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Re: [Phys-L] 'Unorthodox' propulsion?

View this as a textbook elastic collision between m(ping pong ball) with velocity v, and a stationary M(paddle) ==>

The final momentum and energy of M are respectively 2mv/(1+m/M) and (2/M)[mv/(1+m/M)]^2.

In the limit of a rigid paddle (m/M-->zero), these become 2mv and zero.

Bob Sciamanda
Physics, Edinboro Univ of PA (Em)

-----Original Message----- From: John Denker
Sent: Saturday, August 02, 2014 10:29 AM
Subject: Re: [Phys-L] 'Unorthodox' propulsion?

On 08/02/2014 03:23 AM, Chuck Britton wrote:

Doesn’t any EM beam have momentum given by p = E / c ?

Now THAT is an interesting question, involving some fundamental
physics plus an enormous range of practical applications.

The short answer is no, the "E" that you care about and the "p"
that you care about are not locked together in such a simple way.

Here's an experiment you can do: Suppose we have a ping-pong
paddle a little ways above and parallel to the ping-pong table.
The ball is bouncing up and down between the two.

/ \ o

Every time the ball hits the paddle it imparts some upward
momentum to the paddle. To a good approximation, however,
the energy is unchanged. The ball continues on its way,
and on the next bounce it imparts some more momentum. In
many practical situations, the "E" you care about is the
energy required to set up this situation, and the "p" you
care about is the total transferred momentum. The "p" can
be very large, if the ball bounces many times before it
escapes off to the side or loses its energy to other modes
via friction or whatever.

People guess wrong about this wrong all the time.

One important application has to do with airplanes, namely
the momentum-per-unit-energy relationship for a wing or
propeller, i.e. the lift-to-drag ratio. The ratio is a
lot better than a naïve calculation would suggest. Wings
work amazingly well.

In the limit where the ping-pong ball cannot escape at all,
you end up with a pressurized gas in a cylinder, and the
ping-pong paddle is the piston. Here you get a /force/ i.e.
pressure (not momentum) proportional to the energy. The
momentum is the integral w.r.t time of the force, and grows
without bound.

As for that NASA paper, the abstract is astonishingly badly
written, but the premise is not completely crazy. If you
can find something to push against, the momentum-per-unit-
energy relationship is greatly improved.

Over the years there have been lots of proposals to push
against the interplanetary medium
not to be confused with

Brady et al. propose pushing against virtual particles.
It's hard to imagine a scenario anywhere in this galaxy
where that would be competitive compared to pushing
against real non-virtual particles. I can believe it's
possible; I'm skeptical that it's useful. AFAICT all
we have to go on is the abstract. Presumably a full
paper will come out before too long.

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