Formulae in simple english?

[Rasori]

I'm looking for the following things, for what COULD be considered a school project but truly isn't. Let's say I'm trying to disprove something that I thought up myself that seems too simple to work.

 

Okay, I need the following, simplified down to something that I can hopefully understand. None of this scientific stuff without an explanation, I'm simple-minded sometimes. (*s denote important parts)

 

1. One pound of thrust can hold something weighing one pound suspended in air if I understand correctly (the equivalent of 9.8m/s/s I think). *If a jet engine were providing one pound of thrust, how fast is the air coming out of it?* (*s denote important parts)

 

2. Space has very little friction (I'm restraining from saying none). *If a propellent is shot out of a spacecraft at 20mph (kmph, your choice, hopefully in the same units as above though), then how fast does the craft move in the other direction?*

 

3. 0.1234 LB/FT³@32°F I have no clue what that means, but it's the density of CO2 I believe. Correct me if I'm wrong and use the correct number in the following question. *If a spacecraft is shooting a propellant with the density 0.1234 LB/FT³@32°F at a constant rate of 0.1921296 cubic feet per second, how fast is it theoretically capable of going?* The spacecraft in question would be APPROXIMATELY 77111 kg. Sorry about switching between metric and US Customary, I'm just using the numbers as I receive them.

 

 

I believe that's all for now. And if there's any sort of theoretical improbabilities (what I like to call 'mistakes' ) then point them out.

[VendingMenace]

If a spacecraft is shooting a propellant with the density 0.1234 LB/FT³@32°F at a constant rate of 0.1921296 cubic feet per second, how fast is it theoretically capable of going

 

you are missing one piece of information for this calculation to be made. Specifically, you would need to know how long the "jets" are being fired for.

 

If you mean how fast will the spacecraft go if you let the jets fire forever, then it will approach the speed of light (and it will attain the speed of light after an infinite amount of time).

[Rasori]

Well that's true with any propellant in space if you fire it constantly and forever. Good point.

 

I suppose I meant more like is there a formula of some sort as to how long it takes to get up to a certain speed with that propellant, etc, etc.

 

Like, how long would it take a craft shooting a propellant with the density 0.1234 LB/FT³@32°F at a constant rate of 0.1921296 cubic feet per second to reach 100 m(km)ph, 500, 1000, and so on.

[Rasori]

So THAT'S where the edit button is! I am very :lame:

[swansont]

The formula you want is F=dP/dt, which i the source of the well-known F=ma, or force is mass X acceleration. But that assumes constant mass (so dP/dt =m(dv/dt), or ma), and isn't useful in this case.

 

Rearrange it and you get

F= v (dm/dt), where dm/dt is the rate at which mass is ejected and v is the speed, which is assumed constant.

[Rasori]

Well, in the case I'm thinking of, constant mass is approximately correct, as the fuel would be created on the craft about once a day. So yes, the mass would drop, but then it would increase.

[Sayonara]

What is the fuel created from?

 

Unless matter is converted to energy or vice versa, the only change in mass should be due to propellants or wastes ejected from your craft.

[wolfson]

Rasori just one thing try and keep all the figures in 3 or 4 sf (significant figures), instead of 4, 5 and 6 figures, it works much better!!!

[YT2095]

"1. One pound of thrust can hold something weighing one pound suspended in air if I understand correctly (the equivalent of 9.8m/s/s I think). *If a jet engine were providing one pound of thrust, how fast is the air coming out of it?* (*s denote important parts)"

 

"fast" as you say it is not the issue, it`s in liters per second.

the VOLUME of air being moved over time is key here

----------------------------------------------------------------

"2. Space has very little friction (I'm restraining from saying none). *If a propellent is shot out of a spacecraft at 20mph (kmph, your choice, hopefully in the same units as above though), then how fast does the craft move in the other direction?*"

 

what MASS is "shot out at 20 mph"? I`m sure a little grain of sand ejected from the craft at 20mph wouldn`t make it move as much as ejecting a car at the same speed

------------------------------------------------------------------

3. 0.1234 LB/FT³@32°F I have no clue what that means, but it's the density of CO2 I believe. Correct me if I'm wrong and use the correct number in the following question. *If a spacecraft is shooting a propellant with the density 0.1234 LB/FT³@32°F at a constant rate of 0.1921296 cubic feet per second, how fast is it theoretically capable of going?* The spacecraft in question would be APPROXIMATELY 77111 kg. Sorry about switching between metric and US Customary, I'm just using the numbers as I receive them.

 

please try to keep it conscise and as accurate as possible (someone may go off and do this work for you only to find out that YOU made a mistake!) sorry, but that question doesn`t warrant an answer just yet.

------------------------------------------------------------------

we need more REAL facts before ANY of us is likely to go off and do some calculations for you

[Rasori]

Wee that's what I'm looking for- corrections!

 

It's in liters per second... I understand the point of the whole volume thing there. So then, how many lps equals one pound of thrust?

 

And for two then, it's more like if the density of gases being shot out is 0.1234 LB/FT³@32°F (if it's needed, the temperature of the gas is -109.3°F or -78.5°C) and the combined total is 65,000 lbs of thrust, how fast is it going?

 

And three I believe was solved via "F= v (dm/dt), where dm/dt is the rate at which mass is ejected and v is the speed, which is assumed constant."

 

As for the fuel, my mistake. The fuel is made with things already on the ship, such the mass does decrease. I just need to find out exactly how much.

 

See how unexact I am? And this isn't the worst I've done.

 

Okay, the facts I have now:

Density of propellant: 0.1234 LB/FT³@32°F (I believe 55.973298 g/m³, check it if you can)

Temperature of propellant: Can be controlled most likely, but the easiest assumption is -109.3°F or -78.5°C.

Thrust: 65,000 lbs (if my conversion is right, 29,483.50405 kg)

Mass: 172,000.655049 lbs or 78018.18476 kg

 

Tell me if you need any more, I'll try to find it.

[Rasori]

What, no help? You were helpful before .

[Rasori]

Still nothing? Just tell me if you don't know so I can search for it elsewhere. Just thought this was easier, getting just the information I need.

[YT2095]

lol, soz, I`ve been busy, and it`s been hollidays, don`t take my silence as refusal to help

[Radical Edward]

is it a requirement to keep switching randomly between imperial and metric?

 

anyways. all you do is work out the momentum imparted on the propellant. so say 1000kg is accelerated to 1m/s, then p=1000kgm/s this will equal the momentum of your rocket. say the rocket is 10,000 kg, then it will be accelerated to 0.1m/s.

[Rasori]

Ooh, now that's fast paced there. 0.1 m/s.

But the equation itself is useful.

 

And I didn't take the silence as not being willing to help (I know you people too well already ) but since I'd bumped the thread once I was a little worried. Besides, I needed something to do to pass the time during Study Hall!

[Rasori]

Hmm...

 

I suppose I never asked this straight out, so here goes-

 

65,000 pounds of thrust is being provided in this case, so:

 

1. How many liters per second are being moved with this amount of thrust?

 

2. (Tell me if I didn't realize this was already answered) How can I calculate the approximate acceleration of a vehicle in space assuming enough volume could be created for 65,000 pounds of thrust?

[YT2095]

1.it depends on the fuel used and the ratio s of burn rate, gasses evolved in litres per sec, THEN you factor in the overall weight to fuel ratio.

let me give you an example; BBQ Charcoal is a VERY GOOD fuel, and it will liberate many litres of of CO2 per kilo used, however it would be totaly useless as a rocket fuel due to it`s burn rate, even though the gasses evolved per second are quite good!

 

2. that`s an unanswerable question, how heavy is the craft is the 1`st question that springs to mind (inertia plays a part here).

how long is the burn for for? what is the drop-off weight for the fuel used per second? (it wont be a linear curve, more exponential, due to drop-off weight and inrtia etc...)

 

these are just just the bare bones of the factors needed to be considered, long before going into any sort of depth

[YT2095]

1.it depends on the fuel used and the ratio s of burn rate, gasses evolved in litres per sec, THEN you factor in the overall weight to fuel ratio.

let me give you an example; BBQ Charcoal is a VERY GOOD fuel, and it will liberate many litres of of CO2 per kilo used, however it would be totaly useless as a rocket fuel due to it`s burn rate, even though the gasses evolved per second are quite good!

 

2. that`s an unanswerable question, how heavy is the craft is the 1`st question that springs to mind (inertia plays a part here).

how long is the burn for for? what is the drop-off weight for the fuel used per second? (it wont be a linear curve, more exponential, due to drop-off weight and inertia etc...)

 

these are just just the bare bones of the factors needed to be considered, long before going into any sort of depth