Good point, the horizontal stabilizer in conventional aircraft in most situations is pushing down. That is effectively added weight that must be overcome by the wings’ lift. In a pure canard like the Rutan homebuilts (LongEZ, et al.), there is no horizontal stabilizer. The canards are lifting surfaces. So I can see that would improve rate of climb. But in aircraft with canards AND aft horizontal stabilizers, I agree with Stranger, the new surfaces likely just add weight and drag.
As an aside, higher angle of attack doesn’t equate with higher rate of climb. In the little airplanes I’ve flown (so, much less than 1:1 thrust to weight), the best rate of climb airspeed was a lot faster than stall speed. So best ROC at less than stall angle of attack.
Anyway thanks, Temporary and Stranger, for the long posts.
The source of this information was a video where they interviewed the members of a squadron of F-14 aviators in an operational unit on an aircraft carrier in the middle of nowhere. They flew basically two different kinds of missions day after day for a long period of time steaming around in the middle of the Pacific ocean waiting to see where they would be sent next (striking distance to the Middle East was the most likely future deployment).
The F-14 squadrons had basically two jobs, fly Combat Air Patrols, and train for possible hostile action. There are many interviews with various aviators and also their commanders and higher-ups (guys who seldom get to fly anymore) always followed by video of the thing talked about being demonstrated in real life. Everyone on the ship including the RIO’s (who don’t even fly the planes) mentioned that all dogfights that last past the first encounter devolve into a contest to out turn the other guy and get behind him. Every Air Combat Maneuver is a series of turns in different directions to get the other guy off your tail or to get and stay on the other guys tail. (Split S’s and Cuban Eights are a few that I can still recall the names of, but they all involve using every advantage in each turn to have a smaller radius of turn than the other guy. So you learned to use the lift of your wings to make the turn tighter so if you want to dive for example, you invert so you are diving as tightly as possible. If you want to turn left, you flip the aircraft over with its left wing down so the turn to the left is as tight as it can be. There are also ways to build up pressure in one direction by using reverse rudder so at some point you can quickly snap into another direction)
When you are in identical aircraft with an identical turning radius, the options for getting the advantage is quite limited. Every single person in the video mentioned that the F-14 was nose heavy and actually heavier than almost any other tactical airplane (the Air Force’s F111, which also had variable geometry wings was also a heavy sucker!). When you are light with an ability to climb quickly-- you pull up to save your hide. When you are heavy and your nose automatically wants to go down-- you dive to avoid getting “waxed”. When you are a thousand miles from training against dissimilar aircraft, you do everything you can to get the other guy to go nose down so you can jump on him. At the same time, he knows that too so he is trying to get you to drop your nose so he can jump behind you.
Eventually, these encounters almost always ended with two planes chasing each other lower and lower until the exercise has to just end. But yes, if the guy who is lower and can’t out turn the other guy gets too low in an actual combat situation, he (and now, or she) must pull up and risk gunfire to escape.
My understanding is that missiles are not part of the exercise, especially fire and forget missiles guided by heat signatures, lasers, camera vectoring, or any other technology. ACM or Air Combat Maneuvering drills are about coming up behind another pilot (getting on their six) and waxing their ass (being in firing position), ideally with camera footage to confirm the “kill”. I am certain the Air Force has bombs and possibly missiles that will home in on a signal sent from a separate source like a different plane or a grunt on the ground but I am not sure if the Navy ever developed such a thing. Any old fool can launch a missile, but it takes a real stick and rudder man (or woman) to win a dog fight.
So would a bi-plane have less lift than the same airframe with only one of those wings? That seems unlikely to me but I am not an expert and never was. But I do listen to people who should know what they are talking about and I have read quite a bit on the subject long ago and the things I said above do come from genuine tactical aviators except my speculation about firing above a climbing target.
It also seems unlikely to me that the horizontal control surface near the top of a tail in some aircraft (usually those with engine nacelle at the rear of the airframe) would be affected by any airflow over the main wings. As I recall, that is why the Lockheed NF 104 had a “tee” tail, because it would flame out at super high altitude and there was an electric motor that would adjust it while the engine was shut down so the plane could be aimed nose down and the engine could be restarted once airflow into the engine started the turbine spinning.
I have been told, and I have little trouble believing that canards WITH rear elevators, can add to rate of climb. As long as the rear stabilizers are an airfoil, both the canard in front and the stabilizer in back can be lifting surfaces (as long as they don’t interrupt airflow over any other surfaces. Instead of the rear stabilizer pushing down to balance the plane, balance and attitude of attack can be controlled by adding more lift to front or back as needed.
A group of fighter jocks at an air show told me that every surface under their planes provided lift (because there was more pressure under the wings AND airframe than there was above it) except the rear stabilizer which counteracted the lift to balance things out. By adding a canard, you can change the function of the stabilizer from pushing down (in order to maintain level flight) to being a second pair of wings.
If you want to climb, and the canards will provide lift for the front of the aircraft-- except that it is not what they are “expected to do”, why can’t the rear control surface be adjusted to lift the back end of the airframe? It is just a matter of adjusting the leading edge from below the slipstream to above the slip stream. If thrust is causing air to hit the bottom of the surface instead of the top of the surface – that is lift. (As long as there is no roiling from the main wings which there shouldn’t be or why are they where they are?) And that is just based upon them being flat like a fan blade (which I am sure creates drag due to wind resistance, but if they are also creating lift they can be configured to be a net gain especially at certain speeds).
If they are no longer expected to push down to stabilize because the combined use of lifting canards- and lifting stabilizer can trim the ship when used in the right combination, the rear stabilizers can be an airfoil (even with adjustable slats) that essentially changes them into a lifting surface with lots of flexibility.
This is not a good explanation, it is hard to convey the whole idea without drawing sketches or using hands to show direction of travel combined with airflow at differing angles.
I don’t know about fighter jets but canards on slower plane can be set to have a higher angle of attack than the main wing and would, therefore, stall before the main wing. The nose would drop, lowering the AoA of the main wing and prevent it (or at least make it harder) from stalling.
Biplanes have less lift than a single wing of the same total lift area. The primary purpose of stacking wings horizontally (biplane or triplane configurations) is to obtain greater stiffness of the wing section with less weight and chord ratio by using a truss structure rather than a cantilevered wing, which was crucial in the early days of aviation before lightweight high strength materials (in particular, high strength aluminum alloys) were readily available. Although the multiple wings each provide some amount of lift, air tends of slot in between the wings which reduces lift potential, hence why later biplanes have the upper wing staggered forward of the lower wing. Multiwing planes also have more profile drag, and it is essentially impossible to push them past a a certain airspeed before before the profile drag becomes so great that it compromises the structural integrity of the stacked wing.
It is worth noting that in the development of fighter aircraft (which primarily drove aviation design in the interwar and WWII period) and improvements in structural design methodology and materials, monowing planes (starting with the Boeing P-26 ‘Peashooter’) rapidly took over from biplanes in frontline service and by 1940 essentially all new fighter aircraft (as well as bombers and transports) were monowing aircraft. The increased power and airspeed as well as design and functional efficiencies essentially displaced multiwing aircraft, and biplanes built today are either replica of historical aircraft or ultralight gliders that operate at very low speeds and minimal power.
Stranger
Or…go for nine wings. (it actually flew…barely) 
Heh…I actually referenced the Noviplano as the aircraft equivalent of C++. It seems incomprehensible that someone believed that would be a reliable flying aircraft, but then people had a lot of really strange ideas in the 1920s.
Stranger
Your point is well taken, and I suppose to some degree I am just pushing this because I have this little sliver of information or possibly knowledge that I am trying to hold onto. I will defer to your information on engineering details but will add a few things.
The biplane comment was just to make a point, obviously if they were hyper efficient they would still be in service in some capacity. But getting back to canard design and three different lifting surfaces . . .
If you look at the outline profile from the bottom of almost all canard designed planes, I believe they are mostly on delta wing or modified delta wing aircraft. Which to some degree just incorporates the surface area of the elevators/rear stabilizers into the main wing- hence the need for canards up front to trim. I understand deltas are extremely awkward at slow speeds and also make it damn near impossible to land because of ground effect. So they have to pitch up to land and that is why the Concord had that adjustable birds beak looking nose so the pilots could actually see the runway on approach. (The wings on F15’s and F22’s have that sort of staggered back, modified delta main wing configuration that has a lot of surface area – but less along the trailing edge than a true delta wing. But they DO have stabilizers so the surfaces must accommodate each other.)
These obstacles eventually lead to variable geometry swing wings to give more or fewer (? -less?) feet of leading edge depending upon speed and need. I was going to argue that by sweeping the elevator surfaces some drag would be reduced, but there would always be some. I believe if they would make a model and do wind tunnel tests, they would find that there are ways to minimize drag and create lift across three different sets of horizontal control surfaces similar to what the experimental joint venture NASA F-16 with canards was trying to accomplish. (The fact that they never incorporated the design into production aircraft dissuades me not at all!)
Mostly the flyboys could not wait to get their hands on a Falcon with canards, they were certain they could shoot down a whole squadron with one of those bad boys. It might be that one or more of them had actually flown it (or claimed he had) but just a get acquainted flight, nothing to test its metal.
Try to think of it in these terms, if you were tasked with designing a platform that split the horizontal stabilizer function between front and back how would you do it? You would add swept wing canards up front and smaller than usual, swept wing (nearly identical?) elevators in back and call them all something like forward trim tabs and rearward trim tabs and stagger them so they did not interfere with each other as much as possible.
In other words, instead of proving it will never work, try to think of a way in which it could work. Perhaps you are correct, any benefit would be offset by drag. But then again, maybe a cleaver design could make it a decent design idea. I am not asking you to believe the world is flat or anything. I am suggesting you forget the immutable “laws” you know to be true and see if you can work out a novel solution. It may even be true that once calcs are done an otherwise flawless design has little or no benefit at high cost – or negative impact for low cost.
So that is essentially a Zeppelin with a whole lotta … wing surface instead of a flammable bag of gas above it.
I can picture it in level flight, but how the hell does it take off?? Is it a sea plane, does it have landing gear or does it float upon the waters? In either case it would take a long, long time to build up speed enough to get the wings functional, especially in water. Would take a pretty long runway on land I would think.
Okay, once I watched the video the answer became obvious.