Re: GEV on other worlds

agoodall@att.net wrote:

> The amount of energy imparted by a propellor (or fan blade) on a
> column of air is equal to 1/2mv**2. In order to move the same mass of
> air in a less dense atmosphere in the same amount of time, you have
> to move the air twice as fast. However, that means that the energy
> needed to move the mass goes up due to the formula squaring the
> velocity. So, in order to move the same mass of air in the same
> amount of time, you have to move it more quickly. This means that you
> end up spending more energy to move the same amount of less dense
> air.

I don't want to drag the technical discussion out too much, since it 
doesn't appear to be generating much interest :( -- but I did a little 
scribbling and came up with the following:

I'm just considering a "standard vehicle" which can operate in different

settings characterized by their atmospheric pressure and gravitational 
acceleration.  I'm concerned only with lift and not propulsion, and 
assume the engine will work under any conditions.  The only variables 
are thus gravitational acceleration, atmospheric pressure, and fan 
rotation speed.

Pressure under the skirt is a result of the lift fan moving air, and 
there are two components to this -- how rapidly air mass is moved (mass 
per second) and and how fast those particles are moving.  I.e. we're 
concerned with momentum here.

mass moved = m
velocity of air molecules = v
fan angular velocity = w
atmospheric density = n
pressure under the skirt = p

dm/dt ~ w*n
v ~ w

and

p ~ dm/dt * v ~ w^2 * n

Since the pressure has to balance the weight of the vehicle we have

p = constant * g

or

w^2 * n / g = constant

 From this, the atmospheric density and gravitational acceleration work 
linearly in opposite directions.  Doubling density and doubling grav. 
accel. leads to no net change in operation of the GEV.

If we keep g constant but alter n, then we have to change fan speed to 
compensate, proportional to the square root of 1/n.  E.g. n drops to 25%

then we need to boost w to sqrt(1/0.25) = 2 times faster.  Note however 
that this means that the power required to run the fan, which is 
proportional to w^2, goes up by 4.  Which is to say the power 
requirement to run the fan varies linearly with the inverse of the air 
density (g = constant).

Of course propulsion won't depend on g, so the power requirements to 
actually move will vary according to the previous paragraph.  And then 
there's things like turning radius / rudders etc.

Anyway I started thinking about this in the context of Dirtside 2 
scenarios in the GURPS Transhuman Space setting, particularly on Mars 
(which has g = 0.38 Earth's, and in the setting has an atmospheric 
pressure 45% of Earths after some 50+ years of terraforming) or even on 
Titan.

Cheers,
--Jerry

-- 
Jerry Acord [+] acord@imagiware.com [+] http://imagiware.com/acord/