Chapter 5 Helicopter Performance

1. Chapter 5Helicopter Performance SONG, Jianyu

2. What Can We Learn?

3. Performance: • estimation of required power • maximum level flight speed • endurance range • …

4. The International Standard Atmosphere

5. The International Standard Atmosphere (ISA)  • The rotor performance and the performance of the helicopter as a whole is a function of the air density. • We can not compare the performance metrics between aircrafts unless the data are corrected to some standard condition. • ISA has been established to solve this problem. • It gives the height in a standard atmosphere corresponding to the properties of the air in which the aircraft is actually flying

6. ISA • ISA gives the definition of the standard: at sea level • Air temperature: • A barometric pressure: • Pressure is the function of altitude (h) • Density is the function of both altitude(h) and the temperature(T) • The pressure and the densityin the standard atmosphere is defined relative to the standard conditions: • Remark: “h” is in meters In the lower atmosphere (Below 6 km)

7. ISA • Up to 11 km, temperature and pressure has the relation: Remark: R= the universal gas law constant of 8.3145 m3·Pa/(mol·K) • The temperaturein the standard atmosphere is a linearly decreasing function of altitude: Remark:“h” is in meters:, “T” in ⁰C • Pressure altitude: the height at which a given pressure is found in the standard atmosphere • Density altitude: the height at which a given ambient density is found in the standard atmosphere Remark: the density ratio can be obtained from:

8. ISA • Remark : • the pressure altitude is used more often because it can be read directly off the altimeter in the aircraft • Pressure altitude and density altitude are identical if the temperature conforms to standard conditions • As a rule of thumb, density altitude exceeds pressures altitude by about 9 meters per ⁰C

9. Outline • Hovering and Axial Climb Performance • Forward Flight Performance • Performance Analysis

10. Hovering and Axial Climb Performance

11. Hovering Recall in Chapter 3 for hovering: Κ :the induced power factor :the average profile drag coefficient FM :figure of merit The basic effect of density altitude on hovering performance show on the right: Power required varies with altitude (for 11,ooo lb helicopter UH-60 20% greater power needed at 9,000 ft) Assume FM or K are not substantially affected by ρ

12. Hovering decrease in excess power almost proportional to extra weight. Ceiling ≡ height at which excess power = 0 (it is means that the helicopter can not hovering beyond the height) 700

13. Climb • Recall Chapter 2: ΔP = excess power available (above hover) The climb velocity does not depend on excess rotor thrust but on an excess of power • For low to moderate rates of climb: This is the maximum climb rate

14. Climb figure on the right shows a decrease of maximum climb rates if hp is high

15. Forward Flight Performance

16. Forward Flight Performance total power: Consider a climbing forward flight: For small flight path angle: Equilibrium: Vertical: horizontal:

17. Forward Flight Performance Assume: small angles assuming is independent of the angle of climb The power to undertake a climb and also to propel the helicopter foreword. climb power(Pc) parasitic power (Pp)

18. Induced Power (Pi) • From Chapter 2: • If the forward velocity is sufficiently high i.e. μ > 0.1 • Then the induced velocity can be approximated by Glauert’s “high-speed” formula: • Therefore the power equation can be written as:

19. Blade Profile Power(Po) • In chapter 3 Blade Element Theory • The profile power coefficient with a uniform blade cord is:

21. Reverse Flow At higher advance ratios , a considerable amount of reverse flow will exist on the retreating side of the rotor disk. Compute the locus of the region: So the region is a circular region with diameter μ centered at (μ/2,270).

22. Reverse Flow It also change drag sign in this region If Cd is the same

23. Parasite Power Pp Is a power loss as a result of viscous shear effects and flow separation (pressure drag) drag on the airframe A = rotor disk area f = equivalent wetted area Another approach is to represent drag relative to 100 units

24. Climb Power (Pc) • rate of increase of potential energy

25. Tail Rotor Power • typically 3-5% of the main rotor power • It is calculation in a similar way to the main rotor power, with the thrust required being set equal to the value necessary to balance the main rotor torque reaction on the fuselage. • So the required thrust is : distance of main rotor shaft to tail rotor thrust

26. Induced + propulsive power Total Power Profile power Total power for forward flight: for high μ: λ < μ Tail rotor power Parasitic power Climb power

27. Performance Analysis

28. Effect of Gross Weight Power required is a function of GTOW (MSL conditions) With increasing GTOW, the excess power available becomes progressively less, bust it is particularly affected at lower airspeed where the induced power requirement constitutes a greater fraction of the total power maximum speed is limited by onset of stall and compressibility effects (happens before power required = power available)

29. Effect of Density Altitude(hρ) As discussed at the beginning of the chapter, an important consideration is the effect of altitude on overall helicopter performance increasing hρ increases required power at low speeds at high speeds lower density reduces parasite drag at high altitudes power available also reduces

30. Lift-to-Drag Ratios The lift-to-drag(L/D) of the helicopter can also be calculated from the power required curves Comparison of the forward flight efficiency with other rotor lift force: P: power expended The power: For the rotor : For the helicopter: The L/D rotor alone: complete helicopter: • Figure, L/D increases rapidly as induced power requirements decrease, reaches a maximum , then drops off as the parasitic power requirements rapidly increase.

31. Climb Performance The general power equation can be used to estimate the climb velocity assume that for low Vc, Pi, P0, D ≈ constant ΔP: excess available power Plever is simply the net power required to maintain level flight conditions at same forward speed. Let the installed power available is Pa(maybe vary with flight condition) • Figure ,max rate of climb is shown above • Note that the curve is similar to excess power; • “Translational lift”: the tendency of the helicopter to climb when translating from the hover condition. • Effect of hρ is shown

32. Engine Fuel Consumption Performance can be expressed in Specific Fuel Consumption(SFC) vs shaft power, the unit for them are (kg/kW hr) vs. (kW) For not supercharged piston engines δ(temp. ratio) and σ (density ratio) For a turboshaft engine: Normalizing both the power and the SFC by give a single unique relationship for a turboshaft engine If we multiply SFC by the power we found that the fuel flow rate is a linear function of power output: the parameter A & B depends on particular engine.

33. Speed for Minimum Power max Vc happens at the speed of minimum power in level flight (Vmp) ≈ 60-80 kts Vmp = optimum speed to fly for min autorotation: the least amount of potential energy / unit time) Vmp also gives best endurance The fuel burn per unit time should be minimum So the endurance for a given amount of fuel is Clearly, the time is maximized at the best SFC and lowest power required for flight.

34. T ≈ W; low speeds P0 ≈ 0 Min Forward ratio for maximum endurance Remark:Vmp increases as hρ increases (or h increases, T increases); Vmp = f (GTOW)

35. Speed for Maximum Range The fuel burn versus airspeed curves mimic the power required curves. range = distance for a given GTOW and fuel best range is obtained when P/V min or V/P max or best L/D And the speed is also determined essentially by the variation in induced power and the parasitic power Remark: Vmr increases when hρ increases and W increases

36. Speed for Maximum Range A more accurate estimate of range will take into account the actual SFC curve

37. Range–Payload and Endurance–Payload Range-payload and endurance-payload curves provide information of the effects of aircraft range and endurance when trading off payload of fuel. The fuel flow rate WF w.r.t distance R: Where, Because W decreases as fuel burns, (5.77) needs to be integrated numerically using the approximation: WF = initial fuel weight Estimation of endurance can be found in a similar way:

38. Q&AThank you!