ALT 0 m V/S 0 m/s GS 0 m/s RPM 100% COLL 0% ON GROUND
Ready

How to fly: collective changes the pitch of all blades together, so it moves you up and down. Cyclic tilts the rotor disc, so the helicopter moves forward or back. Pedals turn the nose. Start with the Hover mission: raise the collective slowly until the skids lift.

Power required in level flight

total requiredinducedprofileparasiteavailableyou

Rotor & performance

Gross mass
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Disk loading
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Thrust now
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Induced vi
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Power req.
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Power avail.
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Hover OGE
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Hover IGE
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Tail-rotor thrust
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Yaw rate
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Why it matters: a helicopter holds itself up by throwing air downwards, which costs far more power than a wing gliding forward. That single fact explains why hovering is hard work, why hot high places such as Mount Kenya are dangerous, and why helicopters can still land safely when the engine stops.

1. How a rotor makes thrust: momentum theory

disc area A, thrust T far above: V = 0 at disc: vᵢ far wake: 2vᵢ (contracts to A/2)

Treat the rotor as an actuator disc that pushes air downwards. The mass flow through the disc is $\dot m = \rho A v_i$. Far below, the wake moves at $2v_i$ (a result of energy conservation), so the momentum given to the air each second, which equals the thrust, is

$$T = \dot m\,(2v_i) = 2\rho A v_i^2 \quad\Rightarrow\quad v_i = \sqrt{\frac{T}{2\rho A}}$$

The ideal power is the thrust times the velocity at the disc:

$$P_{ideal} = T v_i = \frac{T^{3/2}}{\sqrt{2\rho A}}, \qquad P = \kappa\,T v_i + \underbrace{\frac{\sigma C_{d0}}{8}\rho A(\Omega R)^3\left(1+4.65\mu^2\right)}_{\text{profile power}}$$

Here $\Omega$ is the rotor's angular speed (so $\Omega R$ is the blade-tip speed), $\sigma$ the solidity (fraction of the disc covered by blades), $C_{d0}$ the blade drag coefficient and $\mu = V/(\Omega R)$ the forward speed as a fraction of tip speed. $\kappa \approx 1.15$ accounts for non-uniform inflow and tip losses. The figure of merit $FM = P_{ideal}/P$ (0.6–0.75 for real rotors) measures hover efficiency. The disk loading $T/A$ is the key design number: a big, lightly loaded rotor needs less power to hover, which is why helicopters have such large rotors and why a Harrier or a rocket, with tiny "discs", burns so much fuel to hover.

2. Density altitude

Thin air is the helicopter's enemy. Hover power scales as $1/\sqrt\rho$, while a piston engine's power falls roughly as $(1.132\sigma - 0.132)$ (Gagg–Ferrar), where here $\sigma = \rho/\rho_0$ is the density ratio relative to sea level (not the solidity). At Wilson Airport on a warm afternoon both effects work against you. On Mount Kenya at 4,000 m a light helicopter may only hover in ground effect with a very light load. Change the site and temperature and watch the "Hover OGE" readout (OGE = out of ground effect, high above the ground; IGE = in ground effect, see section 3).

3. Ground effect

Close to the ground the downwash cannot spread freely; the induced velocity is reduced and the same power produces more thrust. Cheeseman and Bennett's image-vortex estimate is

$$\frac{T_{IGE}}{T_{OGE}}\bigg|_{P} = \frac{1}{1 - \left(\dfrac{R}{4z}\right)^2}$$

where $z$ is the rotor height. The effect fades above about one rotor diameter. The simulator reduces $v_i$ by the factor $1-(R/4z)^2$ (weakened as forward speed sweeps the wake away), which is why the helicopter feels "cushioned" near the pad.

4. Forward flight and translational lift

Tilting the rotor disc forward with the cyclic tilts the thrust vector; its horizontal component accelerates the helicopter. In forward flight the rotor processes a much larger mass of air, so it needs a smaller induced velocity for the same thrust (Glauert):

$$v_i = \frac{T}{2\rho A\sqrt{V^2 + (V_c + v_i)^2}} \;\xrightarrow{V \gg v_h}\; \frac{T}{2\rho A V}$$

Induced power therefore falls as speed rises: effective translational lift, felt at about 8–12 m/s as a sudden surplus of thrust. Profile power rises slowly and parasite power ($\tfrac12\rho f V^3$) rises steeply, giving the classic bucket-shaped power curve. The bottom of the bucket is the best endurance speed and the best speed for autorotation.

5. Torque and the tail rotor

The engine drives the main rotor with torque $Q = P/\Omega$; by Newton's third law the rotor pushes the fuselage the other way. This rotor turns anticlockwise seen from above, so the fuselage tries to yaw to the right. The tail rotor, on an arm $l_{tr}$, cancels it:

$$T_{tr} = \frac{Q}{l_{tr}} = \frac{P_{main}}{\Omega\, l_{tr}}$$

The pedals change tail-rotor pitch. More collective means more power, more torque and more left pedal is needed. Switch off automatic anti-torque to manage it yourself, and watch the top-view inset.

6. Autorotation

If the engine fails, lower the collective immediately. As the helicopter descends, air flows up through the disc. With low blade pitch this upflow drives the rotor like a windmill, keeping rotor speed up while still producing thrust close to the weight: the helicopter descends steadily, like a sycamore seed. The descent rate is set by the power the rotor still needs:

$$V_{d} \approx \frac{P_{i} + P_0 + P_{p}}{T} \qquad\text{(lowest near the bucket speed)}$$

Near the ground the pilot flares (aft cyclic) to convert forward speed into rotor energy and reduce the sink rate, then raises the collective to cushion the touchdown using the rotor's stored kinetic energy $\tfrac12 I_R\Omega^2$. Let rotor speed decay below about 70% and the blades stall: there is no recovery. Rotor RPM dynamics follow $I_R\,\Omega\,\dot\Omega = P_{engine} - P_{required}$.

Vortex ring state. Descending vertically at about the induced velocity, the rotor re-ingests its own wake and momentum theory breaks down. The simulator uses an empirical curve for this region: power rises, thrust becomes erratic, and adding collective can make the descent worse. The cure is forward speed.
About the model. A light, piston-engined two-blade helicopter (rotor radius 5.0 m, tip speed 200 m/s, 200 kW at sea level). Rotor thrust comes from blade-element theory, $T = C_T\rho A(\Omega R)^2$ with $C_T = \tfrac{\sigma a}{2}\big(\tfrac{\theta_0}{3}(1+\tfrac32\mu^2) - \tfrac{\lambda}{2}\big)$, coupled to a momentum-theory inflow model that includes climb, descent (with the empirical vortex-ring curve), forward flight, ground effect and rotor-speed dynamics. Motion is simulated in the vertical plane; yaw is shown in the top-view inset. Flapping, blade stall and lateral (roll) dynamics are simplified away.

Missions are on the right of the simulator. These investigations use the live readouts.

Investigations

  1. Ground cushion. Hover at 1 m and note the collective; climb slowly to 15 m. How much more collective and power do you need out of ground effect? Compare with $1/(1-(R/4z)^2)$.
  2. The power bucket. Fly level at 0, 10, 20, 30 and 40 m/s and note the power required. Plot it against the chart. Where is the minimum?
  3. Torque. Turn off automatic anti-torque. Raise the collective sharply. Which way does the nose go, and why? What does the inset show when you cut the engine?
  4. Hot and high. Find the heaviest payload you can hover out of ground effect at Mombasa, Wilson and Mount Kenya.