GCS Vs 12" Cannons

[m52nickerson]

I'm probably missing something, but how based on distance and time are you calculating acceleration?

Dude, really? Distance equals rate multiplied by time. Even I know that, and I'm no math whiz.

If you know the distance, and the time it took to travel said distance, you can calculate the average speed (rate). Somebody else can take it from there.

Yes that would be rate or speed, acceleration would be the the change in speed over time.

[Tsukiyumi]

Yes that would be rate or speed, acceleration would be the the change in speed over time.

Which is covered by kostmayer's and Seafort's posts after mine.

[m52nickerson]

Given constant acceleration the average is also the median, so doubling it gives you the maximum speed, divide by time and you have the acceleration.

Why are you assuming the ship was accelerating the entire time?

Yes - torpedoes can accelerate to war from sublight ("Emissary" - the TNG one), so they must have mass-lightening ("Deja Q" shows that warp and mass-lightening are linked).

So they have it, but do they need it at sublight speeds?

All irrelevent - it's the change in momentum of the smaller object that matters.

Please explain.

Not that great - the E-D was able to shove the Tsitovsky at the lump far quicker than the lump was approaching.

How could you know that? Remember the Tsitovsky was pushed twords the fragment at the same time it pushed the E away.

Against a physical impact that shouldn't make much difference, as any impact on the shields would be transfered to the frame anyway through conservation of momentum.

We never see that. In Nemisis when the E-E rammed the Scimitar the Scimitar did not move We also see ships rammed as you brought up and the don't show anything such as that. One of two things must be going on, Conservation of Momentum does not apply in the Trek Universe, or there is something with the ships that causes this to take less energy to destroy the hulls then to push the ships.

Yes there is - at 1st Chin'toka the Klingon ships were destroyed by ramming before suffing a single hit.

That we see, but I will have to look again to see how long into the battle that was.

"The Hunted" springs to mind - this simply demonstrates a lower limit for shield effectiveness, rather than "Survivors"' upper limit.[/quote]

Perhaps. It would depend on that ships speed and mass.

[SteveK]

It is possible to use calculus for this problem too...

If "A" is the acceleration then integrating twice with respect to time will give a position function. In this case we have 1/2 A t^2 = 650x10^6 km If we evaluate at t = (3600 *1.8 ) then we get A = 30.96 km.

There is, however, nothing to suggest that the acceleration is indeed constant.

[kostmayer]

Why are you assuming the ship was accelerating the entire time?

Given that the E-nil was attempting to intercept V'Ger as far out as possible, and Kirk later attempted to go to warp against Scotty's advice, it's safe to assume the ship was being driven as hard as possible. Note that in the case the helm order was given as a fractional warp factor

[Mark]

But wouldn't the acceleration have topped out at a certain point? Especially before hitting reletivistic speeds?

[Captain Seafort]

Why are you assuming the ship was accelerating the entire time?

I explained this in the original post - the E-nil was racing to intercept V'Ger, to the extent that Kirk ordered her to warp against Scotty's advice. It doesn't make sense that she'd stop engines and just drift along.

So they have it, but do they need it at sublight speeds?

Of course - no matter how strong the engines are, reducing mass will always make them more effective, and in combat even the slightest advantage can be vital.

All irrelevent - it's the change in momentum of the smaller object that matters.

Please explain.

Imagine a truck is appraoching you at walking pace - it doesn't flatten you, you can simply stand on the front bumper and travel along with it with no ill effects. Now imagine an oil tanker is approaching you at the same speed. Likewise, you can simply grab it, stand on the prow, and be carried along with no ill effects. This illustrates that the effect of an impact is independant of the mass of the larger object.

How could you know that? Remember the Tsikovsky was pushed twords the fragment at the same time it pushed the E away.

The Tsikovsky shrank noticeably as it was pushed away, whereas the approaching solar fragment barely appeared to change size at all, indicating that the Tsikovsky was travelling much quicker.

In Nemisis when the E-E rammed the Scimitar the Scimitar did not move

Two possibilities:

1) The Scimitar is sufficiently massive that the momentum didn't add up to much movement.

2) There was lots of movement, but we didn't recognise it as our frame of reference remained on the ships - they could both have been moving at a fair clip relative to where the impact originally ocurred, but we wouldn't see it.

We also see ships rammed as you brought up and the don't show anything such as that. One of two things must be going on, Conservation of Momentum does not apply in the Trek Universe, or there is something with the ships that causes this to take less energy to destroy the hulls then to push the ships.

That we see, but I will have to look again to see how long into the battle that was.

Right at the start - the Jem'Hadar didn't fire a single shot.

Perhaps. It would depend on that ships speed and mass.

It's inherently a lower limit, as the E-D's shields didn't fail, just as "Survivors" is an upper limit because they did fail. That's not to say that they're hard and fast numbers - other examples may produce lower upper limits or higher lower limits within those boundaries.

[Mark]

Hey Nickerson..........not to change the subject, but I've been wondering for the longest time. Is your avatar a picture of your son?

[m52nickerson]

But wouldn't the acceleration have topped out at a certain point? Especially before hitting reletivistic speeds?

If you get near your maximum speed. Scotty stated that the E could reach 0.8c without her warp engines, and Seaforts calculations are right on.

I don't remember anything that would indicated they could not reach maximum impulse speed.

Hey Nickerson..........not to change the subject, but I've been wondering for the longest time. Is your avatar a picture of your son?

Yes, my 3 year old. Plus we just added a new one(another boy) this past month.

[Mikey]

Congratulations!

[Mark]

Congrats indeed!

[m52nickerson]

I explained this in the original post - the E-nil was racing to intercept V'Ger, to the extent that Kirk ordered her to warp against Scotty's advice. It doesn't make sense that she'd stop engines and just drift along.

Sorry, I read your response to fast.

Of course - no matter how strong the engines are, reducing mass will always make them more effective, and in combat even the slightest advantage can be vital.

More effective is one thing, absolute need it another.

Even with the mass of the torpedo in my example was reduced from 100kg down to 1kg it would still do 6,736,283 exawatts.

Imagine a truck is appraoching you at walking pace - it doesn't flatten you, you can simply stand on the front bumper and travel along with it with no ill effects. Now imagine an oil tanker is approaching you at the same speed. Likewise, you can simply grab it, stand on the prow, and be carried along with no ill effects. This illustrates that the effect of an impact is independant of the mass of the larger object.

Thank you!

The Tsikovsky shrank noticeably as it was pushed away, whereas the approaching solar fragment barely appeared to change size at all, indicating that the Tsikovsky was travelling much quicker.

....but the fragment had enough energy to destroy that ship and would have destroyed the Enterprise as well.

Two possibilities:

1) The Scimitar is sufficiently massive that the momentum didn't add up to much movement.

2) There was lots of movement, but we didn't recognise it as our frame of reference remained on the ships - they could both have been moving at a fair clip relative to where the impact originally ocurred, but we wouldn't see it.

I don't see ether. The Scimitar had begun to move forward just before impact, unless it did not have mass-lightening, it mass would have been reduced. Plus we don't see movement when the Scimitar backs away from the E-E.

Looking at that pat of the film again there is no movement. During the rest of the battle we can clearly see the ships moving against the back drop of stars and clouds. We don't see that during the impact.

Right at the start - the Jem'Hadar didn't fire a single shot.

....and since we don't see any shield affect on those impacts of the Nemesis impact perhaps the shield don't "flash" if they instantly fail.

It's inherently a lower limit, as the E-D's shields didn't fail, just as "Survivors" is an upper limit because they did fail. That's not to say that they're hard and fast numbers - other examples may produce lower upper limits or higher lower limits within those boundaries.

ok........

[m52nickerson]

@ Mikey and Mark

Thanks guys! Now if I can only get some sleep.

[SteveK]

But wouldn't the acceleration have topped out at a certain point? Especially before hitting reletivistic speeds?

It certainly would. Allow me to demonstrate:

We know that F = MA / (1 -V^2/C^2)

Then A = F(1 - V^2/C^2) / M

We can see from this that as V --> C then A --> 0

Acceleration is the first derivative of Velocity, so by integrating the expression for A with respect to time we can get V(t)

V(t) = integral : F(1 - V^2/C^2) / M dt

V(t) = F/M (1 -V^2/C^2) t

A bit of algebra later (which I can show if asked) we have:

V(t) = ( 1/ [ (M^2/f^2 t^2)] + [1/C^2]) ^ 1/2

Now, imagine we have a 1 kg object which we will subject to a 1000 newton force for a period of time. Let's start with 2 seconds.

Classically we expect:

Acceleration: 1000 m/s^2
Velocity: 2000m/s

What we actually have is this:
velocity: 1999.999996 m/s
Acceleration: 1000 * (1- 4.44x 10^-11) ^1/2 which my calculator does not distinguish from 1000

Let's increase the time a bit, and see what happens. Time = 10^6 seconds, or about 11.5 days.


Velocity = 33314830.8
Acceleration = 993.81488 m/s^2

As we can see, a ship will experience its greatest acceleration when its speed is near 0. Therefore the assumption of constant acceleration is false, indeed the acceleration of the Enterprise from rest must be greater than the previously calculated value of 30km /s^2, to account for the slowing as velocity increases.

[Captain Seafort]

Even with the mass of the torpedo in my example was reduced from 100kg down to 1kg it would still do 6,736,283 exawatts.

Continuing to assume that the torp is going at .25c relative to the target (which would take half an hour or so), and indeed that the mass is only reduced by a couple of orders of magnitude - in Deja Q the E-D was able to reduce the mass of the moon by four orders of magnitude.

...but the fragment had enough energy to destroy that ship and would have destroyed the Enterprise as well.

Which goes to show that Fed ships don't handle physical impacts at all well. This is the point I was making.

I don't see ether. The Scimitar had begun to move forward just before impact, unless it did not have mass-lightening, it mass would have been reduced.

Which is why I favour the second explanation

Plus we don't see movement when the Scimitar backs away from the E-E.

Because the image is focused on those two ships, and the viewpoint is remaining stationary relative to them.

Looking at that pat of the film again there is no movement. During the rest of the battle we can clearly see the ships moving against the back drop of stars and clouds. We don't see that during the impact.

For most of the rest of the battle the ships are moving very quicly relative to the camera, resulting in the impression of movement relative to distant objects. Given the scales we're talking about any real movement relative to those objects would be minimal.

...and since we don't see any shield affect on those impacts of the Nemesis impact perhaps the shield don't "flash" if they instantly fail.

Quite possibly.