How are forward and aft CG limits calculated?

I have been tasked to create a POH for my aero engineering coursework and part of this task is to create the CG envelope for the theoretical 65 passenger aircraft. I have figured out weight, moment and cg for all loading scenarios but I am wondering how to create the actual envelope using forward and aft limits, as surely not all these scenarios will be able to fly? TIA

• Aft CG is primarily stability margin (say, 10%). For forward CG, you can use the ability to rotate at V_rotate as a good approximation. – MikeY Mar 23 at 14:33

You have done half of the way. Since you have computed the CG variations in all loading scenario, you know approximate limits. This limits are the ideal limit from loading and unloading point-of-view. But in real application, the design of the aircraft does not allow such broad limits.

There are many factors that limits the aircraft aft CG movement:

1. MLG load: The loads on MLG increases as the aircraft weight is increased or the CG is moved aft. Since in most of cases, the MLG's are designed for touch down loads at maximum landing weight, which is lower that the maximum ramp/take-off weight, the static loads at maximum ramp weight may exceed the dynamics load at touch down. So, a limitation may be imposed on aft CG location regarding this issue.
2. Take-off Tip-Up: At the take-off conditions, the engines are producing their maximum thrust. If the engines are located below the CG, which is the case for under-wing mounted engines, this thrust produces pitch-up moment. This pitch-up moment reduces the load on the NLG. From the other hand, as the aircraft weight decreases combined with aft cg movements, the load on the NLG will be further decreased. At light enough NLG loads, steering effectiveness is reduced, and eventually, the NLG load can become negative causing the airplane to tip up. So an aft CG limits may be imposed to maintain enough loads on the NLG.
3. Static Stability: Too far aft CG may cause neutral or negative stability, so a margin (normally 10% of MAC) should be provided between the CG and the aerodynamic center.
4. Go-Around: At go-around condition, the engines are producing the maximum thrust, and a huge pitch-up moment. Elevator deflection are required to counter this moment with pitch down moment. This moment is proportional to amount of upward acting load on the tail a the arm of this acting load. The distance between the tail and the CG is the arm. As the cg moves aft, if the tail reaches its maximum lift the aircraft can not maintain its path. So a limit may be imposed to prevent pitch-up at go-around.

By combining the above limits, and other limits that may arise from that specific configuration, an aft CG limit can be estimated.

• Another is the ability to stall the aircraft (forward CG limit). Stick force during go-around could also limit the forward CG is the engines are tail mounted. – JZYL Jul 16 at 1:07
• Of these, (3) is by far the most important and should be #1. Other things sometimes may be a factor that imposes further limit, but static stability always applies. Sometimes, the aft limit is imposed by things like spin recovery, but it's broadly the same category. (4) is not practically an issue: the arm change is not very significant (esp. for aircraft with underwing engines), while reduction of the aerodynamic moment due to relaxed stability is. It is the forward limit (which you didn't cover) that is largely determined by controlability (i.e. available elevator control). – Zeus Jul 16 at 1:22

For conceptual design, the longitudinal CG limits can be evaluated with:

1. Static Margin: you probably want at least 10% static margin at aft CG at the early conceptual stage for at least the flaps in configuration.

2. Trimmability: the amount of elevators or stabilizer (if movable) required to trim both full power and power off, for all flaps. For tail mounted engines, full power may limit the forward CG; for wing mounted engines, full power may limit the aft CG.

3. Takeoff Rotation: ensure your aircraft can rotate at $$V_R-10kt$$ or $$V_R-7\%$$ at takeoff flap at forward CG. This assumes the landing gears are positioned to give adequate tip-over margin.

Once you are in the preliminary design, then you have lots more things to look at.