Re: Safe speeds (FT)

Thomas Barclay wrote:

> Just a general comment on FT speeds:
> 
> People like Oerjan are incredible (no, don't blush!) - flies fast,
and
> measures distances like 0.2 mus when an MU is a cm... (that's be 2
> mm - a tough call).

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?
> 
> Here is an answer for all you captains who wish to avoid courts of
> inquiry followed by flogging...
> 
> Assume we have the formula
> S(t) = Vo*t + 0.5 * A * t^2  where S is distance, t is time, Vo is
> initial velocity, and A is acceleration - a very standard Newtonian
> thing. This describes the movment of a ship from some initial value
of
> time, based on velocity at that point, plus acceleration.

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
> Th-4 Vmaxsafe = 20
> Th-6 Vmaxsafe = 25

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
> right. I seem to recall seeing sensor ranges of 54" and 72". And
> thrusts are typically 2/4/6.

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
> entirely correct: many times you could dodge an object without
> needing to stop, so you could go faster.

Yep. Particularly in Cinematic <g>

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

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,

Oerjan Ohlson
oerjan.ohlson@telia.com

"Life is like a sewer.
  What you get out of it, depends on what you put into it."
- Hen3ry