A coaxial counter-rotating rotor system places two rotors on the same axis at different heights. Separate concentric shafts drive them in opposite directions. Equal opposing torque loads balance the net reaction; an unequal split leaves a reaction moment. This tool illustrates that torque balance and calculates delivered shaft power.
Coaxial Contra-rotating Rotor Interactive Calculator
Explore a steady torque split between two equal-speed, counter-rotating rotors. Enter the combined torque before losses referred to rotor speed, drivetrain efficiency and a load-split bias. The diagram keeps both shaft paths and rotor planes distinct.
Equation Used
- Equal constant rotor-speed magnitudes; upper clockwise and lower counter-clockwise from above.
- Equivalent total input torque expressed at rotor speed.
- One overall efficiency applies before torque split.
- Bias does not change total delivered torque or rotor speed.
- No thrust, clearance or yaw-rate calculation.
Steady-speed torque accounting with equal and opposite rpm. Input torque is referred to rotor speed before the entered losses. Blade count, spacing and gearbox enclosure are schematic; pitch actuation, aerodynamics and flight dynamics are not simulated.
Animated Diagram
Separate shafts, opposite rotation
The blue inner shaft reaches the upper rotor. The bronze hollow outer shaft drives the lower rotor. The longitudinal cutaway makes both paths visible; bearings support the assembly. The gearbox housing marks the drive connection; its internal gearing is not shown.
The upper rotor turns clockwise when viewed from above and the lower turns counter-clockwise at the same rpm. The illustration uses three blades per rotor and exaggerated vertical separation for clarity. It is a schematic arrangement, not a reconstruction of a specific aircraft. Both motions are slowed thirty times.
The torque-bias input changes the load split, not the angular speed. NASA’s Mars-helicopter control paper explains differential collective as opposite pitch changes that alter rotor drag and produce a yaw moment. This calculator starts from an entered torque split; it does not solve the aerodynamic relationship between collective pitch and torque.
Coaxial drive and control
Coaxial rotorcraft use concentric, counter-rotating rotors in a compact arrangement. Rotor and wake interactions make performance more involved than adding two isolated rotor calculations. Torque balance describes the opposing shaft loads. It does not by itself determine aerodynamic efficiency or aircraft performance.
Separate cyclic and collective controls, blade deformation and transmission design are outside this animation. The schematic separation between the planes is not a clearance specification.
Torque split and combined shaft power
Let T be the combined equivalent torque before drivetrain losses, expressed at the selected rotor speed. This is a reference quantity: an actual engine-shaft torque at a different rpm needs its gear ratio before it can be used here. Let η be drivetrain efficiency, b the bias as a fraction, and ω = 2πn/60 for the common rotor-speed magnitude.
T upper = ηT(1+b)/2 and T lower = ηT(1−b)/2 are positive delivered torque magnitudes. Their sum is ηT. Delivered power is (T upper + T lower)ω/1000 in kilowatts.
With the upper rotor clockwise and the lower counter-clockwise when viewed from above, the drive reaction on the airframe is T upper − T lower, positive counter-clockwise. This assumes steady rotor speeds and represents the drive contribution, not a complete flight-dynamics equation.
Worked torque-balance example
For a rotor-speed-referred input torque of 10,000 N·m, 95% efficiency and 250 rpm, the delivered combined torque is 9500 N·m and delivered power is 248.7 kW. At zero bias, each rotor receives a 4750 N·m torque magnitude and the net drive reaction is zero.
At +20% bias the upper value becomes 5700 N·m and the lower 3800 N·m. The airframe reaction is 1900 N·m counter-clockwise in the stated view. The total torque and delivered power remain unchanged because only the split changed.
Interpreting torque and power
Increasing torque or efficiency increases delivered torque and power. Increasing rpm increases power at the same torque. Changing bias transfers the load between rotors; it does not change total power at equal fixed speeds.
The results do not predict thrust, hover efficiency, flight speed, yaw rate, safe blade separation or structural limits. A nonzero torque moment is not an aircraft rotation rate. Aircraft inertia, aerodynamic loads, rotor controls and transient effects are needed for that calculation.
Coaxial torque calculator questions
Why do the rotors keep equal speed when I change bias?
This is a fixed-speed torque-split model. Bias changes the load carried by each rotor; differential rpm is not the control represented.
Can I enter engine torque directly?
Only after referring it to the selected rotor speed using the appropriate transmission ratio. The input here is a combined equivalent torque at rotor speed before the entered losses.
What is the sign of airframe reaction?
Positive means counter-clockwise viewed from above, for the pictured upper clockwise and lower counter-clockwise rotors. It is the upper torque magnitude minus the lower magnitude.
Does zero reaction prove the aircraft is stable?
No. It shows torque balance under this steady assumption. Stability and control require a flight-dynamics model.
Does the illustrated gap establish safe blade clearance?
No. It is exaggerated to show the two planes. Blade deflection, coning, flapping and structural limits are not modeled.
References & further reading
- Grip and colleagues, Guidance and Control for a Mars Helicopter, AIAA 2018-1849: coaxial rotors, collective/cyclic control and differential collective.
- NASA, The Wind and Beyond, volume III: coaxial configuration with concentric shafts and differential rotor torque.
- NASA, Computations of Torque-Balanced Coaxial Rotor Flows: rotor interaction and torque balancing require aerodynamic analysis.
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