How much force can a speaker and one-way valve system produce?

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McKay

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How much force can a speaker and one-way valve system produce?
« on: 09/11/2015 16:24:06 »
Greetings, naked scientists. I am wondering about alternatives to propellers for thrust production. What I have in mind is this:
The inspiration being a speaker cone, I get a square plate full with one-way valves (say, thin stripes covering the length of the square, all right next to each other. Or something.) and hook it up to a system that, similar to a speaker cone, vibrates it/ moves it back and forward. Now, if the valves open and close fast enough, it will be pushing air in one direction, producing some thrust, wouldnt it?

How much thrust could it make? Lets say, 1m^2 at 20Hz with the amplitude (that is, the total distance traveled by the plate in one sweep) of 2 cm? The air moved in one sweep would be 0.02m^3 and the mass of air would be 25.5 grams, according to WolframAlpha.

What would be the optimal frequency and amplitude before the plate or the valves just couldnt move that fast? And how much thrust would that give?

I did some simple calculations on my own, but I am not sure if they are correct:
I assumed the final air velocity would be the speed at which the plate moves, which is, in case of 20Hz and 2cm amplitude, 20*2=40 cm per second. Or is it twice as fast since it moves 20 times in one direction and 20 times back making it 40*2? I am not quite sure, but I want to know.
If the air is exiting the device 0.4m/s and it took just 1/20 (or is it 1/40) of a second to accelerate it to that speed, then the acceleration would be 8m/s/s (assuming the lower estimates).
Knowing acceleration and mass of the air pushed we get 8*0.0255=0.204 Newtons (or 204 grams?). But since its pushing only half of the time the total force decreases to 0.102 Newtons (?)

Not particularly much, using the lover estimates, it might be 2 or even 4 times as much as this, depending to answers to the questions above. But what if it revs up to 100Hz? Would the force be 5 times as much? 10 times as much? How much could the amplitude be increased? 4 cm?
« Last Edit: 10/11/2015 08:51:28 by chris »

chiralSPO

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Re: How much force can speaker + one-way valve system like this produce?
« Reply #1 on: 09/11/2015 17:00:40 »
There is no air in space, so the speakers will have nothing to push against. If you bring air along with you to be pushed out by the speaker, the thrust generated by releasing the air out to space will dwarf any contributions from the speaker.

One rough way of calculating the thrust you might be able to generate with this system is to look at the wattage of the speaker--this will set an upper limit on the available power. If you blasted a 600 Watt speaker for 100 seconds, and all of that energy was converted into motion of a 500 kg spaceship that was initially at a standstill, the final velocity would be about 15 m/s (34 mph). This is not particularly fast in space terms, and the speed would only increase as the square root of the time the speaker is on v = $$\sqrt{2*wattage*time/mass}$$

This is also likely a huge overestimate of the efficiency of a speaker as an engine (probably an order of magnitude or so, if you're lucky), and ignores the mass of the propellant (rocket equation).

McKay

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Re: How much force can speaker + one-way valve system like this produce?
« Reply #2 on: 09/11/2015 19:06:31 »
I am not talking about spacecraft. Why did you think I was? Inner atmosphere thrust is what I am talking about. Alternative to propellers, as i wrote.

chiralSPO

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Re: How much force can speaker + one-way valve system like this produce?
« Reply #3 on: 09/11/2015 19:25:34 »
Sorry, my mistake. I read "thrust" and immediately thought of spacecraft. I still don't think that a speaker-type driver would be more effective than a propeller, mostly because the diaphragm has to move back and forth, essentially starting and stopping repeatedly, while the propeller just does one unidirectional motion.

McKay

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Re: How much force can speaker + one-way valve system like this produce?
« Reply #4 on: 09/11/2015 19:34:47 »
Well, yes, but the propeller also has a very small surface area (and a square has even more than a circle)

evan_au

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Re: How much force can speaker + one-way valve system like this produce?
« Reply #5 on: 09/11/2015 20:14:02 »
If you pushed against a denser medium (like water), you would get more thrust - but it would take a lot more power to move the plate by the same displacement. And moving through a denser medium requires higher force (for the same frontal area).

Speaking of frontal area, the area of a 1m2 square plate is 1 m2 (or less when the valves are open). Passing water through thin pipes instead of a free-flowing mass causes frictional losses. The shape causes a lot of turbulence, which causes a additional loss of power.

However, a propeller on a boat or aeroplane presents a much thinner profile to the oncoming medium (water or air), gently diverting its path, and creating a moderate amount of turbulence.

The old paddle-wheel steamers effectively pushed a 1m2 square plate through the water in a single direction, with a stroke of several meters, before returning via the air. In an historic contest, there was a tug-of-war between a propeller ship and a paddle-wheel steamer; the propeller-heads won.

alancalverd

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Re: How much force can speaker + one-way valve system like this produce?
« Reply #6 on: 09/11/2015 23:39:05 »
Problem is that you waste a lot of power accelerating the plate and slowing it down again to repeat the cycle. Plus you need to consider what fraction of the plate would be "open" and how much would need to be rigid structure to support the valves. The V1 pulse jet used a "venetian blind" valve that offered about 50% open area at cruise speed and you'd find it difficult to construct anything like a square meter with more than 50% opening.

If you "unwind" a propellor locus you will see that it is actually a continuous form of what you have designed, with up to 90% open area, 100% duty cycle (your plate only produces thrust on the "push" stroke, not the "pull"), less microturbulence losses,  and no loss of energy in starting and stopping the moving mass. And a rotating machine is a lot quieter and more comfortable for the passengers than an oscillating one, which is why we prefer jets and turbines to big piston engines.

The V1 engine certainly worked but it was designed to be light, cheap and simple, not efficient. Modern drones use Wankel engines driving propellors, or small jets.
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