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Science of formation drag reduction

scsmith

Well Known Member
OK, now that we got everyone excited, I thought I would write just a bit on the science of what is going on, and especially, how it is that the lead plane benefits in a V formation.

The first thing to understand is simply that there is a circulating field around an airplane because of the trailing vortices. There is generally upwash outboard of each trailing vortex, downwash inboard, and sidewash above and below. Mathematically, we can compute what the induced velocity is, based on the distance from the vortex -- for a vortex that starts at one point and trails downwind to infinity (they almost do!;)) the tangential velocity drops off as 1/r, r being the perpendicular distance from the vortex. But also significant is that the effect extends significantly upwind of the origin point of the vortex. As you would expect, the farther upwind of the origin point you go, the weaker the induced flow is, but it is important to understand that it does extend upwind - the tangential flow can't just abruptly stop at some point, it decays slowly with distance. If you want to look up the actual math equation for the tangential flow, its called the Biot-Savart Law.

Next, why does flying in an induced upwash field reduce the drag? Mathematically there are couple of different ways to illustrate this, each gives the same answer. For those of you that have some technical background, it comes from the Kutta-Joukowski theorem that describes the force acting on a vortex in cross-flow. Just as the lift comes from rho x U x gamma, induced drag (or thrust) comes from rho x W x gamma. So if W is positive upward, you get thrust on the bound vortex. For lay folks, perhaps easiest to understand is to consider a glider flying along a ridge where the wind is turned upward by the ridge, and the glider is able to fly level along the ridge because of the upward flow. You could say that the glider is still descending through the air at its normal sink rate, but the whole parcel of air, with the glider in it, is being carried upward at the same rate. The glider doesn't know that it is flying level, it thinks it is decending through the air. So, a powerplane flying in an upwash field can reduce the amount of power needed to fly level at the same speed, because it thinks it is descending through the flow.

OK, now to formation flight. One interesting case is line-abreast formation. In this case, each airplane feels some upwash from its neighbors. There is a superposition effect. The tip vortex from my neighbor's nearest tip is producing a lot of upwash for me, but the vortex from my neighbor's far tip is producing some downwash for me. But it is farther away, so it is not as strong; there is a net upwash. If there is another airplane beyond him, I feel weak effects from those vortices too - each airplane in the line adds some upwash from its near tip, and less downwash from its far tip. The guy in the middle is feeling net upwash from every single airplane in the formation, and he gets the most benefit in the formation.

Another interesting case is a very pointy V formation, where the 'sweep angle' of the V is large. In this case, the lead plane feels very little benefit, because it is too far upstream of its neighbors. Each plane is flying in the strong upwash of the neighbor in front of it, and getting a MUCH weaker benefit from the neighbor behind it. The planes near the tail of the V are feeling the accumulated upwash of the whole family of trailing vortices, and get the most benefit.

Now here is where it gets cool -- at least I think its cool: There is an optimum V angle, in between the two cases I described above, where the accumulated benefit of all the vortices produces EQUAL benefit for each plane in the formation. The V angle is flat enough so that there is enough upwind effect from each airplane to benefit the neighbor in front of it just enough so the net benefit is equal for each plane. This result, mathematically optimized, was first published by Peter Lissemann in 1970 in a science journal. You might recognize Peter Lissemann's name as one of the co-founders of Aerovironment along with Paul McCready. So this explains why we measured a substantial benefit for the leader.

Anyway, the cool thing about this ideal V angle is that it is self-seeking. In a flock of birds, if the ones near the middle of the formation are stronger, they pull ahead, making the V angle steeper, thus benefiting the birds out toward the tails of the V so they can catch up. If the birds near the middle of the formation get tired and drop back, making the V angle flatter, then they, near the middle, feel more benefit, so they can rest. So the V angle is stable -- birds naturally fall into the right angle that allows all the birds to keep up the same speed.

As far as the actual fuel saving....one wild card in our method is fuel-air mixture. Carburetors and fuel injection don't necessarily maintain constant fuel-air mixture as you change throttle setting. On my Bendix FI, if I lean to peak EGT at cruise power, the mixture lever is not as far back as if I lean to peak at idle. We got very significant reductions in manifold pressure in formation, and I think on some of the airplanes, the fuel flow reductions were similar. In some of the planes, the fuel flow reduction seemed less than I expected based on manifold pressure reduction. What I can say is that the actual fuel flow measurements from the instruments in the West Coast Ravens airplanes were extremely accurate. We were down to counting pulse-widths and averaging over significant lengths of time.

The other variable, of course, is how well each airplane stayed in its "sweet spot". The best position actually has some wingtip overlap, which is a position that the formation guys are not used to. Although the flow is smooth in that position (not the difficult task of holding in perfect trail), it is fairly dynamic - the roll moment and side force are changing as you move around in the vortex. And of course, there are throttle excursions all the time to hold position, which tend to offset some of the benfit.

All told, I was really pleased that we got the results we did, about 3-5% benefit for each plane. When we did the two-ship F-18 test, with some cockpit display aids using differential GPS to help hold the optimum position, we saw more like 12% (and there are some good stories about those tests too!)

Anyway, glad you all enjoyed the show. Not RV-related, but I also worked on an upcoming episode called Fireworks Man #2, so watch for it.
 
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One of the most interesting and informative posts I've seen in VAF. Good stuff here for the tech and lay person alike. Thanks!!
 
Thanks, Steve

I never heard this before and it makes sense.

Now all we need is a way to slave the autopilot to the optimal spacing in the formation and we will save big bucks when going to fly-in's.

Kent
 
So this is why the Jedi says, "May the FORCE be with you!" [also an old engineering school joke]

Seriously, Steve, I thank you for posting enough of the science to make it interesting and also enough of the practical to help us understand and accept it.
Please post again.
 
Excellent post Steve! Now here is a question I have always wondered about (but never heard enough to look it up). Geese have eyes on the side of their heads - not the front, like humans. SO their normally "relaxed" look angle is somewhere to the side of straight ahead. I have always wondered if their "relaxed" look angle corresponds to the angle of the V - and if it does, and that angle is the same as the optimum angle (which as you point out is naturally stable), it sure would be an interesting argument in the direction of evolutionary optimization.

I guess we need an ornithologist to chime in here.... ;)

Paul
 
aerodynamics for dummies?

Steve, great explanation, even without pictures and diagrams!

some day I hope to be able to make up stuff like "....Kutta-Joukowski theorem that describes the force acting on a vortex in cross-flow. Just as the lift comes from rho x U x gamma,.....
that is sweet!...

I like Paul's idea ....what was it? ....that as our eyes evolved to the front of our faces, our ability to fly tight formation has diminished? No wonder I washed out of air cadets....too far evolved!!! :)

..something like that, or, I could be completely wrong here, eh?
 
Bird's field of view

I remember seeing drawings depicting the view angles of various animals, including birds. They have a wide enough field of view that they do have some stereo vision straight ahead (which makes sense, it would be hard to land without depth perception, let alone pluck a kernel of corn off the ground). If the relaxed focal axis of their eye orientation just happened to coincide with the optimum V angle for formation, that would be just AMAZING, but not impossible, whether you think of it as the blind watchmaker of evolution or the wisdom of a creator.
But of the various tasks that birds need to use their vision for, watching the red-head in the lead plane is probably farther down on the list than, say, finding food. So I kind of doubt there is a connection.
Intriguing idea though!

By the way, I should have mentioned that the optimum V angle varies with the number of members of the formation. Although, for populations above 5 or 7, it pretty much converges to a certain angle. With RV's, we could not safely fly at the optimum V angle with the optimum overlap, because it put wingtips too close to horizontal tails. So we flew a bit more steep V than would be best. Nice that the lead still showed benefit.


Excellent post Steve! Now here is a question I have always wondered about (but never heard enough to look it up). Geese have eyes on the side of their heads - not the front, like humans. SO their normally "relaxed" look angle is somewhere to the side of straight ahead. I have always wondered if their "relaxed" look angle corresponds to the angle of the V - and if it does, and that angle is the same as the optimum angle (which as you point out is naturally stable), it sure would be an interesting argument in the direction of evolutionary optimization.

I guess we need an ornithologist to chime in here.... ;)

Paul
 
...But also significant is that the effect extends significantly upwind of the origin point of the vortex...

But that only holds for subsonic speeds, right? Not that it has much relevance to the RV community, but that must have had some bearing on the F-18 application.

Thanks, Bob K.
 
But that only holds for subsonic speeds, right? Not that it has much relevance to the RV community, but that must have had some bearing on the F-18 application.

Thanks, Bob K.

The F-18 tests were all done subsonic. I don't think they spend any time in formation going supersonic - well, at least what we think of formation. They might have a combat spread that puts them a quarter-mile apart or something? A bit of thread drift, but maybe some figher-jocks can chime in?
 
Do you feel this relates to RV's flying in formation? I offer that we are too far apart to feel these effects
 
It's all a lot of bunk.

The only guy who will save fuel is the lead because he is not pumping the throttle to stay in position. :) :)
 
Steve,

Great explanation, it was fun to read it here after learning it from you and flying it with you!

I'll post my impressions of the experience with the science from a formation flyer's perspective...I figure you guys might want to hear what it was like to fly this position.

By the way, for those that don’t know Steve, he’s an RV-8 builder and flyer (nice 8!) and an accomplished glider pilot as well. He knows the practical as well as the theoretical…and is a fun guy to fly with too!

First, I will say that when Slick contacted me after Steve approached him about doing the show I was, of course, enthusiastic about doing the show, but pretty skeptical about being able to show a benefit. My gut said that the throttle movement to stay in parade would mean decreased fuel efficiency for a wingman (as Dave postulated above). Then Steve explained the optimum position to us, some of the science behind it, and we went out and did some proof of concept flying. Doggone it if it didn't work...and pretty darn well!

First, to answer Stripes' question: It would not apply to our standard RV formation position. I'd have to defer to Steve to define where the standard parade position exists in the flow around the aircraft, but it is definitely not in the optimum drag reduction spot, which we started calling "the sweet spot", in our practice and in the filming hops.

The sweet spot, using formation terms, is sucked (aft), inboard, and stepped up from the normal 45 degree parade position. To get there, we moved aft from the lead (or the aircraft ahead in the formation) to gain a little extra nose to tail (about a plane length). Then we stepped up very slightly above the aircraft ahead, and then moved inboard to find the sweet spot. In the larger formations, we actually started out in a wide route position, then moved up, over and in, in sequence...and we each called "in" when we found the spot and were stable, so the next wingman could move in.

That spot turned out to be about where the pilot's eyes are sighting up the outer edge of the wingtip of the aircraft ahead (perhaps just outside of that), and looking slightly down at the top of the wing of the airplane ahead. So there was significant wingtip overlap, but nose to tail spacing was maintained for safety.

As you move the airplane into the sweet spot, you can feel the roll forces change, and when "in", it requires inboard aileron and outboard rudder to stay "in". It was very controllable, but very noticeable. If you were "in" and released the controls, it would roll you out of the spot, away from the aircraft ahead. We did that in early tests, but not with the big group. As we moved around, in and out of the sweet spot, the roll forces changed quite a bit, sometimes going away, sometimes reversing, as we moved around the spot and practiced staying “in”.

Our early tests with Steve coaching us were with Slick Cone, Spike Randolph and me in a small V formation, taking turns finding and flying in the sweet spot. We then put two in the sweet spot in a V, and we even played with a "reverse V" with Spike and I line-abreast, but split just enough to put Slick behind and between us, and in the sweet spot from both of us. That position showed a huge benefit to the trail guy, as you would expect. We didn't measure the fuel flow closely on that practice run, but we had Slick freeze his power hand, and then Spike and I widened out to remove the benefit...and Slick quickly disappeared in our rear view mirrors...impressive! That exercise was scrubbed from the filming list as not fitting for the V formation myth in a clear way for the TV audience, but it was eye-opening!

During practice, we played with lead at a constant power, and lead at a constant airspeed, to see the results. When I was lead (in practice), at a constant speed, my fuel flow decreased very slightly, but was hard to see a big drop. However, at a constant power setting as lead, with just two wingmen "in", my speed as lead increased 2-3 knots (110 knot baseline speed). I then slowed back to baseline when they left the sweet spot. As a wingman, in practice and during filming, my fuel flow decreased from the low 13 gph range to the high 11 to low 12 gph range, as noted by Steve in my right seat…a decrease somewhere in the 7-8% range, which was slightly above average for the group. Steve felt that may be because my wings are clipped slightly, and I may have benefitted more from the “assist”.

We also practiced the line abreast position in close formation, and showed that all aircraft did benefit, but lead benefitted more, as was shown in the show. That formation was challenging, as we maintained close wingtip to wingtip clearance, but we approached it very carefully and slowly. We used a decreased formation size for that part of the show, and were fortunate to have very smooth air for filming, allowing us to close in pretty tight.

The last formation we did was the trail formation, or what was termed “drafting” or "conga line". We used a smaller formation for that as well, and moved into position one at a time for that as well, until we were all in. Since we were in the prop wash of the aircraft ahead, it was really not much fun at all to fly, and it took a lot of control force and lots of big corrections to stay in place. We held it for 2 minutes once all were in, and it was asked more than once on the radio, “how much longer?”! We had plenty of nose to tail on that one for safety, and were happy to be done with it after the 2 minutes!

All in all, it was quite an education, and it was a great exercise in precision flying with trusted friends and RV formation colleagues!

It anyone has questions about the flying, the techniques, or the results, please do ask away…I’m sure the WC Raven gang would love to share their experiences with the science we experimented with! We approached it very methodically and professionally, kept safety as our primary concern, and had a lot of fun in the process!

Cheers,
Bob
 
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Disclaimer and "Vortice?"

"Don't try this at home."

Before any RV pilots go out for the Saturday morning breakfast flight tomorrow morning with the thought of flying V formation, please reconsider. I think it's obvious you should be a skilled and pre-briefed group of pilots before trying to save a few quarts of gas by flying in V formation.

I thoroughly enjoyed the show, but I'm also reminded of the loss of an XB-70 and two test pilots due to wingtip vortices so long ago. The video is dramatic. Of course I wouldn't expect an RV to roll inverted when flying close to another RV but those Air Force pilots were professionals.

Y'all be careful out there.

P.S. Just as a reminder, the grammar lesson for today is "Plural forms of English words derived from Latin." "Vortex" is singular, and "Vortices" is the plural word. An alternate plural form is "Vortexes," but there is no such word as "Vortice" often pronounced "Vor-ta-see" as a singular form of "Vortex." English is so confusing.
 
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Welcome to VAF!!!!

Jake, first post I see:D

Welcome to VAF.

Rosemond, seems that there may be an RV or two close by you;)
 
Birds

Anyway, the cool thing about this ideal V angle is that it is self-seeking. In a flock of birds............

This reminds me of one of my favorite jokes with laymen when a discussion of bird aerodynamics arise.

"Y'know how birds fly in a V?"

"Yep"

"Ever notice that one leg of the V is always longer? Know why that is?"

"Nope"

"There's more birds on that side......"
 
"Don't try this at home."

Before any RV pilots go out for the Saturday morning breakfast flight tomorrow morning with the thought of flying V formation, please reconsider. I think it's obvious you should be a skilled and pre-briefed group of pilots before trying to save a few quarts of gas by flying in V formation.

I thoroughly enjoyed the show, but I'm also reminded of the loss of an XB-70 and two test pilots due to wingtip vortices so long ago. The video is dramatic. Of course I wouldn't expect an RV to roll inverted when flying close to another RV but those Air Force pilots were professionals.

Y'all be careful out there.

I almost said "Please don't try anything you see at home. We're what ya call...experts!"...ahem! But I think Adam and Jaime might have a copyright on that! ;) The filming was 4 months + of preparation, from early briefings to planning, to practice, to execution. Practice and filming hops were fully briefed, just as any Raven formation hop is...mucho detail. All participants were/are carded FFI Wingmen or Flight Leads, as Shady (Joe Blank) posted in another thread on the MB flying.

Joe's point is good...hope it didn't sound like I was saying go out and play with it. It definitely should be approached with due caution, and one should have a solid foundation in formation flying. "In" is not actually in the vortex, but is using the vortex. However, while finding "in", it is possible to get pushed around in the vortex. The vortices of the RV are to be respected, as with any airplane, and we approached it very carefully. We practiced multiple times locally and enroute to a formation airshow we flew, so we had a lot of time practicing this.

Would it be something we would use to save fuel...not likely...too much work and too much beautiful country to see out there!

Now if I coulda found 3 more knots at Reno and closed the gap to Greg Nelson and his F1 Rocket, would I have used it...I aint sayin'! ;)

One more OBTW...the trail, or "drafting" (as the producers called it) position was used in the show to prove that what we were doing in the sweet spot is not like drafting in a car. It used more fuel, and was very uncomfortable. Not worth experimenting with at all out there, IMHO.

P.S. Just as a reminder, the grammar lesson for today is "Plural forms of English words derived from Latin." "Vortex" is singular, and "Vortices" is the plural word. An alternate plural form is "Vortexes," but there is no such word as "Vortice" often pronounced "Vor-ta-see" as a singular form of "Vortex." English is so confusing.

I used it correctly in the above passage, right Don!?!? As an Aero major, I looked back at my first post here to make sure I didn't say vortice...I would have been aghast! :p

The F-18 tests at NASA were actually able to get up near 20% drag reductions. They also used an automated control system that used differential GPS to hold the trailing aircraft in precise locations.

A technical report on the results are published here for anyone wishing to see more details:
http://www.nasa.gov/centers/dryden/pdf/88749main_H-2505.pdf

Steve told us quite a bit about the Hornet experiment. He said that they were able to find the spot at quite a long nose to tail distance. We worked with that, and tried finding the sweet spot at longer trail distances. It was there; however, it was quite elusive, and hard to stay in long enough to show any benefit. We used a nose to tail that was safe, yet easy to find...and stay...in the right position.

This reminds me of one of my favorite jokes with laymen when a discussion of bird aerodynamics arise.

"Y'know how birds fly in a V?"
"Yep"
"Ever notice that one leg of the V is always longer? Know why that is?"
"Nope"
"There's more birds on that side......"

Of course, as formation pilots, we were conspicuously concerned with symmetry...especially with the entire RV community...and Kari...watching! ;)

Cheers,
Bob
 
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no one said it!

"Don't try this at home."


P.S. Just as a reminder, the grammar lesson for today is "Plural forms of English words derived from Latin." "Vortex" is singular, and "Vortices" is the plural word. An alternate plural form is "Vortexes," but there is no such word as "Vortice" often pronounced "Vor-ta-see" as a singular form of "Vortex." English is so confusing.

I checked using the search feature. You are correct of course, and it is a common error. But cudos to the RV gang that no one made that error. As Bob said, I would be agast.;)
 
The Germans Worked on this too... in WW2

Great post Steve!

When I frist heard about this I remembered that there is a short article on it in Hoerner's "Fluid Dynamic Drag." I scanned it and would be happy to email it to you if you don't have it, as well as anyone else who might want to look it over. He has some curves that show drag reduction as a function of lateral and vertical separation as well as number of planes in the formation. I find it interesting that he didn't think there was any benefit to the lead, and your explanation is right on!

If anyone wants a copy, PM me.
 
Hoerner

Thanks Brent,

Yes, Hoerner is one of my standard desk references.

The journal article by Peter Lissemann is very good, although of course very technical. But if you are interested, some Google work should find it.

Steve.
 
What he said....

Steve, Nasty, All, Great thread so far and hugely informative. And, yes, Don't try this at home unless you've had training...

A couple of observations that I had while doing these flights...

The postion of "Thuh Sweet Spot" in a 2-3 ship trail position for me was to line up the H/S tip with the NACA duct on the side of the fuselage of the preceding aircraft. At 110 Kts, this put the trailing aircraft just about exactly in the Vortex (just one, right):rolleyes: Very controlable and maintainable. Nasty's description on how to fly that was spot on.

Another observation I made, was when KK (Ken Kreuger RV-4) and I (RV-6) were commuting down to Tracy from the Mother Ship, we had a long time (3+ hrs) to play with this. At RV cruise speeds the effect is not quite as pronounced but it was still there. KK played most of the time while I led. What I found as Lead blew me away. :eek: While at cruise power/speeds and KK in trail he was able to affect my heading! At first I thought, 'No Way'... At that altitude the air was glass though and danged if he didn't keep pulling my nose to the left and off course. From then on I could tell when he was effectively playing in "Thuh Sweet Spot" and draggin' me around the sky... Pretty weird...:cool:

I again had a chance to try this today while flying the RV-9A on a reposition flight with Gus, who was flying the factory 7A. Even at cruise speeds I was able to easily locate the spot and get in it. The 9A seemed to be a bit more controlable in that spot, possibly due to that wings different airfoil, aspect ratio, etc. I want to say that it felt just more efficient too, but without any data capture capability I can't document it. Just sayin' maybe we should instrument a -9 airframe and try it.

Great science project! Thanks to all for participating and watching. The VAF community Rocks!
 
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They missed something.

Just finished watching it.

I can't believe that they got through the entire myth without drawing attention to the fact that all the aircraft involved had "EXPERIMENTAL" written on them.

Wouldn't that have been perfect for Mythbusters? :)

- mark
 
smoking vortex?

Would be interesting to see this with smoke coming off of the wingtips. It might be easier to SEE the sweet spot, (but might not be so easy to see the lead!)
 
Big Wakes



This close formation was very difficult.
Aircraft weights would be 750,000--- 385 RV's and 250,000--125 RV's.
The bow wave of the C-5 would push the 135 around
like a rag doll. Thanks for autopilot.

Joe----It would roll left and right from bow wave alone and was
controlled by autopilot.

Very hard on Boom controls in back at 50 feet back it would
fly boom up to stowed position with no help.

Just thought I would share.

Great show and thanks to the guys and
Slick----Get a hair cut.

Boomer--OUT
 
Boomer,

I cut both of them, what more do you want?

I've tried tanking in a c-5 sim and it's lots tougher than most would think...who'd think a puny little kc-135 could toss three quarts of a million pounds around like that?
 
This is all fascinating.

There's a good movie, "Fly Away Home," which led me to Operation Migration - you can look it up, it's about leading migrating birds with ultralight aircraft.

And that led me to a posting that caught my attention:

"After twenty years of leading birds, some of my memories run together, but I have a vivid one from this location. It was Richard?s turn to lead or maybe he drew the short straw. One of our birds that year had developed a habit of turning back shortly after takeoff. One of us would always swoop in to pick him up and he soon learned that if he broke from the crowd, he would eventually get his own personal aircraft to carry him to the next site.

That day I was in position to collect this savvy bird. Like clockwork, he broke and I moved in to collect him. With only one bird on the wing, you can climb better than if you have an entire string...."

Neat, eh?

Dave
 
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