Ground school lesson
Weight and balance
Two numbers decide whether the aircraft flies the way the designer promised: how much it weighs and where that weight sits.
What you will be able to do
- Run the weight-times-arm computation for a loaded aircraft.
- Check a result against maximum weight and the CG envelope.
- Know the gyroplane-specific reasons this is not optional paperwork.
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Step 1 of 3
The whole method in three lines
Every item aboard has a weight and an arm, its distance from the datum, a reference point the manufacturer fixes. Multiply each weight by its arm to get a moment. Then:
The computation
- Total weight = sum of all weights. Must not exceed the maximum in the flight manual.
- Total moment = sum of all moments.
- CG = total moment ÷ total weight. Must fall inside the manual's CG envelope.
That is the entire method, for a gyroplane or an airliner. Everything else is bookkeeping.
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Step 2 of 3
A worked example
Invented round numbers, to show the arithmetic only. Your aircraft's real empty weight, arms and limits are in its flight manual and nowhere else.
Item Weight (lb) Arm (in) Moment (lb-in) Empty aircraft 700 100 70,000 Pilot 190 90 17,100 Passenger 170 110 18,700 Fuel (17 US gal) 102 105 10,710 Totals 1,162 — 116,510 CG = 116,510 ÷ 1,162 = 100.3 inches aft of datum. Now two checks: is 1,162 lb at or under the maximum weight, and does 100.3 sit inside the envelope? Both yes, and the aircraft is legal to load exactly like this. Note aviation gasoline is figured at 6 lb per US gallon.
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Step 3 of 3
Why a gyroplane cares so much
The rotor hangs the fuselage
A gyroplane's fuselage hangs under the rotor head, so where the CG sits directly sets the aircraft's hang angle and how much control authority you keep, especially in pitch. Some types verify it physically with a hang test at weighing.
Small aircraft, big fractions
In a two-seat machine, one heavy passenger or full versus empty tanks moves the numbers by a large fraction. The airline habit of never checking does not transfer: run it whenever the load changes.
Overweight or out of envelope is not a fine-print violation; it is degraded climb, altered handling, and test-pilot territory the designer never cleared. Ten minutes with the manual beats all of it.
Check yourself
3 questions. Pick an answer to see whether it is right and why.
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How is centre of gravity computed?
Sum every item's weight-times-arm moment, sum the weights, and divide moment by weight. The result must land inside the flight manual's envelope.
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Aviation gasoline is normally figured at what weight?
6 lb per US gallon is the standard planning figure for avgas, so 17 gallons is about 102 lb of load that burns off as you fly.
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Your computed CG falls just outside the envelope. The flight is short. What now?
The envelope is where the designer demonstrated safe handling. Outside it you are the test pilot. Move weight, drain fuel or leave something behind until the number is inside.
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FAA Pilot's Handbook of Aeronautical Knowledge, weight and balance chapter, and the FAA Weight and Balance Handbook (public domain). Your aircraft's real figures are in its flight manual.