What is the air velocity here?

I'm trying to find the lift force to what I have here in the system that shown below in the attached picture. I found some parameters to solve the equation of the left, but I couldn't find the air velocity. How could I find this velocity?. Could anyone help me with this matter, please?.

%The given aircraft characteristics are defined below

m= 4.6;                % Aircraft Mass [kg]

S= 0.85;               % Wing surface  [m^2]

k= 0.0095;             % Induced drag parameter

Cd0=0.118;             % Zero-lift drag coefficient

alpha=2.75;            % Angle of attack[deg]

p0=945.15;             % Air pressure[hPa]

rho=1.225;             %Air density of (ISA)standard[kg/m^3]

alpha0 = -4;           % zero lift angle of attack (Found from given graph)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%Q1:How much is the lift force?

%The lift force can be found by the below equation:

L=(1/2)*rho*(v^2)*S*CL

The system

[darova]

I think lift force and mass of an aircraft has to be equal: m == L

[HAITHAM AL SATAI]

@ darova Could you explain it to me? How they could be equal sir?

[Walter Roberson]

The gravitational force downward F = m * a, and a = g (possibly reduced due to altitude). That has to balance the lifting force or else the plane will either ascend or descend.

However, this is a force, and a force is not a mass, and a force is not a velocity. Do your units analysis!

[HAITHAM AL SATAI]

@ Walter Roberson I didn't get the idea Sir. So, what should I do?

[Walter Roberson]

darova thought that the lift force and mass has to be equal, but a force is mass times acceleration whereas the mass of the plane is just a mass, so the units between the two are not the same. Therefore lift force and mass cannot be equal. However, lift force and downward force must be equal.

[HAITHAM AL SATAI]

@ Walter Roberson I got your idea sir

[darova]

But an aircraft don't fall down. Why there is acceleration?

[Walter Roberson]

Gravity causes downward acceleration, which is countered by the upwards acceleration of the lift.

Answer 1

[PIYUSH AGGARWAL]

As per your diagram , the aircraft experiences T (I guess its forward propelling/throtelling force)and D (backward drag force) in the horizontal direction (x). You need the velocity to apply this equation :-

L=(1/2)*rho*(v^2)*S*CL

A possible solution maybe :-

(T-D)/m = A = Gives you the acceleration of aircraft in positive x direction.

If T and D are not time varying forces then velocity calculation will be pretty straight forward :-

v = u + A*t

where t is time lapsed from the initial point till now and u the velocity at initial time

If these forces are not constant you have to go for integration:-

[HAITHAM AL SATAI]

@ PIYUSH AGGARWAL Thank you so much sir for your answer, but after your persmission how could I get the values of D, T , u, t?

[PIYUSH AGGARWAL]

@HAITHAM AL SATAI :) Anytime. Look I don't know much about areodynamics but the solution which I told you was based on pretty basic mechanics only. There must be some formulae for calculating Drag Force D and Throttle T, as for the initial velocity u and time t, you are the observer of the frame of reference so you must be knowing the time interval length and initial states of the system such as velocity (u) before hand.

Drag Force D:- refer this link

I can see that Drag also depends on velocity, So you have a differential equation of the type where force is proportional to velocity squared.

Or I can say the derivative of velocity wrt time depens on Velocity squared. So you will have to rearrange terms, Bring similar terms together on one side and then integrate both the sides. Pretty much how you solve the basic diff eqns.

Well in ideal case if the aircraft needs to move with constant speed/velocity , T = D.

[HAITHAM AL SATAI]

@ PIYUSH AGGARWAL Thank you so much sir for your help. ?