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I'm upgrading the propulsion of a standard WW-I biplane with new technology. It can generate nearly limitless power for the same weight and dimensions of the original power plant. The propeller, shaft, and bearings are also indestructible.
The plane: Assume a biplane like the Sopwith Camel. In another post, I learned that biplanes can't go 700mph
With the airplane specified exactly like the SC, but given unlimited power, What is the physical breaking point of the plane?
A Sopwith Camel had a listed top speed of around 180kph. This was mainly due to potential damage to the engine in a dive, however period accounts of dives by pilots of Camels record the IAS being pegged at 180kph, but the aircraft still increasing speed somewhat.
However, if we discount engine damage, a Camel might begin to suffer from structural damage at 190+kph, and it is highly unlikely that any period Camel could survive an airspeed of 250+kph without suffering a catastrophic structural failure rendering it unflyable. A modern replica of a Camel might be able to withstand a bit more speed, but would probably not be able to exceed 300 kph safely.
Short version : Maybe Mach 10 regardless of the number of wings.
the engine has no upper limit(that matters at least), how fast can I make a biplane go before it breaks?
A "biplane" is just a plane with two wings, normally in the configuration we're all familiar with from WW1 planes. However the shape and functionality of WW1 era wings would be quite unsuited to making a very fast plane. The reason swept wing designs appear on (almost) every jet airliner and (almost) every military jet, and all jets designed to exceed the speed of sound is down to physics. You cannot use old biplane style wings to do that. Any wing generates lift and drag. It is a delicate balancing act trading off these things to be efficient.
Wings also have to be able to work at all speeds. This is why landing and taking off in some aircraft (and particularly landing) is difficult. Wings designed to do well at high speeds do not necessarily have good low speed stall characteristics, so these aircraft sometimes have poor safety records.
If you want an example of extreme wings, have a look at the Lockheed Starfighter which has wings that barely look capable of generating lift. Could you make a "biplane" version - probably. Would you ? Probably not. But the wings would not be the limiting factor The Starfighter also had a bad reputation for landing issues - it was designed for one type of flight and was not at all easy to fly at low speed when landing.
Wings have to have control surfaces in them and this makes them complex, but the control surfaces themselves have to be designed to work reasonable well at all flight speeds.
So designing wings is far more involved than just the number of wings - that's the least of your problems. And note that other elements of the control surfaces are not on the wings and it all has to work together in a wide range of flight conditions.
Likewise the engine has a huge effect on the aerodynamics of the plane. All engines in use in the real world have some kind of air flow through them. Propeller aircraft use the propeller to drive the air and generate thrust. Jet engines, surprisingly, do the same, they just do it in a different way. All of these engines not only generate thrust, they generate drag.
And here is where your first unknown starts.
If the engine uses air and is exposed to air (and from your earlier question this may not be the case), then it has drag. So just slotting it into the aircraft is much harder than it seems. Air intake shave to work at all speeds and this is a significant issue on supersonic aircraft (e.g. see Diverterless supersonic inlet. So you cannot just slot an engine into an aircraft, you have to build an aircraft around an engine or an engine for an aircraft. This is why upgrading aircraft engines (when making a new version of a plane) is quite complex.
If the engine does not use air (e.g. is a rocket or similar) it is still a problem if it uses fuel. This is because the balance of the plane will change as you use fuel. This is a common, everyday issue for all aircraft.
Traveling through the air at high speed also generates heat. A lot of heat. The legendary SR-71 at Mach 3 had skin temperatures higher than 400 C and some parts of it went to over a 1000 C. That's high enough to melt Aluminium which is why they didn't use Aluminium (and that's the correct spelling in my part of the world, BTW :-) ).
So what's the bottom line ?
In principle you can push a plane through the air as fast as you like. In practice, biplane or not, you start running out of materials and techniques that allow it stay in one piece as you hit low teens in Mach numbers. The fastest I'm aware of was NASA's X-43 at about Mach 9.6. The space shuttle did exceed that for brief periods but I would not describe that as flying so much as re-entry - to get to that speed in the first place requires what is basically a space launch. Once you hit air (even very thin air at high altitude) you are going to convert all of that speed into heat and slow down doing it. So at present maybe Mach 10 is a good number for your top-speed.
Will they break Mach 10 someday - sure. Will it be practical for sustained flight without some sci-fi engine and materials - no. With handwavium - anything you like.
The wire-braced, fabric and wood (possibly with a steel tube fuselage frame) construction common to WWI fighter aircraft was as good as it could be with the materials and knowledge of the day. As noted in another answer, few if any of these aircraft could exceed 200 km/h (about 120 mph) even in a dive.
Warplane design at that time was more about maneuver than speed. Since all of the planes were slow (by modern standards, even by the standards of the day -- they were barely faster than a record-setting steam train!), the ones that could climb and turn best and hold together were hailed as "best" -- and the Camel was one of those. With its rotary engine, it turned much better to the right than the left, but it climbed well.
As noted in a comment a while back, however, there were aircraft models in that period that were known to lose the fabric off the upper wing or even lose the entire upper wing by structural failure if overstressed by speed or maneuvering. Trying to say how fast you could push a re-engined Camel airframe before it breaks up is like asking if you could get the Titanic up on plane if you just converted her to turbine power and doubled the boiler capacity: it's unanswerable, but also somewhat silly to ask.
If someone has the near-limitless engine you describe, they'll need to start from ground up, as it were, designing an airframe to take advantage of all that power -- and assuming the engine outputs rotary torque at relatively low RPM like an aircraft engine, after a number of generations of new designs they're likely to wind up with a machine that resembles one of the last generation of fighters from the Second World War -- P-38, P-51, Corsair, Spitfire, etc. -- and their limitation on speed is more about Mach number than structure. This kind of aircraft becomes uncontrollable as soon as shock waves start to move over the control surfaces, which normally occurs around Mach .8-.9. This is the speed range in which compressibility was blamed for killing pilots in the days before the X-1, and the airframe breakups that did occur happened because of the loss of control, not because of simple speed.
