General equations
Center of mass motion in wind axes is described by the following equations used at flight characteristics calculation (disregarding sliding)
where
H - is flight altitude;
V - is aircraft speed;
dV/dt - is acceleration;
θ - is flight path angle;
ψ - is heading;
P - is engine thrust;
Qsec - is second fuel consumption;
G - is aircraft weight;
φ - is angle between thrust vector and axe x;
γ - is angle of roll;
q - is dynamic pressure;
Cx - is drag coefficient;
Cy - normal force coefficient.
Sliding is described by the following equation:
When moving on the ground friction force is added: Ffriction = kfr * G * (1 - Ny).
When calculating Mach number and dynamic pressure the table of standard atmosphere is used.
At present in FM the following dependences are accepted for aerodynamics and engine characteristics:
Cy = Cyalfa(M) * α + Cyflaps * k(q) + nonlinear correction(α); Cy ≤ Cymax(M);
Cz = Czbeta(M)* β ;
Cx = Cx0(M) + Cxflaps + Cxpld(M) + Bpol(M) * Cy ** 2 + Dpol(M) * Cy ** 4 - Czbeta * β ** 2;
P(M,H,Dr) = F1(M)*F2(H)*F3(Dr);
Qsec = Ce * P / 3600
where:
M - is Mach number;
α - is angle of attack;
β - is slide angle;
Dr - is engine operating mode.
Dependences Cyalfa(M), Cymax(M), Czbeta(M), Cx0(M), Cxpld(M), Bpol(M), Dpol(M), F1(M), F2(H), F3(Dr) are set by the tables with linear interpolation.
To get real aerodynamics characteristics of aircraft and engine flight characteristics is rather difficult due to secrecy of such information. When there is not enough information on aerodynamics characteristics and engine flight characteristics we have to correct various table dependences to agree then with known flight characteristics (accelerations, turns, climb, flight range, etc).
