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Part 1 - Recap

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- We looked at the history of helicopters.
- We studied ways of overcoming reactive torque – tail rotors, co-axial rotors, tilt-rotors, tip jets, NOTAR etc.
- We looked at a number of ways predicting helicopter performance in hover, and climb.

V

The excess velocity in the

Far wake is twice the induced

Velocity at the rotor disk.

To accommodate this excess

Velocity, the stream tube

has to contract.

V+v

V+2v

Now we can compute the induced velocity at the

rotor disk in terms of thrust T.

T=2rAv(V+v)

Use this during conceptual design to size rotor, select engines

In hover, ideal power

- Figure of merit is defined as the ratio of ideal power for a rotor in hover obtained from momentum theory and the actual power consumed by the rotor.
- For most rotors, it is between 0.7 and 0.8.

dT

r

dr

R

Root Cut-out

Use this during preliminary design, when

You have selected airfoils, number of blades,

Planform (taper), twist, solidity, etc.

- Let us assume that every section of the entire rotor is operating at an optimum lift coefficient.
- Let us assume the rotor is untapered.

Rotor will stall if average lift coefficient exceeds 1.2, or so.

Thus, in practice, CT/s is limited to 0.2 or so.

Use this to select solidity s, during design.

Total Inflow Velocity from Combined

Blade Element-Momentum Theory

- We also looked at modeling the tip vortices from the rotor using a prescribed form, and computing induced velocity v due to these vortices using Biot-Savart law.

- What happens when a helicopter vertically descends, perhaps due to a loss of engine power.
- The rotor may grow through four phases:
- Hover
- Vortex Ring State
- Turbulent Wake State
- Wind Mill Brake State

- We mentioned that the rotor is as good as a parachute with drag coefficient 1.4

- Coning Angle of the blades
- Lock Number

Lock Number, g

- We studied how to compute the induced velocity v through a rotor in forward flight.

We studied a simplified picture of Force Balance

Rotor Disk, referred to

As Tip Path Plane

Flight Direction

aTPP

Force Balance in Forward Flight

Thrust, T

Vehicle Drag, D

Flight Direction

Weight, W

We refined the Horizontal Force Balance

HT

HM

DF

V∞

Total Drag= Fuselage Drag (DF) + H-force on main rotor (HM)

+ H-force on the tail rotor (HT)

We included fuselage lift inVertical Force Balance

LF

GW

Vertical Force = GW- Lift generated by the fuselage, LF

We discussed how to estimatePower Consumption in Forward Flight

Total Power

Power

Parasite Power

Induced Power, Tv

Blade Profile Power

V∞

- Three coordinate systems
- Shaft Plane
- Tip path Plane
- Control Plane

- Blade Flapping Dynamics Equation:

Natural frequency= W

If a first harmonic input at the resonance frequency is imposed,

The blades will respond 90 degrees later!

- Sectional angle of attack
- This angle of attack can be achieved either by flapping or by cyclic pitch.
- One degree of pitch is equivalent to one degree of flapping as far as the blade is concerned.

- How to compute the sectional loads.
- How to integrate them radially, and average them azimuthally to get total thrust, total torque, power, H- force, and Y- force.

- How to trim an entire vehicle, taking into account fuselage lift and drag characteristics.
- We also discussed how to trim an entire vehicle, when it is in autorotative descent.
- Trim means all the forces and moments on the vehicle are balanced, and the power required equals power available.

Vehicle Performance Methods

An Overview

How high? - Service altitude

How fast?- Maximum forward speed

How far?- Vehicle range

How long?- Vehicle endurance

- Engine performance data is available from engine manufacturer.
- This information comprises of variation of shaft horse power and fuel consumption with altitude, forward speed, and temperature at various settings (max continuous power, max take-off power, etc.)
- Estimates of installed power losses are available.

- Inlet duct total pressure losses due to skin friction (1 to 4%)
- Inlet total pressure losses due to particle separators (3 to 10%)
- Exhaust duct total pressure losses due to skin friction (2%), and due to infra-red suppressors (3% to 15%).
- Exhaust gas reingestion (1 to 4 degrees inlet temp rise)
- Compressor bleed (1 to 20%)
- Engine mounted accessories (addition 100 HP)
- Transmission losses

Segments

This is done experimentally, or by modeling the fuselage

as a series of bluff body segments.

- Main rotor-tail rotor interference. The tail rotor is immersed in the downwash of the main rotor.
- The tail rotor will need to generate more thrust than estimated, because some of the thrust generated is lost by the interference effects.
- Empirical curves that plot this interference effect as a function of separation distance between the main and tail rotor shafts are constructed.

- Ground effect: This reduces the inflow through the rotor, and has the beneficial effect of reducing the torque needed.
- Fuselage plus hub Parasite Drag coefficient (or equivalent flat plate area, f) as a function of fuselage angle of attack.
- Miscellaneous drag due to antennae, Pitot probes, hinges, latches, steps, etc.
- One of the major efforts in performance studies is an accurate fuselage drag estimate.
- The fuselage drag is expressed as equivalent flat plate area.

0.95

vIGE/vOGE

When operating near ground, induced

Velocity decreases. Induced power

Decreases. Performance increases, since

Total power consumed is less.

IGE: In ground effect

OGE: Out of ground effect

0.6

1.0

0.1

Height above Ground/Rotor Diameter= z/D

- Sum of:
- Rate of change of potential energy
- Main rotor power (based on Thrust equals Gross weight plus fuselage vertical drag)
- Tail rotor power taking into account extra thrust needed to overcome interference
- Transmission and Installation Losses

- This is compared against the available power, to determine the maximum GW that the vehicle can lift.
- When power required equals power available under zero climb rate, absolute ceiling has been reached.
- When there is just enough power left to climb at 100 ft/min, service ceiling is reached.
- These calculations are plotted as charts.

- Gross Weight = 16000 lb
- Main rotor
- R=27 ft, c=1.7 ft,s=0.082, b=4, WR=725 ft/sec

- Tail rotor
- R=5.5 ft, c=0.8 ft, s=0.19, b=4, WR=685 ft/sec

- Distance between main and tail rotor= 32.5 ft
- Use k=1.15, Drag coefficient=0.008
- Available power less losses = 3000 HP at sea-level less 10%
- Neglect download.
- Find absolute ceiling as density altitude.

Variation of Power with Altitude:

- Assume an altitude, h. Compute density, r.
- Do the following for main rotor:
- Find main rotor area A
- Find v as [T/(2rA)]1/2 Note T= Vehicle weight in lbf.+ download
- Insert supplied values of k, Cd0, W to find main rotor P.
- Divide this power by angular velocity W to get main rotor torque.
- Divide this by the distance between the two rotor shafts to get tail rotor thrust.

- Now that the tail rotor thrust is known, find tail rotor power in the same way as the main rotor.
- Add main rotor and tail rotor powers. Compare with available power.
- Increase altitude, until required power = available power.

Hover

Ceiling

Standard Day

95 deg F

Gross Weight

R/C, ft/min

Standard Day

95 deg F

Altitude, ft

R/C, ft/min

Standard Day

95 deg F

Gross Weight

High Altitude

Low Altitude

Engine HP

Gross Weight

- Power required is the sum of
- Induced power of the main rotor, kTv
- Profile power of the main rotor
- Tail rotor induced power and profile power
- Fuselage parasite drag times forward speed

High altitude

Intermediate altitude

Low altitude

Severe Stall

Onset of stall

Power

Forward Speed

- Select GW, atmospheric density, density ratio= r/r at sea-level
- Use engine charts to find total power available at sea level
- Divide power by density ratio to find excess power needed at higher altitudes.
- Match power required to (Power available at sea level + Excess Power needed at high altitudes), to get a first estimate for forward flight.
- If compressibility effects are present, correct sectional drag coefficient to include wave drag.
- Iterate on the maximum speed.

GW ~10,000 lb

GW ~ 24,000 lb

Altitude

Take-off Power

Take-off Power

Continuous Power

Continuous Power

120 knots

180 knots

Maximum speed in ft/sec or knots

- It is at times of interest to compare a rotor with that of a fixed wing.
- This comparison is done in terms of L/D of the rotor.
- Fuselage effects are excluded in this comparisons.
- L is the vertical component of rotor thrust
- D = Main rotor power/Forward Speed – Fuselage Drag

10

L/D

160 knots

Forward Speed

- Distance traveled per unit fuel.
- Similar to miles per gallon on automobiles.
- Generally expressed as nautical miles traveled per pound of fuel.
- If one knows the power required by the helicopter as a function of forward speed, and the fuel consumption of the engine as a function of horse power, we can compute fuel flow rate at any given forward speed.
- For multiple engines, divide power required by the number of engines to obtain power required per engine.

Fuel Flow

Rate lb/hr

Best SR=1/slope

Best speed for maximum specific range

Relative Forward Speed including head or tail wind, knots

Range is found by numerical integration of the curve below,

Generated by computing the best SR for various gross weights.

99% of

Best SR

Take off

Landing

Gross Weight

- Provides an indication of the helicopter for carrying useful loads.
- This information can be extracted from the range calculations described previously.
- Plotted as Range vs. Payload, for various payload conditions, for a fixed maximum take-off weight.
- As payload increases, the amount of fuel that can be carried decreases, and the range decreases.

GW=28000 lb (auxiliary tanks)

Payload, lb

20,000 lb

10,000 lb

1600

400

Range, Nautical Miles

- In some military missions and search and rescue operations, loiter is more important than range.
- Endurance is defined as the hours of loiter per pound of fuel.
- Loiter is done at the forward speed where power consumption is minimum.

Power

HP

Power loiter

Best speed for Loiter

Forward Speed

- Specific endurance is defined as 1 / (fuel consumption in lb/hr) under loiter conditions.
- Once we know the power consumption at loiter speed from the previous chart, we can use engine performance data to find fuel consumption in lb/hr ar this power.
- The inverse of this is SE.

SE

Gross Weight

Power Available

Power Required

Power

Maximum

Forward Speed

Forward Speed

Absolute Ceiling

Altitude

Service ceiling

Gross Weight

Helicopter Performance

Special Performance Problems

- Turns and Pull-Ups
- Autorotation
- Maximum Acceleration
- Maximum Deceleration

T

CF

W

Radius of Turn, R

Power needed to perform a turn is analyzed in the same way

as steady level flight. The gross weight is multiplied by n.

- In some cases, the engine can not supply the power needed to perform a steady level turn at a constant altitude.
- The pilot will lose vehicle velocity, and altitude.
- In other words, some of the vehicle kinetic energy and potential energy are expended to perform the turn.
- In that case, the average velocity may be used to compute the load factor n and the thrust/power needed.
- From the energy required to perform the turn, subtract off the energy extracted from the change in the vehicle kinetic energy during the turn, and subtract off the energy extracted by a change in the vehicle potential energy.
- The rest is the energy that must be supplied by the engine.
- Divide the energy by time spent on the turn to get power needed.

R

T

V

W+CF

Power is computed as in

Steady level flight.

T+CF

R

W

- In the case of power failure, the RPM rapidly decays. How fast, how much?
- The vehicle supplies power to the rotor by descending rapidly. How fast?
- The vehicle continues to move forward. How far?

A high J and high W0 needed to keep rotor

spinning at a high enough speed.

1

W/W0

tKE= 4 sec

tKE= 1 sec

0.4

3 to 4 sec

Time

Vdescent. t

Descent Angle

Ground

VForward. t

Vortex ring state

Encountered..

Too steep a descent

Rate of Descent = P/GW

Best descent

angle

Speed for minimum

Descent angle feasible

Forward Speed

Best Forward Speed

For minimum descent rate

Pilot zooms to

higher altitude,

trading kinetic energy

for potential energy.

Autorotative

descent is

attempted.

Aircraft has high

forward speed when

power failure occurs.

Vehicle is too low.

Ground

Avoid!

Height

Power consumption

Is too high.

Vortex ring state

possible

Avoid. High speed

Impact with ground likely

Velocity

Cyclic Flare:

Cyclic pitch

is increased to

Increase lift, tilt rotor

Aft, slow down

descent rate.

Vehicle pitches up.

Collective Flare

Increase collective.

Bring nose down.

Touch down as

slowly as possible

Steady

Autorotative

Descent

Thumb Rule: For safe autorotative landing employing flare,

the autorotative index must be higher than 60 for

single engine helicopters, and higher than 25 for twin- engine

aircraft (assuming only one engine Is likely to fail).

- We first find the highest fuselage equivalent flat plate area, fmax at which steady level flight is possible.
- This is done by assuming various values of f, and computing power needed in forward flight using methods described earlier.
- f is increased to its maximum value fmax until power needed=power available.
- Compute maximum thrust= maximum drag=1/2rfmaxV2
- Compute actual thrust needed1/2rfmaxV2
- The maximum acceleration= (Maximum thrust-Actual Thrust)/m, where m is the mass of the aircraft.

- When the vehicle decelerates, the pilot tilts the rotor disk aft, so that thrust is pointing backwards, and vehicle slows down.
- If deceleration occurs too quickly, autorotation may occur, and the rotor RPM may increase too much, and structural limits may be exceeded.
- To avoid this, only a 10% to 20% overspeeding of the blade RPM is permitted.
- Compute the H force, tip path plane angle, T, fuselage drag fq, etc. at this higher permitted RPM, for autorotative condiitons.
- Compute the maximum permissible rearward directed force = -TaTPP+H+f q
- Maximum deceleration is this force divided by helicopter mass.

Airfoils for Rotor Blades

- High maximum static and dynamic lift coefficients to allow flight at high speeds or at high maneuver loads.
- A high drag divergence number to allow flight at high advance ratios without prohibitive power requirements or noise.
- Low drag coefficient at moderate lift coefficients and Mach numbers to minimize profile power.
- Low pitching moments at moderate lift coefficients.
- Enough thickness for structural strength.

High altitude

Intermediate altitude

Low altitude

Severe Stall

Onset of stall

Power

Forward Speed

1.6

1.2

Dynamic Stall

Shape depends on

Many factors.

Causes vibrations,

Due to the large

Changes to lift.

Cl

Static

Alpha

Cm

Nose up is

Positive

Dynamic Stall

Alpha

Static, moment stall

High nose-down pitching moment

May stress the pitch links too much

And cause fatigue.

High Pressure

Low Pressure

Dynamic Stall

Cd

Alpha

Laminar Drag Bucket

Drag Divergence Mach No, MDD

M

Drag rise due to formation of shock waves on the

Advancing side, near the tip.

MDD: Mach number at which drag rises at the rate of

0.1 per unit Mach number. Curve slope=0.1

Rotorcraft Noise, MTip > 0.9

High-Speed-Impulsive noise

UH-60A Black Hawk

Factors to consider in thePreliminary Design of the Rotor

- Payload
- Range or Endurance
- Hover ceiling
- Vertical Climb
- Maximum speed
- Maximum Maneuver load factor

- Advantages of High Disk Loading:
- Compact size
- Low empty weight
- Low hub drag in forward flight

- Advantages of Low Disk Loading:
- Low induced velocities
- Low autorotative rate of descent
- Low power requirements in hover.

- If it is too high, shocks will form, shock noise will rise, power consumption will go up.
- If it is too low, there will be inadequate storage of energy when autorotative descent is necessary.
- If it is too low, rotor may stall sooner.

Noise

800 ft/sec

Wave drag, high power

Tip speed

Stall

400 ft/sec

200 knots

Stored energy

Forward Speed

- Advantages of high solidity
- Allows hover at high altitude and temperature.
- Permits high forward speed without stall on the retreating side.
- Permits maneuvers at high load factors.

- Disadvantages:
- Increased profile power consumption
- Increased weight
- Increased cost of ownership

- Advantage of fewer blades
- Low rotor weight, cost
- Ease of folding and storing
- Low vulnerability to combat damage

- Disadvantages of fewer blades
- High rotor induced vibrations
- Distinctive noise

- During the first three days, we have looked at engineering methods for predicting
- Hover and vertical climb characteristics
- Forward flight characteristics
- Rotorcraft Performance

- During the next two days, we will look at representative CFD techniques for a more accurate modeling of the hover and forward flight loads.