Helicopter EngineeringVI Semester Aeronautical Engineering

1. Show that for a hovering rotor with blades that operate at constant lift and drag coefficients, thrust on the rotor is proportional to the square of the tip speed, and the power is proportional to the cube of the tip speed.

2. A helicopter weights 30,000 N and has a single rotor of 16m diameter. Using momentum theory estimate the power required for level flight at a speed of 20 m/ sec at sea level. Take CD=0.0065 based on rotor disc area.

3. Using Bernoulli’s equation of the general energy equation, show that the induced velocity in the fully contracted wake of a rotor climbing with a vertical velocity if twice the induced velocity in the rotor plane.

4. A helicopter with gross weight of 1600 kg, a main rotor radius of 6 m, and a rotor tip speed of 210 m/s has 225 kW delivered to the main rotor shaft, the tail rotor radius is 0.8 m and the tail rotor is located 4.8 m from the main shaft. Calculate the thrust and power required by the tail rotor for hovering conditions at 7500 ft. Assume that the FM of the tail rotor is 0.70.

5. The simple momentum theory assumes that the jump in pressure across the disk of a hovering rotor is the same everywhere. By considering an elemental annulus of the rotor disk prove that

λ i=σ⋅a16 [√1+32

σ⋅aθ⋅̄r−1]

6. How the Blade Element Theory does relate induced inflow, Pitch angle, Airfoil shape and Solidity ratio?

7. Explain the following with respect to a Helicopter.a. Ideal Rotorb. Optimum Rotorc. Mean Lift Co-efficientd. Root cutout

8. Given that the inflow distribution over a rotor with rectangular untwisted blades is approximately triangular and assuming no tip-loss effects (a) Compute the variation with radius of inflow angle and section AOA for such a rotor. (b) Derive the relation between the blade element lift coefficients andCT /σ . (c) Derive an expression for the hovering power of such rotor in terms of CT /σ andCd0.

9. Using Blade Element Theory, derive the following expression.

CT=σa2 [ θ

3− λ

2 ]10. Explain the performance of the rotor at different flow states in axial flight.

11. Estimate the inflow value in turbulent wake region using induced velocity curve diagram.

12. A helicopter with gross weight of 1400 kg, a main rotor radius of 4m, and a rotor tip speed of 208 m/s has 210 kW delivered to the main rotor shaft. For hovering conditions at 3 km, compute: (a) the rotor disk loading (b) the ideal power loading (c) the thrust and torque co-efficient, and (d) the figure of merit and actual power loading.

13. A large helicopter of 45359 kg of weight is to be designed with a rotor diameter of 40 mm. The operating altitude is 4 km. Rotor speed is restricted to 200 m/s. Assuming same blades, Calculate the chord of the rotor. Assume reasonable values for data not specified in the problem, but clearly state the assumptions.

14. In a coaxial rotor design, the rotors are spaced sufficiently far apart such that the lower rotor operates in the fully developed slipstream of the upper rotor. Show by means of the momentum theory that the induced power factor resulting from interference is 1.28 compared to 1.41 when the rotors have no vertical separation. Assume that the thrusts of both rotors are equal.

15. Using the momentum theory for an overlapping rotor configuration with unequal

rotor thrusts, find an expression for the overlap induced power factor κov in

terms of the overlap area Aov=m' A where

m'= 2π [cos−1( d

D )−( dD )√1−( d

D )2]

16. For helicopter operations at high speed, it is possible that a “reverse flow” region can exist at the root end of the blade on the retreating side of the rotor disk. Show that the reverse flow region on the rotor disk is a circle of diameter

μ with a center located at (r,ψ ) = (

μ2

,3 π2 )

17. Show that for a rotor producing constant thrust in non-axial translation moving

at a speed of V 0 and, at an angleα , the induced velocity υi and the ideal power Pi are given by the following equations.

( υi

υh)

4

+2 ( υi

υh)3

(V 0

υh)sin α+( υi

υh)2

(V 0

υh)2

−1=0

Pi

P i , h

=(V 0

υh)sin α +( υi

υh)

18.

Starting from an expression for the figure of merit for an optimum hovering

rotor, show that the figure of merit is a maximum when the blade sections are

operating at the highest values of

C l3/ 2/Cd

19.

A tilt rotor has a gross weight of 25,500 kg. The rotor diameter is 12 m. On the

basis of the simple momentum theory, estimate the power required for the

helicopter to hover at 2 km altitude. Assume that the figure of merit of the

rotors is 0.80 and transmission losses amount to 5%. If each of the two turbo-

shaft engines delivers 4,500 kW, estimate the maximum vertical rate of climb at

sea level.

20. For the autorotation in vertical flight, prove that

1.

−CP pd

CT3 /2/√2

∝Cd 0

Cl3 / 2

21. Based on what the Figure of Merit of rotor system of a Helicopter will be decided? Explain briefly with set of mathematical relations and graphs.

22. Assuming an optimum hovering rotor, rewrite an expression for the figure of merit in terms of rotor tip speed, disk loading and airfoil lift-to-drag ratio.

23. By means of the blade element theory in forward flight show that the profile power co-efficient can be written as

CP 0=σCd 0

8( 1+3μ2)

Neglect the radial component of velocity.

24. Given a helicopter of weight, W=2700 kg, calculate the power required in hover and up to 600m/min axial rate of climb. The radius of the main rotor is 12m and the rotor has a figure of merit of 0.70. Assume sea level conditions. Plot your result in the form of power required versus climb velocity.

25. Derive the condition for auto-rotation of a particular blade element on rotor and prove mathematically how the acceleration and deceleration of the blade region takes place on a single rotor.

26. A preliminary design of a tandem rotor helicopter with a gross weight of 9,000 kg suggests a rotor diameter of 14 m, a blade chord of 0.6 m, three blades, and a rotor tip speed of 220 m/s. Estimate the total shaft power required to hover if the induced power factor for the front rotor is 1.20 and that for the rear rotor is 1.15. The rotor airfoil to be used has a zero lift drag co-efficient of 0.01. Estimate the installed power if transmission losses amount to 5% and the helicopter must demonstrate a vertical rate of climb of 310 m/min at 5 km altitude.

27. An understanding of the vortex ring state is necessary to explain certain aspects of helicopter performance. Describe, with the aid of diagrams, what is the mechanism behind the vortex-ring state. Under what flight conditions is the vortex ring state important to pilot and why?

28. An understanding of “ground effect” is necessary to explain certain trends in helicopter behaviour. Describe the mechanism of ground effect in hover. How does ground effect influence the performance of the helicopter during the transition from hover to forward flight?

29. Explain why in reality the variation of inflow through a helicopter rotor in forward flight is highly non-uniform. Explain the source of non-uniformity.

30. If the coning angle of a blade is given by

β0=

12

ρac R4 [ θ0

4( 1+μ2 )+ λ

3 ]I b

Write the above expression in terms of the Lock number. What does the factor represent?

31. A rigid rotor blade with a uniform mass distribution has its flapping hinge located at a distance e from the rotational shaft axis. If the shaft is rotating at an angular velocityΩ, calculate the natural frequency of the blade about the flapping hinge.

32. From Glauert formula, How to calculate induced velocity and inflow ratio in forward flight? Also show the exact analytical solution of inflow ratio for the special case whenα=0.

33. Justify that, the rotary wing will act as fixed wing in high forward speed.

34. Using coordinate transformation or rotation matrix, Derive the aerodynamic loads acting on blade element at an arbitrary location in terms of hub fixed non-rotating coordinate system.

35. By considering the blade thrust, blade weight, centrifugal force, and blade inertia of a centrally hinged flapping untwisted untapered blade, find an expression for co-efficient of thrust

CT=σa2 [ θ0

3 {1+ 32

μ2}+ θtw

4{1+μ2 }+μ

θ1 s

2−

λTPP

2 ]36. Derive an expression for coning angle β0 for the helicopter with centrally

hinged rotor system in forward flight.

37. By considering the blade thrust, blade weight, centrifugal force, and blade inertia of a centrally hinged flapping untwisted untapered blade, find an expression for the coning angle of the blade in forward flight. Assume uniform inflow.

38. A helicopter is operating in level forward flight at 210 ft/s under the following conditions: shaft power supplied = 655 hp, W = 6,000 lb, ρ= 0.00200 slugs/ft3. The rotor parameters are R = 19 ft, σ = 0.08, ΩR = 700 ft/s, k = 1.15, Cd0 = 0.01. (i) How much power is required to overcome induced losses? (ii) How much power is required to overcome profile losses? (iii) What is the equivalent flat plate area, f ? (iv) If the installed power is 800 hp, estimate the maximum rate-of-climb possible at this airspeed. (v) If the installed power is 800 hp, estimate the maximum level flight speed.

39. Estimate the vertical autorotative rate-of-descent in forward flight at sea-level

conditions for a small light-weight helicopter with the following characteristics: Weight = 1370 lbs, rotor radius = 12.6 ft, rotor solidity = 0.030, tip speed = 700 ft/s. Estimate the autorotative rate of descent for the same helicopter in forward flight as a function of forward flight speed. Repeat the calculations for a density altitude of 10,000 feet and comment on your results.

40. Derive the following expression for power required in forward flight using Blade Element Theory

P=kT υi+σ Cd 0

8ρ (ΩR )3 π R2 (1+4.65 μ2 )+∑ (C D S ) 1

2ρ V 3+Pmisc

A helicopter is operating in level forward flight at 63.6 m/s under the following conditions: shaft power supplied = 488.4 kw, W = 2722 Kg, ρ = 1.038 Kg/m^3. The rotor parameters are R = 5.75 m, σ = 0.08, ΩR = 212.2 m/s, K=1.15, Cd0 = 0.01.

(a) How much power is required to overcome induced losses?(b) How much power is required to overcome profile losses?(c) What is the equivalent flat-plate area, f?(d) If the installed power is 596.56 kW, estimate the maximum rate of climb

possible at this airspeed.