Off By Three

So we're talking at StarfleetJedi.net about the Death Star exhaust port and who could hit it with the proper intel.   I noted that "Given the accuracy concerns of Malcolm Reed in "Fight or Flight"[ENT1], when a 0.02% (three meter) inaccuracy on a target was grounds for him to have a panic attack, I'd wager Enterprise NX-01 could take care of it, if they had all the intel.  And it'd be fun to see them try to get in range."

I decided to have a further look at the spatial torpedo test.




With love to Chakoteya.Net:

REED: Ready.
TRAVIS: Fore and aft target scanners are aligned.
REED: Activating simulation J6. Target acquired.
TRAVIS: Simulated launch.
REED: Five seconds to impact. Three, two, one.
(It misses.)
REED: Wonderful.
TRAVIS: We're only off by three meters.
REED: Only three meters. Three meters could mean the difference between hitting a weapons port and a warp core. Instead of disabling a vessel we'd end up destroying it, and probably ourselves in the process.
TRAVIS: We'll get it right.
REED: All this should have been dealt with before we left Earth. Have they detected any inhabited planets or vessels?
TRAVIS: Not yet.
REED: Good.
TRAVIS: I hope you don't expect everyone we run into out here to be hostile. In twenty three years I don't think my folks ran into a problem more than a half dozen times.
REED: I don't believe you were ever out quite this far.
TRAVIS: Do you think that makes a difference?
REED: All I do know is until we get these targeting scanners working properly, the further we are from everyone else, the better.
TRAVIS: Seems like everybody else on board is itching for a first contact.
ARCHER: How's it going?
REED: Not well, sir. We've corrected the problem but we're still off by point oh two percent. It's unacceptable.
ARCHER: Are you sure it's not the simulations that are off?
REED: There's only one way to find out.
ARCHER: How long would it take to arm a few torpedoes?
REED: Moments, sir.
ARCHER: Archer to T'Pol.
T'POL [OC]: Yes, sir.
ARCHER: Prepare to drop out of warp. It's time for a little target practice.
T'POL [OC]: Acknowledged.
REED: Thank you, Captain.
ARCHER: Come on, Travis. We've got to find Mister Reed something to blow up. 

Let's ponder that 0.02% for a moment.   We don't have a stated range, so one would presume that 0.02% is directly tied to the three meters . . . this suggests that we can apply a little trigonometry to determine the range.

Let's bear in mind, though, that for consistency's sake, it appears that all the ranges in Enterprise are on the order of 100km or less  . . . probably more like 10 in combat with maneuvering vessels.   Matter of fact, I don't recall of the top of my head right now any orbital bombardment type hits (other than the one against the mountain in "Silent Enemy") or beyond-visual-range shots.

And indeed, applying a touch of trigonometry, we find the range to have been approximately 2400 meters, or 2.4 kilometers.  This assumes 0.02% of 360 degrees, resulting in 0.072 degrees as the error radius.

sin(A)=a/c

The sine of 0.072 degrees is .0012567 or so, and if we divide three meters by that to work the formula, we get 2,387.325 ... or 2400ish.

Little wonder that he'd be concerned about blowing themselves up.

Of course, I consider this calculation to be more an exercise than a firm value, though I consider it to be about right in line with Enterprise ranges.  Still, I can think of no good reason for someone to give degrees in percent, for instance, suggesting that he may have been talking about something more esoteric.  Further, the beauty of missile weapons is that they should have the capacity to guide themselves and not rely on the ship's targeting capability alone ... just upload a pic with a crosshair and send it in the general direction of the badguy, for pete's sake.  And as a thermal exhaust port, IR targeting would suffice.

Nevertheless, rolling with what we came up with would mean Enterprise would have needed to get extremely close to make the shot given the then-"unacceptable"-condition of her targeting scanners.  If 2.4km equalled a possible six meter diameter hit area, then if we wanted to get close enough for a 1.5 meter diameter area (to hit the two meter exhaust port and give wiggle room for the torpedo size), the ship would have to get within 600 meters.  That's less than three ship-lengths.

And, of course, this ignores the fact that the torpedo still has to make it 60km without hitting the sides of the shaft, but we'll pretend the torpedo is smart enough to manage that.