# The Naked Scientists Forum

### Author Topic: What velocity would be achieved with 1/10G applied for one hour.  (Read 4181 times)

#### litespeed

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##### What velocity would be achieved with 1/10G applied for one hour.
« on: 16/11/2009 14:57:23 »
I am brainstorming interstellar exploration and believe normal ion type engine could push a probe into the relativistic velocities.  For instance, at 86 percent the speed of light, it seems that mass dialation would be no more then 100 perchent, which means the acceleration might only be effectively reduced by half.

#### Vern

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##### What velocity would be achieved with 1/10G applied for one hour.
« Reply #1 on: 16/11/2009 21:09:04 »
It would be nice to accelerate at one G. Then accelerate half way to destination then decelerate the other half.

It may be completely unreachable, but what if all the loose atoms and ions could be gathered in from frontward and released as pure energy for propulsion?

Maybe a good angle for SF.

#### Geezer

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##### What velocity would be achieved with 1/10G applied for one hour.
« Reply #2 on: 17/11/2009 00:27:47 »
It would be nice to accelerate at one G. Then accelerate half way to destination then decelerate the other half.

It may be completely unreachable, but what if all the loose atoms and ions could be gathered in from frontward and released as pure energy for propulsion?

Maybe a good angle for SF.

It would certainly avoid the problems associated with being weightless. The sanitation arrangements could be just like on Earth. No need to make artificial gravity by spinning the thing around. The only tricky bit would be during the transition from positive to negative acceleration.

#### wolfekeeper

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##### What velocity would be achieved with 1/10G applied for one hour.
« Reply #3 on: 17/11/2009 01:53:05 »
It would be nice to accelerate at one G. Then accelerate half way to destination then decelerate the other half.

It may be completely unreachable, but what if all the loose atoms and ions could be gathered in from frontward and released as pure energy for propulsion?

Maybe a good angle for SF.
I worked out a few ways to do this for travelling around the Earth; actually faster I pegged it at 3g; because nearly everyone can take that g-force.

For example vacuum tube maglev trains can do this, you could accelerate at 3g down the tube, and go from London To New York in about 45 minutes. One of the limits is the curvature of the Earth; if you go too fast, you end up standing on the ceiling(!)

But for travelling to Mars, it's difficult to get enough power to put through your engine to do this; with normal power sources ion drives give you disappointing milli-gee accelerations, and normal rockets can only burn for up to about 20 minutes at 1g.

#### litespeed

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##### What velocity would be achieved with 1/10G applied for one hour.
« Reply #4 on: 19/11/2009 17:38:54 »
Pardom my abominable math skills. But I assume the speed of 2.2 miles per second may simpy be multiplied by 10 for 22 miles per second after ten hours? I get about 19,000 mps after one year.

One G is ten times that = 190,000 mps, if you set aside mass dialation. We established earlier that time dialation of 50% would only require 86% the speed of light. Assuming starship with nuclear reactor, I just wonder how much mass would be need to be carried on board to push out the back!

Theoretically, if you are generating 1G by squirting mass out the back of your ship, then your mass will decrease as you speed up, perhaps offsetting mass dialation?  At 86% speed of light the starship travelor is aging one half the speed as those who sent him on his way. In effect, he observes himself traveling FASTER then the speed of light.

Setting asside one year of acceleration, the travelor would traverse about eight light years distance from us in ten years of travel, but experience only five years of aging.

« Last Edit: 19/11/2009 17:41:20 by litespeed »

#### Geezer

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##### What velocity would be achieved with 1/10G applied for one hour.
« Reply #5 on: 19/11/2009 18:45:13 »
Pardom my abominable math skills. But I assume the speed of 2.2 miles per second may simpy be multiplied by 10 for 22 miles per second after ten hours? I get about 19,000 mps after one year.

One G is ten times that = 190,000 mps, if you set aside mass dialation. We established earlier that time dialation of 50% would only require 86% the speed of light. Assuming starship with nuclear reactor, I just wonder how much mass would be need to be carried on board to push out the back!

Theoretically, if you are generating 1G by squirting mass out the back of your ship, then your mass will decrease as you speed up, perhaps offsetting mass dialation?  At 86% speed of light the starship travelor is aging one half the speed as those who sent him on his way. In effect, he observes himself traveling FASTER then the speed of light.

Setting asside one year of acceleration, the travelor would traverse about eight light years distance from us in ten years of travel, but experience only five years of aging.

Here's "Geezer's easy math" version. (Geezer can only do easy math!)

G/10 = 3.2 ft/sec/sec = 2.2 MPH per second (3.2*3600/5280=2.2 approximately!) In other words, the speed increases by 2.2 MPH every second.

2.2 MPH per second means it will accelerate to 69.3 Million MPH in one year (2.2 multiplied by the number of seconds in a year)

69.3 Million MPH is around 19,250 miles per second

In SI units:

G/10 = 0,98 m/s/s (Let's call it 1,0)

In one year, velocity = 1*3600*24*365 m/s
= 1*3,6*24*365 km/s
= 31.536 km/s

Note the "." is a thousands separator rather than a decimal point, so the SI answer seems to agree with the Imperial answer.

Accelerations are typically expressed in distance/(time)squared

e.g feet per second squared, meters per second squared etc.

This is because acceleration is the rate at which speed changes. As speed is itself a rate, 32 ft/second every second is the same as 32 ft/sec/sec

This can be expressed as 32 ft/sec x 1/sec, or 32 ft/sec^2 (32 ft/second squared)

Now, consider that you are trying to understand this and someone says "The acceleration is 32 feet per second squared". To most people, that will mean almost (pardon my language) bugger all. It's mathematically quite correct and very clever, but it does not help to convey the concept at all. In other words, it's techno babble. A form of code speak that helps to divide the "insiders" from the "outsiders".

Now, if you say something like "Every second, the speed of the body increases by 3 kilometres per hour" a lot more people will immediately be able to determine the speed of the body after one hour, or after just about any amount of time come to that.

"So what Geezer?" you might say. Well, if we want more people to get interested in science, we should de-obfuscate it as much as possible. I'm not suggesting we try to over simplify, but let's not get carried away with the brilliance of our analysis. If we do, we will probably lose the attention of a lot of people along the way.

« Last Edit: 20/11/2009 07:24:05 by Geezer »

#### LeeE

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##### What velocity would be achieved with 1/10G applied for one hour.
« Reply #6 on: 20/11/2009 21:59:36 »
DiscoverDave's solution is correct for acceleration over a period of one hour.

However, the question as posed does not take into account the fact that for a constant thrust, the rate of acceleration will increase as the mass of fuel (which also needs to be accelerated) is used.

Ultimately, the answer to the question comes down to Newton's equal and opposite forces and the only relevant factor is how fast the fuel mass is expelled.

As long as the same fuel mass is expelled at the same speed you'll end up at the same final speed, regardless of whether you expel a little fuel over along period, or lots of fuel over a short period.

#### Geezer

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##### What velocity would be achieved with 1/10G applied for one hour.
« Reply #7 on: 21/11/2009 00:45:03 »
Also, Lightspeed's calculation was quite correct for a period of one year, but that was not the question asked. Come to that, the question was clear that the acceleration was constant, regardless of mass.

#### LeeE

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##### What velocity would be achieved with 1/10G applied for one hour.
« Reply #8 on: 21/11/2009 17:13:35 »
As we're really talking about ion thrust reaction motors, constant acceleration doesn't make sense as you'd have to reduce thrust as you use the fuel; the only purpose of this would be to increase the journey time.

#### Geezer

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##### What velocity would be achieved with 1/10G applied for one hour.
« Reply #9 on: 21/11/2009 17:25:08 »
Well, if you want to be so practical about it, that's true!

#### wolfekeeper

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##### What velocity would be achieved with 1/10G applied for one hour.
« Reply #10 on: 25/11/2009 02:18:37 »
You can normally adjust the engine to give less thrust (i.e. throttle it back) as you use up the fuel. Rockets do that all the time, and I'm pretty sure ion drives can as well.

Actually an ordinary 2-stage rocket could give this much thrust for 2.5 hours, with only minor modifications, or one stage about half that.
« Last Edit: 25/11/2009 02:20:28 by wolfekeeper »

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##### What velocity would be achieved with 1/10G applied for one hour.
« Reply #10 on: 25/11/2009 02:18:37 »