Mass and balance, drawn in the envelope

Pick an aircraft, load it, and see where the centre of gravity falls in its envelope for the take-off, landing and zero-fuel cases. Six training aeroplanes and one helicopter, the Robinson R22 Beta II, whose page changes shape because a helicopter is balanced in two axes. Built as a study aid for pilots learning to work the numbers rather than trust a memorised loading.

The CG envelope

Choose an aircraft preset — its empty mass and arm are representative figures, not your airframe's weighing report — then enter the crew and passengers, the baggage and the fuel, and the calculation gives the take-off and landing mass with the moment and the resulting CG arm. The result is drawn inside the aircraft's published envelope, so a load that is legal on mass but out of limits on balance is visible rather than arithmetic.

Fuel burn moves the CG during the flight, which is why the landing case is shown alongside the take-off case — an aircraft can start inside the envelope and finish outside it.

A helicopter is balanced in two axes

For the Robinson R22 the form asks for the pilot in the right seat, the passenger in the left seat, the baggage under each seat and the fuel in the main and auxiliary tanks, because every one of those sits off the centreline. The loading table carries a lateral arm and a lateral moment beside the longitudinal ones, and the page draws both charts the POH draws: gross weight against fuselage station, and lateral CG against the same station, with the POH's inch scale folded onto the metric axes. The per-seat maximum includes the baggage under that seat, and the placard minimum solo pilot weight is checked.

There is no runway card for the helicopter. The R22 flight manual publishes no take-off or landing distance — its performance limits are the hover ceilings in and out of ground effect and the height–velocity diagram — so the page quotes those as reference and describes the hover power check instead of drawing a runway. Nothing computes whether the helicopter can hover today; that is the POH chart and the power check.

An illustrative look at runway distances (aeroplanes)

For the aeroplanes, an illustrative graphic scales typical sea-level ISA take-off and landing figures with the computed mass. It applies no wind, temperature, slope or surface corrections and knows nothing about any particular runway — it exists to show how strongly mass alone moves the distances, not to clear you for a strip.

This is a study aid. The aircraft's own flight manual is the authority on its mass, balance and performance limits — always work the real numbers from it before flight.