FF2017 Int. Race Pace Plane: Beck-Mahoney Sorceress

[Craftydan]

So . . .

I promise, last post of polar charts. I need to show one more thing, but in the process, I noticed something . . .


Pulling up the polar charts of each airfoil over several Re, something popped out:



If you look, the tan line is for 50k Re, which equates to roughly 10mph for this wing . . . notice on several of the charts it separates from the others -- it's particularly obvious on the Cl v. Alpha. What's going on? This airfoil can't maintain laminar flow over that low of an Re -- it's going to work very poorly at low speeds, which is decidedly not-friendly in a landing.

So GOE 611, it was an interesting run, but you're out!

. . . and then there was one . . .

So the last thing I wanted to show with the charts was how to set the AoA on the airframe. We'll assume everything else is streamlined to the fuselage in cruise. Two of the Alpha charts become handy for setting the angle -- Cl/Cd v. Alpha, and Cd v. Alpha -- depending on what we want from the plane:



So if we wanted to go for an efficient flight -- glider or cargo planes -- we look at the Cl/Cd v Alpha. Find the peak and we have roughly the most efficient AoA for that airspeed (Re). The wing will be generating the most lift there for the same drag cost, and the peak doesn't shift much with airspeed. For a glider this means it can create the most lift per unit drag at that AoA, so in strong lift, this is an ideal angle to take in lift (for streamline out of lift we'll pick a different AoA on the airframe, but in flight it will set this my pitching up). For a cargo plane, it sets this angle in cruise and can adjust it's airspeed to balance the lift with it's weight. For this airfoil, it happens just over 6 degrees . . .

. . . and is totally wrong for a racer.

A racer is about speed at all costs. Efficiency isn't the mountain to climb, instead drag is the enemy to conquer. For that, we look at the Cd v. Alpha. Find the bottom of the trough, and there we are. Pulled up the numbers and Cd hit's bottom about 0.5 degrees. At other Re, it varied between 0.5 and 0.75 degrees . . . so 1/2 a degree it is!

Not a huge surprise, but if you look at the foil, the centerline has an upward tilt to it already, pushing the nose down . . . anyone want to guess by how much?


So we import the foil, rotate it up 0.5 degrees (BTW, the bottom is now flat and level), draw a line off the cockpit to the top of the wing, nudge the airfiol a bit to line up . . .




and the wing has a cross section

'bout time

Now we're ready to trace some points, and flatten a few of the primary structures . . .

 

[willsonman]

How embarrassing it would be if you go to fly this and it does not go as planned Just razzing you Dan.

This is an exxcellent write-up on a very math-based approach to design. While my approach is more purely scale-based, I fully appreciate the efforts here. It would make an exceptional FT article. I'm curious though how you incorporate airfoil selection and incidence in relation to tail plane foil selection. A flat plate (foam board) essentially has no lift where a foiled tail can cause lift. Are you just assuming a flat plate at zero incidence?

 

[Craftydan]

Give as good as you get, eh? How'd the Bugatti progress go last night?

To drive this point forward once more (for sanity, more than anything else) anything that resembles an airfoil will do. Practice bears this out and the theoretical experts (in both senses) agree. I've been told already "fold it up already", "pick that one", and "just use a Clark Y and be done with it", and all three were good advise . . . but this was as much about learning than anything else.

I will disagree -- not a math based approach. So far I've only done one calculation -- calculating thickness from T/C, and calculating T/C in terms of "sheets of foamboard". This method involves connecting the Renyolds numbers back to a real-world airspeed (using a handy-dandy calculator), loading up the selected polars in comparison (from a database), understanding what the trends are . . . and the rest is TLAR -- "A" looks better than "B" because squiggly lines. Way more about reading a chart than crunching the math.

Analytical based? Absolutely. A lot of math and experimentation involved in the background? Sure, but I didn't do a lick of it. The key to this method is someone else has done the heavy lifting, all the user needs to do is read the results.

Daunting? sure, but doable.


Now that you've brought it up however . . .

Stupid Polar Math Tricks

So given a polar, can it give some specific answers about how it will perform? Say . . . how much lifting force can we get at straight and level?

If you know Cl, you can

L = (1/2) d v² s CL

Where d is density, V is velocity, s is wing area, and Cl is the coefficient.

read the chart (ok, I cheat and looked at the data set) and at 0.5 degrees, Cl = 0.468. Using the chart here from NASA, d = 0.002377.
We'll try V = 40mph (59 fps), and assuming the full 32" span, twice (biplane), with 6.25" chord, s = 2.9sqft.

So the lifting force = (1/2)(0.002377)(59)²(2.9)(0.468) = 5.6lbs.

20mph? 1.4 lbs.

Change that up a bit . . . if the plane weighs 2lbs, what speed would it fly level?

The Cl was already selected for level flight, so rearrange the equation: V = sqrt(2L/(d*s*Cl)) = 35 fps = 24 mph.

One more change . . . if we're maintaining altitude on this 2lbs plane at 20mph, what's it's AoA?

Solve for Cl, then look up it's Alpha on the chart: Cl = 2L/(d*s*v²) = 0.69

Go back to the chart, and that lands right at 2.75 degrees . . . subtract off the 1/2 degree of incidence and the airframe is sitting at 2.25 degrees nose up at 20mph.

This naturally ignores ALL of the lift contributions on the rest of the plane, and the Venturi effect between the biplane wings, but it's a stupid polar math trick . . . what more can you expect?



As far as tail feathers go . . . yeah, there I'm going to "wing it". Those will be TLAR. Picking a good foil to get matched performance out of it would be the next step, but I'm ready to move on. I'll bevel them for sure -- not sure if it'll just be an edge ironing, or whether I'll shave and re-cover, but the airfoil will not be precise. As far as incidence, it will be set to zero, but the same kind of "minimum drag" analysis I used on the main wing would work for setting that.

Article? Perhaps, but I've got a Sorceress to finish first

 

[DamoRC]

Crafty Dan,

Thanks for the write up of the process for the airfoil selection - a lot of good info and food for thought.

Quick question - can you comment on the difference between building in the AoA for the wing installation versus installing the wing with zero AoA and trimming it out in flight with some up elevator? Are there advantages to building it in versus trimming it out?

Thanks

DamoRC

 

[Craftydan]

Damo,

Glad you're enjoying my bumbling through this mess

Since we're talking modeling, we don't have to worry about a passenger sitting at a negative angle -- funny thing about people, they get fussy about the noise pointing down even though the plane is still rising. Important for full scale, but so long as it's not so extreme it's obvious from the air, it's not a big concern for us.

Streamlining becomes the next major concern incidence addresses. To minimize the drag from the fuselage, you'd prefer the cruise attitude to be aligned with the fuse. Setting your incidence to the preferred cruise AoA, the fuselage presents the smallest profile, and the least drag.

So . . . what about the tail? "Decalage" is the relative angle between two surfaces, which could refer to either the angle between the biplane wings (hey, for once we're actually talking about a biplane!) or the angle between the main wing and the H-stab. In this case, decalage between the wings will be 0 (I've got no reason to dink with that, and I'm not positive what I'd accomplish if I did -- I've read some empirical analysis of it . . . still digesting that and positive I didn't understand it all), but decalage between the wing and tail is up for grabs. If you adjust the wing incidence up by a few degrees, but keep the wing-to-tail decalage at 0, you set the aircraft's cruise angle down by that amount from neutral. This will impact the streamlining -- you present more of the fuselage to drag -- but it might add a benefit: lifting the horizontal stabilizer out of the main wing's wake, making it more effective for it's size. Some airframes this is significant, some it's not, but this little tweak can turn some squirrely plane into something more friendly . . . so long as this is the problem you need to fix.

One last consideration: "Trimming it out" instead of setting incidence and decalage will cause a loss of elevator range, and increase drag form your tail. If you've got elevator throw to waste, with sufficient resolution to make you happy, then trim away. It will costs you a bit in streamlining, but generally models are overpowered and efficiency isn't the primary goal. When efficiency IS the primary goal, then it's time to set both to minimize drag on the wing at cruise.

A spin-off from this . . . as mentioned in the "stupid polar math tricks", if the designed cruise speed were 20mph, and AUW were 2lb, the wing's AoA would need to be at 2.75 degrees to maintain altitude. Yes, there's a lot I didn't account for in that calculation -- I expect the actual angle is likely 50-75% of that -- but if my target was 20mph and I accounted (modeled) the remainder of the airframe, the 1/2 degree would not be the best "cruise" AoA, and therefore, not the best incidence.

Long story short, with my incidence pick, I aligned the wing's least drag with the fuselage's least drag, without considering this might be way below my designed cruising speed for this AUW -- I'll have to angle up the nose to generate the lift I need to stay aloft . . . and I'm fine with this. I don't yet know my AUW, nor do I know how much lift I threw away in those back-of-the-envelope calculations. The wing's least drag is known, so I've used it. The rest . . . TLAR will do in place of the rigorous modeling that I've decided isn't worth further effort . . .


Which leads to the point I'm bouncing around . . . how much of this kind of effort is worthwhile? As a thought exercise, it's invaluable. As practical design? Depends. Usually not this much, but the cutting edge sometimes needs more. It's all up to the designer, builder and tweaker, how deep down this rabbit hole they want to go.

 

[ViperTech]

OK! OK! OK! Pull the rabbit out of the hole and cut some foam man I want to this bird already!

 

[JimCR120]

I have a question. What happens in the competition if the Sorceress, once she enters the race, has an unfortunate (for her) "accident"?

 

[wilmracer]

I have a question. What happens in the competition if the Sorceress, once she enters the race, has an unfortunate (for her) "accident"?

Send up the bugatti to chase folks down?

Things like that are always possible, but Dan won't be constrained by the restrictions on mAh and can just fly in a relaxed style. I'm betting on Dan to finish... the other racers I'm not so sure about

 

[JimCR120]

If a midair collision were to happen and bring Dan down, then a well flown glider could do rather well... hmmm. Maybe a team of racers, some running endurance, others running intercept.

 

[willsonman]

There is a contingency plan. I'll let Dan elaborate as it was his idea.

 

[Mid7night]

There is a contingency plan. I'll let Dan elaborate as it was his idea.

I hope it includes slingshots...

 

[wilmracer]

If a midair collision were to happen and bring Dan down, then a well flown glider could do rather well... hmmm. Maybe a team of racers, some running endurance, others running intercept.

Now there is an idea I like. Like one of those zombie runs or some mad max or death race movie. You get a few racers and a SWARM of guys trying to take them out combat style.

 

[SlingShot]

Now there is an idea I like. Like one of those zombie runs or some mad max or death race movie. You get a few racers and a SWARM of guys trying to take them out combat style.

Flying "tanks" with nozzled props? Something like that could maybe swap paint a little bit.

 

[PsyBorg]

Is it safe? Are the maths gone? Can I come back in here to see where this is at?

Cool stuff though really. It all gives insight as to just how technical things are to make something fly well and fly safe. Unlike our little hobby where you can make anything flt if given enough power to drag it thru the air. I flashed back to math class and the trusty old graphing calculator seeing them plots. I also flashed back to the tiny blond teacher erasing the black boards during class. And I thank you Dan.

 

[Craftydan]

Sorry to drop out for a bit . . . been fighting a cold . . . and a broken sink . . . not fun to do at the same time


Psy,

Your welcome. You apparently had prettier Math teachers than I I still respect most of my math teachers, but easy on the eyes, they were not.


Jim,

This isn't the first time this issue has been discussed (mostly in private), but it's a good point to address -- thanks for asking the question. The contingency plan is "more of the same". I was planing to see if I could get someone willing to standby as an alternate, in case of a failure in the pace plane. Doesn't have to be a crash that sets her on the ground, but in either case something needs to go up in her place to keep the ball rolling.

Until Wilsonman mentioned that we're opening the ranks for "FT Racers" to run in the races (which I fully support -- it's a good way to include more aspiring builders) I was thinking about coning someone into building a Ripslinger for this task . . . might still do that, but it'll need to stand-out among the others. Perhaps taped up with mylar for an all silver finish? Dunno . . . plenty of time between now and then to iron that all out, but I'm willing to take suggestions.



As for demolition derby . . . it may happen -- if we're all trying to *NOT* hit each other, we probably will -- but for some of these airframes a lot of time and care have been put into them.

I'm all for throwing the slapped-together, ragged-out, broken-but-mended, mad-max-worthy beast into combat to watch it live or die, but this is not the same kind of contest. I've done it many times, and I'll gladly do combat again . . . but these races are a test of the fastest or most efficient among 1/6 scale models of a specific era, not the hunt for the most nimble or durable among the worn-out-warriors.


So . . . back to the Sorceress . . . I'm blocking out the fuse as we speak into more foldable shapes . . . I should have something presentable soon.

 

[JimCR120]

Well answered as usual, Dan. Thanks for the clarifications.

I just tonight conferred with my better half and she's saying "yes" to FF'17! So it seems I will finally get to meet everyone in person and their flying artwork.

 

[Craftydan]

Fantastic!

One more reason to look forward to FTFF

 

[willsonman]

Excellent news, Jim! Make your rounds and you will for sure become closer friends with us all.

 

[Craftydan]

Ah, poor abused, neglected thread

2 months is a bit overdue for an update, so I think I'll leave this here:



Naturally, more to come soon . . .

 

[willsonman]

Looks like you could use my printer right about now Good to see some progress here. I'll be pushing the race registration more once FFW is over.