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REVESE ENGINEERING HELICOPTER PERFORMANCE USING THE ROTORCRAFT FLIGHT MANUAL

James M. Eli Birch Bay, WA

Email: JamesEli@earthlink.net November 10, 2008

INTRODUCTION Aircraft weight and atmospheric conditions (comprised of temperature and pressure altitude) embrace the basic performance issues for a hovering helicopter. For pilots that routinely work over a range of weight and atmospheric conditions, awareness of these factors are essential and they define the boundaries for safe and efficient operation. But it is difficult at best and sometimes impossible for the civil operator to get the required performance information from manufacturer supplied charts.

Figure 1 – Example Maximum Power Available Chart

To completely understand the issue two separate charts are needed. The first, with an example shown in Figure 1, provides the engine power available (typically as a function of temperature and pressure altitude). Figure 2 represents the second, which supplies the power required to hover at a range of weights versus density altitude. Additionally, this chart usually provides for hovering at several heights above ground (in ground effect to above ground effect). Military helicopters normally incorporate these two charts into their operator’s manual, while civil helicopters rarely do. In fact, there is no civil certification requirement for manufacturers to provide either of these basic but crucial charts.

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Figure 2 – Example Hover Performance Chart

Fundamentally speaking, the hover chart provides the aerodynamic contribution to the dilemma, while the engine performance is embodied in the maximum power chart. Lacking either of these charts makes it virtually impossible for the operator to determine helicopter hover performance. However, armed with the right information and utilizing some basic equations, a civil operator can reverse-engineer the provided data in order to calculate the required numbers or in a more elaborate case, self-construct these basic charts. ENGINE PERFORMANCE Obviously, the Rotorcraft Flight Manual (RFM) is the primary and fundamental source of information. And an excellent place to start is the Power Assurance chart, like the one from an AS-350B2 RFM1 shown in Figure 3. This is an example of a typical rotorcraft maximum power check diagram. While this chart packs a wealth of useful information, it needs to be used in conjunction with other charts and data. And, the RFM should not be the sole source of information. Certification data, maintenance documents, flight test reports, and in some cases, actual aircraft performance can be used to supply the necessary background data. This example will start by dissecting the lower portion of the AS-350B2 Power Assurance Check chart.

1 The example chosen here is without Sand Filter. The Sand Filter is an option which slightly alters the power output of the engine.

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Figure 3 - AS-350B2 Power Assurance Chart

The lower portion of the chart (Figure 4) defines the relationship between main rotor rpm (Nr), indicated torque (%) and power (kW). Based upon the F.A.A. Type Certificate Data Sheet2, 100% torque corresponds to 641 shaft horse power, which converted is 478.1 kilowatts. A brief study of the chart reveals an excellent correspondence between power in kilowatts and the underlying scale of the horizontal axis of the grid (note added highlights). Utilizing values from the chart,

Figure 4 - RPM, Torque and Power

and inserting them into the standard equation for power,

( ) ( )000,60

2 rpmNmtorquekWPower

⋅⋅=

π

Substituting and solving for torque (at 100%),

2 The EASA Type-Certificate Data Sheet contains similar information.

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2.767,11000,60

3882)(1.478 =

⋅⋅=

πNmtorque

which can be rearranged for our purpose,

( ) ( ) ( )rpmNrtorquekWPower ⋅⋅= %239.1

Skipping the middle portion of the chart for now, let’s examine the upper portion next. For our purposes, we can ignore the shading and the division of the graph into correct and incorrect regions. At first glance this scatter plot appears unmanageable, since it’s a plot with three variables. But, lucky for us the relationship between temperature and Ng for a turbine engine is fundamental and well established. Follow along…

Figure 5 - Ng vs. Temperature

Table 1 contains the data extracted from this area and includes the calculated values of theta, corrected NG and corrected kW (equations discussed below).

Corrected Ng FAT kW T Ng kW 98 -20.00 552.50 0.87854 104.2 589.5 98 -10.00 527.75 0.91324 102.3 552.2 98 0.00 501.25 0.94795 100.5 514.8 98 10.00 473.30 0.98265 98.8 477.5 98 20.00 442.00 1.01735 97.2 438.2 98 30.00 409.25 1.05205 95.7 399.0 98 40.00 374.00 1.08676 94.2 358.8 98 50.00 336.00 1.12146 92.8 317.3

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96 -30.00 538.00 0.84384 104.1 585.7 96 -20.00 513.00 0.87854 102.1 547.3 96 -10.00 486.60 0.91324 100.2 509.2 96 0.00 456.67 0.94795 98.5 469.0 96 10.00 424.00 0.98265 96.8 427.7 96 20.00 390.00 1.01735 95.2 386.7 96 30.00 354.00 1.05205 93.7 345.1 96 40.00 315.00 1.08676 92.3 302.2 96 50.00 273.00 1.12146 90.9 257.8 94 -30.00 498.00 0.84384 101.9 542.1 94 -20.00 471.00 0.87854 100.0 502.5 94 -10.00 440.00 0.91324 98.1 460.4 94 0.00 408.00 0.94795 96.4 419.1 94 10.00 372.00 0.98265 94.8 375.3 94 20.00 334.00 1.01735 93.2 331.1 94 30.00 295.00 1.05205 91.8 287.6 94 40.00 250.50 1.08676 90.4 240.3 92 -30.00 456.00 0.84384 99.7 496.4 92 -20.00 424.75 0.87854 97.8 453.2 92 -10.00 391.00 0.91324 96.1 409.2 92 0.00 355.00 0.94795 94.4 364.6 92 10.00 316.60 0.98265 92.8 319.4 92 20.00 274.00 1.01735 91.3 271.7 92 30.00 230.00 1.05205 89.8 224.2 91 10.00 287.50 0.98265 91.8 290.0 91 20.00 242.50 1.01735 90.3 240.4 91 -20.00 401.00 0.87854 96.8 427.8 91 -30.00 434.00 0.84384 98.6 472.5

Table 1 - Ng and kW Relationship The temperature ratio, or theta (?),

16.28816.273+

=fat

θ

is computed for the ambient temperature and utilized in the following equations for correcting Ng and kW to standard day conditions. The equation used for correcting Ng here uses a tweaked exponent 3 of 0.475,

475.0θNg

Ng corrected =

and the equation for corrected kW,

θkW

kWcorrected =

3 Theory states the exponent should be 0.5. However it is well established that manufacturers often tweak these values in order to achieve better correlation with reality.

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results in the following plot of corrected NG vs. corrected kW,

kW vs. Ng

R2 = 0.9999

200

300

400

500

600

89 93 97 101 105

Ng -Corrected

kW

- C

orr

ect

ed

A quadratic fit of this data (with a very good coefficient of determination of R2 = 0.9999) yields the equation,

( ) 7.693678.1265237.0 2 −⋅+⋅−= correctedcorrectedcorrected NgNgkW

Figure 6 is an enlargement of the center section of the chart which applies the pressure altitude correction to the available power.

Figure 6 - Pressure Altitude Adjustment

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The pressure ratio, or delta (d),

( ) 256.5

16.288001981.0

0.1

⋅

−=feetaltitude

δ

defines the curve of the lines in this section. However, as with most data slight tweaks are applied to generate a better fit for the data. In the case of the pressure ratio, we find the best fit here by adjusting the exponent from the usual 5.256 to 5.125. This completes the process of reverse engineering the Power Assurance Check. With the help of the above equations, we can now calculate the specified power of the AS-350B2 Turbomeca 1D1 engine for any combination of ambient temperature, pressure altitude, Ng and rotor rpm. A byproduct of this effort is the ability to mathematically compute a power assurance check, thus eliminating the inherent errors in tracing a long and admittedly convoluted path through a very confusing chart4. However, before we can determine the maximum available power, we need to extract some additional data from the Rotorcraft Flight Manual. This data is supplied in tabular format and titled, Theoretical Maximum Takeoff Power. Tabular data eliminates the inherent errors involved in scale, interpolation and accuracy when extracting values from charts.

4 Appendix A contains the complete method for calculating the PAC.

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Since this data is based upon temperature and pressure altitude, now is an appropriate time to introduce the density ratio, or sigma (s),

θδ

σ =

In this case, delta is computed in standard fashion, without a tweaked exponent. A plot of the referred maximum Ng versus sigma is shown below.

Theoretical Maximum Ng for Takeoff

R2 = 0.9999

65

70

75

80

85

90

95

100

105

0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1

Sigma

Ng

* D

elt

a^

0.5

25

/ T

heta

^0

.47

5

Performing a quadratic fit of this plot results an excellent coefficient of determination of R2 = 0.9999,

( ) 852.28494.92744.19 2 +⋅+⋅−= σσreferredMaxNg

We can now calculate the maximum power available for any combination of temperature and pressure altitude. HOVER PERFORMANCE The ability to determine the maximum power available for any ambient condition now unlocks the possibility of reverse engineering the hover chart. For our example we will utilize the OGE chart (Figure 7), however, the same procedure is equally valid for the IGE chart. The goal is to develop a plot of power vs. thrust. This is accomplished through a well establish process utilizing the referred parameter of power and weight (see equations below). The work above supplies the power values while the O.G.E. chart supplies the weight variables.

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Figure 7 - AS-350 B2 O.G.E. Hover Chart

The equation for referred power is,

( )( )3

3

test

stdreferred

R

RESHPESHP

⋅Ω⋅

⋅Ω⋅=

σ

The equation for referred weight is,

( )( )

2/3

2

2

⋅Ω⋅⋅Ω⋅

=test

stdreferred

RRGWt

Wσ

where,

θπ

⋅⋅

⋅=Ω60

2rpm

Displayed below is a plot 5 constructed from a sampling of values extracted from the O.G.E. chart married with the corresponding values computed for maximum power.

5 A better fit could be achieved if compressibility effects were accounted for. However, the additional complexity distracts from the value of this discussion.

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Referred Power vs. Referred Weight

R2 = 0.9982

500

600

700

800

900

1000

4700 5200 5700 6200 6700 7200

Referred Weight

Ref

erre

d P

ower

Figure 8 – O.G.E. Hover Power

A quadratic6 fit derived from this plot is,

( ) 0.1140988.0066 2 −⋅+⋅−= refrefreferred WtWtEESHP

It becomes a simple matter of rearranging the equation for referred ESHP in order to determine the power required to hover O.G.E. under any conditions.

( )( )3

3

std

testreferred

R

RESHPESHP

⋅Ω

⋅Ω⋅⋅=

σ

One must take note, when substituting values for low density altitudes and low helicopter weights the process involves extrapolation. However, by conducting a simple hover test, an operator could easily validate and refine these equations by anchoring the chart at lower values.

6 While a quadratic fit produces a coefficient of determination of 0.9982, the fit theoretically should be a straight line, a linear fit yields an R2=0.9976 for the same data.

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APPENDIX A. AS-350 B2 POWER ASSURANCE CHECK It is not easy to explain why the manufacturer constructed this chart with the correct/incorrect shaded areas and the bizarre and convoluted path needed to determine a valid Power Assurance Check. The entire process could have been established with a much easier and less confusing method. Regardless, here are the steps to mathematically calculate the power assurance check:

(1) Complete an in-flight power assurance check in accordance with the procedures outlined in the RFM. Note the values of Free Air Temperature, Pressure Altitude, Torque, Nr, and Ng.

(2) Calculate theta and (tweaked) delta,

16.28816.273+

=fat

θ

( ) 125.5

16.288001981.0

0.1

⋅

−=feetaltitude

δ

(3) Calculate the power produced from the observed torque and main rotor rpm,

( ) ( )rpmNrtorquekWactual ⋅⋅= %239.1

(4) Calculate the minimum specified power for the Ng and ambient conditions,

475.0θNg

Ng corrected =

( ) 7.693678.1265237.0 2 −⋅+⋅−= correctedcorrectedcorrected NgNgkW

δθ ⋅⋅= correctedkWkWmin

(5) Compare kWactual with kWmin. If kWactual is greater than or equal to kWmin, the

engine is producing sufficient power.

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APPENDIX B. EUROCOPTER AS-350 B2 HELICOPTER SPECIFICATIONS

Weights Empty (typical) 2,736 lbs. Maximum takeoff 4,960 lbs. Maximum takeoff (with sling load) 5,512 lbs. Fuel capacity 143 gals. Engines Type Turbomeca Arriel 1D1 Maximum T.O. rating 478 Kw Maximum continuous rating 441 Kw Rotor Parameters Radius (3 blades) 35.07 ft. Chord 13.78 in. Rotor RPM 390 (+4/-5) Main rotor airfoil (asymmetrical) ONERA OA 2.09

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REFERENCES

1. Aerospatiale SNI, 1990, Flight Manual AS 350 B2, Marignane, France. 2. Eurocopter, 2009, AS350B2 Technical Data (350 B2 09.101.01 E), Marignane,

France. 3. European Aviation Safety Agency, 2007, Type-Certificate Data Sheet AS 350,

Koeln, Germany.

4. F.A.A., 2007, Type Certificate Data Sheet No. H9EU, Washington, DC.

5. F.A.A., 2006, Type Certificate Data Sheet No. E19EU, Washington, DC.

6. N.O.A.A., 1976, U.S. Standard Atmosphere, Washington, DC.

7. U. S. N., 1996, Rotary Wing Performance, USNTPS-FTM-No. 106, Patuxent River, MD.

8. Volponi, A. J., 1998, Gas Turbine Parameter Corrections, ASME, 98-GT-947.