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Another important factor is speed. The faster a plane is moving, the more extra lift for you gain from pitching up. The faster you're going, the more air you can push on with the same size wings.

So combining all these factors, fighter jets get a lot out of their wings by moving fast, having sturdy wings that can take high loads, and by being light so the wings don't have as much mass to turn.

Another important factor is speed. The faster a plane is moving, the more extra lift for you gain from pitching up. The faster you're going, the more air you can push on per wing area. At high speed, you don't need as much wing area to produce the max ~9G of acceleration a pilot can handle.

In terms of turning-radius, this is more than cancelled out by the centripetal force needed for a constant-radius turn increasing quadratically with speed. (Thanks @Todd for catching this). Degrees-per-second (angular velocity, ω) is similarly not helped by moving faster, once you're going fast enough to make a max-G-force manoeuvre.

F = lift-factor * v = ma.

$m \omega^2 r = mv^2/r = F$
$\omega^2 r = v^2/r = F/m = a = 9G$
$\omega^2 = v^2 / r^2$
$\omega = v/r$. But for constant $a$, $r$ is proportional to $v^2$.
$\omega = v / (v^2/a) = a/v$ (where $a$ is constant)

So at speeds fast enough for max acceleration to be the limiting factor, turn rate ~= 1/v. At lower speeds, where achievable $a$ increases ~linearly with speed, ω is about the same at any speed up to $a = 9G$. High thrust is needed to overcome the high drag of high lift / high angle-of-attack turning.

So combining all these factors, fighter jets get a lot out of their wings by moving fast, having sturdy wings that can take high loads, and by being light so the wings don't have as much mass to turn.

Lift is proportional to wing area, not just wingspan.

Fighter jets typically have narrow wings (as you noted), but they run most of the length of the fuselage (low aspect ratio). Larger slower-moving planes typically have long skinny wings.

Low aspect ratio wings are usually used on fighter aircraft, not only for the higher roll rates, but especially for longer chord and thinner airfoils involved in supersonic flight.
-- wikipedia's Aspect Ratio article

Many jet fighters, esp. the F15 as noted in several answer, generate lift from the fuselage, significantly increasing effective wing area. The entire wingtip-to-wingtip span is wing, because there's no non-wing fuselage in the middle.

So even though the premise of the question is somewhat flawed, there are reasons:

I'm not sure if fighter jets have more or less wing area per mass than larger craft. It's reasonable to assume they have less area per nose-to-tail length, though, because mass increases with the size³, while surface area increases with size².

Compared to a big plane, 1/2 length -> 1/8th mass, requiring only 1/8th wing surface area, not the 1/4 area you'd have from a proportional scale-model.

To turn, you need to get the entire mass of the plane moving in a different direction. To pull into a loop, you not only need to change attitude quickly (large control surfaces); you also need lift from the increased angle of attack to change the plane's motion vector. (With large control surfaces but not enough lift, you pitch up but keep moving horizontally, and stall).

"Enough lift" depends on the mass of the plane, because $F = m a$. Keeping proportions the same, a larger plane would have less lift per mass, because of the cube vs square issue.

Another important factor is speed. The faster a plane is moving, the more extra lift for you gain from pitching up. The faster you're going, the more air you can push on with the same size wings.

Small planes also make it easier to make wings strong enough to not snap them off at a high angle of attack (difference between heading and facing, whether it's in the vertical plane, or turning horizontally after rolling to near 90 degrees.) Low aspect ratio wings spread the load over a longer attachment point with the fuselage, helping with this.

In a high angle-of-attack, the engines are contributing some of the necessary centripetal force to bend the plane's momentum vector, because they're pushing the plane in the new direction, not just along its current trajectory.

So combining all these factors, fighter jets get a lot out of their wings by moving fast, having sturdy wings that can take high loads, and by being light so the wings don't have as much mass to turn.

Appropriately sized control surfaces are obviously a requirement, to hold a figher jet in a high-angle-of-attack turn.

I think vectored thrust contributes mostly in this area. In a (non-inverted) loop, a jet would have its thrust vectored upward, along with the elevators, pushing the tail down. This means less thrust is contributing to centripetal force; instead it's helping to hold the plane in a higher angle of attack so the wings can pull the plane in a tighter loop.

I'm sure there are some mistakes here, since I don't actually design airplanes, or even fly them outside of video games. I'm just applying simple physics and making stuff up.

Lift is proportional to wing area, not just wingspan.

Fighter jets typically have narrow wings (as you noted), but they run most of the length of the fuselage (low aspect ratio). Larger slower-moving planes typically have long skinny wings.

Low aspect ratio wings are usually used on fighter aircraft, not only for the higher roll rates, but especially for longer chord and thinner airfoils involved in supersonic flight.
-- wikipedia's Aspect Ratio article

Many jet fighters, esp. the F15 as noted in several answer, generate lift from the fuselage, significantly increasing effective wing area. The entire wingtip-to-wingtip span is wing, because there's no non-wing fuselage in the middle.

So even though the premise of the question is somewhat flawed, there are reasons:

I'm not sure if fighter jets have more or less wing area per mass than larger craft. It's reasonable to assume they have less area per nose-to-tail length, though, because mass increases with the size³, while surface area increases with size².

Compared to a big plane, 1/2 length -> 1/8th mass, requiring only 1/8th wing surface area, not the 1/4 area you'd have from a proportional scale-model.

To turn, you need to get the entire mass of the plane moving in a different direction. To pull into a loop, you not only need to change attitude quickly (large control surfaces); you also need lift from the increased angle of attack to change the plane's motion vector. (With large control surfaces but not enough lift, you pitch up but keep moving horizontally, and stall).

"Enough lift" depends on the mass of the plane, because $F = m a$. Keeping proportions the same, a larger plane would have less lift per mass, because of the cube vs square issue.

Another important factor is speed. The faster a plane is moving, the more extra lift for you gain from pitching up. The faster you're going, the more air you can push on with the same size wings.

Small planes also make it easier to make wings strong enough to not snap them off at a high angle of attack (difference between heading and facing, whether it's in the vertical plane, or turning horizontally after rolling to near 90 degrees.) Low aspect ratio wings spread the load over a longer attachment point with the fuselage, helping with this.

In a high angle-of-attack, the engines are contributing some of the necessary centripetal force to bend the plane's momentum vector, because they're pushing the plane in the new direction, not just along its current trajectory.

So combining all these factors, fighter jets get a lot out of their wings by moving fast, having sturdy wings that can take high loads, and by being light so the wings don't have as much mass to turn.

Appropriately sized control surfaces are obviously a requirement, to hold a figher jet in a high-angle-of-attack turn.

I think vectored thrust contributes mostly in this area. In a (non-inverted) loop, a jet would have its thrust vectored upward, along with the elevators, pushing the tail down. This means less thrust is contributing to centripetal force; instead it's helping to hold the plane in a higher angle of attack so the wings can pull the plane in a tighter loop.

I'm sure there are some mistakes here, since I don't actually design airplanes, or even fly them outside of video games. I'm just applying simple physics and making stuff up. It looks like a lot of what I said is pretty much what wing loading is.

Lift is proportional to wing area, not just wingspan.

Fighter jets typically have narrow wings (as you noted), but they run most of the length of the fuselage (low aspect ratio). Larger slower-moving planes typically have long skinny wings.

Low aspect ratio wings are usually used on fighter aircraft, not only for the higher roll rates, but especially for longer chord and thinner airfoils involved in supersonic flight.
-- wikipedia's Aspect Ratio article

So even though the premise of the question is somewhat flawed, there are reasons:

I'm not sure if fighter jets have more or less wing area per mass than larger craft. It's reasonable to assume they have less area per nose-to-tail length, though, because mass increases with the size³, while surface area increases with size².

Compared to a big plane, 1/2 length -> 1/8th mass, requiring only 1/8th wing surface area, not the 1/4 area you'd have from a proportional scale-model.

To turn, you need to get the entire mass of the plane moving in a different direction. To pull into a loop, you not only need to change attitude quickly (large control surfaces); you also need lift from the increased angle of attack to change the plane's motion vector. (With large control surfaces but not enough lift, you pitch up but keep moving horizontally, and stall).

"Enough lift" depends on the mass of the plane, because $F = m a$. Keeping proportions the same, a larger plane would have less lift per mass, because of the cube vs square issue.

Another important factor is speed. The faster a plane is moving, the more extra lift for you gain from pitching up. The faster you're going, the more air you can push on with the same size wings.

Small planes also make it easier to make wings strong enough to not snap them off at a high angle of attack (difference between heading and facing, whether it's in the vertical plane, or turning horizontally after rolling to near 90 degrees.) Low aspect ratio wings spread the load over a longer attachment point with the fuselage, helping with this.

In a high angle-of-attack, the engines are contributing some of the necessary centripetal force to bend the plane's momentum vector, because they're pushing the plane in the new direction, not just along its current trajectory.

So combining all these factors, fighter jets get a lot out of their wings by moving fast, having sturdy wings that can take high loads, and by being light so the wings don't have as much mass to turn.

Appropriately sized control surfaces are obviously a requirement, to hold a figher jet in a high-angle-of-attack turn.

I think vectored thrust contributes mostly in this area. In a (non-inverted) loop, a jet would have its thrust vectored upward, along with the elevators, pushing the tail down. This means less thrust is contributing to centripetal force; instead it's helping to hold the plane in a higher angle of attack so the wings can pull the plane in a tighter loop.

I'm sure there are some mistakes here, since I don't actually design airplanes, or even fly them outside of video games. I'm just applying simple physics and making stuff up.

Lift is proportional to wing area, not just wingspan.

Fighter jets typically have narrow wings (as you noted), but they run most of the length of the fuselage (low aspect ratio). Larger slower-moving planes typically have long skinny wings.

Low aspect ratio wings are usually used on fighter aircraft, not only for the higher roll rates, but especially for longer chord and thinner airfoils involved in supersonic flight.
-- wikipedia's Aspect Ratio article

Many jet fighters, esp. the F15 as noted in several answer, generate lift from the fuselage, significantly increasing effective wing area. The entire wingtip-to-wingtip span is wing, because there's no non-wing fuselage in the middle.

So even though the premise of the question is somewhat flawed, there are reasons:

I'm not sure if fighter jets have more or less wing area per mass than larger craft. It's reasonable to assume they have less area per nose-to-tail length, though, because mass increases with the size³, while surface area increases with size².

Compared to a big plane, 1/2 length -> 1/8th mass, requiring only 1/8th wing surface area, not the 1/4 area you'd have from a proportional scale-model.

To turn, you need to get the entire mass of the plane moving in a different direction. To pull into a loop, you not only need to change attitude quickly (large control surfaces); you also need lift from the increased angle of attack to change the plane's motion vector. (With large control surfaces but not enough lift, you pitch up but keep moving horizontally, and stall).

"Enough lift" depends on the mass of the plane, because $F = m a$. Keeping proportions the same, a larger plane would have less lift per mass, because of the cube vs square issue.

Another important factor is speed. The faster a plane is moving, the more extra lift for you gain from pitching up. The faster you're going, the more air you can push on with the same size wings.

Small planes also make it easier to make wings strong enough to not snap them off at a high angle of attack (difference between heading and facing, whether it's in the vertical plane, or turning horizontally after rolling to near 90 degrees.) Low aspect ratio wings spread the load over a longer attachment point with the fuselage, helping with this.

In a high angle-of-attack, the engines are contributing some of the necessary centripetal force to bend the plane's momentum vector, because they're pushing the plane in the new direction, not just along its current trajectory.

So combining all these factors, fighter jets get a lot out of their wings by moving fast, having sturdy wings that can take high loads, and by being light so the wings don't have as much mass to turn.

Appropriately sized control surfaces are obviously a requirement, to hold a figher jet in a high-angle-of-attack turn.

I think vectored thrust contributes mostly in this area. In a (non-inverted) loop, a jet would have its thrust vectored upward, along with the elevators, pushing the tail down. This means less thrust is contributing to centripetal force; instead it's helping to hold the plane in a higher angle of attack so the wings can pull the plane in a tighter loop.

I'm sure there are some mistakes here, since I don't actually design airplanes, or even fly them outside of video games. I'm just applying simple physics and making stuff up.