude above mean sea level.
The International Standard Atmosphere (ISA) is a model for the variation with altitude of pressure,