Here is VK1OD's analysis of the original "Cobra Jr." antenna:http://www.vk1od.net/antenna/cobra/index.htm
Notice there are some frequencies where the losses in the antenna itself are very high.
That's because the currents in the folded wires mostly cancel each other, requiring a
large current to flow to get much power radiated.
This analysis is for a 72' antenna, so for a 41' version with the same construction you
would scale the frequencies by 72/41 = 1.756. So, for example, the performance that
VK1OD shows at 10 MHz would apply instead at 17.56 MHz. (In both cases it means
that efficiency would degrade significantly just below one of the WARC bands.) It
also means that frequency below which the efficiency is generally poor, shown as about
6 MHz, would translate to 10.5 MHz on your antenna.
So basically 20m would fall on about 8 MHz on the chart - just below a major problem
range, but perhaps not too
bad as long as environmental factors don't shift the
resonance downwards. The spike shown between 8 and 9 MHz would fall between 20m
and 17m instead, and 10m comes in just short of the bad area shown starting at 17 MHz.
So, as long as the antenna is far enough from other objects (such as roofs, buildings, etc.)
that might shift the resonant frequency in an unfortunate manner, the antenna may work
reasonably well on the ham bands from 20m through 10m.
On those frequencies where efficiency is poor, the impedance presented to the tuner at the
end of the ladder line can be pretty extreme, and it wouldn't surprise me if you find it
difficult to match for some line lengths.