Weight, Power and Span Loading

Both safety and utility are thereby enhanced. A short take off run is .... both model airplanes and sail- planes are designed with endurance uppermost in mind.
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Weight, Power and Span Loading By Bob Whittier Based on NACA TM No. 311 and TM No. 326, "The

Light Airplane", Driggs

F perimenters was to get into the air in a reasonably rom 1900 to 1914 the main objective of aviation ex-

safe and controllable machine. Between 1915 and 1919

the entire purpose was to fly higher, faster and with a greater load than the enemy, regardless of cost, and engineering progress was tremendous. This spurt of development left in its wake a flood of surplus aircraft

which were often high-strung tactical aircraft, costly-tooperate bombers and short-life trainers. Because they were available at give-away prices, airmen bought them

and used them for civilian purposes in spite of their shortcomings.

today thousands of experimenters are starting all over

again to design and build airplanes under 50 hp. It is pertinent for us to take a close, hard look at the subject of flying with minimum horsepower. Too few amateurs have done this. A common daydream seems to be that an ideal cheap airplane could be made by combining a simple little affair of twelve or fourteen-foot wingspan with a motorcycle or outboard engine. Such a craft would be easily demountable, readily stored, cheaply built and certainly inexpensive to operate. But it won't work that way. If you want very small span

you must have high power, and if you want very low

Nevertheless, from 1920 to this very day there has been a persistent interest in many countries in the design and construction of small, very inexpensive aircraft for sport flying. Off and on, the ultra-light airplane has been regarded as the wave of the future, the salvation of civil aviation, and also as nothing but an impractical toy. We have all heard airport characters scoff at various airplanes with less than 50 hp! The popularity of small, low-powered planes has waxed and waned and really, it

power you must have generous wingspan. Do it any other way and you will achieve an airplane which will land too fast for safety, which will not climb out of small

airfields, or which just won't fly at all. The Germans have a well-deserved reputation for

their ability as mathematicians, and many years ago men like Dr. Prandtl of Gottingen University conducted

seems there is a regular cycle to be discerned. In the 1920's there was much interest in motorcycle-engined aircraft both in Europe and America and it was obviously a reaction to the ownership problems posed by surplus military planes with gas-gulping engines, engines designed for 50-hour service lives, and the periodic recovering and rerigging of forty-foot biplanes. This led, in the 1930's, to a spate of 30, 35 and 40 hp airplanes which were manufactured in large numbers. You could buy a safe, enjoyable little two-seater for only $1200 or $1300 in 1937! These ships flew quite

well but as competition existed between various manufacturers, power grew to 50 hp and to 65 hp and, in late years, to 90 and 150 hp. This, plus the steady increase of all costs, has put two-seaters very much out of the reach of those who love flying and airplanes but have families to support on average incomes.

And so

In the early 1920's England held a series of light airplane trials at Lympne, for the purpose of developing sport and training aircraft of very low power and cost. One of the outcomes was the de Havilland "Humming Bird" shown here. Powered by a little 22 hp engine, it had to follow the rules of span loading to get acceptable takeoff, climb and cruising speed, and the broad wings were the result. Very low power and short wingspan just do not work.

advanced mathematical studies of airplane design, laying down basic theorems which hold true today as much as do Newton's laws of motion. After World War I the Germans were severely limited by treaties as regards what they could fly. Interest turned to gliders as a

means of keeping alive the skill and interest of airmen. German gliders and sailplanes soon amazed the world

If for any reason a designer wishes to keep his airplane's wingspan short, he must then use plenty of power to gain satisfactory takeoff and climb characteristics. This Boeing P-26 has a wingspan comparable to the de Havilland "Hummingbird", but it is much heavier and the resulting

greater span loading demands a lot more horsepower. In this case it is 575-600 hp. It would be ridiculous to put 65 hp on the nose of this airplane; it is just as ridiculous to put 20 or 25 hp on the nose of a plane of 12 or 14 ft. wingspan. Either it won't fly at all, or its performance will be hopelessly poor. 24

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with their flights, but this wasn't luck, it was the outcome of applying scientific design principles. Dr. Prandtl's theorems enabled designers to design directly for the required performance. In other words, they had been given a formula by which they could design directly for the size and shape required to achieve the desired results. Since the German gliders did so well, it was assumed that if small engines were installed the result would be excellent and practical sport airplanes. And right here the thinking of thousands of aviation fans took the wrong road. There is a big difference between the basic

circumstances of gliding and powered flight and if you ignore this truth, you will become lost in a fog of uncertainty. Is an ultra-light airplane a powered glider, or

is it an underpowered airplane?

Guesswork is no good

when we are attempting to get into the air on mini-

mum power or at minimum cost . . . we have to be scientific about it or we will miss the mark widely. A person who does not know how to design directly for the required size and shape and who cannot even answer the foregoing question is ... well, he isn't going to be flying!

The problems of gliding and the problem of flying from place to place under power are distinct. The aim in soaring is to stay off the ground for the longest possible time, and a sailplane is designed for duration. The purpose of powered flight is to become disengaged from the limitation of wind and thermals so that useful work may be done, transporting a useful load over an acceptable distance at satisfactory speed and cost. An airplane differs from a sailplane essentially in that it is designed for range. By the very nature of its way of flying a sailplane cannot divorce itself from the air's currents, but an effective airplane is one which is least affected by the wind. It is said that a practical airplane should have a top speed as much greater than its cruising speed as the average velocity of the winds in which it will fly. A common top speed for an ultra-light airplane is 80 mph and if it can safely be flown in winds of 10 mph, its cruising speed of 70 mph will be acceptable, because it can still plug along at 60 ground mph against a 10 mph headwind. That may not be exciting but at least you can get home! If, however, an ultra-light airplane tops 70 mph, cruises at 50 and can be managed in 10 mph winds, it will make only 40 ground mph

and that may make getting home problematical.

The glider is designed for duration and so has a

very high aspect ratio wing. Such a wing has a very high

The 9-to-l aspect ratio of the old Aeronca C-3 resulted from the fact that a long wingspan was needed to get acceptable performance from a small engine, and chord had to be kept narrow to keep wing area and hence wing loading within practical limits for windy-weather operation. Sometimes an airplane's aspect ratio turns out to be only the result of the designer's compromise between span loading, wing area and structural requirements. It is commonly supposed that aspect ratio is chosen first but this is not always so!

An airplane is underpowered only when it is unable to properly perform the service for which it was designed. If we wish an airplane to carry a pilot and baggage 200 miles at 75 mph and cross over a mountain range 12,000 feet high en route, and it fails to do so, it is underpowered whether it carries 15 Ibs. or 30 Ibs. per horsepower. In the final analysis airplane performance can be increased in one of two ways: by increasing the horsepower or by decreasing the power required for

flight. You can make a Cub faster by putting 90 hp in place of 65 hp on its nose. When designing a small

plane to take a particular low-powered engine, the latter course is naturally open to you because the plane does not yet exist. It is logical and scientific. And when

you design to get the greatest useful work out of the

least power, the result also happens to be a plane which is relatively cheap.

From the standpoint of safety an airplane designed

ratio of lift to drag at a very low speed. Put an engine on such an aircraft and the craft no longer rides the winds, it is dragged through the air. At the angles of attack and airspeeds thus attained, its wing has a lot of drag and the cruising speed is low. Please note very carefully that we are talking of small engines installed on sailplanes to convert them to airplanes, and not of retractable engines meant only to boost them to soaring altitudes. But now it is obvious that a correctly-designed ultra light airplane must have a wing which has a very high ratio of lift to drag at high speed in order to get the highest possible cruising speed with low power. A powered glider will have a phenomenal duration but it will not be a practical airplane. Therefore, to call a low-powered airplane a "power glider" is illogical. Shake this notion out of your head, stomp on it and bury it six feet deep! This is the first step toward learning to design to attain a specific result. Likewise, divorce yourself from the notion that ultralight airplanes are "underpowered". They are not underpowered in the true sense of that term. It is true that the number of pounds carried per horsepower is greater

this way can rate very well. Most of today's cross-country airplanes are fast and powerful and usually fly at a considerable altitude. From a height of 5000 or 10,000 feet

than in most commercial planes, but actually this high

rate of climb in feet per minute and the forward velocity

power loading is the basic reason for being of the ultralight airplane. For economical sport or even profitable commercial flying, the greatest possible load should be carried by the minimum practical amount of power, so that income will cover investment with some profit left over. Everything else being equal, an airplane with the highest power loading will be the cheapest both in first cost and operation. That is our goal.

it is possible to glide a considerable distance to a suitable emergency field in the event of engine trouble. But it

is monotonous to fly at such altitudes in a slower airplane. If only to make progress seem faster, the sport pilot may choose to fly at a lower level, say 1000 to 2000 feet. Not only is the plane's motion more apparent, but it is much more amusing and interesting to drift along

seeing all the sights on the ground clearly. Naturally the gliding range is less should the engine fail, but the lowpowered airplane is still quite safe to fly at such low levels because if correctly proportioned, it can safely land in any small area. If badly proportioned, it can be hazardous.

The ability to set down in a small place should be matched by the ability to take off from small fields. Both safety and utility are thereby enhanced. A short take off run is desirable, followed by a good rate of climb. It is essential here to understand clearly that the ability to clear obstacles depends on two things; the of the airplane. Any airplane goes up at some vertical velocity, while at the same time moving forward at some horizontal velocity. One which moves forward at 100 mph will cover more distance than one which is moving at 50 mph and if both ascend at a vertical rate of 700 ft. per minute, obviously the faster one is going to reach the end of any particular runway at a lower altitude than Continued on next page SPORT

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the slower one. Superficially one would think a plane with a rate-of-climb of 1000 ft. per minute would get out of small fields better than one which climbs at 500 ft. per minute. But the crux of the matter is that a high rate of climb is of little value if it takes place at a high forward velocity. A good small-field airplane should combine a good rate of climb with a low forward speed.

As a wing moves through the air it forces air particles downward to produce lift. Do not be mentally sidetracked by the familiar saying that most of the lift comes from the top surface of the wing; we just try to reduce pressure on the upper surface to make the lower surface push up better, speaking in a loose way. We all know of wing "downwash" and it is this downward acceleration of air which really gives the reaction called lift. Secure a length of string to the trailing edge of an airplane's wing and fly it level. The string will maintain an angle with the wing considerably greater than the wing's actual angle to the relative wind. This demonstrates the downward deflection of air. And this deflection is obviously equivalent to the airplane flying at all times in a current of air directed downward. The fact that it is caused by the airplane itself does not invalidate the basic assumption. If an airplane is flying in such a downward current, it must have an upward vertical velocity equal to the vertical velocity of the air downward. In other words, it must be climbing. This is exactly what is happening in level flight; the airplane is continually climbing away from the air that it has passed through and forced downward.

This is where a lot of engine power goes to in level flight. Your propeller does not simply pull the plane forward, it also supports the airplane by making the wings move through the air and develop lift. The power required to maintain a plane in level flight in the downwash created by its wing is called induced power. True, some power is expended in overcoming parasite drag caused by nonlifting members exposed to the air such as wheels, struts and tail, and more is used to overcome profile drag, or friction of the air over the wings, but the power required to "manufacture" lift is of prime concern here. What matters is that induced power is determined solely by the ratio of weight to wingspan. Engineers call it span loading. Span loading is the key to scientific ultra-light airplane design. Induced power

performance from low power you must have a low span loading.

If a 4000 Ib. airplane has a span of 50 ft., it has a span loading of 80 Ibs. per foot of wingspan. On this basis one would assume that since it flies all right, a span loading of 80 Ibs. per foot would work on a 500 Ib. lightplane. This would result in a span of 6.2 feet. Ridiculous! We have to go into rather light span loadings when we go down to light, low-powered airplanes, more on the order of 18 to 20 Ibs. per ft. On this basis a 500 Ib. airplane would thus have a span of 25 ft., which is obviously much more reasonable.

The Prandtl theory is built around a rather simple formula for Induced Power:

„„

Induced Power =

W-^

3b2pV

where:

W b p V

= = — =

plane weight in Ibs. span in ft. density of the air speed in mph

Calculations based on this formula have resulted in

a number of interesting graphs. Fig. 1 shows the relation of power and span for various slopes of the angle of climb. It shows the height of obstacle which may be cleared 1000 feet after the plane leaves the ground. As a fair average take the curve marked 100' in 1000', and study it well. You will see that for this climbing ability to be realized with a given power, a very definite wingspan is required, and also that as power decreases to low values the span must be increased at a rapid rate. Thus the fallacy of trying to build a very low-powered airplane with a wingspan of only 10 or 15 feet.

It also shows that if a practical climbing angle is to be realized, a definite relationship exists between power and span which will be the most effective and cheapest For example, a rate of 100' in 1000' calls for 31J/2 hp with a span of 16 feet. If the span is increased to 20 feet, only 24 hp is required. It will usually be cheaper and lighter to build the slightly larger wing and use the smaller, lighter, cheaper engine. Reading further, it is seen that a 28 foot span needs 19 hp and a 32 foot span needs only 18V4 hp. Now we are getting into the range

varies as the square of the span loading. To get good

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where considerable increases of span result in but a very small reduction of required power. As between a 28 foot span and 19 hp, and a 32 foot span and 18V4 hp, engine cost will vary but little but wing cost may grow rapidly. Hence the fallacy of sailplanes-with-engines as ideal cheap powerplanes. The very low wing, fine for soaring, costs too much to be logical for a cheap powerplane and will have too much drag at cruising speed to give good cross-country performance from a small engine. One of the commoner objections to low-powered airplanes is that they climb very slowly. Sometimes it is tiresome to wait many minutes as the ship struggles up to a useful cruising or traffic-pattern altitude. There are

other times when a sluggish climb can be dangerous,

such as when crossing a range of hills where downdrafts are encountered, when trying to climb over a patch of fog, or when trying to get out of a small airport on a very hot summer day. Besides a good angle of climb (for clearing obstructions) an ultra-light airplane should

have the best possible rate of climb (for getting upstairs quickly). As 5000 feet is a good average altitude for crossing hills and practicing maneuvers, this figure has

been chosen for the graph in Fig. 2, which shows the time to climb to 5000 feet. The very marked influence of span is to be noted. As span increases (for a given

power) the time to climb to 5000 feet drops rapidly. This shows again the fallacy of hoping for a useful airplane having low power and short wingspan. Keep the

span large!

This talk of large wingspans naturally leads to the question of where aspect ratio enters the picture. We hear the model airplane fans talk so much of it! But always remember that both model airplanes and sailplanes are designed with endurance uppermost in mind. A model is often hand-launched, and the sailplane is

hauled rapidly aloft by a winch or towplane. Here there is obviously no need to be concerned with how well the craft will lift itself out of a small field and rise to a

30-ft. wings they took off and climbed better. The Ercoupe chances to have a 30-ft. span because that was the

best compromise between good climb and structural requirements.

When aspect ratio, through our choice of span loading and wing area, gets to be around 8-to-l or 9-to-l, structural problems begin to appear. The Aeronca C-3's long, narrow wing had so much overhang outboard of the external brace wires that double internal drag wires had to be used to gain torsional rigidity. One set of

"X" wires ran from the top of the front spar to the top of the rear spar, and another set ran from the bottom of the front spar to the bottom of the rear spar. You figure what happens to cost and weight when the aspect ratio climbs.

To cite another example, assume we want a plane of 30 ft. span to suit our horsepower, and of 100 sq. ft. wing

area to suit our wing loading goals. A monoplane wing to fill these requirements would have a chord of 3.3 ft., but a pair of biplane wings of the same span and total

area would have chords of 1.65 ft. Consider the shallow

spar depths and short distance between the two spars of a wing of such small chord, and you will see that the

cost and weight of a biplane truss will be greater than for a monoplane of the same span. This is why the vast majority of successful airplanes under 50 hp have been monoplanes. It is perfectly true that all biplanes suffer from wing interference, that they suffer from the drag of four

wing-tip vortices instead of two, and that a biplane wing arrangement can be lighter and stronger than a monoplane wing when power is reasonably high. But it should also be clearly understood that when very low power is under discussion, wingspan should be large and the monoplane wing is then lighter, cheaper, and has the best chance of giving acceptable performance. The sensational Lockheed U-2 airplanes have an enormous wingspan so that with a given power they could climb to the

safe altitude.

utmost possible altitude. A low-powered Sportplane sel-

It is perfectly true that many low-powered airplanes have aspect ratios noticeably higher than the oft-recommended 6-to-l ratio for powerplanes. The Aeronca C-3,

off, a steep climb, a useful cruising speed, and a low

Fig. 3, is a good example, as it had a 9-to-l aspect ratio and 36 hp. Our popular Piper Cub and similar airplanes have aspect ratios of around 7-to-l. There is a tendency

to assume this means that high aspect ratios are chosen because they suit low-powered craft. Of course the lower induced drag of a high aspect ratio wing helps in climb and glide, but that obscures the real reason. If wing span is chosen on the basis of what span loading best

suits the power, then it follows that wing area can be selected only by varying the chord. If we have a 36-foot wing and arbitrarily choose a 6-to-l aspect ratio, its chord will be 6 feet and it will have 216 sq. ft. of area.

This will give a lightplane of average weight a very low wing loading and the result is a plane which is overly sensitive to rough air. To get an airplane with a

wing loading high enough to make it reasonably comfortable and controllable in average winds, the only way to reduce wing area is by reducing chord. Not much is sacrificed by reducing chord as compared to what would be lost by reducing the span. A 36-foot wing of 5 ft. or even 4 ft. chord will have an area of 170 or 144 ft., respectively. Span and span loading are preserved and wing loading is increased to a suitable figure. The aspect ratio is simply the outcome of this choice. Many early lightplanes with motorcycle power and 25 ft. wingspans were painfully poor climbers, but when fitted with

dom goes over 10,000 ft., but it does need a quick take-

landing speed.

A reasonably long span is the answer,

just as with the high-climbing U-2. Forget about clippedwing jobs . . . they are for the racers.

"GIZMO" . . . Continued from page 17 A foam rubber and leather upholstered, removable bucket seat would go very nicely with the varnished mahogany

plywood interior, adding much to a sporty appearance

with little more effort. In fact, the builder could wax fancy and come up with a top-notch machine in the looks department. One nice thing for sure, there will not be acres of surfaces to keep clean and presentable!

The engine that is suggested in the 3-view is the VW. This would be a fine powerplant for this rig. It would be utterly dependable and would go a long way towards removing the onus that has beclouded the future of the small homebuilt Giro. This does not preclude the usage of target drone engines for preliminary evaluation and

general hayfield flying, but we as experimenters should have as our prime motivating force, the desire to constantly improve and upgrade our projects. Greater

reliability and its' attendant safety will help insure our

continued freedom to use what our forefathers took for granted as being a God-given heritage; Our freedom to

make use of land, sea and air in our daily pursuit of happiness! A SPORT AVIATION

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