HOW MUCH ASPECT RATIO? By John W. Thorp spect ratio is the ratio of total A span to mean chord. It is expressed as span squared. For a reelarea

angular wing, aspect ratio is span. It chord is a dimensionless ratio. While it is generally understood that high aspect ratio wings have

ever, it is possible that the wing model tests were conducted at aspect ratio = 6 simply because this

was a good practical compromise proportion between structural and aerodynamic state of the art of the period.

Since wing weight and

airplane

less drag than low aspect ratio wings,

weight empty increases rapidly with increases in span it behooves the de-

how this is evaluated and applied to airplane design is almost completely

si^ner of small airplanes to hold the

misunderstood outside aerodynamics

circles. Induced drag is the drag required to produce lift. At a given speed induced drag of any airplane is inversely proportional to its wing aspect ratio. Induced drag is also inversely proportional to speed squared, so the faster the airplane flies the less important becomes induced drag and aspect ratio. Actually it is convenient to think in terms of aspect ratio while dealing with airfoil characteristics in coefficient form, but once this phase

of the design is passed the physical span becomes the most important

single factor in airplane design. Aspect ratio of a given design then becomes the result of proportioning rather than the cause. Wing area is dictated by take-off distance calculations or by minimum speed calculations. Wing span is dictated by rate of sink calculations, rate of climb calculations or ceiling

calculations which are really interrelated or by maximum cruising range calculations of long range airplanes. Aspect ratio is what results when the calculated span is squared and

span to no more than the value which provides the desired rate of climb with the power available and weight that the airplane is expected to car-

ry.

1000 ft/min. the climbing power equals 1300x1000 = 39.4. If climbing 33,000 propulsive efficiency is 60% and we have a 100 hp engine the total thrust horsepower available will be .60

x 100 = 60.0 and the thrust horsepower available to fly level will be 60.0 — 39.4 = 20.6.

If the speed for best climb is 75 M/H we may calculate the required span: 1300 \ span / 75

K

20.6=

From this it may be deduced

/ 1300 \ .0111 . s pV span a n /

that the best span for a given airplane design can vary greatly with

20.6 = .0111

available power. In the days of 35-40 hp engines, spans of light airplanes

1860 ~~

V span / / 1300 \ \ span /

43.1 =

1300 -span

Span =:

43.1

_

frequently were as much as 40 ft. to provide minimum acceptable climb. With today's 90 and 100 hp

engines better with only half the airplanes maintain and

climbs are achieved the 40 ft. span and are easier to build, store. Even shorter

spans will result from

tomorrow's

light powerful turbines.

Wing areas for a given take-off distance with a given weight also diminish with increases in power but

since light airplanes are also getting heavier the wing areas have not been coming down as fast as span hence the aspect ratio trend of light airplane wings has been coming down. In the 1930's aspect ratios of 7, 8

and 9 were common where today 5, 6, and 7 are in about equivalent usage. Since aspect ratio per se doesn't mean anything performance wise, this

//JL300 1300 \ 2

= 30.2 ft.

If we substitute a 125 horsepower engine, assuming the gross weight goes up 100 pounds to 1400 pounds and the speed for best climb increases to 85 M/H, the same kind of calculations will specify a span equalling 24.3 ft.

If in each case we have chosen a

wing loading of 12 #/ft 2 for reasons of minimum speed the wing area in the first case would be 1300=108 ft.2 ' 12 and in the second case it would be 1400=116 ft.2 12 The resulting aspect ratio in the

first case would be 30.22

=

g.4 and

108

in the second case it would be 24.32 -5.1 116

—————

area.

trend simply reminds us that power is now relatively cheaper and more emphasis is being placed upon mak-

While the foregoing calculations are legitimate for airplanes of a class

ing airplanes go faster which is as

This concept may come as something of a shock to some who are accustomed to think in terms of conventional aspect ratios of 5, 6, 7, 9, or 12 as an order of merit.

it should be.

suitable for home building there are cases for other performance types

is divided by the calculated wing

Actually a large number of good airplanes have been designed with an aspect ratio of 6 simply because many of early wing model tests were made at aspect ratio = 6 and it was convenient to apply these wing characteristics directly to designs. How22

JULY

1960

At the speed for best climb, the

thrust horsepower (brake horsepower times propulsive efficiency) required is proportional to / weight \ 2 - For \ span / most small airplanes, thrust horsepower required equals /____.83____\/weight \ 2

\best climb speed/' span / at sea level. If our airplane weighs 1300 pounds and we want it to climb

where more sophisticated calculations are made to provide appropriate proportions for wings. Such calculations are beyond the scope of this paper.

The object of this paper has been

to emphasize the importance of physical span as a performance factor and to show aspect ratio as a less important proportion of design.