These are all generalities, and as usual there are exceptions to almost every rule.
Cheers,
Biff
Amen to that.
Aircraft design is
always the selection of compromises.
A significant factor against cannons in the wings is that these guns are much heavier with a much greater recoil. That has three major downsides and one upside.
First you must realize that aircraft design is always the selection of compromises. In simple Newtonian physics every action has a equal and opposite reaction. In aircraft design every "minor" change has the potential to have major consequences and changing gun size and position is a classic example of how this can pan out.
The first downside is that the wing must be made much stronger to withstand the loads that the gun installation provides. While adding strength to compensate for the big holes in the main spar (the main structural member of the wing) and leading edge (another primary structure) are obvious it is easy to forget about the fact that you have to cut
big holes in the top and/or bottom of the wing for fitting and removing the guns and ammunition.
Think of it this way - the area of the wing where the guns are to be fitted
was like a taped cardboard box. It was very difficult to twist and crumple. You now remove all the tape from the top or bottom of the box. You know how dramatically that reduces the strength of a box and it is no different on an aircraft wing except on the aircraft you must now replace all the rigidity you removed or you will have a dramatic structural failure.
The doors that you fit to the aircraft to allow access to the guns and ammo are not considered as structural members and way back in those days one common rule of thumb was that for every square inch of the hole you had to surround that hole with not less than the same number of square inches of the same thickness metal as an internal doubler. Then of course you must make the door and that must also have structure to have any strength against aerodynamic loads. And the ribs that were riveted to the skin are now sitting there unsupported so they must have flanges fitted to prevent them buckling under load, etc etc etc. All these things add weight and that means the overall structure may need to strengthening to compensate for that already growing weight increase.
The second downside is that the guns are outboard of the main gear so that the wing has to be strengthened inboard and outboard to allow the wing to remain structurally sound during g loads caused by the weapons during maneuvers and landing. The easy way to understand that is to hold a heavy unbalanced object like a hammer with your hands held out in front of you (weight wise the handle is the barrel and the head is the rest of the gun). Now get a friend to lift that hammer say 1/2m (20 inches) horizontally above your open hand and and let go. Even after such a short drop at the moment of impact the hammer feels far heavier. The same happens with a gun in a wing when the wheels hit the ground. That part of the wing now wants to drop because of all the extra weight there so the wing from the gear pivot out has to be stronger or it will break. The other part of the reaction is that the wing inboard of the gear now has the fuselage pushing it down and the outer wing trying to bend it back up like a seesaw. Again more strength is required.
The third downside is harder to visualize but if you have done basic science you will know that it takes a lot of energy to move an item "at rest". When you are flying straight and level you are basically at rest. With an aircraft with guns in the nose the force needed to roll the aircraft will be X, When you now have a wing that is much heavier PLUS it contains heavy guns/cannons and the even heavier ammunition in them it will take a far greater force to start and to stop the same rolling action. In simple words your roll rate is going to be substantially reduced.
To compensate for this you will need bigger ailerons which means a stronger rear spar where they are fitted and less flap area which means a higher landing speed, etc etc etc.
As I said - aircraft design is always the selection of compromises.
And the upside - you do not need synchronizing gear to stop shooting off your own propeller.