Compressed Air Reverse Thruster

[timmyJACK]

Hello everyone,

I'm attempting to determine the impulse that can be generated by expelling compressed air from a pressure vessel stored aboard a moving craft through nozzles in the nose of the craft. The vessel has a forward momentum of roughly 2,000,000 Ns.

EDIT: For semantics sake, consider that the pressure vessel has an internal volume of ~100-200ft^3 and that the air contained within is of a pressure not to exceed 4000psi. The number of nozzles is variable but I would imagine no more than 10 (I have no actual justification for this number).

I'm trying to figure out how to optimize a reverse air thruster (think a combination of what happens when you shear the valve stem of a compressed air canister and the Reaction Control System which provides attitude control to the space shuttle) so that we consume the least amount of stored compressed air and provide maximum thrust in the opposite direction of the momentum, ideally to slow the craft to a near stop within roughly 10 seconds.

Forces acting on the craft include momentum in the negative x and negligible drag in the positive x direction. Forces in the Y direction negate each other.

Any help you can give in conceptualizing the problem would be appreciated! Thanks!

 

[OmCheeto]

Hello, jimmyMACK, and welcome to the forum.

I'm not trying to be mean, but this looks like a rocket science homework problem, with way too many wishy-washy variables.
You might want to parameterize the problem, and use the homework problem template.

Wishy-washy parameters:

forward momentum of roughly 2,000,000 Ns (aka kg m/s): try and pick a mass and velocity. It may, or may not, have a bearing on the problem.
pressure vessel has an internal volume of ~100-200ft^3: try and pick a volume. 150 ft^3 is good for me. (but, um..., see below*)
a pressure not to exceed 4000psi: is it safe to assume, that this is the initial pressure?
The number of nozzles is variable: 10 is a good number.​

Homework template:

Homework Statement

2. Homework Equations 3. The Attempt at a Solution [/B]

Showing just the slightest attempt at a solution will usually get you a much better response, than mine.*Also, I don't think people appreciate mixed units. You might try sticking with either SI or English.
I think you'd have the best luck with SI, as I can't remember the last time I saw a "slug" mentioned at the forum.

wiki, on impulse; "In English engineering units, they are slug·ft/s"

 

[timmyJACK]

Hey there, a couple things:

I'm an architecture student. This has nothing to do with my curriculum. I'm self teaching for a hypothetical problem. For the purposes of this, consider me a hobbyist - It has nothing to do with homework.

The parameters are 'wishy-washy', because the problem is theoretical with many unknown variables that need to be estimated. The units, sure, apologies for being born in America. Jimmy Carter should have forced us to switch to metric when he proposed it 40 years ago.

The weight of the object is 15000kg. Gravity is negated so the mass of the object is roughly 1530 kg. Revised momentum based on 1223 kph using p = mv is 520k Ns.

I'm attempting to see if compressed air or compressed steam could be utilized to reduce momentum of the object in a timely manner by directing the air or steam in a vector counter to the momentum force via nozzles.

I'm having a hard time formulating the calculations involved in figuring out the amount of force that can be imparted on an object using a nozzle in this manner, and I'm trying to get help with that. I know that my variables are the volume of the pressure vessel, the pressure of the air contained within, and the size and geometry of the nozzle, and how much air flow is allowed to pass from the vessel through the nozzle.

For my purposes, the volume of the pressure vessel, pressure of the air, and number of nozzles should be as few as possible to reduce momentum to 0 kph within 15 seconds. If we want to pick arbitrary numbers for plugging and chugging into a formula and letting me manipulate the variables as I like, let's say 4 nozzles, volume of 5m^3 for pressure vessel, air pressure at 14MPa.

I'm asking for help in laying all of that out and in fleshing out / understanding the problem in more detail.

Thanks, I really hope I can get a better response!

 

[JBA]

I would like to be more helpful but I am can tell you that this thought exercise is doomed from the beginning. There is a potentially erroneous corollary you may be making in your view of the problem. One is that a tank with a nozzle can somehow be related to rocket thrust; and there are two mismatches there. The first, is that rocket fuel stores much more power than you can create with tank pressure alone; and, the second is that the thrust delivered by a rocket has a sustained mass flow, where as, for stored gas discharged from a tank, even though the nozzle sonic discharge velocity will be maintained, the tank pressure and therefore mass flow and resisting force of your nozzle will immediately start declining as soon as the nozzle is activated.

I might suggest that you do a energy balance between your aircraft's kinetic energy plus, if applicable, the thrust of its running engine(s) vs the kinetic energy of the tank nozzle discharge; but, because, accurately calculating the gas thrust of a nozzle with a declining tank pressure against the static pressure of the velocity of the approaching air due to the aircraft's forward motion is going to require you to spend considerable time learning the theory of gases, gas dynamics and sonic nozzle flow.

 

[timmyJACK]

Have you ever seen what happens when the valve stem of a compressed air bottle is sheared off? My question boils down to what are the physics of that reaction? My hypothesis is that if I can replicate that effect (preferably with a nozzle and a valve rather than simply shearing the stem), and attach it to the craft with a thrust bearing, then I can harness the force it generates to create reverse thrust on the craft. This effect only needs to be used once, and for a duration of only a few seconds.

A couple things about the craft itself:

• It is only traveling forward on momentum from an initial impulse.
• There is no other form of motive power aboard the craft. It coasts for the duration of its transit.
• Gravity is not a factor.
• The pressure of the atmosphere that the craft is operating in is a near vacuum (100 Pa)

 

[cjl]

Cold gas thrusters are definitely a thing, and you could definitely make them work. The specific impulse tends to be rather bad though - for nitrogen, specific impulses in the 60-75 second range seem to be typical, and for helium, you could get up around 150-160 seconds (based on some quick back of the envelope math), at the cost of substantially increased tankage volume and lower thrust for the same nozzle size. To achieve a total impulse of 2MN*s, you'd need around 2900 kilograms of nitrogen at this efficiency level, or 1200 kilograms of helium, and because this number is so large, you'd probably have to increase the impulse requirement (since the craft's initial momentum would be larger due to the mass of propellant). Because of their low exhaust velocity (and associated low specific impulse), cold gas thrusters tend to be used when only a small amount of momentum change is required, and simplicity and fine control of the thruster matter more than efficiency.

 

[timmyJACK]

Cold gas thrusters are definitely a thing, and you could definitely make them work. The specific impulse tends to be rather bad though - for nitrogen, specific impulses in the 60-75 second range seem to be typical, and for helium, you could get up around 150-160 seconds (based on some quick back of the envelope math), at the cost of substantially increased tankage volume and lower thrust for the same nozzle size. To achieve a total impulse of 2MN*s, you'd need around 2900 kilograms of nitrogen at this efficiency level, or 1200 kilograms of helium, and because this number is so large, you'd probably have to increase the impulse requirement (since the craft's initial momentum would be larger due to the mass of propellant). Because of their low exhaust velocity (and associated low specific impulse), cold gas thrusters tend to be used when only a small amount of momentum change is required, and simplicity and fine control of the thruster matter more than efficiency.

Thank you! I'm glad you understood what I was saying - I was starting to think I was going crazy. I had figured it had a lot to do with specific impulse but I didn't know how to make the math work.

I was also off on the math for momentum - we're actually looking at more like 500kNs, which I think is a lot more reasonable.

Additionally, I'm only trying to reduce it to a safe speed so that we could deploy a mechanical wheel system and use friction brakes. Assuming this is ~160kph or 100mph, that lops off about another 70kNs bringing us down to 430kNs.

I appreciate that you brought up other gases as well. I specified air, but if I can make a compelling argument for another gas that would have more mass and thus more potential energy, I'm all for it so long as there's no combustion and the gas isn't harmful / corrosive. Thanks again for your help!

 

[JBA]

One advantage of using a denser gas is that, even though the gas payload weight will be greater, the maximum tank pressure and therefore the payload weight of the tank might be reduced.

 

[cjl]

Thank you! I'm glad you understood what I was saying - I was starting to think I was going crazy. I had figured it had a lot to do with specific impulse but I didn't know how to make the math work.

I was also off on the math for momentum - we're actually looking at more like 500kNs, which I think is a lot more reasonable.

Additionally, I'm only trying to reduce it to a safe speed so that we could deploy a mechanical wheel system and use friction brakes. Assuming this is ~160kph or 100mph, that lops off about another 70kNs bringing us down to 430kNs.

I appreciate that you brought up other gases as well. I specified air, but if I can make a compelling argument for another gas that would have more mass and thus more potential energy, I'm all for it so long as there's no combustion and the gas isn't harmful / corrosive. Thanks again for your help!

Why won't wheel brakes work for the full deceleration? The amount of brake mass needed to act as an energy sink will probably be much less than the amount of reaction mass needed to slow down appreciably, and it reduces complexity too. What is the application that this is for? Even at 430kN*s, you're looking at over 620 kilograms of compressed nitrogen, which at 4000 psi would take up about 81 cubic feet (2.3ish cubic meters). This is a huge amount of compressed gas, and there are substantial safety concerns with a tank this size as well. As I said, if you say what application this is for, we can likely recommend something to achieve your objective easily and safely.

 

[JBA]

What is your target or estimated touchdown velocity?