THE BIFILAR PENDULUM
Inertial moment
Two strings. A gentle twist.
A measured moment of inertia.
Measure an RC aircraft’s resistance to rotation about its roll, pitch or yaw axis using a simple suspension test.
Enter measurements01 / PREPARE THE AIRCRAFT
Keep the test configuration fixed
Install the battery, payload and equipment for the condition you want to measure. Secure all moving items, restrain control surfaces and record fuel or battery configuration. Find and mark the center of gravity (CG).
02 / CHOOSE AN AXIS
The measured axis must be vertical
Reorient and restrain the aircraft so the selected body axis through its CG aligns with the suspension’s vertical twist axis. Keep the cradle level in every setup.
These are body-axis moments through the CG. Three tests do not determine products of inertia or the complete inertia tensor.
03 / BUILD & MEASURE THE RIG
Two equal, parallel strings
Hang the rigid cradle from two light, low-stretch strings. At rest, both strings must be vertical, equal in loaded length and equally spaced above and below. Center the aircraft CG and combined assembly CG on the midpoint axis; balance the fixture independently.
- Mass m: weigh everything that twists together: aircraft, cradle, straps and hardware.
- Length L: measure the loaded free length from each fixed upper pivot to its lower attachment. Both lengths must match.
- Spacing d: measure the full center-to-center distance between the strings, not half the distance. Upper and lower spacing must match.
This calculator assumes negligible string mass and torsional stiffness. Unequal strings, tilted axes, off-center CG or a flexible fixture require a different model; do not compensate by averaging dimensions.
04 / TWIST, RELEASE & TIME
Count complete cycles
Twist the assembly gently about the vertical axis, about 3–5°, and release without pushing. It should rotate, not swing sideways. Start at one turning point, count 10–20 full cycles, and stop when it returns to the same turning point after the last cycle. Repeat at least three times.
Use a fixed reference mark or video to review timing. Reject trials with sideways sway, slipping restraints, strong damping or contact with nearby objects.
05 / REMOVE FIXTURE INERTIA
Measure the empty cradle
If a cradle or other moving support is used, test it alone about the same axis and in the same rigid configuration. Balance its CG on the centerline. Record its mass, loaded string length, spacing and timing separately; strings may stretch differently without the aircraft.
The calculator subtracts the empty fixture’s inertia from the combined result. Leave correction off only if moving fixture inertia is negligible or the aircraft is directly suspended with negligible attachments.
06 / REVIEW THE RESULT
From timing to inertia
I = m g d² T² / (16 π² L)
Iaircraft = Icombined − Ifixture
Each trial produces an inertia; the result is the mean of those trial inertias, followed by fixture subtraction. Calculations use SI internally with g = 9.80665 m/s².
Spacing and period are squared: a 1% error in either causes about a 2% error in inertia. Repeatability is a consistency check, not a complete uncertainty estimate. Aerodynamic damping and added-air inertia are not corrected.