Energy question

[consequences]

How much energy would be required to accelerate 8 million tons of ship at 600 Gravities?

[kojikun]

precisely shitloads. but i dont think youre going to get a real answer about energy because constant acceleration requires POWER not energy.

but acceleration from something like an explosion or electromagnetic bursts.. ALOT.

[Howedar]

F=ma

Convert 8 million tons to kilograms, multiply by acceleration in meters per second squared (roughly 6000), you get a joule output.

[Darth Wong]

F=ma

Convert 8 million tons to kilograms, multiply by acceleration in meters per second squared (roughly 6000), you get a joule output.

No, you don't. You get a Newton output. The minimum amount of energy required for any given acceleration depends on the duration of that acceleration. Without that information, it is impossible to produce a figure for joules.

[consequences]

Constant acceleration in the case I'm looking at.

[The Nomad]

Constant acceleration in the case I'm looking at.

I'm proposing you a method ( quickly ) to get an approximate idea, but it requires you to know the relative velocity you wanna get your vessel to. And that the vessel isn't submitted to any other force than the thrust of its reactors.

The initial velocity is considered zero m/s.

Speed is given by v=at=600gt

You derives t.

Know assuming the thrust is a conservative force :

delta(KE)=KE(end)-KE(ini)=.5*m*v² if subrelativistic
=gamma*m*c² if relativistic

( KE(ini)=0 since we consider the initial velocity to be 0 )

were gamma=1/sqrt(1-(v/c)²)

A little bit of calculus leads you to the power in watt.

Or use the last formula if you want the brute energy.

This method is IMHO very approximative.
Comments ?

[kojikun]

constant acceleration requires a power output not energy.

Howwie, yours gives: (1.6e10 kg * 5.9e3 m/s^2) = 9.4e13 Newtons (which is a nice amount, believe you me).

[Beowulf]

You're probably looking to see how much energy a Honorverse ship needs to be able to accelerate to their maximum STL speed, right?

It's more than could possibly be provided using fusion, assuming the mass fraction isn't obscenely tilted towards fuel.

[Dahak]

You're probably looking to see how much energy a Honorverse ship needs to be able to accelerate to their maximum STL speed, right?

It's more than could possibly be provided using fusion, assuming the mass fraction isn't obscenely tilted towards fuel.

That's the beauty of Impellers in Honorverse.
The energy necessary to accel a ship doesn't come from the ship at all. All the ship does is to power the Impeller nodes generating the wedges. The energy for accel comes from hyperspace

[Wicked Pilot]

How much energy would be required to accelerate 8 million tons of ship at 600 Gravities?

You need Power for this. Power is the rate of doing work, or energy over time. Your kinetic energy is gonna equal (m(at)^2)/2. Your power is gonna equal (m(at)^2)/(2t)

If your ship accelerates for one second, the energy output would be 1.26*10^17 Joules. Two seconds would be 5.03*10^17 Joules.

[Howedar]

No, you don't. You get a Newton output. The minimum amount of energy required for any given acceleration depends on the duration of that acceleration. Without that information, it is impossible to produce a figure for joules.

Don't let sleep deprevation happen to YOU!

[Ted C]

Change in velocity is 5880 m/s per second.

Change in kinetic energy is therefore about 138,000 TJ per second, so the ships engines must use at least 138,000 TW.

[His Divine Shadow]

F=ma

Convert 8 million tons to kilograms, multiply by acceleration in meters per second squared (roughly 6000), you get a joule output.

No, you don't. You get a Newton output. The minimum amount of energy required for any given acceleration depends on the duration of that acceleration. Without that information, it is impossible to produce a figure for joules.

Wouldn't it just work to use your KE calculator and use 5883m/s^2 as the speed figure? That way, we ought to see what it requires per second of acceleration, which is 1.384E+17watts.

EDIT:
It seems I was right, if Ted C is to be believed, and I do believe he is.

[Wicked Pilot]

Change in velocity is 5880 m/s per second.

Change in kinetic energy is therefore about 138,000 TJ per second, so the ships engines must use at least 138,000 TW.

Negative ghostrider, the change in kinetic energy is not linear. Energy is based on velocity squared, meaning the ship's energy will increase by a factor of four whenever the time spent accelerating is doubled. This is why power cannot be calculated until a specific time value is given.

[Ted C]

Negative ghostrider, the change in kinetic energy is not linear. Energy is based on velocity squared, meaning the ship's energy will increase by a factor of four whenever the time spent accelerating is doubled. This is why power cannot be calculated until a specific time value is given.

Hmm... seemed perfectly logical to me.

KE = 0.5 * m * v^2

(quickly expands comparison over ten seconds in spreadsheet)

I suppose, in retrospect, that it only works for the first second, though.

[His Divine Shadow]

Hmm, doesn't a constant 600G acceleration always require the same amount of energy? Until you get close enough to C that is?

[Ted C]

Hmm, doesn't a constant 600G acceleration always require the same amount of energy? Until you get close enough to C that is?

That was my thinking, but apparently it's not the case.

In the first second, the KE of the object increases by 138 PJ.

In the second second , the KE increases by 415 PJ (according to my spreadsheet).

Third second: 691 PJ.

And so on.

Seems kinda odd, but constant acceleration doesn't seem to indicate constant power.

[Crayz9000]

It's a power curve approaching infinite power as you approach the limit of c.

[Crayz9000]

I'm proposing you a method ( quickly ) to get an approximate idea, but it requires you to know the relative velocity you wanna get your vessel to. And that the vessel isn't submitted to any other force than the thrust of its reactors.

The initial velocity is considered zero m/s.

Your figures seem a little messed up, though.

v'(t) = a(t) = 600 g/sec

So you take the integral of a(t) to find your velocity, and take the integral of v(t) to find the position function s(t).

So, integrating a(t), the velocity should be given by v(t) = 600t + C...

Bah. I can't do anything else right now, I've gotta head to college now...

[Darth Wong]

Seems kinda odd, but constant acceleration doesn't seem to indicate constant power.

Remember: as you accelerate, you are applying the same force on a constant basis, but you are applying it over a greater DISTANCE per unit time. Energy is force x distance, hence the non-linear energy curve. It's really quite obvious when you think about it, even if you don't look at the KE formula.

[Grand Admiral Thrawn]

What is 1 G in m/s²?

[Darth Wong]

What is 1 G in m/s²?

9.806

EDIT: 10 is close enough for most purposes.

[Grand Admiral Thrawn]

What is 1 G in m/s²?

9.806

EDIT: 10 is close enough for most purposes.

In other words it's close enough for lazy assholes who can't take the time to do completely accurate calculations.



Like me.

[His Divine Shadow]

Seems kinda odd, but constant acceleration doesn't seem to indicate constant power.

Remember: as you accelerate, you are applying the same force on a constant basis, but you are applying it over a greater DISTANCE per unit time. Energy is force x distance, hence the non-linear energy curve. It's really quite obvious when you think about it, even if you don't look at the KE formula.

Actually yeah, now I get it too!

[Howedar]

What is 1 G in m/s²?

9.806

EDIT: 10 is close enough for most purposes.

In other words it's close enough for lazy assholes who can't take the time to do completely accurate calculations.



Like me.

Thats not how you phrase it. You say "its within the margin for error already" or mumble something about significant figures. Come on, you gotta look smart