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Ducted fan theory and practice


Richard Sharman
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Dizz,

So am I. It was seeing Richard Sharmans efforts flying at Beaulieu a week or so ago that kicked me off again. I am building a slightly scaled down copy of the old BVM Maverick, originally about 62inches span for an OS or BVM 90, scaled down to 48 inches for a Wemotech 90mm MidiFan. I cut the foam wing and tailplane cores yonks ago and have now fitted the retract mounts and sheeted them with 1/16 balsa., fitted the ailerons, etc. I find wings and tails boring so I do them first.

The fuselage is as yet only a drawing of the side elevation and plan elevation, and the formers. The fan will sit roughly above the wing TE and has to have a hatch anyway for its fitting/removal, which in my case will be towards the front. So I have to remove a portion of the front ducting to get the fan out. Thus it will be easy to try it with smooth ducting ,no bellmouth, and the spinner or a 'plenum chamber' (the bare fuselage structure, near enough, a bellmoth, and with/without the spinner. The rear duct will be 90mm dia all though, but I will be able to slide a tapered one inside to see if it is better. At the front, the intake size is 110 percent of the the full fan area so there will be plenty of air for the plenum chamber and bellmouth. I can always reduce the intake area should it be beneficial.

My slightly smaller RBC all balsa Panther weighs 6.5 lbs and flies quite well on a fan measured at 5.5 lbs thrust on a test rig.

The new motor, a Hacker B50 12XL, better suited to the fan, gives 8.7 lbs thrust using an identical MidiFan on the same test rig and the plane should weigh a bit less that the Panther. hopefully it will be a rocket ship with a nice low wing loading for slow langings. It has a lot more wing area than the Panther..

PS: Didn't see your pictures before I started this post. Looks very nice. I most certainly take your  point about a sharp edge on the intake. I very much like the Super Sabre, but it has a small sharp intake and its too small to have a 'nominal bellmouth' on the inside. So I have given the Super Sabre idea up for the moment.

Edited By Mark Powell 2 on 11/08/2012 13:55:53

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Leibniz certainly developed the calculus, independently of Newton and at around the same time. While Newton may have actually been the first, his methods and notation were not the easiest, which is why we now universally use the Leibniz notation. While Newton may have been handicapped by the absence of chemistry, he was also handicapped in the area of mechanics by the absence of the laws of motion...until he invented them. So perhaps if he had applied the same rational approach to alchemy, instead of adopting a lot of pseudo religious nonsense, he might have made a similar contribution there. Still, I don't think we can really complain about the value of the contributions he did make!

However...I don't think we can neglect compression, at least in the simple case of a duct with constant cross section. For there to be any thrust, there must be a difference in pressure between the area in front of the fan disc and behind. In a static test, that difference in pressure will be the measured thrust divided by the area of the duct. So the fan must be compressing the air...in fact in exactly the same way as the somewhat similar fan in a gas turbine compresses the air. In a similar way a rocket produces thrust which depends on the combustion chamber pressure and the nozzle area, although we do improve on the thrust here by shaping the nozzle to take advantage of the expansion of the gas.

John

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John,

There won't be any compression if the intake, fan, and exit are a constant diameter parallel tube. OK, there is a little temporary compression (or a speed up due to venturi effect and thus no compression) where the centre body is narrowing the area.

And EDFs fly perfectly well with a constant diameter parallel tube. In fact the low speed (take off acceleration) is usually better than a tapered tube.

You can narrow the exit and increase the velocity and down to about 80 percent of the fan swept area this works, presumably giving a better 'match' to external circumstances as the speed increases. But the low speed performance is worse. Any more than 80 percent gives too much back pressure on the fan blades and stalls the fan, though it will unload in the air if you can get it off the ground. The compression ratios are very low, only measurable on sensitive equipment, which I don't have.

A gas turbine compressor is just that, a compressor. Be it centrifugal, like the model turbines, or axial like the modern full size ones, the exit area of the compressor is between a third and a fifth of the inlet area. But in a ducted fan the inlet and exit areas at the front/rear of the fan are identical so there is no compression. They are very different, not 'somewhat similar'.

PS: They are surprising good, too. My OS 46 AX two stroke gives 5.5 lbs static thrust on its claimed 1.6 BHP, which is 1200 watts,  on a Master Airscrew 11x6 prop. which is 4.6lbs/Kw.My 90mm fan gives 8.7 lbs on 2000 watts, which is 4.4 lbs/Kw.  Of course, those figures for the EDF are input power only, not output power, so the shaft power to the fan is actually lower than 2000 watts. The BHP of the OS is shaft power, measured at the shaft, 100% efficient, with input power not considered. So the fan comes out better than it looks. And the thrust in the air of a propellor decreases as the speed increases. On a fan the reverse is true, though only up to an (un)certain point of course. 

Edited By Mark Powell 2 on 11/08/2012 14:29:03

Edited By Mark Powell 2 on 11/08/2012 14:30:44

Edited By Mark Powell 2 on 11/08/2012 14:41:09

Edited By Mark Powell 2 on 11/08/2012 14:44:01

Edited By Mark Powell 2 on 11/08/2012 14:50:34

Edited By Mark Powell 2 on 11/08/2012 14:52:47

Edited By Mark Powell 2 on 11/08/2012 14:54:06

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John

The pressure difference we are talking about in a DF is essentially across the fan. The lower pressure created in front, encourages air to flow in to equalise the general air pressure. The slightly higher pressure, moves to dissipate itself to the general air pressure. In terms of heating due to volume or pressure changes, negligible, this is where the flow is derived, along the duct.

Compression ratios in Gas Turbines are in the order of 20:1. I am hesitant to make a guess but would guess at 1.0001:1 for a DF. Just a few Pascals difference, from atmospheric. In a GT, the compression is further increased by burning a fuel, which rushes to reach atmosperic pressure, the process greatly increasing the volume

I thought the splitter plate on modern jets, was to do with the stagnant boundary layer?

How a system behaves has been predicted in this thread quite nicely I had thought, with respect to air entry, duct sizing, and extit.

I do not disagree with the notion that greater than a 20% reduction reduces performance. I think the general argument expressed in the thread that any reduction in duct area or shape increases losses. Although i do agree with the argument, that a model cannot fly any faster than the outlet velocity from the duct. Seems obvious on reflection.

 

Edited By Erfolg on 11/08/2012 16:13:11

Edited By Erfolg on 11/08/2012 16:15:08

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Cannot fly faster that the jet outlet velocity?

I dont think Concorde's jet efflux was at mach 2 when it was cruising at that speed.

However I would accept that it may be rather difficult to design a ducted fan plane that can exceed its outlet velcity but then who would have thought model gliders can reach 400mph!

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Simon,

Course they can. Forget models and DFs, just think of Mr Newton. And space. A body (spaceship) is going along at a given speed. No drag, and no bodies nearby to affect it. No energy is required for it to continue at its existing speed and direction. (Mr Newton). Then fire a rocket out of the back. Exhaust velocity lower than the vehicles speed. So what? The speed of the body is relevant to nothing, there is no point of reference. The body will accelerate. It must, or where has the energy of the rocket gone? What happened to the law of conservation of energy?

It's only the people who think a rocket/jet/DF works by pushing against the air behind it that think it can't go faster than its exhaust velocity. If that were true, you could have a rocket in space as powerful as you like, with an exhaust as fast as you like, And you wouldn't move an inch. But it does work, it's been done. smiley

.

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Ok you are correct a=f/m

I am not sure that the efflux was not greater than mach 2 though, it certainly would be going at mach 2 along with the aeroplane, plus the velocity it travelled down the duct. How long it remained at this velocity is another matter. Just like firing a bullet from a plane.

On reflection, with a practical duct arrangement, I now believe that the velocity of the air leaving the duct will necessarily faster than the planer. The reason being is that the air has to be accelerated to generate the force. Without some bizarre duct geometry it will be necessary to continuously generate the force due to various drags and losses.

Edited By Erfolg on 11/08/2012 18:00:23

Edited By Erfolg on 11/08/2012 18:17:48

Edited By Erfolg on 11/08/2012 18:18:42

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Whilst I have been relaxing this evening, I have been thinking about some of primarily Marks comments and Simons arguments.

The trouble with Marks argument, there is a fluid called air ( as well as gravity) in our environment. We are not concerned with just accelerating the body (with resistance) but maintaining a steady state velocity, where air (our fluid) resists and gravity, wants to pull our model to the ground.

I imagined that the fan was in a circular duct. The air could be circulated around, the reaction would then be at the point where the duct was fastened to the floor. I then thought about a "U" tube shaped duct. What would happen? To a large extent, it depended where it was fastened (our interface for a FBD).

I then thought about a DF and concluded there are two boundaries which are interesting. The inlet and outlet. You could mount the fan horizontally or inline or any other position which you can think of. Yet in the environment we live in the principal point of interest is the outlet. As suggested by some one other than myself (I think). this becomes a momentum issue, very similar to our firemans hose.

The trouble with our world, the question is not only about statics, but involves dynamics, not is it simple in that there a drag forces which vary with speed as well as form (in level flight). These forces vary in the real world, as profile. induced drag alter by both proportion and value, dependant on velocity (partially due to AoA).

I am increasingly tempted to go into the attic for my very old notes, as my memory is not good enough and I would need to reacquaint myself with my youth. It seems ex-engineers forget.

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Posted by Mark Powell 2 on 11/08/2012 14:25:26: And the thrust in the air of a propellor decreases as the speed increases. On a fan the reverse is true, though only up to an (un)certain point of course.

The static thrust of a fan decreases as the speed of the model it's in increases in exactly the same way as a propellor.

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Posted by Mark Powell 2 on 11/08/2012 17:43:43:

It's only the people who think a rocket/jet/DF works by pushing against the air behind it that think it can't go faster than its exhaust velocity. If that were true, you could have a rocket in space as powerful as you like, with an exhaust as fast as you like, And you wouldn't move an inch. But it does work, it's been done. smiley

.

A ducted fan is not a reaction engine. It is merely a propellor, albeit a small high pitch one, in a duct, it creates no expanding exhaust gasses. It can not drive a model faster than the air stream passing through the duct.

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Taking the rocket situation first...yes, a rocket can certainly accelerate to a higher velocity than its own exhaust. Of course, when operating in free space, the centre of mass of the entire system remains where it started, eg either at the same location, or travelling in the same direction at the same velocity.

An aircraft, once off the ground, can really only propel itself by reaction forces, the viscosity of the air being negligible for practical purposes. To obtain a reaction force, it has to accelerate the air it takes in through the intakes (or through the propellor) in a rearwards direction. So the air that was standing still when the westbound Concorde arrived and took it into the intake must be going east when the Concorde has gone past and it comes out the exhaust. The same actually applies with a propellor plane. Lift from a wing or from a propellor results from a reaction force, to get that force air has been accelerated. So because the reaction mass is being taken in at a velocity relative to the aircraft, it must be accelerated to a greater velocity to obtain thrust. (I am neglecting the mass of the fuel which is burnt here.)

Taking a quick look at a 3 inch ducted fan from one of the well known suppliers, they claim a thrust of up to 2000 grams. Since the units are incorrect anyway, let's convert to pounds...that is 4.4 pounds, over an area of 7.2 square inches, which is about 0.6 pounds per square inch. That is the force that is being applied to the column of air passing through the fan. Naturally that column of air is going to accelerate, and air being light stuff, the velocity acheived will be considerable. One thing to note is that quite a lot of the acceleration will take place before the air reaches the fan, or even before it reaches the duct, which is where the shape of the intake starts to make a difference. So with the fan running, a lot of air will pass through the duct that would not have gone that way if the fan were not there. Some of that 0.6 psi will be a reduction of pressure in front of the fan, some will be an increase behind, but either way the fan is increasing the pressure of the air that passes through it by that much.

Don't confuse this with the changes in velocity that take place in the inlet of a supersonic plane....the compressor cannot accept air that is travelling at a supersonic speed (relative to the compressor.) So the intake is designed to slow the air down to a speed that the compressor can accept. But having done that, compressed the air, then heated it to expand the gas, it will then accelerate down the tail pipe to a greater velocity than it came in at. (still relative to the plane.) So if it arrived at Mach 2, it will depart at somewhat more than Mach 2. If the mass of air only departed at the same velocity that it arrived at, there can be no net thrust. The thrust is needed to overcome the drag of the airframe, which is actually tending to accelerate the air that did not pass through the engines in the same direction as the aircraft. So the overall effect of the aircraft passing is likely to be that the air behind it is somewhat more turbulent and a little warmer than it was before.

So if you carry your reaction mass with you, you are a closed system and your velocity with respect to anything else is purely relative. If you are travelling through your reaction mass and picking it up as you go, your velocity relative to the reaction mass becomes very significant.

John

Edited By John Olsen 1 on 12/08/2012 02:42:19

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John,

Thank you for your detailed post. It was hard to follow (took me several triessmiley) but I got there eventually.

My 'space' analogy was more thinking aloud rather than pedantic 'true' facts, and I am beginning to doubt if it is a valid analogy. However, there are several model EDFs where the measured speed is considerably higher than the exhaust velocity. Two come to mind. The Schubeler Vector and the BVM Electra on 12S power. But we are not told if there was a steep, speed increasing dive first. Possibly with the Vector claims, but not, I believe, with the Electra (I would like my bank manager to buy me one of those).

My very expensive experience has taught me not to believe the claims of most of the 'very high thrust' brigade. Some manufacturers are making ludicrous claims which are simply nonsense. Particularly on 90mm fans that are advertised to provide high thrust at low cost. Also some of the rotors come apart, which is extremely dangerous. Schubeler's claims for their complete fan/motor combinations are genuine, as are BVM's. The Wemotech fans, fairly low cost, are true in the claims as far as they go, but it is only rated to 1000 watts by the manufacturer. In reality they hold together at several times this input power. It is one of the best fans around, despite its low cost.

After extensive trials (and lots of money spent on motor 'false starts' I am now getting 8.7 lbs static thrust on 2000 watts out of the 90mm Wemotec fan. This thrust is nearly as high as an OS 91 two stroke glow motor on its recommended 16x8 prop, which is quite good. And we are told by the 'experts' in the magazines that, up to a poiint, the efficiency increases as the speed increases. Though I don't see how they measure this, as it was stated long before onboard sensors became available and even with sensors you can't measure the dynamic thrust. No wonder they are so fast in practice - we've got the equivalent of a top 91 in a four foot span six pound plane!

Edited By Mark Powell 2 on 12/08/2012 03:24:08

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I would be quite prepared to beleive that the aircraft could reach a higher airspeed than the measured speed of the the exhaust under static conditions on the ground, because once it is moving forward the fan will take in even more air, and so the output velocity will also increase. This would also be why the efficiency can increase...the fan and duct would be designed for the operating conditions in the air so will work better. This is like the way a high pitch airscrew will work better once the plane is going fast enough, the trick being to get a compromise that is good enough to let you get off the ground and up to operating speed.

Your fan is close enough to 10 sq inches, so if the duct is the same that would be a pressure of 0.87 psi.

I am really impressed with the performance of the modern ducted fans, having last been involved in model aircraft when it was a real acheivement for a ducted fan aircraft to struggle off the ground even with a really hyped up glow motor. Coupled with the performance of the modern batteries and motors, it seems hardly worth going to the trouble and expense of a real gas turbine.

regards

John

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Hi John,

Yes, I would have liked a small turbine (I don't really like big and heavy planes) and the Wren 44 Gold came to mind at about £1700. Although I can afford it, one should, I feel, put these things in perspective and do I really want to spend that much on a model plane engine? Would I really enjoy my usual 'fooling around' with that much money, plus the aircraft, at considerable risk (I am not a particularly good flyer). My EDF efforts have cost me about £1000, mainly on motors that turned out not to be ideal for the Wemotec MidiFan, (they won't be wasted, one is already in the Junior 60 below) but I recently found the Hacker B50 12XL and the combination is as good as it gets without directly ordering 'special' motors from the USA as there are no UK distributors. 8.7 lbs on a static test rig is only 1.3 lbs less than Wren's claims for the 44 Gold.And ignoring. my previous motor mistakes, the cost of fan and motor is only £250. So I have achieved, a performance that cannot presently easily be bettered and I am very happy with that. I am only doing it for a change, as I was beginning to feel that, in the end, everything from my electric vintage Keil Kraft Junior 60 to My Great Planes OS 91 Little Tony pylon racer all felt much the same to fly ,and a medium sized EDF would be a new challenge.

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I do agree with John, as he has made the points well that I was struggling to convey.

I have been thinking about the impeller compared to a propeller. Propellers do have considerable tip losses, compared with main part of the blade and is of considerable aspect ratio. Whereas the DF is shrouded at the tips, I have one fan (the only one I have and have ever seen), what is disappointing that there is at least 2mm tip clearance. This is so undesirable. In my youth the gas turbines that we built had spill strips to reduce these losses. I would expect modern jet compressor sections have simpler and just (probably more) effective methods ( blade growth was the issue due to centrifugal forces).

It is desirable that the air approaching the fan is laminar, without swirl, as the AoA will become less predictable than with a propeller. I am beginning to suspect that some poor performance of bifurcated inlets, may complicate the airflow to the fan. Maybe that is why some are claiming a Plenum chamber helps. It just sorts out any significant differences with airflows, maybe?

On reflection I am less convinced that there is any benefit in reducing the outlet size at all. Thinking of our fireman and his hose, he is increasing the jet velocity to gain distance with the water jet. The water jet will have energy, which is felt by any object the jet hits. Although our fireman sees no increase or decrease in force, above that resulting from the force generated at the out let. Which is the result of the mass flowing and the velocity, so anything which reduces this mass flow, such as duct losses is bad news.

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Now this is interesting.

Surely the air molecules are stationary (excluding wind) when they enter the duct. They might start to move in the planes direction as they travel down the duct due to wall skin friction but to nothing like that of the speed of the plane.

The molecules are then accelerated down the duct by the fan. This acceleration produces a force on the fan. The force has nothing to do with the speed of the plane only the degree of acceleration imparted on the air by the fan. The air leaving the fan does not have to be going faster than the plane to generate this force.

The only question is whether the force created by accelerating the air in the duct is sufficient to overcome the drag of the moving plane.

Does this sound logical?

 

Edited By Simon Chaddock on 12/08/2012 13:17:26

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Simon

I think you are getting close. Try this. The blades on the fan are actually wings.They generate lift. The pressure on the top surface (front) is lower than the pressure on the rear surface so the blade moves forward (I think, or hope, that we can all agree on that) carrying the plane with it. So what is happening some distance away, such as in the intake duct or the outlet duct is not particularly important. All the ducts do is to feed the air to the fan and get rid of the 'used' air. The speed the air exists the 'waste' duct is completely unrelated to the speed achieved by the aircraft. All the forces are at the fan, the aircraft is not 'pushed' along by what comes out of the tail.

Edited By Mark Powell 2 on 12/08/2012 13:40:16

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Where the fan is or how it is orientated is not of great importance (other than gyroscopic forces).

What matters is how our duct interfaces withe world. Using engineering jargon, the BOUNDARY rather bizarre duct

img005.jpg

Imagine the air enters the bottom, the duct turns through 180 degrees and passes through a fan, the prime mover, and then goes down the duct and round another 180 degree bend and exits the duct.

Although the fan generates a force towards the bottom of the page, we know by common sense as it self evident from experience that the effective force would be to the top of the page.

This is why the BEB's of the world exhort their students, consider your boundary very carefully, a poorly selected boundary will make solving the problem very difficult.

On that basis, to understand what is happening consider the outlet to the system.

The other technique encouraged was the so called "sausage machine" where the features such as the fan. or airframe etc are considered to be functions. The function supplies values to our FBD (free body diagram) at the outlet, you crank the machine, the answer pops out, just like making a sausage.

Keeping it simple as John has said, the fan generates the force which is used at the outlet to move the airframe. Note, I do not say push against or any such thing.

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Erflog,

Yes, you are right. If it worked my way your tube would move in the opposite direction from what it actually does.

In my computer programming days we had 'bounds' of the limits of possible answers so that incorrect input would be rejected if the resulting answer was silly. It was also useful in development if our programming was wrong and gave silly answers to good input.

Note: in my 'push the aircraft along' I did not mean to imply any 'pushing against the air'.

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I was also thinking about Simon and the molecules are stationary.

I know what he means as a description.

I also know that BEB and maybe a few others are also restraining themselves. From our chemistry lessons, we were given some pretty incredible speeds for molecules at ambient. The hotter the environment the faster they are moving, conversely get to -273 C and the world stops still. Then it stops at about -5C for me!

I know useless, no it all info.

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Posted by John Olsen 1 on 11/08/2012 06:23:05:

Tony K asked a question a few posts back about a constant section duct with therefore a constant mass flow before and after the fan, the question being how could it create thrust?

John, the point I was trying to make is that the equation often quoted, ie. thrust equals mass flow x acceleration (dv) is incorrect. Thrust is mass flow x mean or average velocity (I am not sure which so I use the average) through the system.

The equation is: T = kg/s x m/s = kg.m/s^2

The system is that between the inlet and the outlet. The average velocity is inlet velocity plus outlet velocity divided by two. The frame of reference being the model in flight.

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Tony, the dv figure is not actually acceleration, it is change in velocity, so the equation you give is actually correct for the thrust from a mass flow, eg thrust is mass flow per second times change in velocity. The units come out correctly, eg your result is in kg.m/s^2 which is force in Newtons. A change in velocity is not in itself an acceleration, although it does imply that one must have taken place.

The tricky part is that we have to think of the system as being more than just the duct and the fan. This is because some of the acceleration will take place before the air reaches the duct, and the intake of the duct will affect air not just directly in front of it, but also around it. (Think of those diagrams showing the streamlines of air going into an opening.) We tend to think of the fan sucking air in, although of course this is not what is really happening.

So if you try to measure the air velocity at the entrance to the duct and at the exit, there is not going to be as much difference as you might think. For practical purposes though, we could measure the speed of the aircraft and regard that as the starting speed of the air. Then if we measure the speed of the air at the exit, there should be a difference. Given then that we know the diameter of the duct and the speed of the air leaving it, we should be able to come up with a reasonable figure for the mass flow, and then have some idea of how much thrust the system is producing.

It is kind of dangerous to say that the fan is not pushing on the air. In a sense it is pushing on the air, but only on the air that is passing through it. In the same way, a rocket is pushing on its exhaust, and the reaction to that push is what moves the rocket. But of course either would work extremely well exhausting into a vacuum, provided of course one can imagine the ducted fan being able to receive air in at the intake when there is a vacuum at the exhaust.

One thing this is leading me to think is that what happens ahead of the fan and even ahead of the duct intake is going to be extremely important. Anything that interferes with the flow here is going to limit the amount of air that is able to accelerate into the fan. If it does not reach the fan you are not going to get thrust from it.

On the speed of the molecules...at ambient temperature, they have an average speed of something like 330m/s. However, they have an average velocity of zero, assuming no wind is blowing. The difference comes in the a speed is a scalar, eg direction is not taken into account, while velocity is a vector. So although the individual molecules are travelling at high speed, the direction is random, and is randomly changing with each collision. This is why the fan is not really sucking. It is moving air behind itself, and the air in front then finds that there is not so much to collide with in that direction, so it is less likely to bounce back to where it came from. This all works fine until something tries to move through the air at a speed approaching the mean free speed of the molecules, otherwise known as the speed of sound.

John

Edited By John Olsen 1 on 14/08/2012 01:45:59

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I think we, as modellers, are getting very good at ducted fans. Though not much of a theorist, I am finding it very interesting and learning a lot.

On the practical side, using easily obtainable and not too expensive commercial equipment I am now getting almost the same static thrust from a 90mm Wemotec fan as from an OS 91 two stroke driving its recommended 16x8 propellor. At 2000 watts the input power to the fan motor is the same as the claimed output BHP of the OS 91, so the fan system itself is more efficient than the propellor system when you take electric motor losses into account. Statically at least. And it is less than half the weight including the ESC.

That is why I say we are getting good at it. The 'standard works' say that a small ducted fan will be less efficient than a large propellor but this is demonstrably not the case, on static measurements anyway.. I suspect that we have reached a point that minor details of fan theory and design won't make much difference. I have found negligible performance difference between the old Wemotec fan and the much newer 'advanced and sophisticated' Schubeler fan of very different design.

It will not be the first time that modellers have been ahead of full size practice.

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John, I totally agree in your supersession that what happens at the entry of the duct is very important to the system as a whole. Unfortunately this is an area where scale modellers are very atracted to the notion of a small scale inlet. Often with sharp edges, odd shapes etc.

As with the inlet, I do think that the careful design/construction of the inlet or outlet duct is important, particularly when bifurcated.

As for theory and practise, it is often the case that theory is driven by observation of actual things. It is then the theory which often helps in the understanding and optimisation of actual/real systems.

Even my hero, Newton, observed and then theorised. Even Isaac, with a brain the size of a planet, got some things wrong. That is Isaac put forward that it was repulsion of molecules which lead to pressure, where as (someone else, ermmembarrassed) suggested that it was the velocity of molecules and there energy which gave rise to pressure.

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