An explanation of speed to fly theory in gliding. Based on the work of Paul McCready, this presentation examines the reasons that the optimum speed to fly between thermals is higher than the best Lift over Drag speed of the glider. The speed to fly theory is presented geometrically to show how the average cross-country speed is maximized during a thermalling flight. The presentation also compares the speed to fly theory when thermalling with speed when ridge soaring to allow comparison of ridge conditions with thermal strength. The presentation is focused on the theory and does not go into strategies to improve cross-country speeds or how to predict thermal strength. These aspects are left for other presentations.

1. Speed to Fly Theory
Using the Polar Curve

2. The polar curve
0 50 100 150 200 250 300
-6
-5
-4
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-2
-1
0
1
2
Horizontal Speed (km/hr)
Vertical
Speed
(m/s)
●
Shows rate of sink for a
given horizontal speed
– In equilibrium
●
Speed is constant
– Air is still
– Shape of the curve is
dependent on the aircraft
design

3. In a moving air mass
●
Mostly concerned with
motion relative to the ground
●
Add the air mass movement
to the polar
– Sinking air moves the polar
down
– A headwind will move the
polar to the left
0 50 100 150 200 250 300
-7
-6
-5
-4
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-2
-1
0
1
2
Effect of 1 m/s sink on the polar
Still Air
-1 m/s sink
Horizontal Speed (km/hr)
Vertical
Speed
(m/s)

4. Glide Ratio
●
Vector sum of the horizontal speed and
vertical speed (sink) gives the cruise
speed
– In still air, cruise speed ≈ TAS
●
Ratio of horizontal speed to vertical
speed gives the glide ratio
●
Glide ratio and lift/drag ratio are the
same
●
The angle between the horizontal and
cruise vector is the glide angle or glide
slope
⃗
vh
⃗
vs
⃗
vh
⃗
vc
⃗
vh+ ⃗
vs= ⃗
vc
|⃗
vh|:|⃗
vs|=GR :1
Glide Angle

6. 0 50 100 150 200 250 300
-7
-6
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-2
-1
0
1
2
Still Air
-1 m/s sink
Horizontal Speed (km/hr)
Vertical
Speed
(m/s)
Max Lift/Drag
●
Max lift/drag is max glide ratio or
minimum glide angle
●
Speed to fly given by the tangent to
the polar curve passing through the
origin
– In still air, max L/D at 89 km/hr with
sink of 0.8 m/s
– In 1 m/s sink, max L/D at 134 km/hr
with sink of 2.4 m/s
●
Note if moving the polar, the speed at
the tangent point is ground speed,
not airspeed
Minimize angle

7. Alternate method
0 50 100 150 200 250 300
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-5
-4
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-2
-1
0
1
2
Horizontal Speed (km/hr)
Vertical
Speed
(m/s)
●
To read the glider air speeds
in headwind conditions, move
the origin instead of the polar
– Headwind moves origin right
– Sink moves origin up
●
1 m/s sink and 25 km/hr
headwind implies 148 km/hr
speed to fly to achieve max
L/D
1 m/s sink, 25 km/hr headwind
STF

8. Thermal Flight
●
Two phases
– Cruise (c) & Thermal (t)
●
Cruise follows the polar curve performance
●
Thermal is vertical only
– No horizontal movement (assuming no wind)
●
One cycle is a cruise followed by a thermal climb back to
the starting altitude
– Zero height lost or gained
– Distance covered is x
●
The cycle repeats to cover task distance
– Frequency doesn’t matter
●
Overall time to cover the distance determines the average
speed
●
What cruise speed gives the fastest average speed?
Cruise (c)
Thermal
(t)
Distance (x)
⃗
vt
⃗
vh
⃗
vs
⃗
vc
Speeds
⃗
vavg ?

9. Thermal Flight
●
Some relations we can deduce from the
model
1 Total time (t) of the cycle is the cruise time (tc) plus the
thermalling time (tt)
2 Distance (x) covered is the horizontal speed times the
cruise time
3 Average speed is the distance divided by the total time
4 Substituting 1 & 2 into 3 gives another form of average
speed
5 Distance climbed must equal total sink during cruise
– Or total vertical distance in one cycle is zero
– Average speed vector must lie along the x-axis
t = tc+tt (1)
x = vh
⋅tc (2)
vavg =
x
t
(3)
(1)(2)→(3) vavg =
vh tc
tc+tt
(4)
vt⋅tt = vs⋅tc (5)

10. The Relation of Climb and Sink speeds
●
Rearranging (4) and (5) gives
(4) vavg =
vh tc
tc+tt
vavg⋅(tc+tt) = vh tc (6)
(5) vt⋅tt = vs⋅tc
tt =
vs⋅tc
vt
(7)
(7)→(6) vavg⋅(tc+
vs⋅tc
vt
) = vh⋅tc
vavg +
vavg⋅vs
vt
= vh
vavg⋅vs
vt
= vh−vavg
vavg
vt
=
vh−vavg
vs
(8)
Not related to
time or
distance!

11. McCready Theory
vt
0 50 100 150 200 250 300
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-1
1
3
5
Horizontal Speed (km/hr)
Vertical
Speed
(m/s)
vavg vh−vavg
vs
●
Relation of speeds implies that the
blue line is straight
– Similar triangles
– Average speed determined by the
intersection of the blue line with the x-axis
●
Maximizing average speed requires the
blue line be as flat as possible
– Best speed to fly given by line from the
expected thermal climb rate tangent to
the polar
– This is McCready Theory
vavg
vt
=
vh−vavg
vs
STF

12. Speed to Fly in Thermals
vt
0 50 100 150 200 250 300
-7
-5
-3
-1
1
3
5
Horizontal Speed (km/hr)
Vertical
Speed
(m/s)
vavg
●
Vt is the expected average climb speed
– An educated guess (and another presentation!)
– Based on start to stop times of thermalling – not the best
climb rate
●
Speed to fly given by the tangent point on the polar
●
Glide slope between thermals determined from the
origin
●
Note: STF on this chart is horizontal speed, not cruise
speed
– You’d need to convert to cruise speed if doing this
manually
●
Difference is <8% for glide ratios of 20:1 or better
– Flight computers and the instrument rings should have
this factored in
STF
Glide slope

13. Speed to Fly
●
For a given thermal strength,
there is a range of workable
speeds
– Very small impact on the
average speed within this
range
– Means you don’t have to
follow the MC STF too closely
●
Consider a dead-zone around
the indicated STF
vt
0 50 100 150 200 250 300
-7
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-1
1
3
5
Horizontal Speed (km/hr)
Vertical
Speed
(m/s)
vavg
STF
Glide slope
STF
Range

14. And on a Ridge?
●
Ridge flying does not follow
the McCready theory as
there is no stopping to climb
●
Climbing isn’t as important as
staying at the ridge height
– Accelerate in strong ridge lift
to not gain height
– Slow down in weaker lift to
not lose height
●
BUT the glider still flies along
the polar curve and there is
an equivalent in the average
speed
●
So which is better: a working
ridge or a thermal?

15. The Polar on the Ridge
●
Ridge lift will cause the polar
to move up
●
Assuming a flat straight
ridge, speed to fly is the
fastest speed that has zero
sink
●
Average speed will be equal
to the speed to fly while on
the ridge
vavg
0 50 100 150 200 250 300
-6
-5
-4
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-2
-1
0
1
2
Still Air
1m/s lift
Horizontal Speed (km/hr)
Vertical
Speed
(m/s)
STF =

16. So Ridge or Thermal?
●
In deciding to fly a ridge or
thermal, consider the average
speed
●
Using the MC theory, what is
the equivalent thermal strength
required to match the speed
along the ridge?
– For this glider, 1 m/s ridge lift is
equivalent to a thermal of 3.5
m/s 0 50 100 150 200 250 300
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1
3
5
Still Air
1m/s lift
Horizontal Speed (km/hr)
Vertical
Speed
(m/s)
Equivalent Thermal
Polar in 1 m/s
ridge lift
vavg

17. Ridge or Thermal?
●
If the ridge is working enough to
glide at or better than the smooth
air max L/D speed, ridges will do
better than thermals most of the
time
– Small increases in ridge lift match
much stronger thermal lift
– It doesn’t take a very strong ridge to
match the avg speed of MC 5m/s!
●
A strong ridge is better than the
strongest thermal
MC Setting
(m/s)
Avg Speed
(km/hr)
Equivalent
Ridge lift
(m/s)
0.5 36.2 0.61
1 56.0 0.61
1.5 70.3 0.66
2 81.7 0.73
2.5 91.4 0.82
3 100.0 0.90
3.5 107.7 0.99
4 114.8 1.09
4.5 121.4 1.18
5 127.6 1.28

18. This work is licensed under a Creative Commons
Attribution-ShareAlike 3.0 Unported License.
Slide design makes use of the works of Mateus Machado
Luna.
Presentation by Michael McKay