Safe speeds (FT)

> Thomas Barclay wrote:

> Just a general comment on FT speeds:

A 2mm measurement (after movement, that is) isn't *that* difficult -
not
when many of the ship bases are semi-tranparent, at least (GW flying
bases, only lightly sprayed black so they won't glitter so much)... and I only
manage to place salvoes with that kind of precision against immobilised
targets (though I admit to counting anything moving at less than 8
mu/turn
as "immobilised" <g>)

> But what are reasonable speed limitations?

Why stop? Why not just dodge far enough to allow you to bypass the obstacle?

The distance I need to dodge is equal to or less than the radius of the
obstacle (depending on whether or not I'm going towards the very centre of it
or not).

Small individual obstacles are not a serious problem - as someone
pointed out, two FT ships won't collide even if they occupy the same spot on
the table unless at least one of the ships actually wants to ram, and even
then it's difficult. If there are numerous small objects (eg the satellite
cloud around Earth), you're talking about things very similar to meteor swarms
and debris for which MT already has rules; the safe
speed there is 5 mu/turn. (I don't normally use the "Battle Debris"
rule, though - with a mean distance of 3mu (3000 km in the scale we
use) between ships in formation (mainly due to base sizes), you'd need an
utterly outrageous amount of debris from each destroyed ship to put
its neighbours at any serious risk - but if you do use it can be quite
interesting against Banzai Jammers :-/)

So that leaves large objects - ie, asteroids, planets and the like. How
big these obstacles are depend on the game scale you use, but in the 1mu =
1000km Earth has a radius of about 6mu while the gas gigants in our star
system have radii of some 20-72mu.

Assume that you detect this huge obstacle at range Rs while you're moving at
the initial velocity Vo. Call your thrust rating A, and the radius of the
obstacle R. If you don't do anything at all, you'll hit the obstacle at the
time Tbang = Rs/Vo.

If your ship obeys the Vector movement rules (and has a maneuvering thrust
of A/2), you'll immediately turn it perpendicular to Vo and start
accellerating as hard as you can. After the first maneuver point used to turn
the ship, you'll also be able to use your lateral thrusters to reduce your
velocity towards the obstacle. Ignoring that initial thrust point for
the sake of simplicity - I'm way too tired to take it into account now
-
you'll reach, or pass, the obstacle at the time

t = 2*(Vo/A - sqrt(Vo^2/A^2 - Rs/A)).

(It is -sqrt(...) and not +sqrt(...), 'cause otherwise you'd get
t=4*Vo/A
when Rs=0 (ie, when you detect the obstacle by ramming it). Also note that
if Rs > Vo^2/A there is no solution; in this case you'll stop moving
towards the obstacle before you reach it.)

By this time you will have moved the distance

A/2*t^2 = 4*(Vo^2/A - Vo*sqrt(Vo^2/A^2-Rs/A)) - 2*Rs

towards the edge of the obstacle. If this distance is greater than the
radius R of the obstacle, you're safe. Replacing A/2*t^2 with R and
solving for Vo, I get

Vo = (R+2Rs)*sqrt(A/8/R)

but I'm not entirely convinced I got this right - it behaves strangely
when R is much bigger than Rs. Better take an extra safety margin to account
for the maneuvre thrust point you used to turn the ship and to avoid clipping
the edge of the obstacle, though.

Examples: Using the 1mu = 1000km scale, 1 turn = 7.5 minutes scale, Jupiter
has a radius of about 71mu. Assume that you can't detect Jupiter from a range
of more than 54 mu and that you can ignore its gravity well.

If your ship is thrust-2, the "safe speed" using this way of avoiding
the
crash is only 10; thrust-4 ships have a safe speed of 15 and thrust-6
18. IOW, if you're crashing into Jupiter you're somewhat better off turning
all the way around to use your main engines to brake since that'd give you the
following safe velocities:

> Th-2 Vmaxsafe = 14

However, if the planet you wish to avoid is Earth (R = 6mu), the "safe"
speeds are 23 for a thrust-2 ship, 32 for thrust-4 and 40 for thrust-6.
In this case you're obviously much better off just dodging a little to the
side. Mind you, these velocities are rather high even for me since we're
talking Vector movement rather than Cinematic.

'Course, I suspect that you will be able to detect Jupiter at slightly
longer ranges - it is visible from Earth, after all (and Earth itself
is definitely visible at range 380mu, ie from the lunar surface) The gravitic
pull of Jupiter at 54000km is approx. 0.8g - ie, thrust 0.8 - so you
can't
really ignore it either, particularly not for the thrust-2 ship, but
since it varies with the distance to the planet it'd take too long to include
it
in the analysis (since I'm doing it by hand rather than numerically .-/
).

*******

If your ship follows the Cinematic movement laws, things are a bit different.
In order to avoid an "infinitely wide" object, you need to turn your course 90
degrees to avoid hitting it. By turning and braking as hard as the ship's
thrust allows a ship with...

Thrust-2 to turn 90 degrees in 2.5 game turns over a forward distance
of
(Vo*(3+2*sqrt(3))-(7+3sqrt(3)))/4 mu

Thrust-4 to turn in 1 game turn over a forward distance of
(Vo-2)*(sqrt(3)+1)/2 mu

Thrust-6 in half a game turn over a forward distance (Vo-3)*sqrt(3)/4
mu towards the obstacle.

IOW, for *infinitely wide* obstacles, the safe Cinematic speed for a ship
with...

thrust-2: Vo = (4*Rs+7+3*sqrt(3))/(4+2*sqrt(3))
thrust-4: Vo = Rs*4/(1+sqrt(3))+2
thrust-6: Vo = Rs*4/sqrt(3)+3

Assuming Rs = 54mu, Vo becomes 30, 81 (!) and 127 (!!) mu/turn for
thrust-2, 4 and 6 ships respectively. That is quite enough to keep even
me satisfied <G>

With a smaller than infinite obstacle it often isn't necessary to turn the
full 90 degrees, and the safe speed gets correspondingly higher. For
example, a Cinematic-moving ship with a thrust rating of 4 or better
will be able to dodge an Earth-sized planet (R=6mu) at *any* speed as
long as Rs > 12 mu and it is able to change its orders "immediately" (ie, it
either doesn't need to wait until the Order Writing Phase of the game turn or
it ends its movement more than 12mu away from the planet).

[Big snip]

> So, let's plug in some numbers I vaguely recall, but might not be

In FT2, the sensor range for detecting Bogeys (ie, detect that a ship
of some kind, and its general class - Escort/Cruiser/Capital/Merchant)
is not specified - it covers the entire board, so is "effectively
infinite". Active military sensors, ie those you scan things with to get more
detailed information (as in the MT sensor rules) have a max range of 54mu.

However, unless your scale is very different from the one I use you should be
able to detect planets and large asteroids at rather longer
ranges than 54mu :-/

[Another big snip]

> Last point: I picked my definition for max safe speed. It isn't

Yep. Particularly in Cinematic <g>

> Conversely, an object with its own velocity cuts your reaction time

Also remember that objects large enough to be difficult to dodge tend to have
gravity wells which try to suck you in, so you're not always able to brake as
fast as our calculations have assumed.

Regards,