Examples for using the four point kite model

Create a test project

mkdir test
cd test
julia --project=.

Don't forget to type the dot at the end of the last line. With the last command, we told Julia to create a new project in the current directory.

You can copy the examples to your project with:

using KiteModels
KiteModels.install_examples()

Plotting the initial state

First, an instance of the model of the kite control unit (KCU) is created which is needed by the Kite Power System model KPS3. Then we create a kps instance, passing the kcu model as parameter. We need to declare these variables as const to achieve a decent performance.

using KiteModels
kcu::KCU = KCU(se())
kps = KPS4(kcu)

Then we call the function find_steady_state which uses a non-linear solver to find the solution for a given elevation angle, reel-out speed and wind speed.

find_steady_state!(kps, prn=true)

Finding the steady state of the 4-point model is difficult and it only works when we artificially reduce the stiffness by a factor of 0.035. In the function init_sim! this factor is slowly increased to 1.0.

To plot the result in 2D we extract the vectors of the x and z coordinates of the tether particles with a for loop:

x = Float64[] 
z = Float64[]
for i in 1:length(kps.pos)
     push!(x, kps.pos[i][1])
     push!(z, kps.pos[i][3])
end

And finally, we plot the position of the particles in the x-z plane. When you type using ControlPlots you will be asked if you want to install the ControlPlots package. Just press \<ENTER\> and it gets installed.

using ControlPlots
plot(x,z, xlabel="x [m]", ylabel="z [m]", scatter=true)

Initial State

Print other model outputs

Print the vector of the positions of the particles:

julia> kps.pos
11-element StaticArrays.SVector{11, StaticArrays.MVector{3, Float64}} with indices SOneTo(11):
 [0.0, 0.0, 0.0]
 [9.179237622840555, 0.0, 23.842235605018427]
 [18.04995989861643, 0.0, 47.800963572571995]
 [26.562156210544767, 0.0, 71.88939923189402]
 [34.68610302268368, 0.0, 96.11152960655927]
 [42.39897331360162, 0.0, 120.4676716318371]
 [49.681585065247006, 0.0, 144.95590371155842]
 [50.19560621291923, 0.0, 150.01396766608025]
 [51.447158096922415, 0.0, 152.22064860101747]
 [51.269841233250816, 2.823293379900761, 149.7849943282592]
 [51.269841233250816, -2.823293379900761, 149.7849943282592]

Print the unstretched and stretched tether length and the height of the kite:

julia> unstretched_length(kps)
150.0

julia> tether_length(kps)
152.24467154884996

julia> calc_height(kps)
152.18828499538841

Because of the the stiffness_factor of 0.035 we have a longer tether-length then when using the 1 point kite model.

Print the force at the winch (groundstation, in Newton) and at each tether segment:

julia> winch_force(kps)
321.91887139903304

julia> spring_forces(kps)
15-element Vector{Float64}:
 321.90741146969305
 321.90394881639793
 321.90117644298266
 321.8991487686265
 321.89747937647513
 321.8960226182887
  48.63781489453856
 -44.13400039648584
 -38.834017666472626
 128.20126839800218
 149.28336751268995
 149.28336751268995
 128.20126839800218
 -44.13400039648584
  51.39155976906608

Some of the forces are negative which means the segments are getting compressed. This is acceptable for the kite itself (not for the tether).

Print the lift and drag forces of the kite (in Newton) and the lift-over-drag ratio:

julia> lift, drag = lift_drag(kps)
(402.1444777567862, 117.73620926656395)

julia> lift_over_drag(kps)
3.4156397616497047

Print the wind speed vector at the kite:

julia> v_wind_kite(kps)
3-element StaticArrays.MVector{3, Float64} with indices SOneTo(3):
 12.603056847417106
  0.0
  0.0

Example of reeling out the tether

include("examples/reel_out_4p.jl")

In this example, we first keep the tether length constant and at 15 s start to reel out the winch with an acceleration of 0.1 m/s². At a set speed below 2.2 m/s the brake of the winch is active, therefore the "jump" in the v_reelout at the beginning of the reel-out phase.

It is not a real jump, but a high acceleration compared to the acceleration afterward.