McCready Theory , Speed to Fly

Speed-to-fly is a basic precept of soaring flight for unpowered
aircraft. The objective in determining this speed is to find the optimal
airspeed for maximum glide performance under varying conditions of
lift or sink. Use of this concept is not limited to unpowered aircraft
however. It is valuable to the pilots of light airplanes as well. In critical
flight situations such as encounters with mountain wave downdrafts,
correct application of speed-to-fly theory can make the difference
between life and death.

 Paul Mc Cready Aerodinamik Yapı Polar Verisi ve Kullanımı

Background

Speed to fly is explained in detail in virtually every textbook on
soaring. It is defined in Conway's Joy of Soaring as "The indicated
airspeed which produces the flatest glide in any situation of convection
without considering the effect of wind." It is obtained for each type of
glider by plotting the performance polar (i.e., the sink rate at each
airspeed in the glider's operating range) and adding a scale for
vertical motion of the airmass. A line drawn from the airmass motion
scale to a tangent point on the glider performance curve crosses the
airspeed scale at the airspeed that will yield the flatest glide while
flying through the airmass (least altitude lost per unit of distance
traveled).

Such charts are useful for understanding the performance of a glider
but are difficult to apply in flight. Various devices have been
developed that aid the glider pilot in applying this data, including the
MacCready Speed Ring and final glide computers. Glide computers
allow the addition of wind speed to the equation to find the speed for
the flatest glide over the ground.

These devices are very useful to glider pilots as they enable the
pilots to obtain maximum performance from their aircraft. They are not
found in airplanes however, as airplanes rarely have to maximize their
glide performance -- they have engines that eliminate concerns over
vertical motion of the airmass.... in most cases.

There are situations that do require the airplane pilot to be able to
maximize the airplane's performance while flying through a
descending airmass. One of these is an encounter with mountain
wave, and these are not all that rare when flying in mountainous
areas, particularly during winter months.

Mountain wave is an atmospheric phenomenon in which an
obstruction (typically a mountain ridge) excites air currents into a
standing wave pattern of up and down vertical flow. It can be
visualized as ripples downstream of a stone in water. Waves typically
begin to form when winds across mountain peaks exceed 25 knots,
with the wind direction being within 30 degrees of perpendicular to the
line of the mountain ridge. The vertical rates of flows in mountain
waves have been reported to 8,000 feet per minute, with rates of
several thousand feet per minute being common.

These rates greatly exceed the climb performance of most light
airplanes, particularly at the high elevations at which they are
encountered. In the western United States, wave is generally
encountered in mountainous areas at altitudes above 7,000 feet.
Climb performance in still air at these altitudes is on the order of 300 to
500 feet per minute.

Most airplane pilots react to downdrafts by attempting to climb. This
works as long as the intensity of the downdraft is not too severe. If the
downdraft is moderate, the airplane may be able to maintain altitude.
Once the downdraft exceeds the airplane's climb capability it will
begin to descend. At this point the airplane pilot is faced with the
same problem as the glider pilot -- at what point is it beneficial to
speed up in order to obtain the shallowest possible descent? The
problem is that determination of that point is not simple, and most
pilots don't even know how to find a reasonable approximation of the
speed to fly for their airplanes under such conditions.

Factor's in Determining Speed-to-Fly

The starting point in determining speeds to fly for a glider is the
performance polar of that glider, i.e., a plot of the descent rate of the
glider in still air (no vertical currents) over its range of airspeeds. A
similar plot can be made for airplanes although it will look somewhat
different, as the airplane climbs under power. There are actually a
continuous series of curves for airplanes as the climb performance
changes with altitude. A further complication is that climb speeds and
rates change with aircraft weight. Thus the curves change
continuously as altitude and weight vary.

In thermal soaring the aircraft polar plus airmass motion is all that's
required to determine the speed to fly. Mountain wave flying adds
another parameter, namely that of wind speed. In thermal flying the
aircraft moves with the airmass, thus no compensation for the speed of
the airmass is necessary. In wave flying, lift and sink are oriented in a
standing wave and the aircraft glide must be considered relative to the
ground. Thus wind speed and direction and direction of flight are all
significant factors.

Given the inputs of aircraft performance information, weight,
temperature, altitude, heading, airspeed, and ground track and speed,
a flight computer could easily determine the downdraft intensity and
suggest an optimum speed (and direction) to fly to escape from the
downdraft. Such computers are not available, so the pilot must use
some technique to approximate the optimal solution.

Several factors can be used to reduce the complexity of the problem
and thus simplify in-flight calculation and decision making. . First, the
conditions under which mountain waves form are known, so only the
data for those conditions need be considered. These include wind
speed and direction, the likely orientation of waves, and the altitude at
which they will be encountered.

Next, a performance polar for the airplane is needed. This presents
a problem in that polars are rarely available for light airplanes. What is
available is the aircraft operating handbook which usually includes
two points on the polar. These are the climb and cruise performance
at a given weight and altitude. Every pilot should know the
approximate performance level of his or her aircraft, and these
numbers can be verified empirically during climb and flight outside of
mountain wave conditions.

The climb and cruise data are not sufficient to find the optimum
speed to fly given a downdraft of arbitrary intensity. However it is a
simple matter to determine which of these speeds produces better
performance for downdrafts of various strengths. If the downdraft
intensity is expressed as a ratio to the expected climb performance of
the airplane, then given a set of wind conditions, we can determine
when it is better to fly at best rate of climb speed (Vy) or to speed up
and fly at cruise speed.

The attached downdraft performance study presents data for 26
different types of airplanes ranging from 100 horsepower trainers to a
medium twin of 750 total horsepower. Conditions represented are for
winds aloft of 30 knots (an approximate minimum for formation of
mountain waves) and 60 knots (a higher value to show the trend at
significantly higher wind speeds) at an altitude of 8,000 feet, which is
representative of downdraft encounters that have resulted in
accidents. For each of these conditions the point is calculated at
which flight at Vy and cruise airspeed yield the same descent angle.
This is expressed in terms of vertical speed down versus expected
vertical speed up in still air conditions.

For example, for a 1980 Cessna 172, in a 30 knot headwind, if the
airplane is flying at Vy and is descending at a rate of 1.08 times the
expected rate of climb in still air, it will descending at the same angle
as it would if it were flown at cruise speed (it would be descending at a
higher rate at cruise speed, but at the same angle). If the airplane is
descending at a rate greater than 1.08 times the expected rate of
climb, then the airplane will descend at a shallower angle when speed
is increased to cruise speed.

A table of numbers of this type would be very difficult to memorize. A
simpler approach to utilizing this information is necessary.

An examination of these data show that the point at which it is
preferable to fly at cruise speed versus Vy is fairly consistent across
this wide range of types. For headwinds of at least the velocity
required for formation of mountain wave, the point where Vy and
cruise speed yield the same results is approximately where the
descent rate while flying at Vy is equal to the expected climb rate in
still air. When flying downwind, the tradeoff point occurs when the
descent rate is about three times the expected climb rate. We can
derive from these data general rules that are very easy to use in flight.

Rules of Thumb

The most critical case in dealing with a mountain wave downdraft is
when flying directly into the wind, as ground speed is greatly reduced
thus increasing the length of time the aircraft spends in the downdraft,
the altitude lost in the downdraft, the forward progress of the aircraft
and hence the angle of descent. Thus if only one rule is to be
remembered, it is this:

If you're at Vy, and YOU ARE GOING DOWN
FASTER THAN YOU SHOULD BE GOING UP,
SPEED UP TO CRUISE SPEED.

A refinement of this rule takes into account wind direction and
velocity versus direction of flight. This results in three rules, plus an
observation....

If flying into a headwind and you're at Vy, and
YOU ARE GOING DOWN FASTER THAN YOU
SHOULD BE GOING UP, SPEED UP TO CRUISE
SPEED.

If flying with a tailwind and you're at Vy, AND YOU
ARE GOING DOWN THREE TIMES AS FAST AS
YOU SHOULD BE GOING UP, SPEED UP TO
CRUISE SPEED.

THE GREATER THE HEAD WIND, THE SOONER
YOU SHOULD INCREASE TO CRUISE SPEED.

All else being equal, IT'S BETTER TO FLY
DOWNWIND AND FAST.

A pilot who primarily flies one or two airplanes could use the exact
numbers shown in the attached table or calculate numbers that are
closer to the actual altitudes and winds expected. The exact point at
which to speed up is not critical though. It will not make much
difference if the vertical rate decision point is off by a few percent. The
important point is to recognize the trend and to know that increased
speed is beneficial under conditions of strong downdrafts.

In the case of the accident that motivated this study the speed of the
headwind was nearly 60 knots, and while the airplane was flying at Vy
it was descending at nearly three times its expected climb rate. In this
case the descent angle would have been greatly reduced had the
airplane been flown at cruise speed instead of Vy. It probably would
have cleared the ridge by about the same distance above the peak as
the distance below the peak that it actually impacted while flown at Vy.