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Gyroscope Math Page

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Notes and Reference Section


6.283185308 (approx) radians = 1 revolution
(2 * Pi radians = 1 revolution)

gyroscopic couple, C = I * W * Omega

Force on the bearings, F = (I * W * Omega) / L

Basic Gyroscope Measurements

 
Basic Gyoscope Measurements
Density of material
Radius (Meters)
Diameter (Meters) (Radius * 2)
Circumference (Meters) (2 * Radius * Pi)
Depth (Meters)
Volume (Meters Cubed) (Pi * (Radius ^ 2) * Depth)
Mass (Kilograms) (Volume * Density)
Pi
 
Cut-Away Measurements
Radius (Meters)
Diameter (Meters) (Radius * 2)
Circumference (Meters) (2 * Radius * Pi)
Depth (Meters)
Number of Cut-Aways
Volume of Cut-Aways (Meters Cubed) (Pi * (Radius ^ 2) * Depth)
Mass of Cut-Aways (Kilograms) (Volume * Density)
 
Gyroscope Measurements
(After Cut-Aways)
Volume of Gyroscope (Meters Cubed) (Gyro volume - cutaways)
Mass of Gyroscope (Kilograms) (Gyro mass - cutaways)
 
Inertia
Gyroscope Inertia (without cut-aways) (Mass * (radius ^ 2) / 2)
Inertia Cut-Aways (Mass * (radius ^ 2) / 2)
Omega (Gyroscope interia after cut-aways) (without cutaways - cutaways)
 
Speed of Gyroscope
W (radians per second) (rps * ((2 * pi))
Revolutions Per Minute (RPM)
Kilometers Per Hour (KPH) (((rpm * circumference) / 1000) * 60)
Degrees Per Second ((rpm * 360) / 60)
Revolutions Per Second (rpm / 60)
 
Speed of Main Structure
Degrees Change
Time in seconds
Radians Change (degrees / (360 / (pi * 2))
Degrees Per Second (degrees / seconds)
Revolutions Per Second (dps / 360)
Revolutions Per Minute (RPM) (rps * 60)
Omega (Radians per second) (rps * ((2 * pi))
 
Details of Precession
Gyroscopic Couple
C (Gyroscopic couple force) (Inertia * W * Omega)
 
Force
Gyroscope Axle Forces
Distance between bearings (Meters)
Force on bearings (Newton Meters) (C / L)
Force on each bearing (Newton Meters) ((C / L) / 2)
Force on bearings (Kilograms) ((C / L) * 0.1)
Force on each bearing (Kilograms) (((C / L) * 0.1 aprox) / 2)
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