NASA/CR–2012-216037

Aircraft Design Considerations to Meet One Engine 

Inoperative (OEI) Safety Requirements

Mark W. Scott

Sikorsky Aircraft Corporation

Stratford, Connecticut 

August 2012

Prepared for Ames Research Center under 

Contract No. NAS2-01065
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NASA/CR–2012-216037

Aircraft Design Considerations to Meet One Engine 

Inoperative (OEI) Safety Requirements

Mark W. Scott

Sikorsky Aircraft Corporation

Stratford, Connecticut 

August 2012

National Aeronautics and

Space Administration

Ames Research Center

Moffett Field, California 94035-1000
Available from:

NASA Center for AeroSpace Information National Technical Information Service

7115 Standard Drive 5285 Port Royal Road

Hanover, MD 21076-1320 Springfield, VA 22161

(301) 621-0390 (703) 487-4650
iii 

TABLE OF CONTENTS 

LIST OF FIGURES ............................................................................................................................. iii 

NOMENCLATURE ............................................................................................................................ iv 

LIST OF FIGURES 

Figure 1. Heliport vertical takeoff profile. ............................................................................................ 2

Figure 2. Vertical procedure total drop down from CDP vs. PDR. ...................................................... 3

Figure 3. Horsepower required ratio vs. speed and disk loading. ......................................................... 3

Figure 4. PDR vs. AI at 15-foot total drop down. ................................................................................ 4

Figure 5. OEI/TRP vs. engine number and hover power ratio. ............................................................ 5

Figure 6. Hover power ratio vs. disk loading and L/D. ........................................................................ 6
iv 

NOMENCLATURE 

A area, sq ft 

ABC Advancing Blade Concept 

AGL above ground level 

AI autorotative index 

av available 

CAA Civil Aviation Authority 

CDP critical decision point, ft AGL 

DL disk loading, psf (GW/Arotor) 

FAA Federal Aviation Administration 

fe equivalent flat plate area, sq ft 

fpm feet per minute 

fps feet per second 

ft feet 

GW gross weight, lb 

HLR heavy lift rotorcraft 

hp horsepower 

Irotor total rotor inertia, slug-ft2

ISA International Standard Atmosphere 

K thousand 

kts knots 

L/D aircraft overall lift-to-drag ratio 

Neng number of engines 

OEI one engine inoperative 

PDR power deficiency ratio, (OEI hp av/HPreq hover) 

ROC rate of climb, fpm 

RPM revolutions per minute 

sq ft square feet 

TOWG takeoff gross weight 

TRP takeoff rated power, hp 

Vbroc best rate of climb speed 

VDTR variable-diameter tiltrotor 

Vtoss takeoff safety speed, kts 

Ω rotor rotational speed, rad/sec 
1 

AIRCRAFT DESIGN CONSIDERATIONS TO MEET ONE ENGINE 

INOPERATIVE (OEI) SAFETY REQUIREMENTS 

Mark W. Scott1

Ames Research Center 

Commercial airlines are obligated to operate such that an aircraft can suffer an engine failure at any 

point in its mission and terminate the flight without an accident. Only minimal aircraft damage is 

allowable, such as brake replacement due to very heavy application, or an engine inspection and/or 

possible removal due to use of an emergency rating. Such performance criteria are often called zero 

exposure, referring to zero accident exposure to an engine failure. The critical mission segment for 

meeting one engine inoperative (OEI) criteria is takeoff. For a given weight, wind, and ambient 

condition, fixed-wing aircraft require a balanced field length. This is the distance to takeoff if an 

engine fails at a predetermined critical point in the takeoff profile, or the distance to reject the 

takeoff and brake to a stop, whichever is longer. Rotorcraft have requirements for horizontal takeoff 

procedures that are equivalent to balanced field length requirements for fixed-wing aircraft. 

Rotorcraft also perform vertical procedures where no runway or heliport distance is available. These 

were developed primarily for elevated heliports as found on oil rigs or rooftops. They are also used 

for ground-level operations as might be found at heliports at the end of piers or other confined areas. 

Figure 1 shows a vertical takeoff profile for an elevated platform. The takeoff procedure starts with a 

vertical climb at takeoff rated power. There is a critical decision point (CDP), which is typically at 

about a 30-foot wheel height. If an engine failure occurs before this point, the aircraft lands back 

atits takeoff point. If an engine failure occurs after CDP, the takeoff is continued by dropping the 

nose and accelerating to takeoff safety speed, (Vtoss). At Vtoss the aircraft must be capable of a 

100- fpm rate of climb (ROC). The aircraft initiates this ROC upon attaining Vtoss and continues to 

1,000 feet above ground level (AGL). The aircraft must remain 35 feet AGL or higher throughout 

the continued takeoff procedure. At 1,000 feet AGL, the aircraft accelerates to best rate of climb 

speed (Vbroc) where ROC must be 150 fpm or higher. Thees values are Federal Aviation 

Administration (FAA) requirements. The Civil Aviation Authority (CAA) has slightly different 

ROC and clearance requirements, but the takeoff method is the same. The drop down exchanges 

potential energy for the kinetic energy required to reach Vtoss. The larger the drop down, the less 

engine OEI power required. Elevated heliports have the advantage of more potential energy 

available for exchange than ground-level heliports. The continued takeoff profile for a ground-level 

heliport is the same as shown in figure 1. However, the CDP could be less than the 35-foot 

clearance, and an aircraft may actually have to climb slightly as it accelerates to Vtoss. 

 

1

 Sikorsky Aircraft Corporation, Stratford, Connecticut 
2 

Figure 1. Heliport vertical takeoff profile. 

Figure 2 shows a parametric trend developed to estimate the total drop down from CDP for 

helicopters as a function of aircraft OEI power available to power required to hover ratio. This is 

called a Power Deficiency Ratio (PDR). Conversely this ratio can be found for a given total dropdown requirement. There have been several papers that trend drop-down distance by the same or 

similar ratio. The points shown are for a variety of helicopters at different gross weights. Results of 

some limited analyses of 50-passenger-class civil tiltrotors as part of past civil tiltrotor and variablediameter tiltrotor (VDTR) work are shown as well. 

The commercial heavy lift rotorcraft (HLR) focus of this study dictates vertical ground-level 

procedures. Selection of CDP is a function of rotor inertia, engine spool-up time, engine control 

delays, pilot reaction time, pilot visibility, and landing gear sink rate capability. For this analysis a 

50-foot CDP was chosen assuming favorable gains in the above parameters and, in particular, highsink-rate landing gear. A 50-foot CDP and a 35-foot clearance requirement allow only a 15-foot total 

drop down. Based on figure 2, a conventional rotorcraft and a tiltrotor require a PDR of 0.80 and 

0.93, respectively. Tiltrotors require a higher PDR due to lower relative stored rotational energy in 

the rotor system and a higher Vtoss. When a helicopter loses an engine abruptly, there is a finite 

amount of time for the second engine to reach full emergency OEI power. During this time rotor 

RPM decays. A helicopter rotor has a high amount of rotational energy relative to the kinetic energy 

required to accelerate to Vtoss. This energy helps keep the rotor close to 100 percent RPM and allows 

more ballooning and forward speed gain just after CDP. A tiltrotor, with its lighter and smaller 

diameter rotors, does not have nearly as much rotational energy, therefore descent starts very shortly 

after CDP. The larger contributor to higher OEI power requirements is the higher Vtoss speed 

associated with higher disk loadings. The physics of induced power dictates the speed for minimum 

power required increases with higher disk loading. A tiltrotor, with its higher disk loading, has to 

accelerate to a higher Vtoss, which requires more energy, and therefore more drop down or engine 

power than a helicopter (figure 3). 

Normal 

Takeoff

Max power 

vertical ascent

35 ft minimum

Rejected 

Takeoff

Critical 

Decision 

Point (CDP)

Continued 

Takeoff

Vtoss

Total 150 fpm ROC

Drop
3 

Figure 2. Vertical procedure total drop down from CDP vs. PDR.

Figure 3. Horsepower required ratio vs. speed and disk loading. 

Total Drop Down from CDP vs OEI hp av/HOGE HP

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00

OEI HP av/HOGE HP Req (PDR)

Total drop down, ft

Helicopters

Tiltrotors

Poly. (Helicopters)

Helicopters

Tiltrotors

Hp req / Hp hover vs Speed and Disk loading

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1.10

0 20 40 60 80 100 120 140

V ktas

HP req/HP hover

DL=10 psf

DL=20 psf

DL=30 psf

DL=40 psf

Locus of 

minimum power 

required points

Typical Vtoss 

speeds
4 

The effect of rotational energy and disk loading is captured in a nondimensional term called 

Autorotative Index (AI) (eq. 1). This parameter relates the rotational kinetic energy stored in the 

rotor to aircraft weight and rotor aerodynamic efficiency. AI is a nondimensional value that is used 

as an index. Pilot-rated flying qualities for autorotation improve with increased AI. The same is true 

for OEI takeoff procedures for a constant PDR. Figure 4 shows how PDR trends with AI at a 

15-foot-total drop down. Preliminary sizing of a twin rotor tiltrotor meeting mission requirements is 

in the 120K lb takeoff gross weight (TOGW) class. Disk loadings in the range of 30 to 50 psf are 

expected. The AI index was calculated for a 30- and 50-psf tiltrotor and are plotted in figure 4. 

 AI = Irotor * Ω2 / DL / GW (1) 

There is a size effect on AI. Generally, as aircraft size increases, AI is reduced. Therefore, AI values 

for a 120K lb tiltrotor are expected to be lower than the 50K lb tiltrotor points. Figure 4 indicates a 

PDR of 0.945 at an average DL of 40 psf. Knowing that lower disk loadings are sought and some 

advanced flight controls may bring benefits, a PDR value of 0.93 was selected for an HLR tiltrotor. 

An Advancing Blade Concept (ABC) aircraft in the 120K lb class at 17.5-psf disk loading has an AI 

around 12.5. Therefore for a 15-foot drop height, the ABC requires a PDR of about 0.88. 

With the PDR requirements determined, the question is what engine OEI/takeoff rated power (TRP) 

ratio is required? This ratio is a function of how oversized the engines are in hover, and how many 

engines are on the aircraft. Equation 2 relates these three parameters to engine OEI/TRP ratio 

required. The first term in equation 2 is PDR, the second is the hover power margin. 

Figure 4. PDR vs. AI at 15-foot-total drop down. 

Power Deficiency Ratio vs Autoroative Index

0.74

0.76

0.78

0.80

0.82

0.84

0.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Autotaion Index (AI)

PDR (OEIhpav/HP req hover)

Calculated PDR values for a

given AI

Calculated AI for 120K lb TR

and expected PDR's requried

Linear (Calculated PDR values

for a given AI)

Helicopters 50K lb TOGW 

class Civil TR

DL~20 psf

120K lb TOGW class Civil TR

DL=50 psf

DL=30 psf
5 

Plots of required engine OEI/TRP as a function of hover power margin and engine number are 

shown in figure 5 for the selected tiltrotor PDR of 0.93. The most demanding case is where a twoengine aircraft hovers at 100 percent TRP. In an OEI condition, where the remaining engine must 

provide 93 percent of the power required to hover, the engine OEI/TRP ratio must be 1.86. If the 

engines were oversized such that only 75 percent of the available TRP were required to hover, the 

OEI/TRP ratio would be 1.4. A four-engine aircraft hovering at 80 percent TRP does not need an 

elevated OEI engine power rating. 

 (OEI hp av / TRP) = (Hpav OEI / Hpreq over) * (Hpreq hover/TRPav) * (Neng/ (Neng-1)) (2) 

Usually determination of hover power margin is a function of engine OEI/TRP. For the HLR study 

engine ratings ratios are not set, so the benefit of increased OEI/TRP in terms of disk loading 

increase, and weight reduction can be quantified. Figure 6 shows the results of sizing runs for 

various aircraft L/D ratios and disk loadings. A low L/D aircraft requires more installed power to 

cruise. At a low disk loading there is more than enough power to hover. Such an aircraft is said to be 

sized by cruise. Conversely, a high L/D aircraft (which requires less installed power for cruise) with 

a high disk loading may not have enough power to hover. Therefore, more installed power is 

required, and the aircraft is said to be sized by hover. As an example, a tiltrotor with an L/D of 10 

and a 30-psf disk loading only requires 66 percent of installed TRP to hover. If this aircraft had two 

engines, extrapolation of the top line in figure 5 shows an OEI/TRP requirement of 1.2. 

Figure 5. OEI/TRP vs. engine number and hover power ratio.

OEI/TRP ratio vs Number of Engines and Hover Power Ratio

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05

HP req hover / TRP av

Engine OEI/TRP ratio

2 engines

3 Engines

4 Engines

Tiltrotor Ground Level Procedure

OEI Hpav/HP req hover = .93
6 

Figure 6. Hover power ratio vs. disk loading and L/D.

Figure 5 is independent of mission profile and engine lapse rates. Figure 6 was created with hover 

and cruise ambients of 2K-95F and 30K ISA, 350 kts respectively. The engine lapse rates were 

based on a T-406 engine variant. The selected rotor hover FM was 0.81 and vertical drag was 

10 percent of GW for a DL of 25 psf, linearly increasing to 16.3 percent of GW at DL = 50 psf. For 

a given cruise condition, hover ambients and engine lapse rates change the results. For example, 

higher hover density altitude demands more installed power and shifts the curves in figure 6 up. 

Similarly, if the engine were able to retain more power with density altitude the curves would move 

up as well. Figures 5 and 6 indicate that at L/Ds around 12, a four-engine aircraft does not need an 

OEI/TRP ratio greater than one. 

Figures 2 and 5 can be used as part of an aircraft trade study. For a matrix of design disk loadings 

and engine number, PDR values can be found for a given drop down. Then OEI/TRP ratios, the 

associated propulsion system weight and cost, and ultimately the overall aircraft weight, cost, and 

productivity can be found. Similarly, aircraft productivity impact as a function of drop down can be 

quantified. For a CDP of 35 feet and zero total drop down, a tiltrotor will require a PDR close to 

0.97. 

Based on the results shown, historical trends, and past experience, a drag level of 36 sq ft and a disk 

loading of 30 psf are expected for a 120K lb aerodynamically clean civil tiltrotor. Based on figure 6, 

an HPreq hover/TRPav ratio of 0.77 is required. Figure 5 shows an engine OEI/TRP ratio of 1.43 for a 

two-engine aircraft. This is a high rating by today’s standards, but most likely achievable given 

Hover Power Ratio vs. Disk Loading and Aircraft L/D

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

0 10 20 30 40 50 60

DL, psf

HP req hover / TRP av

L/D = 12.5, fe=31

L/D = 11, fe = 41

L/D = 10, fe =51

L/D excludes propulsive efficiency

Engines sized by Cruise

Engines sized by Hover T-406 lapse rates

Hover 2K-95F

Cruise 350 kts, 30K ISA

120K lb TOGW Class tw in rotor tiltrotor
7 

improving engine technology. A two-engine aircraft is also much more attractive from a cost, 

complexity, and weight standpoint. 

Based on extrapolation in figures 5 and 6, an ABC aircraft with an L/De2 of 11 and a disk loading of 

17.5 psf requires only 55 percent of installed TRP to hover. Even at the more stringent tiltrotor PDR 

of 0.93, a two-engine ABC would only require a modest OEI/TRP ratio. Therefore, the OEI 

performance of an ABC should be exceptionally good up to high-density altitudes. 

 

2

 L/De includes rotor induced drag, H force, and profile power converted to a drag.