Aerodynamics of the glide

Ed Williams

presented at SMXGIG '99, Santa Maria Ca

SMXGIG98.tit.cv5
 Only two forces act on an airplane! F=ma

(1) Weight - vertically downward

(2) Air pressure forces:

Static (buoyancy) - negligible for airplanes!
Dynamic forces
Thrust - air motion from prop or jet.
Lift/drag - from relative motion of airplane through the air.

Lift is the component of the aerodynamic force perpendicular to the flight path.
Drag is the component of the aerodynamic force parallel to the flight path.

For convenience, we often say there are four forces:

Lift, weight, thrust and drag

E. A. Williams 4/25/99
SMX99
 Steady flight implies balanced forces Newton (1)

Not just straight and level- any straight line, constant velocity flight!
e.g. Steady climbs and descents.

Throttle or elevator changes unbalances the forces, changing the flight path
or airspeed.

L
L L

D
D T
T D

W W

Straight and level. Descent Climb

In climbs/descents you have excess thrust/drag and less lift. Force components
balance.

E. A. Williams 4/25/99
SMX99
 No trig
Let's focus on power-off glides please!!

L(ift)

β
D(rag)

W(eight)

Glide angle, β, is the angle the total aerodynamic force makes with the lift.

E. A. Williams 4/25/99
SMX99
 The force
The glide angle, β, is determined by L/D is up!

L(ift)

L
β
D(rag)

β
D
W(eight)

Total aerodynamic force (L & D) balance the weight, W.

The glide angle is determined by L/D, in fact tan(β)=D/L.
The optimum (shallowest) glide obtains when L/D is a maximum, or
equivalently, D/L is a minimum.
For a given airplane configuration, this ratio only depends on the angle
of attack.

E. A. Williams 4/25/99
SMX99
 The aero forces, lift and drag depend on:

(1) True airspeed, proportional to v2

(2) Air density, proportional to ρ
(3) Scale size, proprtional to area S
(4) Shape of the body and the airflow direction
(5) Other factors, which often can be ignored (eg viscosity)
In summary:

L= cL(α) ρ v2 S/2
D=cD(α) ρ v2 S/2

All the geometrical information is buried in the lift/drag coefficients cL

and c D. α is the angle of attack. Aerodynamicists define α relative to the
zero-lift line. Others often use the chord line.

Note that L/D = cL(α) / c D(α) is determined by angle of attack.

E. A. Williams 4/25/99
SMX99
 Attack out
Lift and drag vary strongly with angle of attack, α of the sun!

cLmax
cL

cD
cD0
αs
Angle of attack, α

cL(α) has a maximum, cLmax, when α=αs after which lift decreases with
increasing angle of attack. We'll see that this is the stalling α.

The drag coefficient cD(α) is minimum at zero α and increases with α.

cD0 is the parasite drag coefficient. The increase in cD over c D0 with α
is termed induced drag.

E. A. Williams 4/25/99
SMX99
 Stick back,
The wing stalls at its max lift coeff't houses bigger

cLmax

B
cL
A

αs
Angle of attack, α

At A: Momentary increase in AOA -> increase in lift -> climb ->

decrease in AOA. Stable!

At B: Momentary increase in AOA -> decrease in lift -> descent ->

further increase in AOA. Unstable!

There is lift beyond the stalling angle of attack, but no stable flight.

E. A. Williams 4/25/99
SMX99
 What a
"Induced" drag is induced by lift. drag

Parasite drag is independent of lift- frictional and form drag.

Passage of the airplane heats the air and creates a wake. This costs energy.

Induced drag is a consequence of the tip vortices present when the

wings create lift. The wings are flying in a self-induced downdraft.

Flight path
Tip vortex
downdraft

"Lift" perpendicular to the relative wind is tilted back with respect to

the flight path. Larger aspect ratio -> less induced drag.

E. A. Williams 4/25/99
SMX99
 Drag
Combining Cl and Cd gives us the glide angle. polar!

cLmax α=αs Stall

cL

cL α=αLD Best glide

Lift
cD
cD0
β
αs α=0 Vertical dive
Angle of attack, α cD Drag
Glide Angle β

The (no-wind) glide angle β is determined by the angle of attack α.

The optimum glide occurs at αLD, tangent to the "drag polar".
Here induced drag ~ parasite drag.
At a given weight, each AOA α corresponds to a definite IAS.
The POH will list vLD at max gross.
At other weights, vLD=vLDmaxgross (W/Wmaxgross )1/2

E. A. Williams 4/25/99
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 Gear up!
Increasing drag lowers VLD

α=αs Stall α=αs Stall

cL cL α=αLD Best glide

α=αLD Best glide

Lift Lift

β β
α=0 Vertical dive α=0 Vertical dive
cD0 cD Drag cD0 cD Drag
increase parasite drag, cD0

Retractables (gear up!) typically have higher best glide speeds than fixed
gear. Lowering the gear reduces the best glide speed.
A36 Bonanza - 110 kts
Cessna 182 - 70 kts.

E. A. Williams 4/25/99
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 Stopped
Rate of descent vs. IAS for the Schweitzer I-26 glider. prop.

IAS (mph)
10 20 30 40 50 60 70 80 90 100

10 Schweizer I-26
0

20
0

30
VLD
0

400

Vminsink
50
0

Descent angle = 180*60/48 =225 ft/mile

60
0

700

Should really be forward speed - nearly the same as airspeed for shallow angles.

Vminsink (35 mph) gives the slowest descent rate.

VLD (48 mph) gives the shallowest still-air glide.

E. A. Williams 4/25/99
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 Glide faster
In a headwind VLD increases! in headwinds

IAS (mph)
1 20 3 40 50 60 70 80 90 100
0 0
VLD
10
0

20
0
Schweizer I-26
30
0

400
30 mph headwind
50 VLD 62 mph
0
VS 280 ft/min
60 GS= 32 mph
0 Angle of descent 280*60/32 =525 ft/mile
700

At the no-wind VLD of 48 mph, angle of descent would have been

180*60/18=600ft/mile - even steeper.
As a rule of thumb, add one half your headwind to your still air VLD

E. A. Williams 4/25/99
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 Not too
In a tailwind VLD decreases a little. much!

IAS (mph)
10 20 30 40 50 60 70 80 90 100

10 Schweizer I-26
0

20
0
VLD
30
0

400

Vminsink
50
0
20 mph tailwind
60 38 mph V LD
0
58 mph GS
700 155 fpm VS
angle of descent = 155*60/58=160 ft/mile

It never pays to fly slower than Vminsink

The recommended rule is to subtract only one quarter of the tailwind from
your still air VLD

It is better to err by being too fast rather than too slow.

E. A. Williams 4/25/99
SMX99
 Speed up
Up- and down- drafts affect VLD in d-drafts

20
0

10
0
IAS (mph)
1 20 30 40 50 60 70 80 90 100
0

10 Schweizer I-26
0

VLD
20
0
200 fpm downdraft
270 fpm VS -airmass
30
0 470 fpm VS - ground
400 62 mph VLD
Vminsink
50
0

60
0

700

Speed up in downdrafts, slow up in updrafts.

In an airplane add 4-5 knots per 100fpm sink, slow 2-3 knots per 100fpm
rise. Never slow below Vminsink
E. A. Williams 4/25/99
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 Glider pilots chart "Speed to Fly" Mach 3

UP

IAS (mph) Vertical Speed

(Variometer)
100's fpm

DOWN

E. A. Williams 4/25/99 Red curve gives airspeed to fly given (total) vertical speed
SMX99
 What have we learned about L/D max? Huh!

Lift/Drag is a maximum at a specific angle of attack, where

still air glide is shallowest
the angle of glide is the tilt of the lift vector.

This angle of attack corresponds to an IAS which (like other purely

aerodynamic speeds) varies as the square root of the gross weight.

In downdrafts and headwinds the optimum glide speed increases.

Increase glide speed by half the headwind or 4-5 knots per 100 fpm sink.
In updrafts and tailwinds the optimum glide speed decreases.
Decrease glide speed by one quarter of the tailwind or 2-3 knots per 100
fpm rise, BUT not below minimum sink speed.

Know what it is for your airplane!

E. A. Williams 4/25/99
SMX99