Acceleration caclulation request

Alyeska · Post by **Alyeska** » 2003-01-30 07:06pm

I know enough about math that I know I need an equation for this. I am trying to set up my acceleration figures for my own scifi government, but I am running into problems. I am basing the acceleration on how long it takes them to travel a specific distance while accelerating at the same rate the whole time.

So the fixed constant is 7.8 billion kilometers. The Variable is the number of hours. What I am looking for is the acceleration rate in Kilometers Per second. I know that the faster you go the more energy you have to put in, and the closer to light speed you get the harder it is to accelerate (or so I have been told), but I don't care about that. I just want pure acceleration numbers. I want to be able to input the hours on the trip and figure out what constant acceleration rate they had to do to make the trip of 7.8 billion KM.

If anyone can come up with this equation or can point me to where I can find this equation, I would greatly appreciate that.

Alyeska · Post by **Alyeska** » 2003-01-30 07:08pm

(sigh)

Make that 7.4 Billion KM.

Hotfoot · Post by **Hotfoot** » 2003-01-30 07:15pm

Quick question: I'm assuming you actually want to slow down before reaching point B, correct? Otherwise you'll reach point B for all of a fraction of a second before leaving it in the dust, at least if we're talking realspace travel.

Alyeska · Post by **Alyeska** » 2003-01-30 07:21pm

Hotfoot wrote:Quick question: I'm assuming you actually want to slow down before reaching point B, correct? Otherwise you'll reach point B for all of a fraction of a second before leaving it in the dust, at least if we're talking realspace travel.

I already know that. This is only the acceleration phase towards the target. The other half of the trip will be spent deaccelerating at the same aproximate rate. For this caclulation its straight acceleration at the same constant rate for 7.4 billion KM. Thats all I need. I want to be able to input the hours and get the KM/S they are accelerating at.

Post by **AdmiralKanos** » 2003-01-30 07:25pm

Alyeska wrote:I know enough about math that I know I need an equation for this. I am trying to set up my acceleration figures for my own scifi government, but I am running into problems. I am basing the acceleration on how long it takes them to travel a specific distance while accelerating at the same rate the whole time.

So the fixed constant is 7.8 billion kilometers. The Variable is the number of hours. What I am looking for is the acceleration rate in Kilometers Per second. I know that the faster you go the more energy you have to put in, and the closer to light speed you get the harder it is to accelerate (or so I have been told), but I don't care about that. I just want pure acceleration numbers. I want to be able to input the hours on the trip and figure out what constant acceleration rate they had to do to make the trip of 7.8 billion KM.

If anyone can come up with this equation or can point me to where I can find this equation, I would greatly appreciate that.

You can use simple Newtonian equations unless the velocity ends up being a very large fraction of c.

Therefore, distance x=1/2*a*t^2. Therefore, a=2x/t^2.

For example, if they can cover 7.8 billion km in 12 hours, a = 2(7.8E12)/(12*3600)^2 = 8359 m/s^2.

Alyeska · Post by **Alyeska** » 2003-01-30 07:29pm

AdmiralKanos wrote:
Alyeska wrote:I know enough about math that I know I need an equation for this. I am trying to set up my acceleration figures for my own scifi government, but I am running into problems. I am basing the acceleration on how long it takes them to travel a specific distance while accelerating at the same rate the whole time.

So the fixed constant is 7.8 billion kilometers. The Variable is the number of hours. What I am looking for is the acceleration rate in Kilometers Per second. I know that the faster you go the more energy you have to put in, and the closer to light speed you get the harder it is to accelerate (or so I have been told), but I don't care about that. I just want pure acceleration numbers. I want to be able to input the hours on the trip and figure out what constant acceleration rate they had to do to make the trip of 7.8 billion KM.

If anyone can come up with this equation or can point me to where I can find this equation, I would greatly appreciate that.
You can use simple Newtonian equations unless the velocity ends up being a very large fraction of c.

Therefore, distance x=1/2*a*t^2. Therefore, a=2x/t^2.

For example, if they can cover 7.8 billion km in 12 hours, a = 2(7.8E12)/(12*3600)^2 = 8359 m/s^2.

Many thanks. And yes, our ships do get into the high fractions of C, but they are improbability drives so that takes care of it being impossible.

Hotfoot · Post by **Hotfoot** » 2003-01-30 07:30pm

Alyeska wrote:
Hotfoot wrote:Quick question: I'm assuming you actually want to slow down before reaching point B, correct? Otherwise you'll reach point B for all of a fraction of a second before leaving it in the dust, at least if we're talking realspace travel.
I already know that. This is only the acceleration phase towards the target. The other half of the trip will be spent deaccelerating at the same aproximate rate. For this caclulation its straight acceleration at the same constant rate for 7.4 billion KM. Thats all I need. I want to be able to input the hours and get the KM/S they are accelerating at.

Okay, just making sure so that I didn't try doing it at 3.7 or 14.8 or something.

b = travel time (in seconds)
a = acceleration rate (m/s/s)
v = starting relative velocity (m/s) (in this case, zero, so we can ignore it)
D = distance to desired destination

D = v * b + (1/2a * (b*b))

7,400,000,000,000 = v * b + (1/2a * (b*b))
7,400,000,000,000 = 1/2a * (b*b)
7,400,000,000,000 / (b*b) = 1/2a
2 * (7,400,000,000,000 / (b*b)) = a

That should get you what you're looking for, off the top of my head, though I have a nagging feeling it should 7,400,000,000,000/(b/b) for some reason.

Hotfoot · Post by **Hotfoot** » 2003-01-30 07:32pm

I should document my code better. Forgot that I had b*b in there as a kludge for b^2, and that's what confused me. D'oh.

Hotfoot · Post by **Hotfoot** » 2003-01-30 07:32pm

Alyeska wrote:Many thanks. And yes, our ships do get into the high fractions of C, but they are improbability drives so that takes care of it being impossible.

Taking a few pages from E.E. "Doc" Smith, are we?

Alyeska · Post by **Alyeska** » 2003-01-30 07:36pm

I think you have your equation set up for 7.4 trillion. A billion has 9 zeros.

Post by **AdmiralKanos** » 2003-01-30 07:37pm

Alyeska wrote:I think you have your equation set up for 7.4 trillion. A billion has 9 zeros.

A kilometre adds 3 extra zeroes.

Alyeska · Post by **Alyeska** » 2003-01-30 07:40pm

AdmiralKanos wrote:
Alyeska wrote:I think you have your equation set up for 7.4 trillion. A billion has 9 zeros.
A kilometre adds 3 extra zeroes.

Ah. Ok. Let me run these equations just to check for myself and make sure I'm doing them properly.

(whips out old TI-82) This is gonna take me a while.

Hotfoot · Post by **Hotfoot** » 2003-01-30 07:41pm

Alyeska wrote:I think you have your equation set up for 7.4 trillion. A billion has 9 zeros.

*looks at the calcs again* Point. I need more caffiene...

No, wait, that's right, I was converting to m/s, not km/s. Okay, now I really need more caffiene.

Same end result though. If you'd like, I could make you a small spreadsheet which calculates that for you, using whatever values you'd like.

Alyeska · Post by **Alyeska** » 2003-01-30 07:44pm

Damn I love this old calculator. Anyway using both equations I get an acceleration of 161.8445732 km per second.

Thank you very much, this has helped out greatly.

Alyeska · Post by **Alyeska** » 2003-01-30 07:46pm

Hotfoot wrote:If you'd like, I could make you a small spreadsheet which calculates that for you, using whatever values you'd like.

Nah, I already know how to program the stuff into my calculator. Thanks anyway. The equation works perfectly.

Hotfoot · Post by **Hotfoot** » 2003-01-30 07:47pm

Alyeska wrote:Damn I love this old calculator. Anyway using both equations I get an acceleration of 161.8445732 km per second.

Thank you very much, this has helped out greatly.

Heh, same one that I carry around, coincidentally, though it's being phased out by my new Palm, as is the electronic dictionary/thesaurus I usually carry around.

You're welcome, and my offer for the spreadsheet still stands, if you're interested.

Hotfoot · Post by **Hotfoot** » 2003-01-30 07:48pm

Alyeska wrote:
Hotfoot wrote:If you'd like, I could make you a small spreadsheet which calculates that for you, using whatever values you'd like.
Nah, I already know how to program the stuff into my calculator. Thanks anyway. The equation works perfectly.

Hah, gotta love simul-posting.

Sure thing then.

The Dark · Post by **The Dark** » 2003-01-30 09:43pm

I have a Casio CFX-9850G programmed to figure accelerations in percentages of c, in g's of acceleration, the time necessary based on acceleration and distance (either one-way or zero-zero intercept), and a couple for DP9 games to create weapon systems easier than by hand. It's got a very simple form of BASIC (IIRC), and even a relative non-tech guy like me can program the darn thing.

StarDestroyer.Net BBS

Acceleration caclulation request

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