Overimposed movement with friction

[Akrobit]

Homework Statement

I need to describe a glider movement during tow. The tow is based on a single axis displacement (x) with constant speed Ps=5 m/s. The cable length is constant=50 m.. The glider area A, lift and drag coefficients (Cl and Cd) are known as a function of tangential speed (Vt).
The frictional coefficients of the tow line (Cdline) can be known as a function of local velocity. The diameter of the line is known=Ldiam. Y axis is vertical and the problem can be considered to develop only on the X-Y plane. The starting line angle (alpha) respect to x-axis of the movement can be about 20º. The nonconservative force (Px) pulling the tow line along the x-axis is the only external input energy.
Vt= tangential speed of glider
d=density of air
Ar=aspect ratio of glider wing
Cd0=coefficient rapresentative of other glider drag components proportional to square tangential velocity
Vlocal is the cvelocity of a certaion point of the tow line
The goal is to obtain an expresion for Vt and(or) alpha as a function of the other parameters

Homework Equations

Lift of the glider L=Cl(Vt)*d/2*Vt^2*A
Drag of the glider D=(Cd(Vt)+Cl(Vt)^2/pi/Ar+Cd0)*d/2*Vt^2*A
Drag coefficient for the line Cdline:3/log10(Reline)
Reline=65535*Ldiam*Vlocal

The Attempt at a Solution

 

[jbsteele]

I have tried to obtain the expressions for Vt and alpha, but it is not easy because of all the parameters involved. I have been able to find some equations that describe the motion of the glider in terms of the lift and drag forces, but I am not sure if they are correct. I think I need to use Newton's second law of motion to solve this problem, but I am not sure how to go about it.

 

[nlightner]

To describe the glider movement during tow, we must consider the forces acting on the glider and the tow line. The glider experiences a lift force and a drag force due to its motion through the air. The lift force is dependent on the glider's area, lift coefficient, and tangential speed, while the drag force is dependent on the glider's area, lift and drag coefficients, and the square of the tangential speed. In addition, there may be other drag components present, represented by the coefficient Cd0, which also contribute to the overall drag force experienced by the glider.

The tow line also experiences a drag force, which is dependent on its diameter, density of air, and local velocity. This drag force can be calculated using the drag coefficient for the line, which is a function of the Reynolds number of the tow line. The Reynolds number, in turn, is dependent on the tow line's diameter, density of air, and local velocity.

The goal of this problem is to obtain an expression for the tangential speed (Vt) and/or the starting line angle (alpha) as a function of the other parameters. To do this, we can use the equations for lift and drag, along with the known values for the glider's area, lift and drag coefficients, and the tow line's diameter and density of air. We can also use the equation for the drag coefficient of the line, substituting in the known values for the tow line's diameter and density of air, and solving for the local velocity.

Once we have an expression for the local velocity, we can substitute it into the equations for lift and drag to obtain expressions for the lift and drag forces on the glider. Finally, we can use these expressions, along with the known value for the external input energy (Px), to solve for the tangential speed and starting line angle. This will give us a complete understanding of the glider's movement during tow, taking into account the effects of friction on the tow line.