Inertia and Maneuverability

If two airplanes are both rated for 9G's, would a lighter jet have greater maneuverability due to lower inertia? If so, wouldn't it be better to have a lighter fighter for air dominance (F-16 sized or smaller), rather than having a much larger airplane like the F-15

It can be shown that for a fixed load factor at a fixed airspeed, neither turn radius nor turn rate are functions of an aircraft's mass. Load factor can be thought of as "lift per unit weight," so two aircraft of differing sizes are actually scaled identically maneuver-wise when they pull the same number of Gs at the same airspeed.

Turn radius is: V^2/Ng

Turn rate is: Ng/V

...where V is true airspeed, N is load factor (number of Gs) and g is the acceleration due to Earth's gravity (32.2 ft/s^2 or 9.81 m/s^2).

Equations assume a flat turn because it confuses the issue to assume a fighter pilot wishes to maintain altitude during a dogfight (such an assumption would yield the same answer anyway).

Of course, deciding factors come down to drag, thrust and things of that nature. A smaller aircraft might have higher pitch/yaw/roll rates, factors of "maneuverability." But sliced in the specific way you described, aircraft weight does not matter.

Air superiority isn't just about maneuverability. Range is also important, and that is one area where larger aircraft outperform smaller ones (in general) because they can carry more fuel. Also, larger aircraft can potentially carry larger radars which can detect targets further away.

What squirl says is correct, but not complete. 9g is 9g, no question, but the time required to go from 1g to 9g may be affected by weight, or more importantly, pitch axis moment of inertia. To go from 1g to 9g requires a change in angle of attack and pitch acceleration, so in general a lighter airplane can reach 9g quicker than a heavy one.

Another important factor in quickly reaching 9g is pitch stability. In the F-15 / F-16 comparison, the F-15 has positive pitch stability and thus wants to stay at 1g while the F-16 has negative pitch stability (subsonic) and thus wants to diverge to a high g right now. The flight control computer keeps it in check. If you could somehow remove the horizontal tails of both airplanes in flight, the F-15 would lose altitude at a little less than 1g, while the F-16 would abruptly pull up to a positive g.

Also consider that a heavier aircraft with subsequent higher mass moments of inertia will resist maneuvering. Therefore, to get to the 9g level more control forces will be required. This equates to either larger control surfaces or higher control surface deflection. Either produces higher drag. Therefore more thrust is required to maintain energy. Vicious circle...

Lighter is always better, everything else being equal (e.g. the Zero was lighter, but no armor made it highly vulnerable)

Roscoe: Don't forget static stability. Heavier F-16 will require LESS control force for 9Gs than, for example, a lighter MIG-21 (It CAN pull 9Gs, but not many times .

But of course your final statement remains true: EVERYTHING ELSE being equal light is better.

Doesn't matter that much. a heavier aircraft takes more force to move it...F=ma and it's rotational equivalent at play here. More inertia means less agility.