> As for wingspan/weight ratios. . .I thought the purpose of an Air Frame
> was to make the entire craft like a Lifting Body. Then again, I don't
> have BL. . .
Regardless of exactly how it works, lift is roughly proportional to the area
of the lifting surface. For a given shape, this increases with the square
of the size. Mass (hence weight) goes up with the cube. The lift/weight
ratio thus decreases with increasing size (for given speed). That's why
large birds need disproportionately larger wings in order to fly.
- -*-*-*-
> The other nit is a bit more significant, if you're in combat near a Gas
> Giant: The size of Jupiter is wrong.. it's radius is 4.76. It's diameter is
> 9.52 hexes.
Jupiter is about 143 Mm across. How big is a BL hex? 15 000 km?
This gives your figures. I had the idea it was 60 Mm, though.
> The effects of the gravity well are SEVERELY distorted. I hope
> I'm not putting my foot in it here with lousy calculations, but what they
> say is: What I calc'd it to be:
>
> 1G Threshold Threshold 1G 2G 3G 4G 5G ... 10G
> 1.4 Hexes Hexes 15.5 10.95 8.95 7.75 6.93 4.9
Unfortunately, the 15 Mm hex size is inconsistent with these figures.
The 1G radius for Jupiter is 114 Mm from the centre. That is, 1.6 times
its radius. There is evidently something wrong, since the 'surface'
gravity of Jupiter is only 2.5 G, yet your figures show it to be about
10 G at the 'surface'.
If my faint notion of a 60 000 km hex size is correct, the 1G level should
be 1.9 hexes from the centre.
> And with the size of the maps, this 1G threshold covers about one of the
> maps, and since Jupiter is supposedly swinging about at .78 hexes per
> turn... It's going to make REALLY difficult for players (assuming they're
> not using Jupe as a frame of reference).
Jupiter's orbital speed is 13 km/s. This is consistent with a 60 Mm hex and
a 1 hour turn. Just what are the real numbers, anyway? I'll stick with
these because they sound nice enough.
I expect the player's *would* be using Jupiter as a reference - the Sun's
tidal effects are negligible at that distance. Its gravity is small -
48 uHex/turn^2 - so it could be ignored anyway.
> Since I'm curious about orbit periods, can any of you physics wizards
> suggest a calculation to determine orbit period around a planet given
> distance and mass of central planet (or star?)
It depends on the distance from the planet - here's a derivation:
Circular orbit is achieved when the acceleration due to gravity is exactly
that required to keep the satellite in circular motion.
Gravity: a = GM/r^2.
Circular: a = w^2 r. w = 2pi/T.
G ~= 6.67e-11 SI units (kg^-1 m^3 s^-2 for anyone who cares), the
gravitational constant.
M is the mass of the planet. Jupiter's M ~= 1.90e27 kg.
R is the radius of the orbit. eg. 72 Mm - just above Jupiter's atmosphere.
w is the angular speed of the orbit, related to the orbit time (T).
Equating the a's, you get
GM/r^2 = w^2/r
GM = w^2 r^3
Substituting the formula for T,
GM = (2pi/T)^2 r^3
(T/2pi)^2 = r^3/GM
T/2pi = sqrt(r^3/GM)
T = 2pi sqrt(r^3/GM)
> Here's the various & sundry of my calculations:
>
> The determine the range of effect of Gx...
>
> Gx band = sqrt(M/Gx) / 2.34375 where M is the mass of the central planet
> in "earths" and Gx is the effect band.
For those who want a more 'fundamental' formula; use
a = GM/r^2
to get
r = sqrt(GM/a).
1G is 9.8 m/s^2 (use this for 'a'), the value of 'GM' for Earth is
4e14 SI, to give 'r' in metres. (This confirms that you use 15 Mm/band)
Other useful orbital stuff:
Specific escape energy: I = GM/r.
Combined with the kinetic energy formula I = v^2/2;
Escape velocity: v = sqrt(2GM/r).
Esacpe energy equals half of circular orbit energy.
(Hence escape velocity = sqrt(2) times orbit velocity: about 40% extra)
Sun's mass: 1.99e30 kg.
Earth's mass: 5.98e24 kg.
Earth low orbit velocity is 7.9 km/s.
Moon low orbit velocity is 1.7 km/s.
Moon's orbit velocity is 1.0 km/s.
Earth's orbit velocity is 30 km/s.
- --
Tim Little