Subsonic Airplane Design

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Information about Subsonic Airplane Design

Published on November 16, 2008

Author: ahmad1957

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Subsonic Airplane Design

Subsonic Airplane Design Christopher Weyant Joseph Rebolledo COSMOS at UC Davis Cluster 3 August 3, 2006

Presentation Outline Main factors that allow flight Ratios to interpret these factors Important design considerations Case study- Helios

Main factors that allow flight

Ratios to interpret these factors

Important design considerations

Case study- Helios

I. Factors that Allow Airplane Flight Lift Weight Thrust Drag Center of mass Center of pressure

Lift

Weight

Thrust

Drag

Center of mass

Center of pressure

Forces in Airplane Flight

How Lift is Created Observe streamlines Must be downwards pressure force to hold them to wing

Observe streamlines

Must be downwards pressure force to hold them to wing

How Lift is Created Imagine boxes stacked above and below wing Top of box must have higher pressure than bottom Lower pressure on top of wing than bottom Pressure gradient causes lift high pressure low pressure= next high pressure low pressure pressure force pressure force

Imagine boxes stacked above and below wing

Top of box must have higher pressure than bottom

Lower pressure on top of wing than bottom

Pressure gradient causes lift

Lift Three main ways to increase lift: Increase angle of attack Camber Vortex-Induced Lift

Three main ways to increase lift:

Increase angle of attack

Camber

Vortex-Induced Lift

Lift Change angle of attack 2. Camber 3. Vortex induced lift - Watch for separation

Change angle of attack

2. Camber

3. Vortex induced lift

- Watch for separation

Weight Weight measures the downward gravitational pull on the aircraft Several components contribute to the weight of an aircraft: Physical plane Fuel Payload

Weight measures the downward gravitational pull on the aircraft

Several components contribute to the weight of an aircraft:

Physical plane

Fuel

Payload

Weight Considerations Lift must exceed weight to take off In obtaining lift, drag must be less than thrust to accelerate and take off

Lift must exceed weight to take off

In obtaining lift, drag must be less than thrust to accelerate and take off

How Thrust is Created Propulsive device exerts force on air Equal and opposite force exerted back on plane Makes plane go forward and overcome drag

Propulsive device exerts force on air

Equal and opposite force exerted back on plane

Makes plane go forward and overcome drag

Thrust Pressure and sheer stress distribution on surface area cause thrust Thrust equation T=ṁ(V ∞ - V j ) T; thrust [newtons; kgm/s 2 ] ṁ; mass flow through device [kg/s] V ∞ ; velocity of air leaving plane [m/s] V j ; velocity of air ahead of plane [m/s]

Pressure and sheer stress distribution on surface area cause thrust

Thrust equation

T=ṁ(V ∞ - V j )

T; thrust [newtons; kgm/s 2 ]

ṁ; mass flow through device [kg/s]

V ∞ ; velocity of air leaving plane [m/s]

V j ; velocity of air ahead of plane [m/s]

Thrust Total power generated by propulsive device = TV ∞ +1/2ṁ(V j -V ∞ ) 2 (power available) + (wasted/ KE)

Total power generated by propulsive device

= TV ∞ +1/2ṁ(V j -V ∞ ) 2

(power available) + (wasted/ KE)

Thrust vs. Efficiency Useful power ( η p ) = 2/(1+V j /V ∞ ) 100% efficiency has V j = V ∞ However, then no thrust Tradeoff

Useful power ( η p )

= 2/(1+V j /V ∞ )

100% efficiency has V j = V ∞

However, then no thrust

Tradeoff

How Drag is Created Friction drag Drag due to friction over surface Pressure drag Inequality of surface pressure that causes drag Induced drag Pressure drag associated with wing tip vortices

Friction drag

Drag due to friction over surface

Pressure drag

Inequality of surface pressure that causes drag

Induced drag

Pressure drag associated with wing tip vortices

Center of Pressure Sum pressure forces into a single force Point through which lift and drag act Also, the point at which there is no moment To find, plot distributed load and find centroid

Sum pressure forces into a single force

Point through which lift and drag act

Also, the point at which there is no moment

To find, plot distributed load and find centroid

Center of Mass Average location of weight Balance object on that point Point from which gravity can be drawn To find, cg = ( ∫ [x * w(x)]dx) / ( ∫ [w(x)]dx)   Sum of weights of slices times distances to nose divided by the sum of the weights; weighted average x= distance from nose tip of aircraft back to slice [m] dx= small slices perpendicular to x [m] w(x)= weight of slice contained in dx; newton [kgm/s 2 ] Assume weight is distributed symmetrically around center line

Average location of weight

Balance object on that point

Point from which gravity can be drawn

To find, cg = ( ∫ [x * w(x)]dx) / ( ∫ [w(x)]dx)

  Sum of weights of slices times distances to nose divided by the sum of the weights; weighted average

x= distance from nose tip of aircraft back to slice [m]

dx= small slices perpendicular to x [m]

w(x)= weight of slice contained in dx; newton [kgm/s 2 ]

Assume weight is distributed symmetrically around center line

Centers of Mass and Pressure Center of pressure is behind center of mass Leads to increased stability by correcting for angle of attack Horizontal stabilizer provides downwards force Wing provides upwards lift When angle of attack increases, wing lift increase and horizontal stabilizer rotates nose back down They must be on same line, so as to not create torque along the yaw or roll axes

Center of pressure is behind center of mass

Leads to increased stability by correcting for angle of attack

Horizontal stabilizer provides downwards force

Wing provides upwards lift

When angle of attack increases, wing lift increase and horizontal stabilizer rotates nose back down

They must be on same line, so as to not create torque along the yaw or roll axes

II. Useful Non-dimensional Ratios Mach number Reynolds number Aspect ratio Coefficient of lift Coefficient of drag

Mach number

Reynolds number

Aspect ratio

Coefficient of lift

Coefficient of drag

Mach Number Compressibility effects Ma= speed airplane/ speed sound= V/a Ma<1; subsonic Ma≈1; transonic Ma>1; supersonic Ma>>1; hypersonic Ma 2 =-( Δρ / ρ )/( Δ V/V) = change in density/change in velocity

Compressibility effects

Ma= speed airplane/ speed sound= V/a

Ma<1; subsonic

Ma≈1; transonic

Ma>1; supersonic

Ma>>1; hypersonic

Ma 2 =-( Δρ / ρ )/( Δ V/V)

= change in density/change in velocity

Reynolds number Viscosity effects Re= ρ ∞ v ∞ c/ μ ∞ pressure vs. viscosity ρ ∞ = free stream air density [kg/m 3 ] V ∞ = free stream air velocity [m/s] c= chord length [m] μ ∞ = ambient coefficient of viscosity; [Kg/ms] Less than 2300 is laminar Over 2300 is turbulent

Viscosity effects

Re= ρ ∞ v ∞ c/ μ ∞

pressure vs. viscosity

ρ ∞ = free stream air density [kg/m 3 ]

V ∞ = free stream air velocity [m/s]

c= chord length [m]

μ ∞ = ambient coefficient of viscosity; [Kg/ms]

Less than 2300 is laminar

Over 2300 is turbulent

Aspect Ratio Three dimensional effects Tells how skinny wing is AR= b 2 /S b= wingspan [m] S= planform area of wing [m 2 ]

Three dimensional effects

Tells how skinny wing is

AR= b 2 /S

b= wingspan [m]

S= planform area of wing [m 2 ]

Coefficient of Lift C L = L/( ½ ρ V 2 S) C L =coefficient of lift [dimensionless] L= lift; newton [kgm/s 2 ] ρ = air density [kg/m 3 ] V= velocity; [m/s] S= planform wing area [m 2 ]

C L = L/( ½ ρ V 2 S)

C L =coefficient of lift [dimensionless]

L= lift; newton [kgm/s 2 ]

ρ = air density [kg/m 3 ]

V= velocity; [m/s]

S= planform wing area [m 2 ]

Coefficient of Drag C D = D/( ½ ρ V 2 S) C D =coefficient of drag [dimensionless] D= drag; newton [kgm/s 2 ] ρ = air density [kg/m 3 ] V= velocity [m/s] S= planform wing area [m 2 ]

C D = D/( ½ ρ V 2 S)

C D =coefficient of drag [dimensionless]

D= drag; newton [kgm/s 2 ]

ρ = air density [kg/m 3 ]

V= velocity [m/s]

S= planform wing area [m 2 ]

III. Design of Subsonic Airplanes Stalling velocity Wing design Induced drag Angle of attack Ceiling altitude Evaluating airfoils

Stalling velocity

Wing design

Induced drag

Angle of attack

Ceiling altitude

Evaluating airfoils

Stalling Velocity V stall = √(2/ ρ ∞ )(W/S)(1/C L max ) V stall = stalling velocity [m/s] ρ ∞ = free stream air density [ kg/m 3 ] W= weight; newtons [ kgm/s 2 ] S= planform surface area of wing [m 2 ] C L max = maximum lift coefficient [dimensionless]

V stall = √(2/ ρ ∞ )(W/S)(1/C L max )

V stall = stalling velocity [m/s]

ρ ∞ = free stream air density [ kg/m 3 ]

W= weight; newtons [ kgm/s 2 ]

S= planform surface area of wing [m 2 ]

C L max = maximum lift coefficient [dimensionless]

Implications Gets larger at higher altitudes, due to decreasing air density Increases with weight Decreases with planform wing area Decreases with higher C L max

Gets larger at higher altitudes, due to decreasing air density

Increases with weight

Decreases with planform wing area

Decreases with higher C L max

Different Types of Wings High aspect- ratio straight wing Low aspect- ratio straight wing Swept wing Delta wing Simple delta Cropped delta Notched delta Double delta

High aspect- ratio straight wing

Low aspect- ratio straight wing

Swept wing

Delta wing

Simple delta

Cropped delta

Notched delta

Double delta

Prandtl’s Lifting Line Theory a=a o /(1+(a o /  e 1 AR) a= lift slope for finite wing [per radian] a 0 = lift slope for infinite wing [per radian] e 1 = ratio of tip chord to root chord [dimensionless] AR= b 2 /S [dimensionless]

a=a o /(1+(a o /  e 1 AR)

a= lift slope for finite wing [per radian]

a 0 = lift slope for infinite wing [per radian]

e 1 = ratio of tip chord to root chord [dimensionless]

AR= b 2 /S [dimensionless]

Implications Lift slope decreases with aspect ratio Straight wing to maximize e 1 Experimentally, C L max decreases with aspect ratio

Lift slope decreases with aspect ratio

Straight wing to maximize e 1

Experimentally, C L max decreases with aspect ratio

Prandtl- Glauert Rule a o,comp = a 0 / √1 - M ∞ 2 a o = incompressible lift slope [per radian] M ∞ = free stream mach number [dimensionless]

a o,comp = a 0 / √1 - M ∞ 2

a o = incompressible lift slope [per radian]

M ∞ = free stream mach number [dimensionless]

Combined a comp = a o / √1-M ∞ +a o /(  e 1 AR) a o = incompressible lift slope [per radian] a comp = compressible lift slope [per radian] M ∞ = free stream mach number [dimensionless] e 1 = ratio of tip chord to root chord [dimensionless] AR= b 2 /S [dimensionless] Works well for .3<Ma<.7

a comp = a o / √1-M ∞ +a o /(  e 1 AR)

a o = incompressible lift slope [per radian]

a comp = compressible lift slope [per radian]

M ∞ = free stream mach number [dimensionless]

e 1 = ratio of tip chord to root chord [dimensionless]

AR= b 2 /S [dimensionless]

Works well for .3<Ma<.7

Implications Same as before, but modified to account for compressible flows Lift slope decreases with aspect ratio Straight wing to maximize e 1 Experimentally, C L max decreases with aspect ratio

Same as before, but modified to account for compressible flows

Lift slope decreases with aspect ratio

Straight wing to maximize e 1

Experimentally, C L max decreases with aspect ratio

Equation for Induced Drag C Di = (C L 2 )/(  (AR)e) Where: C L ; coefficient of lift [dimensionless] AR; aspect ratio [dimensionless] e; spanwise efficiency factor, how C Di for wing relates to ideal wing with the same aspect ratio [dimensionless]

C Di = (C L 2 )/(  (AR)e)

Where:

C L ; coefficient of lift [dimensionless]

AR; aspect ratio [dimensionless]

e; spanwise efficiency factor, how C Di for wing relates to ideal wing with the same aspect ratio [dimensionless]

Implications Biggest source of drag for low speed aircraft Wings with the largest possible aspect ratio For low speed aircraft, aspect ratios as high as 15 or more are used

Biggest source of drag for low speed aircraft

Wings with the largest possible aspect ratio

For low speed aircraft, aspect ratios as high as 15 or more are used

Angle of Attack Angle that wing is inclined to flow Want only small angle of attack needed to achieve adequate lift at low speed Can be built into wing through camber

Angle that wing is inclined to flow

Want only small angle of attack needed to achieve adequate lift at low speed

Can be built into wing through camber

Ceiling Altitude ( R/C) max = maximum rate of climb [m/sec] η pr = propeller efficiency; power available/ shaft power [dimensionless] P= power [W] W= weight newtons [ kgm/s 2 ] ρ ∞ = free stream air density [kg/m 3 ] K= Coefficient of Cl 2 in drag polar [dimensionless] C D.O= Zero lift drag coefficient [dimensionless] S= planform surface area of wing [m 2 ] L/D max = maximum lift to drag ratio [dimensionless] (R/C) max =( η pr P/W)–[(2/ ρ ∞ )√K/3C D.0 (W/S)] 1/2 *(1.55/(L/D max ))

( R/C) max = maximum rate of climb [m/sec]

η pr = propeller efficiency; power available/ shaft power [dimensionless]

P= power [W]

W= weight newtons [ kgm/s 2 ]

ρ ∞ = free stream air density [kg/m 3 ]

K= Coefficient of Cl 2 in drag polar [dimensionless]

C D.O= Zero lift drag coefficient [dimensionless]

S= planform surface area of wing [m 2 ]

L/D max = maximum lift to drag ratio [dimensionless]

Implications η pr P/W want big Bigger engine, more efficient propeller, less weight K wants smaller Higher aspect ratio W/S want small - Less weight - Larger surface area of wing L/D max want big Less drag More lift

η pr P/W want big

Bigger engine, more efficient propeller, less weight

K wants smaller

Higher aspect ratio

W/S want small

- Less weight

- Larger surface area of wing

L/D max want big

Less drag

More lift

Limits on Reducing Drag Aspect ratio and surface area have to be within a range Makes aircraft heavier which requires more lift Increases skin friction drag which requires more power If aspect ratio is too high, loose stability

Aspect ratio and surface area have to be within a range

Makes aircraft heavier which requires more lift

Increases skin friction drag which requires more power

If aspect ratio is too high, loose stability

Evaluating Airfoils

Explanation For these graphs, Re= 200,500 First graph shows C D and C L of airfoil Want high C L for given C D Second shows  and  C L Want high C L for given  Third shows  and CM Want low CM for given 

For these graphs, Re= 200,500

First graph shows C D and C L of airfoil

Want high C L for given C D

Second shows  and  C L

Want high C L for given 

Third shows  and CM

Want low CM for given 

Coffin Corner Problem faced by high altitude low speed flight If slow down at high altitude, stall If speed up, break sound barrier and generate too much drag and stall

Problem faced by high altitude low speed flight

If slow down at high altitude, stall

If speed up, break sound barrier and generate too much drag and stall

IV. Case Study- Helios Part of HALE $103 million from NASA $36 million from industry

Part of HALE

$103 million from NASA

$36 million from industry

Goals for Helios Reach 100,000 ft. Have non-stop flight for 24 hours, and to have at least 14 hours above 50,000 ft.

Reach 100,000 ft.

Have non-stop flight for 24 hours, and to have at least 14 hours above 50,000 ft.

Significance of Helios Study atmospheric science Observe the Earth Serve as telecommunication system

Study atmospheric science

Observe the Earth

Serve as telecommunication system

Helios Aircraft Statistics Wing span of 247 ft Length of 12 ft Wing chord of 8 ft Wing area is 1,976 sq ft Aspect ratio of 31 to 1 Gross weight is 1,600 lb Payload of 726 lbs Airspeed of 19 to 27 mph Up to 170 mph at altitude 72 trailing edge elevators

Wing span of 247 ft

Length of 12 ft

Wing chord of 8 ft

Wing area is 1,976 sq ft

Aspect ratio of 31 to 1

Gross weight is 1,600 lb

Payload of 726 lbs

Airspeed of 19 to 27 mph

Up to 170 mph at altitude

72 trailing edge elevators

Helios Propulsion Statistics 14 brushless DC electric motors, 1.5 kW each 62,000 solar cells Endurance of several days to several months

14 brushless DC electric motors, 1.5 kW each

62,000 solar cells

Endurance of several days to several months

Helios Accomplishes a Goal (2001) Unofficial altitude record of 96,863 ft Stayed over 96,000 ft for over 40 min Did not meet flight endurance goal Scientists worked on for 2003 flight

Unofficial altitude record of 96,863 ft

Stayed over 96,000 ft for over 40 min

Did not meet flight endurance goal

Scientists worked on for 2003 flight

Helios Malfunctions 3,000 ft. up in restricted Navy airspace Control difficulties Severe oscillations occurred Structural damage lead to crash No environmental effect, but plane lost 75 percent by weight recovered

3,000 ft. up in restricted Navy airspace

Control difficulties

Severe oscillations occurred

Structural damage lead to crash

No environmental effect, but plane lost

75 percent by weight recovered

Summary Main factors that allow flight Ratios to interpret these factors Important design considerations Case study- Helios

Main factors that allow flight

Ratios to interpret these factors

Important design considerations

Case study- Helios

Acknowledgements Professor Hafez Professor Horsley Michael Paskowitz Margarita Montes Tim McGuire Taylor Roche Beth Kuspa

Professor Hafez

Professor Horsley

Michael Paskowitz

Margarita Montes

Tim McGuire

Taylor Roche

Beth Kuspa

Bibliography www.nasa.gov Aircraft Performance and Design by John D. Anderson, Jr. http://www.nasg.com/afdb/list-polar-e.phtml http://www.aa.nps.navy.mil/~jones/research/gui/joukowski/sample_results/

www.nasa.gov

Aircraft Performance and Design by John D. Anderson, Jr.

http://www.nasg.com/afdb/list-polar-e.phtml

http://www.aa.nps.navy.mil/~jones/research/gui/joukowski/sample_results/

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