I was trying to explain to a non-pilot why increased power is required
with
altitude. She said "isn't the air thinner up there so there isn't as
much
resistance?" I said "yes, but the plane needs to fly fast enough for
the
air
over the wings to feel like it does down low. So the speed required
goes
up
you get higher. More speed need more power."

This didn't really do the trick.

Can someone think of a better way of putting it without resorting to
mathematics and an explanation of IAS and TAS?

TAS increases with altitude for a given power setting due to less
aerodynamic drag at higher altitudes. It does not take more power to go
the
same speed at higher altitudes - at least, not in any of the airplanes
I've
ever flown. Take a look at the speed/power charts for a turbo and you'll
see what I mean - if you maintain 75% power the higher you go the faster
you
go.

If you're talking about altitude effects on the power output of a
normally-aspirated engine, that's a different story. At about 8,000 feet
a
normally-aspirated engine will probably be putting out around 75% power at
full throttle, and it will continue to decrease as you go higher.

BDS

First, I stand by my remarks as mathematically accurate.

Second, you are technically correct that a given power (typically 75%) will
give a greater speed with increasing altitude. However, the increase in
speed will not be as much as many people seem to expect, but instead will be
very close to the square root of the optomists expectation.

The good news is that the graphs in the POH seem to be a good guide.

Peter