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Drag Machine:
Optimal Load and Optimal Operating Speed

We shall now be looking into the experimental results for the drag based machine on the previous page.
You may wonder why we go into such detail with this odd machine. The reason will be obvious, when we get to the next pages, however. Many of these results apply very generally to various kinds of wind driven machines, no matter how different they may seem at a first glance. The graphs below were plotted directly with the drag calculator programme.

Propulsion Speed (Ground Speed) for Constant Load
Propulsion speed vs. wind speedFirstly, we ran the drag machine with a constant load (force) of 2 N (Newton). We then adjusted the tail wind velocity, vT from 0 to 25 m/s.
The graph shows that the propulsion speed, vP (the ground speed) of the vehicle varies almost in proportion to the wind speed, when the machine runs with a constant load (force). As we can see, the machine will not start at very low wind speeds (below 1.53 m/s in the case of a parachute-shaped sail). Once it starts, however, the car will run with a ground speed, which increases by 1 m/s every time we increase the wind speed by 1 m/s.

Power Output for Constant Load
Power versus wind speed
The power output, P for different wind speeds, vT can be plotted from the same set of experiments:
The result is very simple. Since the machine increases its speed in proportion to the wind speed, the work it does per second obviously increases in the same proportion. Doubling the wind speed double the power output, if we keep the load (force) constant. That is not the ideal way to run the machine, however, if we wish to maximise power output.

The Ideal Operating Speed
and Maximum Efficiency
Power coefficient and operating speed ratio
Next, we tried a constant wind speed and varied the load on the machine. Clearly, if the load is zero, the machine produces no power, since it does no work. Likewise, if the load is too large, the machine will not be able to move. Somewhere in between we find the ideal load that maximises the power output.
You can see from the graph, that the machine delivers maximum power with a ground speed of 1/3 the wind speed (i.e. λ = 0.33). The machine with a parachute-shaped sail has a maximum efficiency (power coefficient, cP) of 21 per cent, i.e. the machine is able to extract at the most 21% of the energy of the wind flowing through an area corresponding to that of the sail.
In the case of a flat sail, the maximum efficiency is 16%. In the graph above we have drawn two curves: The upper curve is for a parachute-shaped sail with a drag coefficient of 1.42. The lower curve is for a flat, circular plate with a drag coefficient of 1.1. (You can actually draw both curves in the same diagram with the drag calculator, if you plan your experiments carefully).

Maximum Power Output for Different Wind Speeds
Maximum power for different wind speedsNext, we use the result that we maximise the output of the machine by running it at 1/3 of the wind speed. For each wind speed between 0 and 32 m/s we have found the maximum power output of the machine. (Each time we have deleted the results, which did not give the maximum power output). The graph shows the result for a parachute-shaped sail:
The power output, P, varies with the third power of the wind speed, vT3. At a wind speed of e.g. 32 m/s the power output is 4,222.22 W, while it is only 434.87 W at 16 m/s.

The Ideal Loading of the Drag Machine
Ideal loading of the drag machineFinally, we use the same set of experiments to plot a different graph, i.e. the loading of the machine (the force F) that produces the maximum output for each wind speed, vT. The graph looks like this:
At a wind speed of 32 m/s the ideal loading force, F is 396 N. At half the wind speed, 16 m/s, the ideal loading is 99 N. If we look at the rest of the figures, we can check that the ideal loading of the machine (that produces maximum power) varies with the square of the wind speed.


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© Copyright 2002 Danish Wind Industry Association
Updated 17 November 2002