Ducted fan theory and practice

[Tony K]

 

Quote, "Where is the energy coming from to create this impulse gain ? - only from the ducted fan system, since that is the only energy source around. So the system has an energy loss exactly equal to this unknown inlet energy gain, and the two cancel out."

 

I would suggest that the impulse gain in the static case is balanced by the impulse loss of ejecting the "exhaust" into static air instead of air moving at free stream velocity. Therefore these two factors (outside of the system boundaries) cancel out. The calculations can then use measurable properties from inside the system boundaries.

[Erfolg]

I have returned to this thread, after a short time, much has changed.

 

I have always assumed that Ve=0 refers to the model? It being static, relative to the space, in which it occupies

 

I have then assumed that there is a velocity profile into the inlet that is +ve compared to the model, is that correct? At some distance away the air is apparently static

 

I have assumed that the velocity of the air leaving the duct is greater than the model. But that thrust = drag for zero acceleration or deceleration.

 

I will have to re read to try and understand what is being said and how it relates to both the what is measured and how that relates to the calculated mathematical model.

 

I am of the opinion that the Scharnhorst model relates to the fluid flow static to dynamic, principally concerning himself with the intake performance. He assumes that the fan gets it to the new condition. How much power the fan takes to get it there is ignored, other than what it theoretically takes (a none achievable minimum). Is this your interpretation?

[Keith Simmons]

I think the EDF force works at both ends. The intake as a suction force which tries to move the fan forward, and the exhaust as thrust against static air.

 

In dynamic mode (flying) The suction in front of the EDF would be less, so less resistance for the fans and therefore an increase in speed.

(I am sure that the EDF in vacuum will go to the max rate of revolutions as it's unloaded.)

 

The lifting theory of a wing has that the flow of air moving faster over the top of the wing produces less pressure and so sucks the wing up and that the lifting force is greater over the wing than under. The principle also applies to the EDF, I will be interested in which end the force is greatest? (For a jet turbine, its the thrust, or rear end.)

 

I agree that the velocity of the air has to be greater than the model so to overcome drag.

 

The drag increases the faster you go, and is that correct that the EDF fan tip speeds cannot go supersonic? (same as of 'normal propellers') So that is the max limiting factor?.

[Richard Sharman]

I believe Keith is correct - in the static case there are energy losses at both ends of the EDF unit, and they are not usually equal (see my earlier post).

 

I'm not so sure about the lifting theory of flight, though -- this is a very hotly debated topic in aerodynamics, and I think most aerodynamicists would reject it nowadays. It's the circulation theory of airfoils which is most accepted. But don't let's go there on this thread !

 

As far as EDF fan tip speeds are concerned, I see no reason why they should be any different to normal propellers -- and they can go supersonic, as we all know.

[Tony K]

Posted by Keith Simmons on 25/10/2011 13:36:45:

I think the EDF force works at both ends. The intake as a suction force which tries to move the fan forward, and the exhaust as thrust against static air.

 

In dynamic mode (flying) The suction in front of the EDF would be less, so less resistance for the fans and therefore an increase in speed.

 

 

Keith, in non mathematical terms, there is less "pull" in front of the fan in the dynamic case because incoming air is already moving but there is also less "push" behind the fan because that which is being pushed against is also already moving.

 

Richard, Erfolg, that is the basis for my argument above, "I would suggest that the impulse gain in the static case is balanced by the impulse loss of ejecting the "exhaust" into static air instead of air moving at free stream velocity. Therefore these two factors (outside of the system boundaries) cancel out."

 

I am of the opinion that this is a flaw in Scharnhorst's static model.

 

Furthermore, as "impulse" is change in momentum and we assume (questionably) that in the dynamic case vi equals the flying speed, where is the change in momentum at the intake? The velocity of the mass of air about to enter the inlet has the same velocity after it has entered (ignoring lip geometry).

 

This suggests to me that the impulse gain is zero in the dynamic case and has a positive value in the static case.

 

What do you think?

 

[Keith Simmons]

I agree with Tony K that there is less thrust in dynamic flight in both "pull and push". As the EDF is moving as in flight, Now the question of momentum in the intake at max dynamic speed, I guess the narrower area of the exhaust outlet would speed up the volume of air so to balance the airframe drag so they cancel each other out?

[Tony K]

 

Let me present the following for your consideration.

 

We have an EDF aircraft which draws 350W of battery power to fly at 42 m/s airspeed (Vo).

Assuming an effiency (power out/power in) of 85% we have 296W being used for useful work.

 

By calculation, 296W gives a thrust = 4,955 N and the mass flow = 0,2112 kg/s.

 

The inlet area = 0,003667 m^2 and the outlet area = 0,002463 m^2 so the inlet velocity (Vi) = 48 m/s and the outlet velocity (Ve) = 71,46 m/s.

 

Now look at the impulse calculations. Impulse is change in momentum, so I=m.delta v.

 

Impulse gain at the inlet = (Vi - Vo)m and impulse loss at the outlet = (Ve - Vo)m.

 

So pgain = (48 - 42)0,21112 = 1,2672 N and ploss = (71,46 - 42)0,2112 = 6,22195 N.

 

ploss - pgain = 4,9547 N. This corresponds to the thrust figure above.

 

Now the static case, Vo = 0, with the same mass flow.

 

pgain = (48 - 0)0,2112 = 10,1376 N and ploss = (71,46 - 0)0,2112 = 15,0923

 

ploss - pgain = 4,9547 N

 

Therefore, theoretically, static thrust equals dynamic thrust for the same mass flow.

 

 

Edited By Tony K on 27/10/2011 10:45:37

Edited By Tony K on 27/10/2011 10:47:15

[Tony K]

On to the K/S (K.Scharnhorst or Kinetic energy/S) equation, 1/2 mdot.v^2. Combining the input and exit gives 1/2 mdot(ve^2 - vi^2) which gives a result in Nm/s = Joules/s = Watts, ie the power output. This is not the impulse (change in momentum).

 

Working through the figures:-

 

Power = (0,2112 (71,46^2 x 48^2))/2 = 296 W.

 

But we can also use thrust times average velocity to achieve the same result:-

 

TVav = T((Ve + Vi)/2) = 4,9547((71,46+48)/2) = 296 W.

 

All things considered, I think the Scharnhorst paper is of very little use for designing or refining a ducted fan system.

 

Your comments invited, T.K.

 

[Richard Sharman]

Well, thanks for the posting, Tony, but I have to say, with respect, I don't agree at all. In my opinion you have made some assumptions which may lead to a circular argument, so that your conclusion is perhaps a little premature ?

 

I won't go through your whole argument, but, starting at the begining: You want to solve the question of an EDF plane which draws 350 watts and flies at 42m/s. Remember, these are just approximate figures which certainly have experimental errors in them. Also, it would be nice to develop a theory before plugging in empirical numbers, not after. Nevertheless,...

 

You use Scharnhorst's 85% figure for efficiency getting a useful power of 296W = 350 * 0.85, but this value, 0.85, is not a given -- it is one of the things we are trying to find out ! Even Scharnhorst thinks it is speculative, and different for every example. Your reasoning here is back to front.

 

Now, converting 296W to newtons of thrust to obtain 4.955N you seem to be using the figure of 59.7Watts per Newton, which was the result I quoted from the results of a particular static test, so 296 / 59.7 = 4.955. But if we use a value obtained from a static test to solve a problem about the dynamic case it's highly likely we are going to end up proving that the static thrust equals the dynamic thrust. Anyway, the correlation between watts and Newtons given would only be valid for this specific example, and so is hardly a satisfactory way to develop a general theory.

You haven't explained how you calculate the mass flow from just the thrust, but it seems that you may be using the equation T = M*dv or re-arranging, M = T / dv. Of course, at this point we do not know the value of dv, but you seem to have assumed that it is 23.46, thus giving M = 4.955 / 23.46 = 0.2112. But where this value of dv come from? I suggest that you have taken it from a previous calculation where you suggested an entry speed of 48 and an exit speed of 71 so that dv = ve - vi = 71 - 48 = 23. This assumption is not warranted here unless you have some independent way of obtaining it, but you don't show it.

 

Now, you find the entry speed, vi = Q / Ai where Q = M / rho. So vi  = (0.2112 / 1.22) / 0.003667 = 48 ! This is hardly surprising ! we assumed that in the first place !

 

I will stop there, although I have criticisms of several other steps you make later.

 

May I respectfully suggest some thoughts:

1) we have to be very careful when using observations, not only do they contain errors, but they may not even refer to consistent experiments,

2) arguing from the specific to the general is fraught with difficulties because the system we are trying to explain may be more complicated than we think,

3) conclusions based on arguments like this can be premature.

 

The "black box" treatment of an EDF (or IC, or turbine) system we have been discussing is, in my opinion, an essential first step to understanding ducted fans in more detail. I am hoping to show in future posts how the EDF system can be broken down into its component parts using an extension of the KS theory. Then, energy gains and losses can be attributed to the entry duct, the fan unit itself, and the exit duct (nozzle). This leads directly to a method by which we can adjust the geometry of the ducts, the power of the fan, and so on, to achieve the design characteristics we seek for successful flight. This would make the theory very useful for designing and refining a system.

 

Richard

Edited By Richard Sharman on 27/10/2011 21:03:04

[Tony K]

Richard, the only assumption I have made is that Scharnhorst is correct when he writes (on page 12), "...indicates that the ducted fan (generally) can achieve its best effiency of approx. 82 - 85%..."

 

On the 10th. Oct. you wrote, "Actual consumption as measured by battery depletion is 350 Watts".

 

On the 19th. Oct. you wrote, "Consequently, I claim the value given above (42m/s) for average flying speed is reliable, at least to the level of accuracy we are working here".

 

I did not want to clutter this thread with unecessary calculations but this is how I arrived at the previous figures.

 

As a starting figure I used 296 W as useful power output. I want to know how much mass flow and thrust can be obtained from that power.So I need to know the velocity at a point where I know the cross sectional area.

 

Starting at the inlet, Ai = 0,003667m^2. Vi is unknown, I will call it "u".

The exit area, Ae = 0,002463m^2, so from Ve/Vi = Ai/Ae the exit velocity is 1,4888u (I will use1,5).

I now know that the average cross section Aav = 0;003065 m^2 and the average velocity Vav = 1,2444u m/s (I will use 1,25).

 

The mass flow can be obtained from:- density x Aav x Vav.

 

mdot = 1,2 x 0,003 x 1,25u = 0,0045u

 

Moving on to the thrust, T = mdot x dV or mdot.Ve - mdot.Vi.

 

T = (0,0045u x 1,5u) - (0,0045u x u) = 0,00225u^2.

 

Power can be calculated from P = thrust x average velocity.

 

P = 0,00225u^2 x 1,25u = 0,00281u^3.

 

Using the assumed power figure of 296W I can find the value of u.

 

u = cube root of (296/0,00281) = 47,2m/s.

 

I rounded this up to 48m/s and ran it through the calculations:-

 

Vi = 48m/s. Ve = 48 x 1,4888 = 71,46. mdot = 0,2112 kg/s. Thrust = 4,955N

 

These calculations can be repeated for any power output and will give a theoretical thrust based on the sizes of the inlet and outlet.

 

Quote, "This assumption is not warranted here unless you have some independent way of obtaining it, but you don't show it".

 

I hope it is shown to your satisfaction. T.K.

 

Edited By Tony K on 28/10/2011 09:54:59

[Keith Simmons]

I am happy to obtain from you clever guys and work out the formula for ducted fan and the manufacture's website gives their static thrust per given motor/EDF plus LiPo combination. I am keen for the theorectical thrust at a given flight speed. All those are still theorectical as it depends on the duct losses and how well the ducts are made.

I am interested in the assumed loss of thrust per m or cm in the duct itself, (not the EDF unit) and is there any difference in the rate of losses in the duct in front and behind the EDF? I would assume the longer the duct, the greater the losses and therefore come up with a ideal watts that's required for the EDF unit and look at the manufactures products for a suitable one and check it out to see if it meets my needs.

I understand we need experiments, but i have not got the cash to buy different EDF setups to find out which is best. Plus I don't yet have an EDF unit but I do want to build one or more in the future. (I have a Minifan, but no motor yet.)

Perhaps those of you who have EDF jets can pool their findings to give the rest of us a better understanding.

[Tim Mackey]

I have several, and have been using EDFs for many years - back to the old days of nicd and brushed motors! TBH, I am no mathematician, and only a self taught bodger when it comes to engineering, so the vast majority of all this talk went straight over my head.

However, you asked for those of us with EDFs to give their findings, so here's my .02P.

 

1) I still use the 150 Watts per pound of AUW as a benchmark target for any EDF model.

 

2) I use a simple homemade thrust measuring rig to assess the static comparative performance of different fans with no consideration for the ducting.

 

3) I try to get the ducting and eflux tubing as smooth as possible, and ensure that the inlet area is at least the same as FSA

 

4) Finally, and most crucially, I go and fly the darn thing.

 

If it flies well, I leave well alone. If it dont, then I bump up the watts

[Keith Simmons]

Many thanks Tim. The EDF I would like to build first is the Vampire and with the Minifan I have, then work out which motor once I have the model's weight and try for 150 watts/Lb as a starting point. With your formula, I can work out it's likely max dynamic speed. (being an early jet, I have no need to go ballastic.) but it will give me valuble insight for my next EDF project.

[Tony K]

On the question of Scharnhorst using the kinetic energy equation (1/2 mv^2) to calculate impulse gain or loss.

 

The reason I find this invalid is because there is no delta or varying property in that equation so it can not represent an increase or decrease, only a steady state. I know that combining the equations for inlet and exhaust gives a delta v^2 but this only tells you the difference between the steady state at the inlet and the steady state at the exit, ie. the changes within the system boundaries. There are simpler ways of calculating that.

 

The (what I believe is) correct equation, I = m.dv, gives you the actual gain or loss because a property has changed. It tells you how the "black box" reacts in its environment. For example, in a previous post I suggested that the intake velocity is 6m/s higher than free stream velocity so there is something changing outside of the black box but being caused to change by a mechanism inside the box. That something is a change of momentum, in this case an impulse gain, and by comparing the momentum at the inlet and the momentum of free air (air unaffected by the mechanism) it can be given a value.

 

This, I believe, is a fundamental flaw in Scharnhorst's theory but I know Richard will not agree with me!

 

 

Edited By Tony K on 28/10/2011 11:32:13

[Keith Simmons]

I do know that one scientist never agrees with another..

It makes sense for intake velocity to be 6m/s higher than free stream velocity as it is suction into the intake as shown by Richard on Page 4 with his diagram and I quote a bit of it "because air is being drawn from a much wider area" from his post. I do think this is the effect at all speeds, but maybe the area gets smaller the faster you go.

 

Now I better DUCK out of the way...

[Erfolg]

I think a lot of this discussion is revolving around the effect of the inlet has on the system performance. Ignoring Scharnhorst, there are other sources, which indicate there is an effect dependent on inlet shape on system performance, although not aircraft sources, the Woods fan Guide and the IHVE ventilation books both support the contention. There is also the visual evidence that all subsonic pod type jet installations have the same type bell entry.

 

It would also help if th Microsoft word Equation writer, as the arithmetic would be both easier to recognize and read

 

If I am honest, I am no longer sure what is being disputed. Perhaps some diagrams and both parties submit there arguments, as a single piece of work(individually), any numerical argument being secondary after the concepts

 

[Richard Sharman]

Erfolg,

what we're disputing (in the nicest possible way, I hope) is how to relate the watts of electricity we are putting into the EDF with the effective thrust we're getting out -- and this really matters. For example, I want to build a bigger (better) Hawk, and I need to know what fan/motor/esc/battery to put in, without having to make too many guesses, and therefore possibly expensive mistakes. I know Timbo (along with most other RC modellers) would say "just put in more power" but there has to be a better way ? and I'm grateful to Timbo's EDF test rig design, which I've copied, but it only measures static thrust, and we need to know if that is the same in the air. Scharnhorst says no, TK says yes. Who do we believe ?

 

Back to the topic -- TK: I still think your acceptance of Scharnhorst's 85% is mistaken. My reading of the whole section p11-13 is that it applies to simple cowled fans "of the type shown in Fig.1 and 2" to quote KS. I have posted a copy of his fig 1 earlier, and you can see that it is not like the arrangement in the Hawk, for example, which has long entry and exit ducts. I would be surprised if they were 85% efficient. I suspect this figure is not right for the case we are discussing, and we should be trying to find it out, rather than assuming it.

 

On the numbers I posted, yes, I did post 350w and 42m/sec but they were not with the plane is the same setup: 350W was estimated from the depletion of a 3s battery over a 3 minute flight for which we do not know the average plane speed. 42m/s was a measured airspeed for a flight using a 4s battery for which we do not know the average wattage. I don't think it is wise to use these figures together.

 

You will see from my post of 22/10 that I have repeated the setups to do static tests, for which I can (reasonably) accurately measure the wattage and thrust, and (probably rather inaccurately) measure the exit velocity. One reason I am not keen on your average velocity derivation is because it is not practical to measure average velocity, so we have not way of making an independent check.

 

Now, on your derivation of the thrust calculation, thank you for making your working explicit, that is very useful, and I now see what you are suggesting. I can't fault the logic, but I don't feel happy about the method. The working you have given (first post of 28/10) is (interestingly) independent of the plane's speed, so applies to the static case as well as the dynamic (your argument, I believe?). If I use your method on the data of my 22/10 static results I get (allowing for some rounding ):

 

test1: 368W becomes 312W useful, vi =48.1, ve=71.5, mdot=.216, T=4.95N

test2: 791W becomes 672W useful, vi=62.1, ve=92.4, mdot=.279, T=8.45N

 

(apologies in advance if I have got the arithmetic wrong, I did this with pencil and paper). But these values don't correspond very well with the measurements I made:

 

test1: ve=47m/sec, T=6.1N

test2: ve=58m/sec. T=10.5N

 

so I have some cause for concern. Are the measurements wildly out, or is the theory not right?

 

[Erfolg]

I will try to find the time this week to read, the individual threads. I will also endeavor to put the various relationships into common presentational formats, along with sketches. The sketches will have to be scanned drawings as my old CAD package will not work with Window 7.

It is evident (to me that is) is that the Scharnhorst diagram and calculations are essentially depicting a duct which has no length (I know it is not possible), concerning himself with the inlet and outlet ratio, with emphasis that the inlet and outlet has on the system performance.

It is very evident for anything other than short pods, it does not come close to a realistic configuration, particularly single bifurcated and particularly double bifurcated systems. Conventional practical analysis of these types of arrangement suggest the losses can be massive, particularly where poor transitions are fabricated and significant changes in cross sectional area. shape and geometries exist. In these cases, the Scharnhorst model is very, very optimistic.

 

The great omission and very optimistic assumption (if my memory is correct) is that the fan and motor could be circa 85% efficient. It is possible that under some circumstances the motor could be 85% efficient. I would guess this only happens at one speed and load, the rest of the time, the motor is less efficient. If you consider the efficiency of the fan, it is anyone's guess how efficient any one of them is. To-date, I have seen no data, or scientific analysis, which attempts to quantify the fans performance. Which to my mind is a great pity, as the fan appears to be central to performance. Particularly that the efficiency could be as low as 20% assuming that everything is wrong, and could be as valid assumption as 85%.

 

I do think you are correct in starting the process, although I guess it will be a long road to being able to model reasonably well all the systems which currently exist in models, in any detail.

[Tony K]

 

Posted by Richard Sharman on 28/10/2011 23:03:13:

 

 

I still think your acceptance of Scharnhorst's 85% is mistaken... I would be surprised if they were 85% efficient. I suspect this figure is not right for the case we are discussing, and we should be trying to find it out, rather than assuming it.

 

I agree, 85% is very optimistic.

 

On the numbers I posted, yes, I did post 350w and 42m/sec but they were not with the plane is the same setup.

 

My misunderstanding.

 

One reason I am not keen on your average velocity derivation is because it is not practical to measure average velocity, so we have not way of making an independent check.

 

I do not understand your reluctance to accept this. We can calculate the velocity ratio by rearranging vi.Ai = ve.Ae. So if we know the velocity at one end, we can simply calculate the velocity at the other end and the average.

 

The working you have given (first post of 28/10) is (interestingly) independent of the plane's speed, so applies to the static case as well as the dynamic (your argument, I believe?).

 

Yes that is my argument. I believe the motion impulse calculations show that, theoretically, static thrust and dynamic thrust (at any speed) are equal.

 

Now, a quick look at your test figures: "test1: ve=47m/sec, T=6.1N"

 

Mass flow = ve x Ae x rho = 47 x 0.002463 x 1,2 = 0,139 kg/s.

 

From the velocity ratio, vi = 31,6 m/s, so dv = 15,4.

 

Thrust = mdot.dv = 0,139 x 15,4 = 2,14N

 

ps, "(in the nicest possible way, I hope)" If this discussion was anything other than polite and constructive, I would not take part.

 

 

Edited By Tony K on 30/10/2011 08:09:34

Edited By Tony K on 30/10/2011 08:11:13

[Richard Sharman]

A quick look at the test figures....

 

Yes, this is the problem -- the calculated values and the measured values don't seem to agree ?

 

I have implemented Tony K's method in an Xcel spreadsheet (like I did for the Scharnhorst theory) and so can do the calculations in full precision without any rounding. (By the way, when I did try to follow the rounding shown in the 28/10 posting I tripped over the fact that the area ratio is rounded (1.4888 -> 1.5) in the derivation, but used un-rounded in the calculation of Ve. There is some other rounding and truncation which I tried to emulate but couldn't quite get it right as I don't know the precision with which all the various calculations are made. Anyway, ignoring this issue as "noise" the answers come out close, but not exactly agreeing. Using the full value of density=1.2252 also effects the result slightly. Actually, this is lesson in the use of arithmetic which computer users are well aware of !).

 

For reference, I get vi=47.13 ve=70.16 mdot=0.2202 and T=5.07 for the example given.

So, in test1 using the measured values for input watts (368W) and duct geometry (as before), the spreadsheet version of the theory predicts vi=47.92 ve=71.34 mdot=0.2239kg/s and T=5.25N which is consistent with the reference example above.

 

BUT, while measured T in this case is 6.1N which is similar, but some way off, 5.25N, the measured ve is 47 which is a long way off predicted 71.34.

 

ON THE OTHER HAND, if we look (easy to do with the spreadsheet, iteratively) for the predicted power input which would produce the measured ve=47, and its corresponding predicted T=2.14N (see previous post) then we find that the input watts should only be 96W, not the 368W actually observed.

 

Something is wrong, and I don't know what it is. I suspect the measured values are inaccurate, but the discrepancy is rather large. Maybe there are other considerations ?

 

Richard

PS real testing has come to a halt as the Hawk was damaged on landing yesterday. After a blistering series of flights it happened that on one landing a wingtip was clipped causing the plane to cartwheel on the runway. I will be fully occupied repairing for a bit. For Hawk enthusiasts: this model has an wingtip airfoil section with very low thickness ratio, leading to a tendency to easily tip stall, but keeping the speed up leads to overfast landings - beware ! I have just been punished with an expensive lesson.

[Erfolg]

I can understand Richards reluctance to accessing the average velocity in a duct.

 

Having had practical experience of measuring both velocities and solids contained in the airstream as part of a commissioning process.

 

There is a considerable velocity gradient across the duct.

 

Your first decision is deciding where and how you will take a useful set of measurements.

 

The measuring probe introduces its own errors. There was a lot of expenditure in time and effort in the design and testing of a so called ISOKentic measuring probe.

 

Once you have your data points, there is then the laborious integrating the data to derive the mean velocity.

 

As with many things, it is easy to talk about, more difficult to do satisfactorily. To some extent, it is about assessing the error in measurement that is acceptable, then convincing yourself that the result you have from taking readings is within the acceptable limit.

[Dizz]

And so with that we are back to the point I tried to make on 19 Oct: without a wind tunnel and some decent insturmentation we are not going to be able to improve on what we can already achieve using basic testing and well know rules of thumb.

 

Regardless, I hope you can come up with something solid relevant to the higher power levels available now.

 

Afraid the weather put paid to any hope of flying the P1091 and getting a S&L speed today. However I'm moving along with a FD2 I'm building and should be able to provide a range of figures from that over the next couple of months.

[Richard Sharman]

I take your point, Dizz, but it's a bit of a council of despair..? Admittedly we have some dodgy measurements, and some theories which don't quite add up, but that only means there's work to do. Even if we had the Farnborough wind tunnel, and all the equipment at Cranwell, Warton, whatever, we'd STILL need some theory !

 

I'll look forward to some data from the FD2 someday - your picture looks reminiscent of a H Hunter fuselage, interestingly. What factor will you allow for those triangular shaped inlet ducts? Not simply the gross intake area I should think ?

 

In dismantling the Hawk, I discovered that the inner face of the inlet duct (analogous to the inner flat bit before the ducts join in your picture) has become rather soft (it was quite stiff when built, but being hidden cannot normally be inspected). As a result it could either swell or collapse when in use -- could be a cause of low efficiency ? What's the cure?

[Richard Sharman]

What sort of theory are we looking for ?

 

I thought I would just pen a few musings for the benefit of those with nothing to but read forums, so while I'm not flying (it's raining) and waiting for glue to set (on the Hawk replacement wing to new design), here goes.....

 

There are many properties that a good theory should have, but the primary ones I'm looking for in a "theory of ducted fan propulsion" are:

 

1. It should be based on a sound derivation from plausible assumptions. This means that we can not throw a dice, pluck a formula off the internet, whatever. These are not "plausible", even if they right. The assumptions have to be plausible with respect to what we know about physics, aerodynamics, fluid flow, and so on. Of course we may make erroneous assumptions, but these will be corrected eventually. When we derive something from the assumptions we have to do it by logic and algebra. Sometimes we can't derive anything -- it's too difficult, or too contentious, so we have to wait until it gets sorted out.

 

2. It should make it possible to calculate useful properties which relate to our task. This means that if the theory predicts how many cups of tea we will drink between flights, it may be very amusing, but it won't be very useful. It has to make it possible to calculate, say, the speed the plane should fly for a given number of watts input, or, say, the duration of the flight I will get for a particular plane with a given motor and fan. Sometimes we can't do a calculation because we don't know some important number, and so we have to make "guesses", "approximations", whatever. They may be wrong even though the basic theory is right.

 

3. It should make predictions which agree with observations. This means that if it predicts the flying speed of the plane for a given power input AND I actually get to fly the plane AND measure the speed it flies at, then there should be some measure of agreement between the two. We're not looking for perfect matches to 10 places of decimals. Even a rough order of magnitude would be useful, and agreement of +/-10% is probably fine for model flying. If we were designing the next Airbus I would want to do better than that.

 

Why is this useful ? Only because it gives us some criteria we can use when thinking about a proposed theory. There are two cases which are relevant here:

 

Case A. The theory meets criteria (1) and (2) but not (3). This is the case with a lot of what we have discussed in this thread. We have to try to understand what is wrong - the theory, or the data ?

 

Case B. The theory doesn't meet (1), or possibly (2), but it does meet (3). This is the realm of "the rule of thumb" -- it works, but no one knows why. The rule "use 150 watts per pound of model" falls into this category. It's useful, it works (at least sometimes) but you can't explain it. Sooner or later a model comes along for which it doesn't work, and we say "bother, it didn't work - it always worked in the past". So we use another "rule" and say "up the power a bit more". But will this work? More power means a bigger motor and battery, which means more weight, which means higher wing loading, which means we need a higher flying speed,.....

 

Working towards a theory is therefore a "good thing".

 

So, we need a theory !

Edited By Richard Sharman on 02/11/2011 20:26:40

[Tony K]

"Case B. The theory doesn't meet (1), or possibly (2), but it does meet (3). This is the realm of "the rule of thumb" -- it works, but no one knows why."

 

Chaos theory? There is a butterfly flapping its wings in the Amazon which is upsetting our results.

 

Seriously, to prove a theory we need reliable and repeatable results, which depend on reliable measurable inputs. So what can we measure?

 

1. Power input simply done with a wattmeter.

 

2. Efflux velocity. Difficult to measure accurately. As Erfolg wrote, there is a velocity gradient across the duct. There may be turbulence. The flow might not be axial.

 

3. Static thrust. This should be measurable to a reasonable degree of accuracy. Given the thrust and the inlet/outlet dimensions we can calculate the theoretical values of the other factors. The theoretical values can be "massaged" by making some plausible guesses ( eg.the effect of triangular intakes or bifurcated ducts) until an overall theory emerges.

 

It appears to me that a reliable thrust measurement is essential.

 

So, Richard, how confident are you that your thrust measurement figures are accurate?

Do you have a picture or diagram of the measuring apparatus?