Aircraft Performance, Weight and Balance
Aircraft Performance
Four questions underneath every problem
What are the limiting speeds, what gradient is required, what does the runway give me, and what does the environment take away?
Speeds: V1 (decision), VR (rotation), V2 (takeoff safety), VREF (landing reference, about 1.3 VSO), VMC (minimum control speed airborne), VNE. Certification climb segments with one engine inoperative, gear up, takeoff flap, at V2 require a second-segment gradient of 2.4% (twin), 2.7% (three-engine) or 3.0% (four-engine); approach climb is 2.1% and the all-engine landing climb 3.3%.
Runway: know TORA and the difference between clearway and stopway. A balanced field length equates accelerate-stop and accelerate-go. Any contaminant, standing water, slush, snow or rubber, invalidates dry numbers. Dynamic hydroplaning begins near 9 times the square root of tyre pressure in psi, for a rotating tyre. Tailwind, upslope, high temperature, high pressure altitude and degraded braking all cost distance.
Worked example. An obstacle is 480 ft above the departure end at 2.4 NM. Required gradient = 480 / 2.4 = 200 ft per NM. One percent of gradient is about 60.8 ft per NM, so the requirement is 200 / 60.8 = 3.3%. A twin certified to 2.4% in the second segment cannot meet that without an improved-climb procedure or a different departure route.
Weight and Balance
Moments do the work
Weight and balance is arithmetic plus judgement. The datum, arm (inches from datum, positive aft), moment (weight times arm) and centre of gravity are the building blocks; moment is often divided into index units to keep the figures manageable.
Know the weights: basic operating weight, zero fuel weight, maximum zero fuel weight, maximum takeoff weight, maximum landing weight, maximum ramp weight, and the traffic-load limits that follow from them. Fuel sits at a known arm, so burning fuel moves the CG; in most swept-wing transports the CG drifts aft as fuel is consumed, but verify the specific type.
Limits matter in both directions. Forward CG raises stall speed, lengthens the takeoff roll and increases pitch-control force; aft CG reduces static stability and shrinks the stick-fixed stall margin. Load so that both the takeoff and landing CG fall inside the certified envelope, and check the most critical case, not just departure.
Worked example. 2,000 lb at 100 in gives 200,000 lb-in; 3,000 lb at 150 in gives 450,000 lb-in. Total moment 650,000 over 5,000 lb equals a CG of 130 in. With LEMAC at 120 in and MAC 60 in, %MAC = (130 minus 120) / 60 x 100 = 16.7%.