Safe Speeds [FT]

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). 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.

So how does this relate to safe speed - by sensor horizon! You want to
know the maximum safe speed at which point you can decelerate to zero
after spotting something you absolutely can't avoid by altering your
vector and which you don't want to hit. (Yes, you might pass this
limit, but it seems like a reasonable way to define acceptable
speeds... beyond that, you're taking your crews life in your hands).

So, if we assume sensor horizon is defined by the point at which, with
a 95-99% certainty, you can lock up any object of dangerous size, then
we'll just call this distance Rs.

So we then get
Rs = Vo*t + 0.5 * A * t^2 (and keep in mind, A will be negative since
you'll be decelerating)
We also know
0 = Vo + A*t	(A being negative) (the time it takes to stop)
which is t = -Vo/A

So, we want to solve for the unknown, Vo.

So we combine the eq'n....

Rs = Vo * (-Vo/A) + 0.5 * A * (-Vo/A)^2

Solving this mess leads to
Vo = sqrt( 2 * -Rs * A)   which seems like a bad idea until you
realize, A is negative.
So if we replace our negative A with the term Tdecel (deceleration
thrust), we're left with

Vsafe = sqrt (2 * Rs * Tdecel)

So the maximum safe speed (by my def'n) would be the squareroot of
(twice your sensor horizon multiplied by your thrust rating).

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.

So, if we assume 54"
Th-2 Vmaxsafe = 14
Th-4 Vmaxsafe = 20
Th-6 Vmaxsafe = 25

If we assume 72"
Th-2 Vmaxsafe = 16
Th-4 Vmaxsafe = 24
Th-6 Vmaxsafe = 41

Hmmm. We begin to get an appreciation for high thrust, superior sensor
vessels.
We also get some idea what ludicrious speeds might be given the level
of sensor technology present.

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. Conversely, an object with its own
velocity cuts your reaction time dramatically. So my value was a
compromise. And it makes good sensors something you really want as a
tech advantage as it lets you cook along faster... with far less risk
to your crew. And less chance of a flogging.

Of course, that's just my opinion. Other views are welcome.

Thomas Barclay
Software UberMensch
xwave solutions
(613) 831-2018 x 3008