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Can some one please let me know,if the thrust required on the rotor head increases with the increase in altitude in an Helicopter or decreases with increase in Altitude?.

Thanks in advance, Pawan

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    $\begingroup$ For no vertical acceleration, lifting force (i.e. thrust, as you use the term) = weight. That's independent of altitude and everything else. Now, the power required to gererate that lifting force increases with altitude, which is why helicopters have maximum altitudes for In-ground-effect (IGE) and Out-of-ground-effect (OGE) hover. Those ceilings vary with weight & temperature. $\endgroup$ – Ralph J Feb 3 '19 at 4:00
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    $\begingroup$ In case you would need a strict answer in addition of @Ralph comment, weight and thrust will slightly decrease with altitude due to the gravity gradient (-0.35% at FL350, though there are few helicopters at this altitude) $\endgroup$ – mins Feb 3 '19 at 18:30
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I presume that OP means torque on the rotor, since thrust must always compensate weight to maintain altitude. Thrust T, torque Q and power P equations for momentum theory in the hover:

$$T = C_T \cdot \rho A (\Omega R)^2$$

$$Q = C_Q \cdot \rho A (\Omega R)^2 R$$

$$P = C_P \cdot \rho A (\Omega R)^3$$

with $C_Q$ being identical to $C_P$.

At any altitude, thrust must equal weight. Air density $\rho$ decreases with increasing altitude, so $C_T$ must increase with increasing altitude which it does linearly.

From Leishman

Above graph from Leishman shows the relationship between $C_P$ and $C_T$, which can be approximated as:

$$C_P = \frac{\kappa \cdot {C_T}^{3/2}}{\sqrt{2}} + \frac{\sigma \cdot {C_D}_0}{8}$$

with $\kappa$ = loss factor and $\sigma$ = blade solidity.

So power required increases with $T^{3/2}$, and therefore increases with increasing altitude. Since $C_P$ = $C_Q$, torque does as well. Note that the weight at altitude has decreased due to the fuel burn required to reach higher altitude, which will compensate some of the additional torque required.

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The thrust required from a main rotor to keep the helicopter aloft remains essentially the same regardless of altitude. Thrust must equal weight to keep it aloft. Since you mentioned thrust, we're talking about hovering and not forward flight (where airflow over the spinning rotor disc produces lift).

The thrust produced by a main rotor, assuming a constant torque and blade angle of attack, decreases with altitude. The air gets thinner, but the blades aren't moving any faster or getting any larger.

In the case of a helicopter, the blades can't turn any faster. They're already at the optimal speed, any faster and either the tips go supersonic and lose a lot of efficiency, or the blades depart from the aircraft... definitely Not Good.

Nor can rotor blades become larger to handle higher altitudes without adversely affecting low altitude flight with increased drag and mass.

So the angle of attack of the blades is increased to keep the thrust sufficient... up to a point. Over a certain altitude, can be FL150-200 depending on the particular model, even that won't restore thrust to where it needs to be... the AOA will increase to where the blades stall.

Note that tilt rotor aircraft cruise at altitudes much higher than helicopters, because they are using higher speed and airflow over the wings to produce lift, not downward thrust from the rotors.

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