Flap Effects on Turn Radius

[Chuck_Smith]

So it took me less time than I thought it would to fix the truck, I'm burning off some vacation days and decided to take a swag at looking at the theoretical contribution flaps make to turning radius. Most of the ships I build use the TLAR more than calculations since theoretical analysis will only get you so close and CFD is for guys with no eyes for a good airplane, LOL! I prefer conic lofting to plines any day too... and I still think tubes sound better than transistors and when it comes to cars... there is no replacement for displacement.

But anyhoo, Howard always beats me to show my calculations. Took longer to scan the the danged things and post them then it did to do them.

Use your engineer's eye to look at the results. I don't claim the result to be dead on....just in the ballpark...but the comparison with and without flaps is pretty cool.

Now, also remember, this would be flying on the ragged edge at max AoA. In reality we would be something like halfway through the corner before we reached max AoA.

But it was a fun way to spend a few minutes anyway.

Interested in what the other mad aircraft scientists think about my methodology.

Chuck

[Chuck_Smith]

Pages 3 & 4

[Chuck_Smith]

Pages 5 & 6

[Tim Wescott]

OTOH, real world data from flapless stunters is that they turn just fine.  I have, as a newly minted intermediate flyer, had to work on opening up my corners, even with a (quite flapless) Fright Streak to get decent looking square maneuvers.

What flaps seem to bring to the mix is an impression of smoothness: a flapless plane goes around a tight corner with its nose pointing visibly toward the center, where a plane with flaps, with its center of mass traveling along exactly the same trajectory, does so with its nose pointed along the line of flight.  So a flapped airplane looks more effortless.

And lest you discount what I'm saying because of my beginner-ness: I'm just regurgitating things that Brett Buck and others have said on this subject, backed up by my own observation.  You can search around and find their words.  In particular, there's a note (I think by Brett) to the effect that you adjust your elevator-to-flap ratio to get the nose pointed where you want in that corner, then you trim the rest of the plane around that.

[Chuck_Smith]

Yep, not doubting that. The calcs show what happens at incipient stall. We don't fly there. But what you can see from looking at the curves is that the flapped ship will need less angle-of-attack to make the corner, and it will look smoother on the entry and especially the exit of a corner since it doesn't need to over-rotate as much.

Think of it like this, flaps move the lift slope from side to side, so for the flapless ship to reach the same lift coefficient as the flapped one, it requires a greater angle of attack. But as you go further up ( or down) the curve the flap WILL decrease the minimum turning radius. You just need to be flying in that deep to see the reduction.    

[Howard Rush]

I think we use the extra lift capability of flaps to get away with a higher wing loading for a given loop radius, hence less susceptibility to turbulence.

The other thing that flaps do is to provide direct lift control.  It takes some lag out of the transfer function between elevator movement and lift. 

[Chuck_Smith]

...

The other thing that flaps do is to provide direct lift control.  It takes some lag out of the transfer function between elevator movement and lift. 

Yep, I'd agree with that, and they alter the flow field around the horizontal tail increasing it's effective AoA (due to the increase in downwash) thus increasing its effectiveness. In fact, they increase the fuselage's contribution to the pitching moment - but probably not too much on a profile!

[Howard Rush]

Doing some additional ciphering on the thrust effect, it looks like your engine at that speed and thrust would be putting .053 HP into the air.  If your prop is 53% efficient (a reasonable assumption, I think), thats a .1 HP engine.  I'd reckon a stunt engine would have 3 times or so that power, but T sin α is still puny, as you say.  I think that side force on a prop disk at an angle to the flow is a heap more than T sin α.  I don't know how to calculate it, but I know that the extra line tension you get from 1 degree of engine offset in a combat plane is a lot more than you'd expect from T sin α.  

[Chuck_Smith]

Yep, but remember, with a fixed pitch prop the thrust is a function of airspeed. The propeller's advance ratio is fixed and the RPM is (generally) constant. So as we go faster, the momentum transfer becomes less and less. At some point mdot deltaV = drag and we stop accelerating. mdot is the density* disk area*Deltavelocity. Density and area are fixed, so deltaV is the thrust variable.

Fixed pitch props are cool because they behave similar to jets. The difference being that the exhaust velocity on a prop is determined by advance ratio and rpm, whereas the jet exhaust is determined by the thermal choking point at the end of the combustion chamber and the nozzle geometry and back-pressure.

So the thrust you feel on the ground at launch will be considerably more than what you get at cruise.

[Chuck_Smith]

Another thing to note is the analyis is at pullup. If we are vertical mg has no effect and when inverted it will tighten the radius, i.e., the turn radius is not constant but will vary by some factor of
1/cos(rotation angle)

[Brett Buck]

Yep, but remember, with a fixed pitch prop the thrust is a function of airspeed. The propeller's advance ratio is fixed and the RPM is (generally) constant. So as we go faster, the momentum transfer becomes less and less. At some point mdot deltaV = drag and we stop accelerating. mdot is the density* disk area*Deltavelocity. Density and area are fixed, so deltaV is the thrust variable.

Fixed pitch props are cool because they behave similar to jets. The difference being that the exhaust velocity on a prop is determined by advance ratio and rpm, whereas the jet exhaust is determined by the thermal choking point at the end of the combustion chamber and the nozzle geometry and back-pressure.

So the thrust you feel on the ground at launch will be considerably more than what you get at cruise.

     Depending on the engine/prop, dramatically more, like a factor of 5 for a piped stunt plane running low pitch and correspondingly high RPM. I had a simulation of this  back in the mid-80s, once it had dawned on me what was going on. It resulted in very decent speed control even with no engine response at all. That was like a light bulb over my head and it dramatically changed what I was doing with engine setup since. There are some absolutely epic threads on SSW about this, one of which ended with me throwing up my hands in frustration due to no one wanting to "believe" it. That's also when I started putting the word "power" in quotes.

  I don't really get what you are referring to in the middle - it's almost the reverse of a jet, which is very poor in this regard, in some cases, it works in reverse, where the thrust goes up with increasing airspeed. My simulation also suggested that at prop did this at very low speeds, since portions of the blade was stalled at rest.

    Brett

[Howard Rush]

Another thing to note is the analyis is at pullup. If we are vertical mg has no effect and when inverted it will tighten the radius, i.e., the turn radius is not constant but will vary by some factor of 1/cos(rotation angle)

Constant radius is a more useful assumption for stunt.  Here's some calculation: http://stunthanger.com/smf/index.php?topic=25255.0

[Chuck_Smith]

    Depending on the engine/prop, dramatically more, like a factor of 5 for a piped stunt plane running low pitch and correspondingly high RPM. I had a simulation of this  back in the mid-80s, once it had dawned on me what was going on. It resulted in very decent speed control even with no engine response at all. That was like a light bulb over my head and it dramatically changed what I was doing with engine setup since. There are some absolutely epic threads on SSW about this, one of which ended with me throwing up my hands in frustration due to no one wanting to "believe" it. That's also when I started putting the word "power" in quotes.

  I don't really get what you are referring to in the middle - it's almost the reverse of a jet, which is very poor in this regard, in some cases, it works in reverse, where the thrust goes up with increasing airspeed. My simulation also suggested that at prop did this at very low speeds, since portions of the blade was stalled at rest.

    Brett

Brett, depends on how you look at it with a jet. Yes, at very low speeds we get into capture area difficulties with diffuser or tunnel effects that limit the change in enthalpy to below thermal choking at the end of the combustion chamber(s), but once we get near cruise everything is working like it's supposed to, and if we are running at maximum thrust (with or without reheat) the limit is still the thermal chocking point as the propellent - in this case mostly nitrogen and combusted oxygen and hydrocarbons - reaches Mach 1.  No more heat can be added. So next we go through the turbine stages to extract some energy to run the compressor, and we now can add that energy back in as reheat, up to the sonic choking point. Now it's game over, the flow will take no more energy and it's all a function of how we expand it through the nozzle. So that fixes the exhaust velocity regardless of airspeed, so the thrust becomes the mass flow rate times the difference in exhaust and inlet velocities. Since Vexh is fixed by the laws of thermodynamics... you get the picture. 

But that's a turbojet, and those old zero-bypass low tsfc engines are dinosaurs, today everything is high compression, high-bypass, high tsfc fans, even in new fighter designs.

The next generation of pilots may never be able to look at the lead plane on a night formation takeoff and see shock diamonds in the exhaust. End of an era.

[Eric Viglione]

As I look back on this past Sunday where I scrubbed down my plane after a nice day at the field, what I really want to see is a chart that explains why I had to scrubb as many bugs off of the trailing edge of my flaps as the leading edge of my wing.

EricV

[Tim Wescott]

Yep, not doubting that (that flapless stunters turn as tight as need be -- TaW). The calcs show what happens at incipient stall. We don't fly there. But what you can see from looking at the curves is that the flapped ship will need less angle-of-attack to make the corner, and it will look smoother on the entry and especially the exit of a corner since it doesn't need to over-rotate as much.

So the whole thrust of the thread is misplaced -- the effect of flap on the turn radius is nil, because even with a flapless stunter the pilot is holding the aircraft back from turning as tight as it possibly can in an effort to achieve a smooth maneuver and to not lose too much speed to induced drag.  So (assuming decent turn performance), neither a flapped nor a flapless ship is giving its all in this regard.

Thus, "flap effects on turn", or perhaps better yet "flap effects on turn aesthetics" is the better title for the thread (and direction of the analysis), with perhaps an introductory calculation that shows what you can do with a Skyray, Flight Streak or whatever.

I see the whole discussion of "how do I use flaps to turn tighter" (I think I even asked it myself) being asked, against a background of the guys who've flown flapless extensively stating that you don't need flaps to fly the pattern, and the top dogs giving occasional instruction on tweaking flap to elevator ratio to get a better looking corner, and it all leads me back to thinking that if you think that you're putting flaps on your plane to turn tighter then you're doing the right thing, but for the wrong reasons.

As near as I can tell (and I'm definitely in the wilderness as far as my own direct experience goes, so I'm open to correction here), the tradeoff with flaps is not for maximum lift.  The limitation on lift in the corners seems to be one of induced drag and turbulence, which means that that fight should be fought primarily with aspect ratio (and aspect ratio has its own problems, which is why there's not many semi-scale stunt YO-3's to be seen in the stunt circles).  So thinking that you are aiming for maximum lift with your flaps, rather than for the look of smoothness in your corner, would mislead you in you design quest.

[Chuck_Smith]

Tim, I was never claiming to be saying one  way or the other is better.
 
Please forgive me if I gave that impression. 

I was simply looking at the aerodynamics to explore some equations ...I'm an aerospace engineer so it's an occupational hazard...and gain a better understanding of what's going on. More for my own curiosity than anything else.

Chuck

[Tim Wescott]

Well, knowing that there's margin is good.

I've been getting progressively more fascinated by the whole subject of the stunt ship in a turn, precisely because (at least as far as I can tell) it is this enormous tradeoff between lift, induced drag, power, and handling in the wind.  I suspect that stunt ship design would be considerably different if contest venues were all set up inside of 200 foot diameter wind tunnels operating at sea-level pressures and capable of generating turbulence-free, finely adjustable breezes between 0 and 10 miles per hour.  Instead, we get ships that must work at a variety of air densities, in air that's calm or windy, with wind that's steady or turbulent, etc.

[Howard Rush]

Tim, I was never claiming to be saying one  way or the other is better.

I was. 
 

[Igor Burger]

I think that side force on a prop disk at an angle to the flow is a heap more than T sin α.  I don't know how to calculate it, but I know that the extra line tension you get from 1 degree of engine offset in a combat plane is a lot more than you'd expect from T sin α.  

At least I do not see any theoretical background to calculate it that way. It could be better from static thrust, but it is also not proper because prop can be stalled. :- ))))

[Igor Burger]

Chuck ... why you think the lift of the tail is 20% of wing? I think it is way overestimated. :- )) ... also I did not get that part of larger or smaller tail, I would say that the size of the stab does not affect the lift produced by tail (at least not to degree which can change any result)

BTW what was the conclusion?  

[Chuck_Smith]

Igor, good question. I eyeballed it. based it on:

1) the ratio of the areas
2) the horizontal tail flap is .5c and the wing flap is .2C (generally)
3) I guessed!

To make it better you can replace .8L with 1/2*rho*V^2*Clsubt*tail area  where Clsubt is the 3D lift coefficient for the tail with the correct flap size and deflection.

If you want to go really crazy you can calcuate the downwash angle from the wing and add that to the tail AoA too.

And then add in the time delay for the shed vortex from the flap to reach the tail, but since that about 1/78 seconds I think we can ignore it.

We can fine tune it, but the fun thing that pops out if the whole analysis is that the turn radius is directly proportional to wing loading and inversly proportional to the lift coefficient. 

 Radius = f(1/Cl,m/S),  but what I'm trying to get my head around is that we have V^2 in the numerator and V^2 in the major term in the denominator. I guess it makes sense. The required acceleration as well as the force creating it are both dependent on V^2. It makes sense from a dimensional analysis standpoint too...we remove them both (disregarding the weight) and we end up with the same units - length, so that makes me feel good.

[Igor Burger]

yes I saw in your text that it is from tail to wing area, but it can be only in case that the lift coefficient is the same, I do not see any background for that (and I think it is simply wrong) ... that is my question, why you think it is the same? ... because my calculation tells me that the negative lift on tail of my model im my radius (3.5m) is 1/10 of coefficient of wing, so the lift on tail will be 2% and not 20% ... yes I have large tail, but if I change area of tail to half, I will get twice the CL ... and if I move CG front, I get also higher tail lift ... so how it fits to your eyeballing? ... something is missing I would say, and it is not 3D flow  ... you cannot derive exact numbers like 42.lbs from wrong theory :- ))))

[Tim Wescott]

It seems that the right way to solve for tail downforce is to assert that you are solving for the forces when the plane is in a stable turn with a constant turn rate.  If that is the case, then the sum of all the moments on the plane must be zero.  So, look at the moment generated by the wing around the center of gravity, then solve for the downforce necessary at the tail to zero out that moment.  Or if you don't like that, pick any other point and look at the sum of all the moments including the moment due to the acceleration of the plane.  No matter how you slice it, you'll either end up with zero moments, indicating a solution, or you won't.

Do that, and do you need to assume anything about the tail at all, other than it's supplying whatever downforce is necessary for the constant turn?

While you're doing all these calculations, are you assuming that the effective airfoil shape is equal to its actual shape?  (See Ziac's Circular Airflow).  In a 5-foot radius turn, (if Frank is right), the wing has effectively gained 0.3 inches of negative camber -- how does this affect one's computations?

[Igor Burger]

It seems that the right way to solve for tail downforce is to assert that you are solving for the forces when the plane is in a stable turn with a constant turn rate.  If that is the case, then the sum of all the moments on the plane must be zero.  So, look at the moment generated by the wing around the center of gravity, then solve for the downforce necessary at the tail to zero out that moment.  Or if you don't like that, pick any other point and look at the sum of all the moments including the moment due to the acceleration of the plane.  No matter how you slice it, you'll either end up with zero moments, indicating a solution, or you won't.

Yes, other point is much easier as it gives much better visualization, if you take it to AC of wing instead of CG, then you can easily calculate CG moment from centrifugal force, lift of wing is in AC, so you not need to count it, you know the pitching moment also to the AC of wing from airfoil pitching moment coefficien, the same you have to do for tail aiffoil with deflected elevator and all of that must be ballanced by lift of tail on known arm ... so I mean the lift of tail is independent on its area (if we do not count other minor details like pitching moment of tail of different area) ... the area of the tail will only change its lift cofficient, but not the lift itself, the same radius simply needs the same force to keep it on the same radius of flight ... in my case it was very close to zero (compared to wing or also max cl of tail) ... actually 0.2 ... so it means that radius of the corner is defined more by place of zero lift AoA then induced lift coefficient, 3D flow, lift curve slope or so ... but I wrote in another 2 threads, now I see I did not explain it enough :- )))

[Igor Burger]

While you're doing all these calculations, are you assuming that the effective airfoil shape is equal to its actual shape?  (See Ziac's Circular Airflow).  In a 5-foot radius turn, (if Frank is right), the wing has effectively gained 0.3 inches of negative camber -- how does this affect one's computations?

do you know this picture? :- ))) I posted it some years ago :- )))

[Chuck_Smith]

Igor, good stuff.

I ignored the moments since I was not interested in the pitch rate. I wasn't looking at it as a stability or control exercise, instead more as what happens after the pitch change. Yes, the pitch rate will affect the radius of the turn on the pullup, increasing it. Also, I used data from a split flap which won't give as high a Cl as your CFD, but again, if I use a second-order vortex panel method or similar the analysis will show a pretty optimistic result because it will neglect separation effects.

When you combine low Re's with the vibration from the engine and the flexing of the covering the chances of actually hitting the max Cl (or any theoretical Cl for that matter ) are pretty remote. That being the case, the split flap data seemed ( to this engineer's eyes ) to be a good compromise. That may be a faulty assumption, but I'm old enough to have worked with sections in the wind tunnel so I know that the experimental Cl will be less than the CFD computed. Plus, my wings aren't perfect as I generally use built-up vs foam.

Might be fun to build a trailing edge rake and install a micro data-logger...that way we could get the real numbers on the wing's lift and drag. 

I'm not claiming the numbers to be spot-on, just using ballpark numbers to find the relationships.

[Tim Wescott]

I ignored the moments since I was not interested in the pitch rate. I wasn't looking at it as a stability or control exercise, instead more as what happens after the pitch change.

The point that Igor and I are singing in harmony on here is not directly about stability.  It's about figuring the lift of the stabilizer.  If you assert that the airplane is not undergoing angular acceleration in the pitch axis, and if you know the pitching moment of the airfoil and the moment arm between the MAC of the wing and the CG, then you don't have to know anything at all about the tail in order to know how much lift it must exert as a proportion of wing lift -- because that proportion is dictated by the factors I listed.  This is sophomore ME stuff -- remember Statics?

[phil c]

I was going to point out Igor's airfoil shape problem.  A flapped stunt wing doesn't have a linear Cl/Cd.  Its actually a curve.  0 at 0degAoA, as you give control, the wings camber and AoA change, so you have to pull the Cl number off a curve of the wing with a flap deflected, which is higher than the unflapped foil.  The higher the deflection, the more the lift is increased, vs. an unflapped foil.

Igor posted pictures somewhere showing his very competitive plane in a "corner of tight radius".  It showed that the fuselage AoA was about 7 deg., with flap deflection of about 22deg. giving a total AoA of about 14 deg.  So the approach would be to compute the airfoil with flap deflections of say 1 deg, in 14 increments of deflection, and then pick points off each of the curves to correspond to Cl at each effective AoA, up to say 14 deg.  The result would be a convex curve, since each airfoil generates progressively more lift at the same AoA of an unflapped symmetrical airfoil.

[Chuck_Smith]

Tim,
I see your point. I'm just not convinced the Cm from the curves are reliable at low Re. If we get a separation bubble and vorticity as will happen in the real-world case, and and with it the earlier onset of transitional flow, the Cm can vary significantly from CFD. Unless you are using a program that takes the kinematic viscosity of the air into account, at low Re the curves are not going to match experimental results due to the higher ratio of viscous forces to momentum.  

So ...IF... you could experimentally determine the Cm/alpha yes, you can use statics.

I'll dig around my library. Somewhere...if I can find it... and the papayrus it's written on hasn't crumbled. I have 0016 data I took in the small wind tunnel at very low Re. IIFC it showed a lot of funk around 5 deg. where the curve "bent" and changed slope with corresponding discontinuity in moment. The data has some iffyness too it since I was down at the hairy edge of being able to read the tubes and the force sensors where at the low limits of linearity. Balance for the sting was probably in a friction effected area too. We also did the H2 bubbles in water trick. You could see the separation start at low V's and then straighten out as the flow velocity increased.    

Phil, the flap won't really change the curve much, it will shift it "to the left" and up, but the slope will remain the same.  

 

[Howard Rush]

JavaFoil and XFoil give different results for different Reynolds numbers, so they must have viscosity in 'em.  There are also good low-Reynolds-number airfoil wind tunnel data around now from the U's of Illinois and Stuttgart.  Alas, I don't know of any for flapped stunt airfoils.  

For flap effect on lift curve slope of an Impact airfoil, see the silly discussion we had awhile back on SSW about the definition of angle of attack.  

Using the Cm_o of Igor's airfoil above and the airplane dimensions from the recent stab aspect ratio discussion, it looks like it would take a stab Cl of -.75 to balance the pitching moment due to flaps (=Cm_o ).  Wow.

edit: I changed Profili to JavaFoil, which is what I meant to write.  Profili includes XFoil.

[Igor Burger]

It depends on tail length, tail size and also on wing aspect ratio :- ))))))))))))) ... so the aspect ratio can change maneuvering properties much more by its moment then lift slope angle :- )))

[Howard Rush]

Here I go being two-dimensional again.  For an Impact wing with your Cm_o and tail length = 2 macs, stab Cl to balance Cm_o would be -.56.