Optimal Load and Optimal Operating Speed
We shall now be looking into the experimental results for
the drag based machine on the previous
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.
Speed (Ground Speed) for Constant Load
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.
Output for Constant Load
power output, P for different wind speeds, vT can be plotted from the same set
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.
Ideal Operating Speed
and Maximum Efficiency
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).
Power Output for Different Wind Speeds
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
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.
Ideal Loading of the Drag Machine
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.