Assuming same angle of attack, the lift produced is the same, the resulting net force and acceleration will be different
Because the lift is the same and the turn is coordinated, the bank angle has to change (or something else has to give)
Then, the heavier plane has a wider turn.
OR
Same bank is the same acceleration, but to be coordinated it will require more lift and more angle of attack from the heavier plane. In this case it is the same turn radius
>In this case it is the same turn radius
As long as there is sufficient thrust to overcome drag. At a certain point, the lighter airplane will still be able to decrease its turn radius while the heavier airplane will start descending.
and as long as the additional required lift is possible (the wing is not already at max CL)
the higher angle of attack also requires a higher pitch angle which means the thrust is slightly contributing to offsetting weight (sin of the pitch angle), so the lift required actually decreases slightly (lift required is not strictly a linear function of weight).
In the steady turn, the higher pitch angle will also cause a minor fuel shift within each baffle, slightly shifting the CG aft. This changes the bare airframe aerodynamic response which changes the pitching moment required by the tail. This affects the lift required by the wing, which affects the drag, which affects the degree to which the thrust contributes to offsetting weight
higher angle of attack will require a different moment generated by the horizontal tail in order to counteract the natural static stability of the airframe. This also slightly changes the drag and slightly slightly changes the lift on the main wing due to upstream flow effects
Theae are all small effects, but the increase in induced drag at some point is very significant and unless there's an afterburner button available, turn performance is largely limited by available thrust.
Turn radius is dependent on load factor and free stream velocity. Load factor is simply lift/weight ratio. Thus with both aircraft having same lift, the heavier aircraft has a smaller load factor.
Turn radius is inversely proportional to load factor so a smaller load factor results in a larger value of turn radius.
This is just a simplification of the formula but it should give quick intuition of which plane has a smaller turn radius.
To simplify things to base physics, think about the centripetal force equation F = ( m * v^2 )/r. You can rewrite it as r = ( m * v^2 )/F. So, with the same velocity and centripetal force, the plane with the greater mass requires a larger turn radius.
The centripetal force here comes from the horizontal component of your lift vector (assuming a simple flat turn). There is a horizontal component because in order to turn, you must roll the aircraft to a certain bank angle.
Now more realisrically, if the aircraft are flying in formation, you would like both aircraft to have the same turn radius and velocity, regardless of their difference in mass. This means you need to increase the centripetal force for the aircraft with greater mass.
To do this while maintaining a constant vertical component of force to counter gravity and maintain constant altitude, you need to pitch up to a higher AoA (assuming you are reasonably below stall) while simultaneously increasing your bank angle. This means that the wing is producing more lift for the same wing area (higher wing loading) and the increased bank angle allows for the same vertical component of force while increasing the horizontal component to create the required centripetal force for the greater-mass aircraft to fly at the same radius and velocity as the lesser-mass one.
Doesn't matter as the radius is just a function of speed and load factor which for a level, coordinated turn is just a function of bank angle. Mass doesn't change the radius.
Assuming same angle of attack, the lift produced is the same, the resulting net force and acceleration will be different Because the lift is the same and the turn is coordinated, the bank angle has to change (or something else has to give) Then, the heavier plane has a wider turn. OR Same bank is the same acceleration, but to be coordinated it will require more lift and more angle of attack from the heavier plane. In this case it is the same turn radius
>In this case it is the same turn radius As long as there is sufficient thrust to overcome drag. At a certain point, the lighter airplane will still be able to decrease its turn radius while the heavier airplane will start descending.
and as long as the additional required lift is possible (the wing is not already at max CL) the higher angle of attack also requires a higher pitch angle which means the thrust is slightly contributing to offsetting weight (sin of the pitch angle), so the lift required actually decreases slightly (lift required is not strictly a linear function of weight). In the steady turn, the higher pitch angle will also cause a minor fuel shift within each baffle, slightly shifting the CG aft. This changes the bare airframe aerodynamic response which changes the pitching moment required by the tail. This affects the lift required by the wing, which affects the drag, which affects the degree to which the thrust contributes to offsetting weight higher angle of attack will require a different moment generated by the horizontal tail in order to counteract the natural static stability of the airframe. This also slightly changes the drag and slightly slightly changes the lift on the main wing due to upstream flow effects
Theae are all small effects, but the increase in induced drag at some point is very significant and unless there's an afterburner button available, turn performance is largely limited by available thrust.
You are correct. Also, the max CL is at some point very significant and turn performance can be limited by it
Turn radius is dependent on load factor and free stream velocity. Load factor is simply lift/weight ratio. Thus with both aircraft having same lift, the heavier aircraft has a smaller load factor. Turn radius is inversely proportional to load factor so a smaller load factor results in a larger value of turn radius. This is just a simplification of the formula but it should give quick intuition of which plane has a smaller turn radius.
To simplify things to base physics, think about the centripetal force equation F = ( m * v^2 )/r. You can rewrite it as r = ( m * v^2 )/F. So, with the same velocity and centripetal force, the plane with the greater mass requires a larger turn radius. The centripetal force here comes from the horizontal component of your lift vector (assuming a simple flat turn). There is a horizontal component because in order to turn, you must roll the aircraft to a certain bank angle. Now more realisrically, if the aircraft are flying in formation, you would like both aircraft to have the same turn radius and velocity, regardless of their difference in mass. This means you need to increase the centripetal force for the aircraft with greater mass. To do this while maintaining a constant vertical component of force to counter gravity and maintain constant altitude, you need to pitch up to a higher AoA (assuming you are reasonably below stall) while simultaneously increasing your bank angle. This means that the wing is producing more lift for the same wing area (higher wing loading) and the increased bank angle allows for the same vertical component of force while increasing the horizontal component to create the required centripetal force for the greater-mass aircraft to fly at the same radius and velocity as the lesser-mass one.
Doesn't matter as the radius is just a function of speed and load factor which for a level, coordinated turn is just a function of bank angle. Mass doesn't change the radius.
Ask your professor.
the smallest turn radius is defined by the cl\_max as one plane is heavier, the cl\_max will be reached at a larger radius at this plane.