Will this propeller arrangement have a net force in one direction?

[leviterande]

Hi, I am very sorry if I have posted in the wrong forum, I don't know wether to post in classical physics or aerospace engineering. I have been wondering this theoretical thing a lot lately and I can't figure it out, it should have a simple straight answer though so your help is very appreciated. Its not anything practical of course, or to be built or efficient of course, it is just a theoretical question I have.

A rigid wide t-bar out of plastic/wood etc is made. On it sit 6 individual PERFECTLY identical propellers/pumps with perfectly identical thrusts. The propellers´/pumps´ diameters are smaller than the width of the wood plate that the propellers are sitting on.

Simply, will the propeller/suction pump arrangement have a net force towards one direction as in the picture? or would there be no movement/force at all. (considering ofcourse that in theory each individual propeller/pump give the exact same thrust as the other). The medium is air but also could be water. The air/water motion direction imparted from the propellers are the blue arrows.

The two arrangements are seen in the picture.

Thanks
/Regards

 

[Simon Bridge]

For each configuration, ask how the air flows about the entire structure.
i.e. the air comes from someplace before it interacts with the propellers, and it has to go someplace after it has interacted.

 

[leviterande]

For each configuration, ask how the air flows about the entire structure.
i.e. the air comes from someplace before it interacts with the propellers, and it has to go someplace after it has interacted.

Hi, thanks hmmm, let's see, the board is wider then the diameter so for the "pusher propeller configuration, the incoming air is coming radially from the sides of each propeller. For the pump arrangement the air is pushed out radially.. or this is at least how I think it is going to be? I am trying to see though how the entire airflow is in the entire structure..

 

[Simon Bridge]

Sketch the streamlines in for the incoming and outgoing air ... i.e. in the pusher configuration, you have two pairs of props pushing air into the same volume - where does it go? Does it just stop there and build up?

It may help you to think in terms of changes of momentum rather than directly as forces.

 

[leviterande]

Sketch the streamlines in for the incoming and outgoing air ... i.e. in the pusher configuration, you have two pairs of props pushing air into the same volume - where does it go? Does it just stop there and build up?

It may help you to think in terms of changes of momentum rather than directly as forces.

In the pusher arrangement: The two pushing propellers on top that are perpendicular to each other that are pushing into the same volume result in greater pressure and build up on the top of the board than on the bottom, and thus, the air mass on top of the board that is pushed away by the (two perpendicular props), is greater than the air mass pushed by the bottom propeller. Therefore the whole pusher configuration will move downwards? That is how I can understand this so far but I am not sure. What I just wrote was one view of how it can look in reality but then again I am not really sure as the whole situation could be the complete opposite ?

Thanks

 

[Simon Bridge]

That's pretty much how I was looking at it.
There is a wrinkle that air flows into each prop at the same rate as it leaves (about) ... but he arrangement changes the directions - and the actual design is 3D - there will be other effects (drag, wobble, interference between the fans, turbulence etc) - but the simplistic analysis does lead us to expect the arrows drawn on the diagrams should work.

Where is this from?

May be interesting to test it out - maybe with PC fans?

 

[leviterande]

That's pretty much how I was looking at it.
There is a wrinkle that air flows into each prop at the same rate as it leaves (about) ... but he arrangement changes the directions - and the actual design is 3D - there will be other effects (drag, wobble, interference between the fans, turbulence etc) - but the simplistic analysis does lead us to expect the arrows drawn on the diagrams should work.

Where is this from?

May be interesting to test it out - maybe with PC fans?

Hi thanks, yeah some fans for the pusher arrangement and some centrifugal fans or sucking fans for the sucking arrangement would give a definite answer but you know , it takes some real time and effort just to know this little thing hehe(considering all the involved wires too..) but I have got some model motors and propellers so maybe...although they are only few ..

One more thing however.. looking back at the resultant net force shown by the arrows , the force directions could actually even be the complete opposite and/or therefore Null ? Why? Perhaps, because instead of the pressure buildup at the top between the perpendicular propellers.. thispressure could be actually less or equal to the pressure on the bottom... the reason being is(I think) that the high standing propeller on the middle standing plastic column is moving the pushed air sideways (and doesn't contribute to any vertical buildup) and thus in fact decreases the total net pushed air on the top of platform. So yeah, while clearly the actual pushed air by the 2 perpendicular propellers are greater than the pushed air on the bottom, the greater pushed air on top is not vertical but ANGLED 45 degrees.. all this should make ZERO NET FORCE? Am I a far too off in my thinking here Simon? I tried vectors sum program and it shows of course zero force but the Vectors Sum addition assumes its all about rockets. Which is not the case here where we are dealing with a fluid medium , air, water...

oh BTW I just made the quick drawings in paint, a pic. sais 1000 words. I tend to love to fill all the holes I have in my brain.. things that may look obvious may not be but that's all because of too much thinking maybe..

Thanks

 

[Simon Bridge]

I noticed that I could argue either way too ... the simplistic model is to give each prop one arrow to indicate the air shifted and use laminar flow.

The upper airflow should be diagonal indeed.
The speeds should be unchanged (laminar).
Look at the conservation of momentum.

But you could treat it as high pressure being created above due to the crossed airflows - while the smooth airflows below is a low pressure. So you go down. Reverse it for the pulling props.

If this came as part of a course - you should put it in context of the immediately preceeding lessons.
I imagine the real-life result of building one would get you odd results anyway.

 

[leviterande]

If it was part of a course it would be a lot easier. maybe I could later run a simulation in in simulators like xplane ...

 

[Simon Bridge]

That may be interesting ... though a lot will depend on how such simulators are modelling the props.
What you actually have to do is build one - try using computer cooling fans. You can suspend the rig from a cord looped over a good pulley so weight is not a factor.

I notice the rigs are supposed to work as well in water - which is not compressible - so thinking in terms of rate and direction of flow should get you there.

In the pusher configuration - each pair of props can be replaced by a box that takes fluid in around the sides and pushes it out at the same rate from the faces.
The flows that point into the same space result in a net diagonal flow of both lots of mass.

A quick sketch on my window shows me to expect the net force to be downwards if the inflow is equal all around the sides of each box. (i.e. net momentum from inflowing fluid is zero.)
[You get 3 forces, on up, two at 45deg down (one left, one right).
Net force up is F-2F/√2 = (1-√2)F and we notice that √2 > 1 so the net force is downwards.]

If, however, inflow from the direction towards the intersection of the T-frame is less, then it is possible to get a net upwards thrust.
Is this making sense?

 

[leviterande]

That is what I feared, two alternatives that could eliminate each other .. Nothing would beat a test in the best simulator there is though: real world.

One more thing you reminded me to add, as you said water is incompressible so this will make things little different. For instance, the "directions" of the "relative rotations" of the water propellers will have to be considered since there will be compressions or rarefactions locally depending on the relative rotations in the local areas between propellers. It seems I must run several tests when I have time hopefully. In air that is highly compressed the propeller rotation direction make almost zero difference, it simply is insignificant which way the propeller rotates. what matters in air is the net moved air perpendicular to the propeller disc.

For instance In water if we say two "sucking "propellers are facing each and rotating in the same direction there will as we know be relative "rarefaction" locally between them and thus the propellers will move towards each other. However if these two same sucking propellers were counter rotating there will be more mass of water moved and piled up between the propeller discs which results in that the two propellers will move away from each other.. yea it is certainly a lot of variables indeed

 

[Simon Bridge]

Remember that the pars of props are fixed by a rigid frame. I just stuck the whole thing in a box :)
Sometimes examples like this are used to get engineering students to realize how simplistic their intuitive models are.

 

[leviterande]

Remember that the pars of props are fixed by a rigid frame. I just stuck the whole thing in a box :)
Sometimes examples like this are used to get engineering students to realize how simplistic their intuitive models are.

Simon, hmm I am not sure if I got what you meant here:). Do you mean the whole frame wouldn't wouldn't see any difference when rotation direction changes between facing pairs in an incompressible medium.. Ýes, the pairs are fixed. But in incompressible medium the direction rotation should affect which way the whole frame is going to move up or down that is. When for example a pair of counter rotating propellers is creating a higher volume of water or water pressure or compression between them there will be a higher compression or mass flow of water nearby as well at 45 degrees (all this considering if there would be any net movement at all ofcourse ) ..

now there is a huge risk of me misinterpreting you and you misinterpreting me maybe :)

 

[Simon Bridge]

No - I'm just saying that any tendency for a pair of props to move together or apart is oposed by the frame holding them at fixed distances.